<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. 1** (a) Spatial resolution of EUSTEM at 11 regions (b) EUSTEM database for instance generation</figcaption></figure>

instances, model data is aggregated straightforwardly or via heuristics, e.g., weighted aggregation based on the 2015 statistics (IEA 2016). A “copper plate” approach is assumed for cross-regional trade matrices when zooming out the spatial
<table><caption>**Table 1** Matrix sizes of some of the EUSTEM instances with different spatial and temporal resolution</caption><thead><tr><th>Instance<br>(XXX_YY_ZZ)<br>XXX = timeslices<br>YY = regions<br>ZZ = periods</th><th>Variables<br>(millions,<br>before<br>CPLEX<br>Presolve)</th><th>Equations<br>(millions,<br>before<br>CPLEX<br>Presolve)</th><th>Non-Zeros<br>(millions,<br>before<br>CPLEX<br>Presolve)</th><th>Memory to<br>generate the<br>instance (GB,<br>before CPLEX,<br>Presolve)</th><th>% of<br>equations and<br>variables<br>eliminated by<br>CPLEX<br>Presolve</th></tr></thead><tbody><tr><td>48_1_8</td><td>0.0</td><td>0.0</td><td>0.2</td><td>0.0</td><td>19%</td></tr><tr><td>48_11_8</td><td>0.6</td><td>0.4</td><td>3.2</td><td>0.3</td><td>18%</td></tr><tr><td>48_22_8</td><td>1.2</td><td>0.9</td><td>6.0</td><td>0.7</td><td>19%</td></tr><tr><td>72_11_8</td><td>1.5</td><td>1.7</td><td>10.1</td><td>1.0</td><td>22%</td></tr><tr><td>72_22_8</td><td>4.1</td><td>3.1</td><td>20.1</td><td>2.1</td><td>22%</td></tr><tr><td>144_11_8</td><td>4.6</td><td>3.3</td><td>24.1</td><td>2.3</td><td>17%</td></tr><tr><td>144_22_8</td><td>8.2</td><td>6.0</td><td>42.6</td><td>4.2</td><td>20%</td></tr><tr><td>288_11_8</td><td>8.3</td><td>12.3</td><td>118.8</td><td>10.2</td><td>31%</td></tr><tr><td>288_22_8</td><td>15.5</td><td>22.6</td><td>218.3</td><td>18.9</td><td>31%</td></tr><tr><td>288_11_20</td><td>55.2</td><td>36.8</td><td>551.5</td><td>46.5</td><td>28%</td></tr><tr><td>672_11_8</td><td>19.4</td><td>28.6</td><td>446.4</td><td>38.9</td><td>29%</td></tr><tr><td>672_22_8</td><td>53.7</td><td>36.7</td><td>839.1</td><td>73.1</td><td>29%</td></tr><tr><td>1344_11_8</td><td>57.1</td><td>38.7</td><td>892.3</td><td>77.6</td><td>34%</td></tr><tr><td>2016_11_8</td><td>85.7</td><td>58.1</td><td>1340.6</td><td>116.7</td><td>29%</td></tr><tr><td>4032_11_8</td><td>171.3</td><td>116.1</td><td>2680.8</td><td>237.9</td><td>26%</td></tr><tr><td>8076_11_8</td><td>257.2</td><td>376.2</td><td>5360.1</td><td>359.2</td><td>28%</td></tr></tbody></table>

dimension. Where aggregation of the trade corridors is necessary, we treat them as parallel when adjusting their capacities and technical characteristics.

EUSTEM parameters depending on the intra-annual resolution, such as ramping constraints, minimum online and offline times of power plants, resource availabilities and demand load curves, are adjusted from the 8760 timeslices to coarser timeslices by accounting for the duration of the latter as required in Loulou et al. (2016) and Panos and Lehtilä (2016). The peak reserve margin is also adjusted across instances, as coarser instances need a higher margin than “finer” ones. The adjustment ensures the same maximum available capacity requirements for 2015 in all instances.

Table 1 presents a subset of the EUSTEM instances and their matrix sizes. The last column refers to the percentage of eliminated equations and variables by CPLEX \Presolve because of dependency, substitutions and aggregations. It is worth noting that the reduction percentage of the TIMES model matrices is smaller than for other frameworks, for example, in ELMOD, which also participated in BEAM-ME (Borggrefe et al. 2019). This is because TIMES runs a sophisticated reduction algorithm to substitute variables before GAMS passes the matrix to the solver.
## 2.2 Using the CPLEX/Barrier Interior Point Solver for Shared-Memory Systems

In this section, we discuss features of IBM ILOG CPLEX/Barrier interior point solver (IBM 2017) relevant for speeding up the solution process in a shared memory system; additional solution accelerating insights related to CPLEX/Barrier are discussed in Klotz and Newman (2013). The insights in this section also apply to other commercial and non-commercial implementations of the Barrier algorithm.

In our discussion, we assume a linear programming problem of $m$ equations and $n$ variables. Its standard primal formulation is $\min c^T x$ subject to $Ax = b$ with $x \ge 0$. The corresponding dual problem is $\max y^T b$ subject to $y^T A \le c^T$ with $y \in \mathbb{R}$. A solution $x^*$ and $y^*$ is optimal for both problems if and only if it satisfies the feasibility of the primal and dual problems and the closure of the optimality gap $c^T x^* - b^T y^* = 0$.

### 2.2.1 Accelerating the Cholesky Factorisation of CPLEX/Barrier

CPLEX/Barrier maintains in each iteration $k$ a Cholesky factorisation $(\hat{AA}^T) = \hat{LL}^T$ where $\hat{A} = A \cdot \text{Diag}(x_k)$ with $x_k$ the feasible solution in iteration $k$. The number of non-zero elements (i.e., the density) in $\hat{AA}^T$ influences the complexity of the Cholesky factorisation and the solver run time. Because $\hat{A}$ is derived by multiplying $A$ with the diagonal matrix $\text{Diag}(x_k)$, the number of non-zeros in $AA^T$ and $\hat{AA}^T$ is the same and depends on the structure of $A$. Even if $A$ is sparse the $AA^T$ can be dense. To reduce the density of $(AA^T) = LL^T$, and the number of floating-point operations to factor, the Barrier algorithm spends significant time to reorder $A$. Whether the primal or dual problem formulation results in low solution times depends on the non-zero structure of $A$ as dense rows in primal (i.e., rows with many non-zero coefficients) become dense columns in dual and vice versa. A high number of dense columns reduces the effectiveness of the Cholesky factorisation. CPLEX/Barrier can handle a modest number of dense columns (Wright 1997), but undetected dense columns slow down the algorithm, while many dense columns can cause numerical instabilities (Klotz and Newman 2013).

Thus, reducing the complexity of the Cholesky factorisation is a priority in accelerating the solution time. Table 2 lists the key CPLEX/Barrier options that can be tested to achieve this and provides suitable explanations based on the above discussion.

### 2.2.2 Improving the Starting Point and Avoiding “Wasted” Iterations in Barrier

The performance of interior point methods also depends on their ability to closely follow the central path and avoid prematurely approaching the boundary of the
<table><caption>**Table 2** Overview of solver options relevant to the complexity of the Cholesky factor</caption><thead><tr><th>Option</th><th>Value</th><th>Meaning</th><th>Why this option is relevant for reducing the solution time</th></tr></thead><tbody><tr><td rowspan="3">Predual</td><td>-1</td><td>Do not give the dual to optimiser</td><td rowspan="3">It is not straightforward if the dual problem performs better than the primal, as it depends on the non-zeros in A. Often forcing the primal (i.e. Predual = -1) improves the performance.</td></tr><tr><td>0</td><td>Automatic</td></tr><tr><td>1</td><td>Give the dual to optimiser</td></tr><tr><td rowspan="2">Barcolnz</td><td>0</td><td>CPLEX finds the number of non-zeros above which the column is considered as dense</td><td rowspan="2">Dense columns degrade the performance of the optimiser. They are treated with specific algorithms to mitigate their negative effect. If too many dense columns are detected, they create numerical instabilities; if too few, the performance is not improved much.</td></tr><tr><td>&gt;0</td><td>User-specified value indicating the number of non-zeros above which a column is considered as dense</td></tr><tr><td rowspan="4">Barorder</td><td>0</td><td>Automatic</td><td rowspan="4">The reordering of the matrix A can reduce the fill-in in the Cholesky factor, i.e., the difference in the non-zeros between the Cholesky factor and the lower triangular matrix of AA<sup>T</sup>. The AMD algorithm provides good quality in moderate time spent for the reordering, the AMF usually results in 5-10% smaller factors than AMD, while the ND produces significantly smaller factors but at higher time spent for performing the permutation of the rows of the A matrix.</td></tr><tr><td>1</td><td>Approximate Minimum Degree (AMD)</td></tr><tr><td>2</td><td>Approximate Minimum Fill (AMF)</td></tr><tr><td>3</td><td>Nested Dissection (ND)</td></tr></tbody></table>

feasible region (Gondzio 2012) that will slow down the algorithm by performing small steps to convergence. Maintaining the central path depends on the starting point and convergence criterion. However, in contrast to Simplex, there is no way to use a previous solution as a starting point in Barrier, and heuristics are applied to construct starting points that are: a) close to primal and dual feasibility; b) to be well-cantered; and c) to be as close to optimality as possible (Mehrotra 1992; Skajaa et al. 2013; Gondzio 2016).

The convergence criteria for feasibility and optimality in interior point methods are based on relative measures and tolerances. In Barrier, the feasibility of the primal problem is assessed with respect to the variables' value in the solution: $\frac{\|Ax - b\|}{1 + \|x\|} \le tol$, where $tol$ is a tolerance. The optimality criterion is usually based on a normalised duality gap (Klotz and Newman 2013): $\frac{c^T x - \gamma^T b}{(1 + |c^T x|)} \le tol$. The above implies that: a) interior point methods cannot produce a basic solution; and b) violations of the constraints can occur as long as the feasibility tolerance is satisfied. To transform the
<table><caption>**Table 3** Overview of options relevant to the iterations' performance of the barrier algorithm</caption><thead><tr><th>Option</th><th>Value</th><th>Meaning</th><th>Why this option is relevant for reducing the solution time</th></tr></thead><tbody><tr><td rowspan="5">Baralg</td><td>0</td><td>Same as 1 for MIP, 3 otherwise</td><td rowspan="5">Usually, the standard barrier algorithm performs well in most cases. However, if the problem has numerical instabilities, choosing options 1 or 2 might improve the solution times. The baralg = 1 and baralg = 2 differ from each other in how they compute the starting point.</td></tr><tr><td>1</td><td>Infeasibility-estimate start</td></tr><tr><td>2</td><td>Infeasibility-constant start</td></tr><tr><td>3</td><td>Standard barrier algorithm</td></tr><tr><td>&gt;0</td><td>User-specified value indicating the number of non-zeros above which a column is considered as dense</td></tr><tr><td rowspan="4">Barstartalg</td><td>1</td><td>Default primal, dual is zero</td><td rowspan="4">These are four heuristics for the starting point. Option 1 and 2 might work well when we pass the primal problem. When we pass the dual is worth checking options 2 and 4. Option 3 is usually slower than the others.</td></tr><tr><td>2</td><td>Default primal, estimate dual</td></tr><tr><td>3</td><td>Primal average, dual is 0</td></tr><tr><td>4</td><td>Primal average, estimate dual</td></tr><tr><td>Barecomp</td><td>1E-8</td><td>Convergence and optimality tolerance: default 1E-8</td><td>Reducing the tolerance avoids wasted iterations, i.e., iterations in which the progress to convergence is very slow. Increasing the tolerance might improve the performance of the Crossover, but it risks wasted iterations or reporting the problem as infeasible.</td></tr></tbody></table>

interior-point solution to a basic one, the Crossover algorithm is invoked. However, Crossover does not benefit from parallel hardware, while its performance depends on the “quality” of the interior point solution, which in turn is based on the tolerances *tol*. A small tolerance can improve the performance of Crossover but increases the CPLEX/Barrier iterations; it also entail the risk that the problem is reported as infeasible by the algorithm. A small tolerance can cause the Barrier to be stuck in iterations with low progress towards optimality (see also the discussion on the “wasted iterations” in Sect. 3.1.4).

Therefore, improving the starting point of the Barrier algorithm and reducing the “wasted” iterations can help accelerate the solution times. Table 3 lists key options to achieve this.

### 2.2.3 Accelerating the Crossover Algorithm

The Crossover algorithm has two main phases involving Simplex. In the first phase, Crossover pushes all primal superbasic variables to their bounds. Superbasic is a non-basic variable that is neither at the lower nor at the upper bound. The dual
<table><caption>**Table 4** Overview of options relevant to the iterations' performance of the Crossover algorithm</caption><thead><tr><th>Option</th><th>Value</th><th>Meaning</th><th>Why this option is relevant for reducing the solution time</th></tr></thead><tbody><tr><td rowspan="10">Ppriind (for primal)<br>Dpriind (for dual)</td><td>-1</td><td>Reduce cost pricing</td><td rowspan="10">Option -1 is less compute-intensive and suitable for dense problems. Option 0 is the default. Option 1 might be useful for difficult problems taking many iterations. If Option 1 helps reduce solution times, option 2 can also be worth trying. Option 2 can be used for even more difficult problems than option 1 can tackle, but it is computationally expensive. Option 3 reduces the computationally intensive nature of option 2.</td></tr><tr><td>0</td><td>Hybrid reduced cost and devex pricing</td></tr><tr><td>1</td><td>Devex pricing</td></tr><tr><td>2</td><td>Steepest edge pricing</td></tr><tr><td>3</td><td>Steepest edge pricing with slack initial norms</td></tr><tr><td>4</td><td>Full pricing</td></tr><tr><td>2</td><td>Default primal, estimate dual</td></tr><tr><td>3</td><td>Primal average, dual is 0</td></tr><tr><td>4</td><td>Primal average, estimate dual</td></tr><tr><td rowspan="3">Barcrossalg</td><td>0</td><td>Automatic</td><td rowspan="3">By default, CPLEX invokes primal and dual Crossover when multiple threads are available in a concurrent optimisation. Otherwise, the choice depends on the type of the problem being solved (primal or dual). Although the default option works well in most cases, forcing the primal (when solving the primal problem) or dual (when solving the dual problem) to Crossover might reduce the solution time.</td></tr><tr><td>1</td><td>Primal Crossover</td></tr><tr><td>2</td><td>Dual Crossover</td></tr></tbody></table>

superbasic variables are pushed to the bounds in the second phase. Crossover solves $Ax^* = Bx_B + Sx_s = b$, where $x_B$ is the basis and $x_s$ are the superbasic variables. When there is a superbasic variable $x_j$ between its lower and upper bounds $l_j$ and $u_j$ respectively (i.e., $l_j \le x_j \le u_j$) Crossover either pushes $x_j \to (l_j \text{ or } u_j)$ (push-move) or moves $x_j$ into the basis and pushes another basic variable $x_i \to (l_i \text{ or } u_i)$ (exchange-move). The choice of the variable to be moved is based on the pricing algorithm, affecting the performance. The options shown in Table 4 could accelerate the Crossover algorithm.

### 2.2.4 Using Parallel Mode in Barrier

CPLEX/Barrier can exploit multiple nodes in shared-memory systems during the Cholesky factorisation, to perform simultaneous linear algebra operations (Bisseling et al. 1993; Karypis et al. 1994). However, experience shows that the performance does not improve after a few nodes, or even deteriorates due to CPU-memory communication overhead (Panos 2022) (Fig. 2).
Solution time (in min) for the EUSTEM instance 72_11_8

<figure><img src="image_22.png" /></figure>

Hardware: HPE Apollo XL230K Gen10 blade with 2 Intel® Xeon® Gold 6152 Scalable Processors @ 2.10GHz (2 x 22 cores, 384GB RAM)
Fluctuations in the solution time are due to the variable cluster workload where the tests were made
The number of nodes available to CPLEX/Barrier is controlled using the "Threads" option of the algorithm

<caption>Fig. 2 Performance of CPLEX/Barrier over multiple nodes for one of the EUSTEM instances</caption>

## 2.3 Using the PIPS-IPM++ Parallel Interior Point Solver for Distributed-Memory Systems

PIPS-IPM++ (Rehfeldt et al. 2019, 2022) is a new interior point solver based on the linear programming parallel solver PIPS-IPM (Petra et al. 2014). It exploits the doubly bordered block diagonal structure (Wilkinson 1965) of the typical energy systems model matrices to solve them in distributed-memory systems (Breuer et al. 2018). Figure 3 shows a typical block-diagonal structure of a model matrix. This structure is revealed by permutating the matrix to group variables and equations into blocks assigned to different nodes for parallel solving. Still, some variables and equations span across several blocks. These are called linking variables and equations. For example, if the blocks correspond to the geographical regions of a model, the global carbon budget constraints are of a linking nature.

The PIPS-IPM++ parallel interior point solver uses a Shur Complement decomposition (Zhang 2005), which exploits the block structure of the model matrix to perform efficient inversions and factorisation operations on it. It is combined with a distributed preconditioning of the linear system (Wathen 2015), which transforms the system from $Ax = b$ to $P^{-1}Ax = P^{-1}b$, where $P^{-1}$ is the “preconditioner”; a suitable approximation of $A^{-1}$ to reduce the sensitivity of $A$ to input data perturbations and roundoff errors during the solution process. PIPS-IPM++ also implements multiple-corrector schemes for the interior point algorithm, scaling methods and presolving techniques (Rehfeldt et al. 2022).
<figure><img src="image_23.png" /><figcaption>Fig. 3 Block structure of the model matrix, linking variables and constraints (Rehfeldt et al. 2022)</figcaption></figure>

The performance of PIPS-IPM++ depends on the size of the Schur Complement, which is affected by the number of linking variables and constraints. The implementation of PIPS-IPM++ outperforms the interior point algorithms in shared-memory systems if there are more than 50 individual blocks in the model matrix to offset the message passing overhead between nodes and the number of linking variables and equations is up to 300,000.

### 2.3.1 Annotating Variables and Equations to Reveal the Block Structure of the Model Matrix

The procedure to manually group the variables and equations into blocks or characterize them as linking variables and constraints is called “annotation”. Figure 4a shows the “random” non-zero structure of the original model matrix A. Figure 4b, c show the outcome of the annotation, i.e., the model’s block structure (Fiand 2018). GAMS supports annotation through the `.stage` attribute of variables and equations. When annotating the model, PIPS-IPM++ requires the following (Fig. 4d):

* Linking variables are assigned to block 1 (i.e., `<variable_name>.stage = 1`). By default, all variables are assigned to block 1. The objective variable is a linking variable.

* All non-linking variables are assigned to blocks 2, ..., $k + 1$ (i.e., `<variable_name.stage = 2, ..., k + 1>` where $k$ is the total number of blocks.

* Constraints that contain only linking variables belong to block 1 (i.e., `<equation_name>.stage = 1`). The objective function is a linking constraint.

* Constraints containing variables from 2 or more different blocks are linking constraints and belong to the block $k + 2$ (i.e., `<equation_name>.stage = k + 2`).
Original problem with “random” matrix structure

<figure><img src="image_24.png" /><figcaption>(a)</figcaption></figure>

Permutation reveals block structure

<figure><img src="image_25.png" /><figcaption>(b)</figcaption></figure>

Matrix structure required by PIPS API

<figure><img src="image_26.png" /><figcaption>(c)</figcaption></figure>

Exemplary annotation in TIMES
 blocks are the regions of the model)

* variables
  objz.stage=1;
  var_ucts(uc_n,t,s).stage=1;
  var_ire(r,v,t,p,c,s,ie).stage=ord(r)+1;
  var_act(r,v,t,p,s).stage=ord(r)+1;
  ...
* equations
  eql_capact(r,v,t,p,s).stage=ord(r)+1;
  ...
  eqe_uct("CO2Budget",t,s)=card(r)+2;

<caption>(d)</caption>

**Fig. 4 (a)** the non-zero structure of an original matrix of TIMES model; (b) the same matrix after annotating the model to group the equations and variables into individual blocks; the grey area denotes linking variables and constraints; (c) mapping of blocks to values for the .stage attribute of variables and equations in GAMS; (d) GAMS code example that identifies blocks based on regions. (The images in panels (a)–(c) are reproduced with permission from Fiand (2018))

* All other constraints that contain variables from only one of the blocks 2, ..., $k + 1$ are assigned to these blocks (i.e., `<equation_name>.stage = 2, ..., k + 1`).

Good practices for annotating the model for PIPS-IPM++ are extensively discussed in Scholz et al. (2020). The most important ones are summarised below:

* The blocks should be as many as possible, of equal sizes and as small as possible.

* Linking constraints are preferable to have variables from two consecutive blocks or at least to have variables that belong to non-very-distant blocks.

* The total number of linking variables and constraints should not exceed 300,000.

The modeller shall try different strategies to create blocks of equations and variables. Experience shows that efficient annotations create blocks across multiple dimensions, e.g., regions and periods or regions and timeslices. Finding the most efficient annotation that leads to many small blocks and a small number of linking variables and equations requires good model and domain knowledge.
<figure><img src="image_27.png" /><figcaption>**Fig. 5** The workflow for solving EUSTEM with PIPS-IPM++ on High-Performance computing cluster</figcaption></figure>

### 2.3.2 How to Solve an Annotated Model with the PIPS-IPM++ Solver

Assuming that PIPS-IPM++ is installed on a computer cluster<fnref n="1" /> and the annotation has been performed, a workflow for solving the model is shown in Fig. 5. The main steps are as follows (Fiand 2018; Scholz et al. 2020):

1. The annotated model should be solved with the CONVERT solver<fnref n="2" /> to get the Jacobian.

2. The Jacobian can be checked using the checkanno.gms tool for correct annotation.<fnref n="3" />

3. The annotated Jacobian can be uploaded to the computer cluster, where it can be split into its blocks, linking variables and constraints using the GAMS utility `gmschk`.<fnref n="4" />

4. The PIPS-IPM++ solver can be invoked as described in its latest documentation.<fnref n="5" />

5. The solution can be collected as a `.GDX` file and processed on the local computer.

<footnote n="1">¹For obtaining the solver, documentation and installation instructions: https://github.com/NCKempke/PIPS-IPMpp</footnote>

<footnote n="2">²See https://www.gams.com/latest/docs/S_CONVERT.html</footnote>

<footnote n="3">³The checkanno.gms can be obtained from the BEAM-ME repository: https://gitlab.com/beam-me/simple-pips The tool can check whether the number of linking variables and constraints meets the PIPS-IPM++ requirements</footnote>

<footnote n="4">⁴The `gmschk` is supplied with the Linux GAMS distribution. To split the Jacobian into blocks it should be called as `gmschk -t -X -g '%gams.sysdir%' '%number_of_blocks%' < jacobian_filename.gdx` without the double quotes</footnote>

<footnote n="5">⁵See https://github.com/NCKempke/PIPS-IPMpp</footnote>
# 3 Results

In this section, we first demonstrate a heuristic to find a set of options for CPLEX/ Barrier for accelerating the EUSTEM instance 72_11_8 in a shared memory system, e.g., a personal computer. Then, we demonstrate the parallel solving of a model matrix in computer clusters using instances 288_11_8 and 288_22_8, which are large enough to be solved with PIPS-IPM++. We conclude the section by discussing the analysis value-added by avoiding the model aggregation.

## 3.1 How to Accelerate the CPLEX/Barrier in Shared-Memory Systems

Each section below describes the heuristic steps to identify suitable options for the Barrier solver. It should be noted that the reduction achieved in each step depends on the non-zero structure of the model matrix and, hence, varies in the different models.

### 3.1.1 Step 1: Examining if Passing the Primal Problem Performs Better Than Dual

The ratio of the number of variables to constraints in instance 72_11_8 is such that the CPLEX Presolve heuristic passes the dual problem to Barrier by default. This resulted in solution times exceeding 9 h. However, by forcing **Predual = -1** and passing the primal problem, the obtained solution time dropped to 113 min, of which 30 min were for Barrier and 83 min were for Crossover. Additional tests showed that CPLEX/Barrier for TIMES-based models performs better when solving the primal instead of the dual.

### 3.1.2 Step 2: Identifying the Number of Dense Columns to Minimise Cholesky Factorisation Complexity

To determine the number of dense columns, the column density histogram of the model matrix<fnref n="6" /> can help find a threshold for the number of non-zero elements above which a column is characterised as dense. By default, CPLEX/Barrier detects 319 dense columns for the primal formulation of instance 72_11_8, but by looking at the column density histogram shown in Fig. 6a, the value of 150 non-zeros seems

<footnote n="6">⁶The column density histogram can be obtained by using the interactive CPLEX (see https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXinteractive) and entering the command "display problem histogram c" (without quotes)—see also https://www.ibm.com/docs/en/icos/22.1.1?topic=cplex-table-commands-interactive-optimizer</footnote>
<figure><img src="image_28.png" /><figcaption>**Fig. 6 (a)** the column density histogram for instance 78_11_8; **(b)** the number of floating-point operations required for the Cholesky factorisation as a function of the number of dense columns for the instance 78_11_8</figcaption></figure>

to be a more suitable threshold. Indeed, by setting **Barcolnz** = **150**, the detected dense columns are 2906. This value also minimises the number of floating-point operations to factor (Fig. 6b) and reduces the solution time from 113 to 84 min; of which 29 min for **Barrier** and 55 for **Crossover**. The reduction of almost 20 min in the **Crossover** in this step compared to the time obtained in the previous step of the heuristic algorithm is also a result of **Cholesky factorisation's** reduced complexity, which improved the interior point solution's quality and resulted in fewer primal and dual pushes in the **Crossover**. If multiple peaks exist in a column density histogram, exploring different cut-off thresholds, especially those corresponding to the peaks, is necessary.

### 3.1.3 Step 3: Exploring Different Ordering Algorithms and Starting Point Heuristics for Barrier

The next step is mostly a trial-and-error procedure, examining different options for ordering the matrix A and finding a suitable starting point for the iterations. Based on the examined instances, **Barorder = 0** or **Barorder = 3** produces the best A matrix ordering results for TIMES-based models. Also, the EUSTEM instances (and other TIMES-based instances) performed better when setting **Baralg = 3** than using other Baralg values. Since we pass the primal problem, opting for **Barstartalg = 1** or **Barstartalg = 2** to identify the starting point could help. In our test case 72_11_8, by setting **Barorder = 0**, **Baralg = 3** and **Barstartalg = 1**, we reduced the solution time from 84 to 38 min, of which 23 are for **Barrier** and 15 for **Crossover**.
<table><caption>**Fig. 7** The CPLEX/Barrier log and the calculated normalised duality gap, showing that wasted iterations occur after iteration 182</caption><thead><tr><th>Itn</th><th>Primal Obj</th><th>Dual Obj</th><th>Prim Inf</th><th>Upper Inf</th><th>Dual Inf</th><th>Duality gap</th><th>Itn</th><th>Primal Obj</th><th>Dual Obj</th><th>Prim Inf</th><th>Upper Inf</th><th>Dual Inf</th><th>Duality gap</th></tr></thead><tbody><tr><td>0</td><td>7.99E+11</td><td>-4.50E+10</td><td>8.19E+09</td><td>4.62E+08</td><td>1.39E+10</td><td>1.056385E+00</td><td>183</td><td>6.59E+09</td><td>6.59E+09</td><td>3.81E-02</td><td>4.55E-10</td><td>5.53E+00</td><td>4.552347E-08</td></tr><tr><td>1</td><td>7.24E+11</td><td>-1.08E+11</td><td>7.19E+09</td><td>4.06E+08</td><td>1.12E+10</td><td>1.145917E+00</td><td>184</td><td>6.59E+09</td><td>6.59E+09</td><td>3.81E-02</td><td>4.85E-10</td><td>5.87E+00</td><td>4.552347E-08</td></tr><tr><td>2</td><td>6.12E+11</td><td>-2.03E+11</td><td>5.34E+09</td><td>3.01E+08</td><td>8.69E+09</td><td>1.330828E+00</td><td>185</td><td>6.59E+09</td><td>6.59E+09</td><td>3.81E-02</td><td>5.13E-10</td><td>6.00E+00</td><td>4.552347E-08</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>186</td><td>6.59E+09</td><td>6.59E+09</td><td>3.81E-02</td><td>5.33E-10</td><td>6.15E+00</td><td>4.552347E-08</td></tr><tr><td>170</td><td>6.59E+09</td><td>6.59E+09</td><td>1.98E-02</td><td>1.94E-10</td><td>4.94E+00</td><td>2.124429E-07</td><td>187</td><td>6.59E+09</td><td>6.59E+09</td><td>3.82E-02</td><td>5.57E-10</td><td>6.54E+00</td><td>4.552347E-08</td></tr><tr><td>171</td><td>6.59E+09</td><td>6.59E+09</td><td>2.27E-02</td><td>2.24E-10</td><td>5.11E+00</td><td>2.124429E-07</td><td>188</td><td>6.59E+09</td><td>6.59E+09</td><td>3.82E-02</td><td>5.77E-10</td><td>6.42E+00</td><td>4.552347E-08</td></tr><tr><td>172</td><td>6.59E+09</td><td>6.59E+09</td><td>2.70E-02</td><td>2.26E-10</td><td>4.71E+00</td><td>1.517449E-07</td><td>189</td><td>6.59E+09</td><td>6.59E+09</td><td>3.82E-02</td><td>6.04E-10</td><td>6.76E+00</td><td>4.552347E-08</td></tr><tr><td>173</td><td>6.59E+09</td><td>6.59E+09</td><td>2.73E-02</td><td>2.80E-10</td><td>4.88E+00</td><td>1.517449E-07</td><td>190</td><td>6.59E+09</td><td>6.59E+09</td><td>3.84E-02</td><td>6.19E-10</td><td>6.96E+00</td><td>4.552347E-08</td></tr><tr><td>174</td><td>6.59E+09</td><td>6.59E+09</td><td>2.74E-02</td><td>3.18E-10</td><td>5.36E+00</td><td>1.517449E-07</td><td>191</td><td>6.59E+09</td><td>6.59E+09</td><td>3.84E-02</td><td>6.42E-10</td><td>7.11E+00</td><td>4.552347E-08</td></tr><tr><td>175</td><td>6.59E+09</td><td>6.59E+09</td><td>3.61E-02</td><td>1.97E-10</td><td>5.28E+00</td><td>6.069796E-08</td><td>192</td><td>6.59E+09</td><td>6.59E+09</td><td>3.84E-02</td><td>6.56E-10</td><td>7.57E+00</td><td>4.552347E-08</td></tr><tr><td>176</td><td>6.59E+09</td><td>6.59E+09</td><td>3.61E-02</td><td>2.55E-10</td><td>5.60E+00</td><td>6.069796E-08</td><td>193</td><td>6.59E+09</td><td>6.59E+09</td><td>3.87E-02</td><td>6.63E-10</td><td>7.52E+00</td><td>4.552347E-08</td></tr><tr><td>177</td><td>6.59E+09</td><td>6.59E+09</td><td>3.61E-02</td><td>3.02E-10</td><td>5.54E+00</td><td>6.069796E-08</td><td>194</td><td>6.59E+09</td><td>6.59E+09</td><td>3.87E-02</td><td>6.81E-10</td><td>7.83E+00</td><td>4.552347E-08</td></tr><tr><td>178</td><td>6.59E+09</td><td>6.59E+09</td><td>3.61E-02</td><td>3.47E-10</td><td>5.60E+00</td><td>6.069796E-08</td><td>195</td><td>6.59E+09</td><td>6.59E+09</td><td>3.90E-02</td><td>7.09E-10</td><td>7.80E+00</td><td>4.552347E-08</td></tr><tr><td>179</td><td>6.59E+09</td><td>6.59E+09</td><td>3.62E-02</td><td>3.75E-10</td><td>5.63E+00</td><td>6.069796E-08</td><td>196</td><td>6.59E+09</td><td>6.59E+09</td><td>3.90E-02</td><td>7.28E-10</td><td>7.75E+00</td><td>4.552347E-08</td></tr><tr><td>180</td><td>6.59E+09</td><td>6.59E+09</td><td>3.62E-02</td><td>3.98E-10</td><td>5.65E+00</td><td>6.069796E-08</td><td>197</td><td>6.59E+09</td><td>6.59E+09</td><td>3.90E-02</td><td>7.38E-10</td><td>7.68E+00</td><td>4.552347E-08</td></tr><tr><td>181</td><td>6.59E+09</td><td>6.59E+09</td><td>3.78E-02</td><td>3.98E-10</td><td>5.56E+00</td><td>6.069796E-08</td><td>198</td><td>6.59E+09</td><td>6.59E+09</td><td>3.92E-02</td><td>7.56E-10</td><td>7.87E+00</td><td>4.552347E-08</td></tr><tr><td>182</td><td>6.59E+09</td><td>6.59E+09</td><td>3.80E-02</td><td>4.23E-10</td><td>5.70E+00</td><td>4.552347E-08</td><td>199</td><td>6.59E+09</td><td>6.59E+09</td><td>3.92E-02</td><td>7.70E-10</td><td>8.46E+00</td><td>4.552347E-08</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>200</td><td>6.59E+09</td><td>6.59E+09</td><td>3.92E-02</td><td>7.94E-10</td><td>8.52E+00</td><td>4.552347E-08</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>201</td><td>6.59E+09</td><td>6.59E+09</td><td>3.92E-02</td><td>8.15E-10</td><td>9.53E+00</td><td>4.552347E-08</td></tr></tbody></table>

### 3.1.4 Step 4: Eliminating “Wasted” Iterations

The Barrier output log shown in Fig. 7 for the instance 72_11_8 reveals that after iteration 182, very little progress has been made in the objective function and the normalised duality gap (calculated separately in the figure). Hence, the iterations 183–201 are “wasted iterations”. To eliminate that, we need to change the optimality criterion tolerance, which, for the primal problem, is $\frac{|c^T x - y^T b|}{|1 + |c^T x|}| \le 10^{-8}$. Given that in iterations 183–201 we have a duality gap of around $4.55 \cdot 10^{-8}$, we can increase the tolerance **Barecomp** to $4.7 \cdot 10^{-8}$ and stop at iteration 182. This reduces the total solution time to 36 min, of which 16 is for Crossover and 20 for the Barrier iterations.

### 3.1.5 Step 5: Accelerating the Crossover Algorithm

To further reduce solution time for the instance 72_11_8, we can set **Barcrossalg** = 1, since we pass the primal problem to Crossover (Table 3). This reduces Crossover time by 6 min, and the overall solution time is 30 min. Recalling also that the optimality tolerance affects the quality of the solution passed to Crossover, by slightly adjusting **Barecomp** from $4.7 \cdot 10^{-8}$ to $4.6 \cdot 10^{-8}$, i.e., by accepting some wasted iterations, the starting point of Crossover is improved and the overall solution time drops to 28 min. Finally, changing the pricing algorithm to **Ppriind** = 3, the solution time is 26 min. It is worth noting that avoiding Crossover result in a solution time of 18 min, but in this case we do not have a basic solution – whether a basic solution is needed depends on the problem being solved (sometimes a near-optimal or a non-basic interior point optimal solution is sufficient) or the use of the basic solution e.g., as an advanced starting point.
<figure><img src="image_29.png" /><figcaption>**Fig. 8** Overview of the steps to accelerate CPLEX/Barrier in a shared-memory system for the instance 72_11_8 and the final set of CPLEX options found by applying the heuristic</figcaption></figure>

Figure 8 presents an overview of the steps described in Sects. 3.1.1, 3.1.2, 3.1.3, 3.1.4 and 3.1.5 for the EUSTEM instance 72_11_8 in finding the optimal set of Barrier options to accelerate the instance.

## 3.2 Insights from Parallel Solving with PIPS-IPM++

In BEAM-ME, we found that PIPS-IPM++ cannot efficiently solve all EUSTEM instances due to many linking constraints resulting from the energy system interdependencies represented in the model. The instances 288_11_8 and 288_22_8 were suitable for PIPS-IMP++. They differ in the number of regions, 11 vs 22, and both have 288 timeslices with a time horizon from 2015 to 2050 divided into 8 periods.

### 3.2.1 Annotation Strategy for the Block Definitions

In TIMES models, the annotation strategy can be based on regions, periods, timeslices, sectors and technologies. Our tests showed that annotating with timeslices, sectors, or technologies might increase linking variables and constraints. Thus, the annotation strategy for instances 288_11_8 and 288_22_8 was based on creating blocks by combining periods and also minimising the “global” linking constraints, i.e. constraints having variables from more than 4 blocks or variables from blocks with a “distance” greater than 9, which deteriorate the PIPS-IPM++ performance. An additional effort was made to avoid having more than 2000 linking constraints per block, an additional limiting factor of PIPS-IPM++.
<figure><img src="image_30.png" /><figcaption>Fig. 9 Block definitions and the block structure of the model matrix after annotation</figcaption></figure>

Figure 9 displays the block definitions for the two instances. Each variable and equation of TIMES is assigned, via its .stage attribute in GAMS, to a block or is considered to be of a linking nature. Instance 288_11_8 produced 97,360 linking constraints and 5251 linking variables, while instance 288_22_8 had 162,169
linking constraints and 16,783 linking variables. By examining the annotation based on periods and regions, we observe the following:

* Linking variables are the objective variable and variables holding intermediate calculations for the objective function, slack variables of user constraints that sum over regions or periods, capacity investment variables and retired capacity variables. The number of linking variables can be reduced if the intermediate variables of the objective function and the slacks of cross-regional or cross-period constraints are eliminated from the TIMES code.

* Linking constraints are cross-regional constraints and cross-period constraints. This implies that when creating the blocks during the annotation, special care should be given to avoid including in the same block regions or periods that are very distant from each other: for example, if two regions, A and B, share a trade link they should be included in the same block or close to each other blocks. Similarly, if region C has trade links with regions D, E, F, and G, it makes sense to include region C in a block which is of a distance less than 4 from the blocks where the regions D, E, F and G are included. By taking care that the distance of blocks responsible for linking constraints and variables is less than 4 would avoid having many global constraints.

### 3.2.2 PIPS-IPM++ Solution Times

Figure 10 compares the solution times of the two instances with CPLEX/Barrier and PIPS-IPM++. While the solution time in CPLEX/Barrier scales with the size of the instance, the solution time from PIPS-IPM++ remains almost constant. With PIPS-IPM++ models can be scaled up in size without significantly increasing the solution time. Small instances with less than 50 blocks do not benefit much from PIPS-IPM++.

<figure><img src="image_31.png" /><figcaption>**Fig. 10** Solution times for the instances 288\_11\_8 and 288\_22\_8 with CPLEX/Barrier and PIPS-IPM++</figcaption></figure>
## 3.3 Insights from Different Spatial and Temporal Resolutions in Modelling SDG7 and SDG13

By being able to solve the EUSTEM instances of Table 1 at reasonable solution times, we demonstrate the need for complex energy systems models in SDG assessment and the insights gained from this additional complexity. We do not aim to repeat the literature on the topic, for example (Allen et al. 2016; van Soest et al. 2019; Barbero-Vignola et al. 2020; Aryanpur et al. 2021), but we focus on a concrete example of the value-added obtained in the analysis by having high spatial and temporal resolution in the modelling of SDG7 (Clean and Affordable Energy) within SDG13 (Climate Action) across three axes: new technology uptake, system flexibility needs and energy system costs. We assess a Baseline scenario for the EU continuing the energy and climate policies from 2015 to 2050 and a Decarbonisation scenario of reducing the EU-wide CO₂ emissions in 2050 by 95% from 2015. In the Decarbonisation scenario, and when applicable by the model's underlying spatial resolution, country-specific targets and policies are also imposed as of the UNFCCC pledges of 2015.

It should be noted that the EUSTEM instances of lower numbers of timeslices or regions are derived from the full model instance of 22 regions with 8760 timeslices. This design implies that these aggregated instances are good approximations of the most accurate version of the model since the latter is used as a benchmark to improve the accuracy of the former, e.g., by introducing in the coarser instances additional parameters and constraints or by adjusting some parameters (such as the reserve margin, see also Sect. 2.1.1). This ideal case, which mitigates the negative effects of model aggregation, is an option only if the most detailed version of the model is available and can be solved within a reasonable time. Therefore, the results below should be understood and interpreted in this context.

### 3.3.1 Different Regional Aggregations of “Europe” Yields Different Projections of Technology Uptake

We first test the hypothesis that the lack of regional internal structure and socio-economic, environmental and political contexts in the different geographies results in false signals to investors and decision-makers regarding technology uptake at coarser regionalities. We use the EUSTEM instances 288_1_8, 288_5_8, 288_11_8 and 288_22_8, which have 288 timeslices and 8 periods but different regional resolutions.

As shown in Fig. 11, and looking at the solar and wind power plant capacity, there is a higher deployment of intermittent renewables in the Baseline scenario at coarser spatial resolutions. This is a finding similar to other studies in literature (Aryanpur et al. 2021), which is attributable to the lower accuracy of renewable potentials, lack of transmission constraints, etc. However, looking at the Decarbonisation scenario at the right panel of the same figure, the instances with coarser spatial resolutions
<figure><img src="image_32.png" /><figcaption>**Fig. 11** Generation capacity in "Europe" with different spatial resolution varying from 1 to 22 regions, with 288 timeslices and 8 periods from 2015 to 2050 (instances, 288_1_8, 288_2_8, 288_5_8, 288_11_8 and 288_22_8)</figcaption></figure>

resulted in lower deployment of wind and solar capacity than those with a finer spatial resolution. This is attributable to the lack of accurate representation of the local techno-economic conditions and policy context at coarser geographies, which is particularly relevant in the Decarbonisation scenario that does not only implement the EU-wide CO₂ emissions reduction targets but also national pledges and other energy and climate policies when the spatial resolution is finer.

The above suggests that the heterogeneity of unequal regions in terms of resources and socio-economic and sustainable policy context makes it difficult to find a direct relationship between spatial resolution and technology uptake, as this depends on a case-by-case basis. This example shows that heterogeneous regions must be modelled in great detail to avoid false signals to decision-makers for achieving the SDGs.

### 3.3.2 Different Timeslices Aggregations Yield Different Projections of Flexibility in the Energy System

Next, we test the hypothesis that aggregating the temporal intra-annual resolution smoothens the fluctuations of energy sources and demand and provides misleading signals regarding the additional measures policymakers need to support high integration levels of renewable energy in the system.

We use the EUSTEM instances, which have 11 regions and 8 periods from 2015 to 2050 but with different numbers of timeslices ranging from 48 to 2016, and we focus on the storage capacity deployment in the Decarbonisation scenario.

In line with findings from literature, e.g., in Kannan et al. (2015), Fig. 12 shows that at coarser intra-annual resolutions, storage deployment is less due to the lower supply and demand variability. The underestimation of the flexibility needed in the energy system for integrating renewable energy, here in the form of electricity storage, is notable in Fig. 12. Even when the selection and aggregation of the timeslices are based on advanced approaches, these methods remain sensitive to
<figure><img src="image_33.png" /><figcaption>**Fig. 12** Pump hydro and battery storage capacity in “Europe” in the Decarbonisation scenario with different intra-annual resolution varying from 48 to 2016 timeslices, with 11 regions and 8 periods from 2015 to 2050 (instances, 48_11_8, 72_11_8, 144_11_8, 288_11_8, 672_11_8 and 2016_11_8)</figcaption></figure>

the number and types of curves (Poncelet and Duerinck 2017; Densing and Wan 2022).

The intra-annual resolution is crucial for SDG7, not only for integrating renewable energy but also when modelling electricity access. High temporal and spatial resolution are important for technology integration and moving from a centralised to a decentralised energy system. Understanding technology integration to deliver SDG7 and SDG13, as well as other SDGs, is important when designing policies to achieve these targets. For instance, based on the example shown in Fig. 12, it would provide misleading insights to decision-makers and stakeholders regarding the role of storage and the need for policies that could support storage systems next to renewable energy technologies.

### 3.3.3 Different Regional and Temporal Aggregations Yield Different Projections of Energy System Cost

Finally, we examine the impact of different spatial and temporal resolutions on the costs of the energy system and the intensity of the policies (e.g., subsidies or taxes) required to achieve SDG7 and SDG13 for “Europe”. Figure 13 presents the difference in the energy system cost between the Decarbonisation and the Baseline scenarios in instances of different spatial and temporal resolutions. We use as a metric the difference in the costs because this is an indication to decision-makers on what does it cost to meet the targets. This is important for stakeholders since could help develop measures to mitigate these costs for the vulnerable households to also contribute to SDG1 (no poverty).

The results indicate that coarser resolutions regarding timeslices do not always imply lower costs. For example, the instances with 72 timeslices show lower costs than those with 48 timeslices. This is attributable to the more accurate dispatching of
<figure><img src="image_34.png" /><figcaption>**Fig. 13** Difference in the energy system costs between the Baseline and Decarbonisation scenario at different spatial and temporal resolutions; the colours in the chart are used to distinguish between instances of the same spatial resolution</figcaption></figure>

the power plants when using a higher intra-annual resolution. Still, model system costs vary due to the different treatments for increasing spatial resolution. For example, the disaggregation of the transmission grids and renewable resources when increasing the spatial resolution could lead to higher costs. The clear trend in the obtained results is that higher spatial resolutions are associated with higher costs to achieve the renewable and climate change mitigation policy targets. This is because of the better accounting for the local conditions and constraints when performing the impact assessment of energy and climate policies. However, this result is valid only when the higher spatial resolution is modelled with accurate regional data. Otherwise, misleading outcomes might arise, especially when dealing with linear programming (LP) models. For instance, in LP models, even a slight cost difference between two regions might result in investing all new capacity in that region with the lowest cost. In this regard, additional constraints should be imposed, or reformulation of the objective function is needed to avoid “corner solutions” in the optimisation of a multi-regional model.

Besides the above quantitative insights on the increased accuracy in the solutions obtained with higher spatial and temporal resolutions, we should also note that some SDGs are correlated with subnational administrative divisions. For example, SDG6 on clean water and sanitation or SDG11 on sustainable cities and communities require modelling at prefecture or municipality levels by default. Other SDGs, such as SDG1 on poverty elimination, require high spatial resolution and segmentation of households in energy systems and economic models. While SDG9 on industrial infrastructures by design calls for energy system models with accurate representation of the local conditions at subnational levels for new infrastructure development and sector coupling. Therefore, besides accuracy, also the modelling of the SDG themselves calls for high resolution modelling across all the three five main dimensions of energy systems models: space, time, technology, sector and policy.
All the above are only a few examples of SDGs that require complex energy and economic models, which in turn need sophisticated methods to solve them in reasonable times.

# 4 Conclusions

This chapter introduces two solver-based methods for accelerating the solution of large-scale energy system models that assess the interactions of SDGs. The first method optimises the IBM ILOG CPLEX/Barrier solver for shared-memory systems, while the second method uses the PIPS-IPM++ solver for distributed systems like High-Performance Computing Clusters. We demonstrate the two methods with EUSTEM, a TIMES-based energy system model for Europe, which operates at various spatial and temporal resolutions.

We find that effective parameterisation of the CPLEX/Barrier solver can significantly reduce the solution time compared to using the default options, and this depends on the model matrix's non-zero structure and the Cholesky factorisation's complexity in each iteration of the algorithm. We also find that the solution times with the parallel solver PIPS-IPM++ do not scale with the model size, but this outcome depends on the annotation strategy to reveal the block structure of the model matrix to the solver, on the number of constraints and variables that spanning several blocks, and on the number of blocks of unequal sizes (the fewer, the better).

Solver-based methods can complement model-based techniques and detect model errors. However, applying these methods efficiently requires knowledge of the solver's algorithmic internals and the model's domain and structure. It's important to note that solver parametrisation and model annotation may need to be redone when new variables and equations are introduced. Therefore, solver-based methods may not be equally effective across different models or versions of the same model.

Applying suitable solver-based and model-based methods to reduce the solution times of large-scale energy systems models is important for SDG analysis. SDGs are vastly interlinked and connected to economic, fiscal, energy, environmental and societal variables. Moreover, some targets can negatively influence others, requiring policymakers to undertake arbitrage. Such complex interdependencies require high modelling detail to assess the implications of public policies on SDGs and uncertainty analyses. As energy is at the heart of the economic and social activities to which the SDGs refer, so they are the energy systems models. Without a high level of detail in the modelling, policy impacts might be overestimated, sectoral (and SDG) interdependencies may only be coarsely captured, and there is a misalignment between models with the SDG priorities and policy coherence.

**Acknowledgements** We thank our colleagues from the BEAM-ME project who provided insight and expertise that greatly assisted the research. We would especially like to thank Fred Fiand and Michael Bussiek from GAMS for their helpful hints and support with GAMS language features and CPLEX\Barrier options. We thank Thomas Breuer and Dmitry Khabi for their help with setting up
and using the computers at the Supercomputing Centers in Jülich (JSC) and Stuttgart (HLRS), respectively. Further, we also thank Daniel Rehfeldt from Zuse Institute Berlin (ZIB) for his tremendous support with the parametrization and operation of the PIPS-IPM++ solver, as well as for solving our instances. Finally, we would like to thank Prof. Dr. Russel McKenna and Dr. Tom Kober from the Paul Scherrer Institute (PSI) for their comments that greatly improved the manuscript.

**Credit Author Statement E. Panos:** Conceptualisation; Methodology; Software; Supervision; Writing—original draft; Writing—review and editing; Funding acquisition. **A. Hassan:** Methodology; Data curation; Software; Writing—original draft; Writing—review and editing.

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# Enabling Coherence Between Energy Policies and SDGs Through Open Energy Models: The TEMOA-Italy Example

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Matteo Nicoli, Maria Elena Alfano, Farzaneh Amir Kavei, Alessandro Balbo, Gianvito Colucci, Daniele Lerede, Daniele Mosso, and Laura Savoldi

**Abstract** This chapter highlights the significance of open-source energy system optimization models in enhancing the transparency and accessibility of energy system studies for policymakers. It provides a detailed example of the creation of a robust modeling framework. This includes guidance on selecting appropriate inputs, interpreting results, and connecting them to policy-relevant objectives such as the Sustainable Development Goals (SDGs), particularly SDGs 6 (water), 7 (energy), 8 (work and economic growth), 9 (industry), 13 (climate) and 15 (land). The focus is on the energy system optimization model TEMOA-Italy, a case study for Italy developed within the open-source framework TEMOA. The presented results explore the impact of possible future scenarios and energy policies on the power sector's sustainability, showing that low emissions scenarios perform better than a base scenario concerning environmental aspects, but worse in terms of land use and social aspects like the quality of labor. Import dependence is also affected by the renewables' penetration, due to the criticality of renewable technologies imports. The exclusion of carbon capture from the set of available new technologies improves geopolitical stability and reduces volume shortage risk.

## Key Messages

* TEMOA-Italy, as an open-source and open-data model, allows the evaluation of the effectiveness of energy policies in addressing the system sustainability in a fully transparent and easy to replicate manner.

M. Nicoli (✉) · M. E. Alfano · A. Balbo · G. Colucci · D. Mosso · L. Savoldi
MAHTEP Group, Department of Energy “Galileo Ferraris”, Politecnico di Torino, Turin, Italy
e-mail: matteo.nicoli@polito.it; marialena.alfano@polito.it; alessandro-balbo@polito.it; gianvito.colucci@polito.it; daniele.mosso@polito.it; laura.savoldi@polito.it

F. Amir Kavei · D. Lerede
Department of Economics and Statistics “Cognetti de Martiis”, Università degli Studi di Torino, Turin, Italy
e-mail: farzaneh.amirkavei@unito.it; daniele.lerede@unito.it
* Several sustainability indicators, concerning the environmental, security and social dimensions are investigated in the context of the SDGs.

* Low emissions scenarios significantly reduce most of the environmental impacts (SDGs 6 on water and 13 on climate), to the detriment of land use (SDG 15), import dependence, and quality of labor (SDG 8).

* Excluding the deployment of carbon capture technologies indirectly improves geopolitical stability by forcing a lower reliance on fossil fuels, creating a synergy with the decarbonization target.

# 1 Introduction and Motivation

Crafting sustainable energy policies requires a deep understanding of their environmental, social, technical, and economic impacts to ensure realistic and effective implementation (Perdigão 2023). Historically, energy policymaking has struggled with outdated tools, failing to adequately address emerging challenges such as integrating fluctuating renewable energy sources, adapting to rapid technological changes, and managing the socio-economic aspects of energy transitions. A key obstacle in this process is the information gap between the scientific community and policy-making entities. As noted by (Mohtar and Daher 2016), the “fragmentation between the scientific and policy communities” needs to be addressed. Furthermore, the tools and information used by stakeholders are often not easily accessible or transparent, creating barriers to informed decision-making. This context underscores the need for enhanced communication and transparent, accessible tools in energy policy formulation.

This chapter provides an example of using an open-source Energy System Optimization Model (ESOM) to assess the sustainability of the future system evolution according to several sustainability indicators, including specific Sustainable Development Goals (SDGs) like 6 (water), 7 (energy), 8 (work and economic growth), 9 (industry), 13 (climate), and 15 (land). The proposed model instance is based on Tools for Energy Modeling Optimization and Analysis (TEMOA), and it represents a case study for the Italian energy system. The analysis presented in this chapter focuses on the power sector, given its key role in decarbonization strategies in the next decades (Martins et al. 2022).

Section 2 presents the main features and data needed to develop the model, while Sect. 3 introduces the indicators used to evaluate the system’s sustainability. Results are discussed in Sect. 4 and Sect. 5 reports the main conclusions and perspectives.

# 2 Model Structure

The main techno-economic parameters used to describe a technology in the TEMOA formulation are shown in Fig. 1.
<figure><img src="image_37.png" /><figcaption>**Fig. 1** The main techno-economic parameters associated with a TEMOA technology and connection with physical (energy and material), demand and emission commodities</figcaption></figure>

TEMOA tackles a linear optimization problem comparable to standard TIMES models (Loulou et al. 2016). This problem involves minimizing the objective function, which represents the total cost of the energy system (denoted as $C_{tot}$). The total cost, calculated in Eq. 1, depends on the discount factor (DiscountFactor, representing the discounted value to the beginning of the time horizon of a unitary payment) and the cost values of individual technologies chosen in the optimal technology mix. Three key parameters in technology modeling play a crucial role in computing the objective function: investment cost ($C_{invest}$ [M€/cap.]), fixed operation and maintenance (O&M) cost ($C_{fixed}$ [M€/cap.]), and variable O&M cost ($C_{variable}$ [M€/cap.]). While investment cost and fixed O&M cost are linked to a technology's installed capacity, variable O&M cost is tied to the total flow of output commodities. $LA_{r,t,v}$ is used to annualize a technology's investment cost, determined by the process-specific loan length and discount rate.

$$ 
\begin{aligned}
C_{tot} = C_{loans} &+ C_{fixed} + C_{variable} \\
&= \sum_{r, t, v} (\text{CostInvest}_{r,t,v} \cdot LA_{r,t,v} \cdot \text{DiscountFactor} \cdot \text{Cap}_{r,t,v}) \\
&+ \sum_{r, p, t, v} (\text{CostFixed}_{r,p,t,v} \cdot \text{DiscountFactor} \cdot \text{Cap}_{r,t,v}) \\
&+ \sum_{r, p, t, v} \left( \text{CostVariable}_{r,p,t,v} \cdot \text{DiscountFactor} \cdot \sum_{s, d, i, o} \text{FO}_{r,p,s,d,i,t,v,o} \right)
\end{aligned} 
\quad (1) $$

The TEMOA-Italy database is rooted in energy statistics provided by the International Energy Agency (IEA) for the year 2006 (the “base year” of the time horizon), as extensively described in Nicoli (2021) and Nicoli (2022). It explores future energy scenarios on a time scale up to 2050, subdivided into several time periods. The model is fully calibrated (i.e., it matches actual energy statistics) from the base year up to 2020. Each time period is split up into refined time slices considering four seasons (winter, spring, summer and fall) and four times of day (night, morning,
<figure><img src="image_38.png" /><figcaption>Fig. 2 Graphical representation of the TEMOA-Italy reference energy system (MAHTEP Group 2023). Note: The interconnection between the upstream, power sector, hydrogen module, CCUS module, and demand-side sectors is visualized through energy commodities and arrows which represent the direction of the energy flows</figcaption></figure>

noon and afternoon) to capture the different behavior of, e.g., intermittent electricity generation technologies.

A schematic view of the TEMOA-Italy reference energy system is reported in Fig. 2. The upstream sector generates the fossil and renewable commodities required to feed the demand sectors on the right-hand side, after a series of transformation processes (central part of Fig. 2). The demand-side considers buildings (including residential and commercial buildings, and the agricultural sector), industry (in five energy-intensive subsectors characterized in full detail plus other energy-intensive industries) and (road and non-road) transportation.

The energy service demands to be satisfied, defined for the abovementioned demand sectors, are projected along the analyzed time horizon according to Eq. 2, wherefor two time steps t and t−1, Demand_t and Demand_{t−1} are the service demand levels, δ_t and δ_{t−1} are the driver values, and e_t is the elasticity of the driver to the demand associated with time step t. The demands need to be satisfied for every time step and are projected according to the methodology described in Oliva et al. (2021).

$$ \text{Demand}_t = \text{Demand}_{t-1} \cdot \left[ 1 + \left( \frac{\delta_t}{\delta_{t-1}} - 1 \right) \cdot e_t \right] \quad (2) $$

The upstream sector belongs to the supply side of the RES and includes the primary production of energy commodities, their transformation into refined fuels, and the
<figure><img src="image_39.png" /><figcaption>**Fig. 3** Import prices of coal, oil, natural gas, and LNG modeled in release 3.0 of TEMOA-Italy (MAHTEP Group 2023)</figcaption></figure>

eventual foreign trade in terms of import and export (Fig. 2). Concerning fossil fuels, coal, oil, and natural gas extraction are modelled, considering as maximum availability constraints the so-called proved, probable, and possible reserve data. Then, the production of refined fossil fuels is accounted for, including primary and secondary transformation processes. The primary production of biofuels encompasses solid biomass, bioethanol, biodiesel, and biogas, it also includes the upgrade of the latter into biomethane—more details are provided in Colucci et al. (2023). Besides, secondary production regards the gasification and liquefaction of natural gas. The availability of the other renewables, namely solar, wind, hydroelectric, biomass and geothermal, is defined through potentials that are constrained elaborating the values from Ruiz et al. (2019). The trade of refined fuels and electricity is modeled through fictitious import and export processes characterized by trade prices. The import prices for the main fossil fuels are shown in Fig. 3: the price spikes due to the recent energy crisis are accounted for. The complete set of data implemented in release 3.0 of the TEMOA-Italy upstream sector is available in MAHTEP Group (2023).

The structure of the main energy sectors constituting the model is described in Nicoli (2021) for buildings and agriculture, Lerede (2021) for industry, Lerede (2020) for transport, and Balbo (2023) and Colucci et al. (2023) for the hydrogen and CCUS modules.
## 2.1 Power Sector

Focusing on the power sector, Fig. 4 shows the main technology groups and their input/output commodities and highlights the connections with the other sectors of the model, namely, the hydrogen and CCUS modules and the demand sectors (including electricity and heat consumption options). Table 1 shows a summary of the main parameters used for the modeling of the existing technologies aggregated by plant category (power, CHP, and heat production plants) and input resource (more than one technology is associated with each resource). The capacities of existing technologies lead to a total gross capacity in 2006 equal to 91.80 GW (including heat plants), as from statistics by the Italian TSO (Terna).

The complete techno-economic characterization of new technologies included in the power sector is available in Mosso et al. (2024) and MAHTEP Group (2023). The time dependent parameters (e.g., renewables capacity factors) are modeled as presented in Nicoli (2024). While several technology groups are present in the sector, the main technology categories are electricity generation plants, CHP and micro-CHP plants (combined electricity and heat production), and heat generation plants (heat production). More specifically, the possible energy inputs for the power sector are fossil fuels, biofuels, renewables, and hydrogen. The techno-economic parameters of power plants with CCS and the hydrogen fuel cell are taken from the JRC-EU-TIMES Model (Simoes et al. 2013). The discount rates are from Laera (2024).

<figure><img src="image_40.png" /><figcaption>Fig. 4 The TEMOA-Italy (release 3.0) power sector (MAHTEP Group 2023)</figcaption></figure>
<table><caption>**Table 1** Calibration of the existing technologies in the TEMOA-Italy (release 3.0) power sector (MAHTEP Group 2023)</caption><thead><tr><th>Category</th><th>Resource</th><th>Efficiency (%)</th><th>Existing capacity (GW)</th><th>End of life</th><th>Fixed O&amp;M cost (M €<sub>2009</sub>/GW)</th><th>Variable O&amp;M cost (M €<sub>2009</sub>/PJ)</th><th>Capacity factor (%)</th><th>Capacity credit (%)</th><th>CHPR</th></tr></thead><tbody><tr><td rowspan="7">Power plants</td><td>Coal</td><td>32</td><td>7.73</td><td>≈2030</td><td>31</td><td>0.46</td><td rowspan="7">≈40</td><td rowspan="7">100</td><td rowspan="7">–</td></tr><tr><td>Oil products</td><td>35</td><td>9.28</td><td>≈2030</td><td>32</td><td>0.47</td></tr><tr><td>Natural gas</td><td>46</td><td>28.03</td><td>≈2050</td><td>18</td><td>0.49</td></tr><tr><td>Biofuels</td><td>27</td><td>0.76</td><td>≈2030</td><td>13</td><td>0.36</td></tr><tr><td>Geothermal</td><td>10</td><td>0.79</td><td>≈2030</td><td>94</td><td>3.48</td></tr><tr><td>Hydroelectric</td><td>–</td><td>21.38</td><td>–</td><td>25</td><td>0.08</td></tr><tr><td>Solar</td><td>–</td><td>0.02</td><td>≈2025</td><td>31</td><td>13.89</td></tr><tr><td rowspan="4">CHP plants</td><td>Wind</td><td>–</td><td>2.12</td><td>≈2020</td><td>34</td><td>–</td><td rowspan="4">≈60</td><td rowspan="4">100</td><td rowspan="4">27</td></tr><tr><td>Coal</td><td>37</td><td>0.91</td><td>≈2030</td><td>221</td><td>0.83</td></tr><tr><td>Oil products</td><td>35</td><td>3.23</td><td>≈2020</td><td>32</td><td>0.47</td></tr><tr><td>Natural gas</td><td>48</td><td>14.83</td><td>≈2050</td><td>29</td><td>0.61</td></tr><tr><td rowspan="3">Heat plants</td><td>Biofuels</td><td>39</td><td>0.82</td><td>≈2050</td><td>221</td><td>0.83</td><td rowspan="3">50</td><td rowspan="3"></td><td rowspan="3">125</td></tr><tr><td>Natural gas</td><td>80</td><td>0.77</td><td>≈2035</td><td>–</td><td>–</td></tr><tr><td>Geothermal</td><td>80</td><td>1.13</td><td>≈2035</td><td>–</td><td>–</td></tr></tbody></table>
## 2.2 Constraints

The main sources of data for the applied set of constraints are:

- TERNA Statistics (Terna), Eurostat Energy Balances (Eurostat 2023) and GSE Statistics (Gestore Servizi Energetici (GSE)) for the calibration of the historical period 2006–2020.

- Integrated National Energy and Climate Plan 2019 (Ministry of Economic Development et al. 2019), Long term Italian strategy for greenhouse gas emission reduction (Ministry of the Environment and Land and Sea Protection et al. 2021) and Fit for 55 (European Council 2021) with respect to stated future policies implemented in the model. This includes the phase-out of coal power plants no later than 2030.

- Elaboration from ENSPRESO Database (Ruiz et al. 2019), for renewable future potentials.

Concerning the minimum and maximum constraints applied to import and export technologies, they are equal to 95% and 105% of the historical data (Eurostat 2023) respectively for the 2006–2020 period, while are linearly projected from 2020 to 2050 assuming a minimum equal to 0 in 2050 and a maximum equal to 1 ~ 2 times the 2020 value. The complete set of constraints is available in MAHTEP Group (2023).

## 2.3 Emissions Accounting Methodology

The emission accounting methodology adopted for the model is dynamic. Indeed, it is capable of accounting for the avoided emissions from the low-carbon fraction in blends with fossil fuels, with a variable composition across the time horizon. That would not be possible by using the commodity-emission factors (CEFs) traditionally adopted to compute fuel combustion emissions which are based on a given static fuel composition. The dynamic method presented in Colucci et al. (2023) and Colucci et al. (2022) is currently applied to CO₂ emissions, while the combustion of low-carbon fuels (LCFs), namely hydrogen, biofuels, and synfuels is not considered to affect the atmospheric CO₂ concentration. Hence, when they are mixed with fossil fuels (at the level of the fuel technologies (FTs)), the CO₂ emissions due to the consumption of the sectorial commodities produced by the FTs are lower than in the case of pure sectorial fuel: this is accounted for in the dynamic methodology by using negative process emission factors (PEFs) proportional to the LCF fractions. This logic is schematized in Fig. 5: these PEFs are applied to the FTs for the hydrogen and biofuel fractions, while for synfuels they are used at the level of the production technologies. The net sectorial CO₂ is the sum of the CEF-CO₂, that is computed through the static CEFs applied to the sectorial fuel, and the PEF-CO₂ (FT), that is computed through the PEFs applied to the fuel technology while
<figure><img src="image_41.png" /><figcaption>**Fig. 5** Scheme of the dynamic emission accounting methodology applied to a generic demand-side sector (dashed box). *Note*: The bigger grey clouds represent the CO₂ emissions due to the consumption of the sectorial fuel, while the smaller ones are the CO₂ fractions associated to the low-carbon fuels (with filling pattern correspondence)</figcaption></figure>

accounting for the hydrogen and biofuel fractions. The synfuel contribution is already compensated through a negative PEF at the level of its production, namely PEF-CO₂ (SF). The methodology is flexible, such that it can be extended to other greenhouse gases and is also applicable in the case of non-null emission contributions from the LCFs (e.g., possible global warming potential of biogenic CO₂). Moreover, it allows to adequately assess the decarbonization potential of using low-carbon fuels in current existing infrastructure. Indeed, under certain mixing shares, conventional technologies can be used without the need for retrofitting: this would contribute to achieving the short-to-medium energy transition targets, whilst also considering the SDG 7 of the United Nations aiming to ensure affordable and clean energy for all by 2030.

## 3 Sustainability Indicators

Enhancing coherence between energy policies and sustainable development is an intricate task, since the proper definition of sustainability is hardly agreed upon, when referring to the energy perspective (Muniz et al. 2020). In the energy domain, integrating various elements of the SDGs into energy system models is crucial (Niet et al. 2021). This integration enables the identification of policy trade-offs and the discovery of synergistic benefits between goals.

Despite the different sectorial, spatial and time horizons of energy models, the integration of sustainability-related aspects within ESOMs raises the question of how sustainability is accounted for and computed (Martín-Gamboa et al. 2017). Attempts have been performed for a direct integration of sustainability measures in the optimization strategy (endogenous integrations), or by conducting sustainability
assessments on the outcomes of the energy models (ex-post analysis) (Blanco et al. 2020). In the given context, a post-processing approach is developed because it can be easily applied to ESOMs, without necessitating modifications to the model structure.

A broad scientific consensus exists about the aspects that are required to be accounted for in ex-post sustainability assessments. Notably, an environmental dimension is acknowledged in relation to factors such as global warming, deforestation, and pollution of air, land, and water (Gayen et al. 2023). Additionally, an economic dimension is considered, including energy profitability and affordability. Moreover, attention is increasingly directed towards the capability of energy systems at providing reliable energy, with a focus on both short-term grid security and long-term geopolitical considerations (Brodny and Tutak 2023). Lastly, a noteworthy trend in recent studies is the emergence of social sustainability, denoting the impacts of energy on society. This dimension encompasses aspects such as acceptability and social impact (Marrero et al. 2021). The economic and the technical dimensions are endogenously considered by ESOMs during the optimization process.

With those premises, Table 2 provides an overview of the selected indicators to conduct the sustainability analysis presented in this chapter. Selected indicators directly align with electricity production (expressed in ESOM by plants activity). Some include an Impact over Activity format, by definition (e.g., environmental indicators). Others necessitated mathematical treatments, assumptions, and simplifications, detailed in (Mosso et al. 2024) alongside supporting data, ensuring transparency, and facilitating interpretation within the broader analysis.

In the next step, such indicators should be translated in policy relevant information (OECD 2008). In particular, the focus is on comparing the performance of different energy scenarios. In other words, it is necessary to establish a quantitative or a qualitative measure derived from a series of observed outcomes that can reveal relative positions (e.g., of a scenario) in a given area (e.g., sustainability) (Miola and Schiltz 2019).

Two primary approaches are usually proposed to develop the SDG metrics (Miola and Schiltz 2019): either creating various distinct pieces of information or condensing information into a single, integrated indicator (OECD 2008). This reflects a common challenge in measuring complex concepts like sustainable development, and a trade-off occurs between the comprehensiveness of a single indicator and the specificity and detail of multiple metrics (OECD 2008).

This study follows the first approach and focuses on multiple aspects analyzed separately. The temporal variation of the indicators of Table 2 within predefined scenarios is analyzed. The data source and the detailed data gathering procedure for the calculation of the indicators are based on Mosso et al. (2024).

Firstly, individual power sector technologies are characterized using the 12 impact/activity indicators presented in Table 2. However, since transitioning from technology-specific analysis to scenario-level insights is the goal of this analysis, a transformative step is necessary. To achieve this, a weighted average approach is adopted which takes activity share as a proxy to perform the average.
<table><caption>**Table 2** Description of sustainability dimensions and indicators</caption><thead><tr><th>Sustainability dimension</th><th>Sustainability indicator</th><th>Overview</th><th>Unit of measure</th></tr></thead><tbody><tr><td rowspan="5">Environmental</td><td>Global warming potential (GWP)</td><td rowspan="5">Environmental impact is measured in a cradle-to-grave approach, considering the full life cycle of the plant, as specified in ISO 14040 (International Organization for Standardization (ISO) 2006) and United Nations Economic Commission for Europe (UNECE) (2021). They express the average impact for each unitary output of electricity.</td><td>(kgCO<sub>2</sub>,EQ) / MWh</td></tr><tr><td>Acidification Potential (AP)</td><td>(gSO<sub>3</sub>,EQ) / MWh</td></tr><tr><td>Eutrophication Potential (EP)</td><td>(gPO<sub>4</sub>,EQ) / MWh</td></tr><tr><td>Land use</td><td>(m<sup>2</sup>) / MWh</td></tr><tr><td>Water use</td><td>(m<sup>3</sup>) / MWh</td></tr><tr><td rowspan="4">Security</td><td>Reliability</td><td>Reliability is represented by the capacity factor of the technologies (Nock and Baker 2019).</td><td>Capacity Factor (%)</td></tr><tr><td>Import Dependence</td><td>The share of imported critical commodities (energy and materials) over total commodities needed for the technology operation is used, taken from Ministry of Environment and Energy Security (2023).</td><td>(%)</td></tr><tr><td>Volume shortage risk</td><td>Volume Shortage Risk is represented by the percentage of supply not affected by the possible unavailability of the biggest energy or material supplier, using the "N-1" criteria (Carrión et al. 2021).</td><td>N - 1 Residual Supply (%)</td></tr><tr><td>Political stability index</td><td>This indicator is based on the political stability index of countries supplying energy and materials, weighted on the import shares of the commodities (Mosso et al. 2024).</td><td>Political Stability Index (-)</td></tr><tr><td rowspan="3">Social</td><td>Human health damage</td><td>This indicator is expressed in Disability Adjusted Lifetime Years (DALY), estimating the number of years lost due to ill-health, disability, or early death, due to the technologies over their lifetime (Mosso et al. 2024).</td><td>(DALY) / MWh</td></tr><tr><td>Fatalities</td><td>This indicator estimates the number of deaths due to power plants construction, material supply and operations (United Nations Economic Commission for Europe (UNECE) 2021).</td><td>(Deaths) / MWh</td></tr><tr><td>Quality of labour</td><td>The Human Development Index (Mosso et al. 2024) is used as a proxy of the quality of labor.</td><td>Human Development Index (-)</td></tr></tbody></table>

Equation 3 summarizes the calculation, where each technology's indicator value (units per MWh) is multiplied by the corresponding electricity production share within the scenario (%) and then summed across all technologies.
$$AI_{s,i} = \sum (AS_{t,s,i} \cdot TI_t) \quad (3)$$

While AI<sub>s,i</sub> represents the Average Indicator for scenarios in year i, AS<sub>t,s,i</sub> is the Activity Share of technology t in scenarios in the same year, and TI<sub>t</sub> is the Technology Indicator for technology t. The sum is made over all technologies involved in the scenario.

This method ensures each technology's contribution to the scenario-level indicator profile reflects its relative importance in electricity generation. The outcome is an indicator profile for each scenario, resulting from the activity of all of the technologies composing the scenario. This methodology is valid even for indicators lacking units, such as the security ones, with the underlying assumption that their impact is proportional to the technology's activity.

# 4 Scenarios and Results

Summary results from TEMOA-Italy together with the selected scenarios are presented in the following.

## 4.1 Scenarios

Table 3 shows the main features of the selected scenarios implemented in TEMOA-Italy. The mentioned emission limit was developed by merging the “Fit for 55” (Erbach et al. 2022) for 2030 and the “Italian long-term strategy for greenhouse gases emission reduction” targets (Ministry of the Environment and Land and Sea Protection et al. 2021) for 2050. This results in emission limits of 194 Mt in 2030 and 29 Mt in 2050. Residual emissions are allowed in 2050 so as to be consistent with the absence of Agriculture, Forestry and Other Land Uses (AFOLU) options in the models, which are expected to contribute up to 45 Mt of CO<sub>2EQ</sub> removal in 2050 (equal to the historical peak reached in 2015) (Ministry of the Environment and Land and Sea Protection et al. 2021).

The reason for also investigating the “No CCUS” scenario resides in its relatively low readiness levels (with respect to other technology sectors). Moreover, the fact that CCS technologies significantly contribute to emission reduction in the “Net0”

<table><caption>**Table 3** Features of the selected scenarios</caption><thead><tr><td>Scenario</td><td>CO<sub>2</sub> emission limit</td><td>Hydrogen availability</td><td>CCUS availability</td></tr></thead><tbody><tr><td>Base</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Net0</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>No H<sub>2</sub></td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>No CCUS</td><td>Yes</td><td>Yes</td><td>No</td></tr></tbody></table>
scenario makes exploring the model’s behavior in their absence interesting, as is also the case for the “No H₂” scenario, excluding hydrogen production and consumption technologies.

## 4.2 Energy and Emissions

Figure 6 presents the yearly final energy consumptions and emissions for the selected scenarios together with a result validation (referred to as “Cal. 2020” in the figure) against historical data for 2020 (referred to as “Hist. 2020” in the figure).

Concerning the comparison with historical data, no significant differences emerge neither for the final energy consumption by energy source (Fig. 6a), nor the total CO₂ emissions in 2020. Looking at the “Base” scenario, an 8% increase in the 2050 final energy consumption can be appreciated with respect to 2020, mainly driven by a growing oil products consumption (in the transport sector, mostly due to the increasing aviation demand). This is also reflected in the emissions breakdown (Fig. 6b) for “Base” in 2050, showing an increase in the emissions from the transport sector, partially compensated by efficiency improvements in the other sectors and higher penetration of renewables (as the power sector emissions reduction also suggests).

A non-negligible role in reducing emissions in the “Net0” scenario is also played by biofuels (mainly biomethane, blended with fossil natural gas) and hydrogen (mainly consumed by aviation technologies accounting for 8% of the final energy consumption, while the Italian Hydrogen Strategy aims for 20% (Ministry of Economic Development 2020) (Fig. 7). Synfuels seem not to be competitive in the studied scenario.

Concerning the three decarbonization scenarios, they are all characterized by complete power sector decarbonization and high electrification of end-uses (Fig. 7). The latter also allows a significant reduction of the total final energy consumption (despite the increasing final service demands) attributable to the higher efficiency of electric technologies compared to thermal options (e.g., in the transport sector).

While the “No H₂” and “No CCUS” scenarios are characterized by a higher degree of electrification and (consequently) a lower final energy consumption with respect to “Net0”, the main difference occurs in the emission levels (Fig. 6b). Indeed, the lack of availability of hydrogenin “No H₂” implies higher emissions from the transport sector and requires a deeper decarbonization of industry to be consistent with the emission limit. The carbon capture moves from the upstream sector in the “Net0” scenario (hydrogen production with carbon capture) to direct air carbon capture in “No H₂”. Eventually, the absence of capture options in the “No CCUS” requires the complete electrification of buildings (residential and commercial) through heat pumps, while the residual emissions are from agriculture, industry, and transport. More detailed results are discussed in Colucci et al. (2023) for the “Net0” scenario only.
<figure><img src="image_42.png" /><figcaption>**Fig. 6** TEMOA-Italy final energy consumption by energy commodity and scenario compared to 2020 historical data (a) and emission levels by energy sector and scenario compared to 2020 historical data (b)</figcaption></figure>
<figure><img src="image_43.png" /><figcaption>**Fig. 7** TEMOA-Italy electricity production mix by energy commodity and scenario compared to 2020 historical data</figcaption></figure>

**4.3 Sustainability**

The evaluation of the sustainability indicators for the applied energy scenarios is shown in Fig. 8. This evaluation reflects the indicators described in Table 2 applied to the scenarios of Table 3. Due to the similarity of profiles among the 12 indicators, “No H₂” and “No CCUS” have been incorporated into the “No H₂ – No CCUS” profile.

Considering the environmental indicators, they collectively demonstrate a downward trajectory, with the GWP and AP averaging 50–60% reduction in 2050 and Eutrophication Potential decreasing by approximately 40–50%. These declines happen for the “Net0” scenario, which aggressively targets emissions reductions, although the benefits come at the expense of a dramatic increase in Land Use. This indicates a significant environmental trade-off, where lower impacts with respect to global warming may lead to heightened land resource demands for renewable deployment. Finally, water use exhibits a significant reduction in Net0, driven by the reduced reliance on fossil fuel plants, characterized by a higher water footprint.

Security indicators within the energy sector present a nuanced landscape. Reliability and Volume Shortage Risk show negligible changes under the “Base” and “No CCUS” scenarios, indicating a “status quo” in these areas. However, under the
<figure><img src="image_44.png" /><figcaption>**Fig. 8** Evaluation of the 12 sustainability indicators evolution from 2020 to 2050 according to the considered scenarios. *Note*: Solid blue for “Base”, dashed red for “Net0”, dashed green for “No H₂” and “No CCUS” (Color figure online)</figcaption></figure>

“Net0” scenario, these indicators diverge, with Volume Shortage Risk registering a positive shift with a reduction potentially ranging from 10% to 15%, denoting a decrease in the risk of supply shortages. This trend is supported by the growing integration of photovoltaic and wind energy in the Net0 scenario, as these technologies offer superior commodity diversification compared to their counterparts. Conversely, Reliability experiences a negative variation, driven by the higher share of variable renewables, notably characterized by lower capacity factors. Import Dependence decreases almost 20% across all scenarios, due to the lower reliance on critical imports associated with new technologies deployment. Geopolitical Stability presents a general improvement, culminating in an increase to a value of 0.5, where the “Net0” scenario again shows a better performance, potentially reflecting the benefits of a diversified energy strategy relying on more trustable partners.

Human Health Damage, closely related to environmental quality, shows a significant decrease, particularly under scenarios that prioritize emissions reduction, emphasizing further the positive intersection of environmental policy and public health outcomes. Fatalities, even if they result in a minimal difference between scenarios by 2050, exhibit a peak in 2030 in Net0 while they are smaller in No
CCUS, with the latter appearing to be the safer option. This is driven by a lag in
renewable installation by the CCUS. Indeed, especially for wind and hydro, fatalities
are relatively higher compared to other model technologies.

Conversely, shifting to Net0 initially coincides with a decline in measured
Quality of Labor (using the Human Development Index). This trend implies poten-
tial challenges in transitioning towards power systems heavily reliant on renewable
energy, leading to a shift in the labor demand within countries marked by unfavor-
able labor conditions, particularly in critical supply chains for renewable materials.

Conclusively, the “Net0” scenario emerges as the most favorable in terms of mitigating environmental impacts, exhibiting marked improvements across the key environmental indicators such as GWP (by definition), Acidification Potential, Eutrophication Potential, and Water Use, which aligns with its intrinsic emphasis on stringent environmental policy and energy transition measures. However, the “Net0” scenario presents the highest Land Use compared to the other considered scenarios, due to the necessity to allocate land for renewables deployment. Simultaneously, socio-economic benefits are visible under this scenario, particularly with respect to diminishing Import Dependence and the Volume Shortage Risk, indicating a strategic reshaping of energy reliance patterns. However, the “No H₂” and “No CCUS” scenarios, by relying less on fossil fuels, unveils unique trends, particularly enhancing Geopolitical Stability.

# 5 Conclusions and Perspectives

## 5.1 Conclusions

The chapter illustrates how to properly evaluate the implications of energy scenarios as to the overall system sustainability and achievement of the SDGs, using the open-source and open-data TEMOA-Italy combined with a set of indicators reflecting environmental, security, and social dimensions of the transition. These findings underscore the complexity of energy transition pathways and highlight the importance of balancing environmental, social, and economic considerations in shaping sustainable energy futures.

The analysis illustrates the synergies between the net-zero emission target, the limitation of acidification and eutrophication risks and public health. However, this achievement comes with a notable increase in land use, indicating a trade-off between environmental benefits and land resource demands for renewable deployment.

Moreover, the net-zero scenario demonstrates promising strides in enhancing energy security and geopolitical stability and reducing supply shortage risks, although facing increased challenges in maintaining reliability. However, the transition to renewable-heavy systems poses initial challenges to labor quality and import dependence due to critical reliance on imports of renewable technologies.

If the net-zero emission scenario emerges as a frontrunner in addressing environmental concerns and reshaping energy reliance patterns, alternative scenarios like
"No H₂" and "No CCUS" offer unique advantages in terms of geopolitical stability and reduced volume shortage risk.

## 5.2 Perspectives

Several model improvements are on-going to contribute to better understanding crucial issues towards sustainable development of energy systems.

The link between energy and water resources is multifaceted. Water is an essential element in the energy value chain (Siddiqi and Anadon 2011) and, conversely, energy is indispensable for water withdrawal, treatment, and delivery to the end-users (Carter 2017). The study of water in ESOMs is not just about their reciprocal uses but extends to its central roles in realizing different SDGs directly (6, 7, and 13) and indirectly (2, 8, and 9). While a single resource modeling approach fails to capture the interconnection dynamics effectively, considering both water and energy resources enables the incorporation of additional inter and intra-sectoral factors, thus obtaining a more accurate present layout and future evolutions (Alfano 2022). For instance, integrated methodology can highlight the key role of the water supply sector in shaping both water system and the energy system demand side. By bridging the gap between energy and water modeling, integrated assessment paves the way to a substantial planning uplift for policymakers and researchers engaged in water and energy resource management, in the perspective of achieving the SDGs 6 and 7. As a future improvement, the integrated approach implemented in the TEMOA framework is also planned to be enriched by extending water-sector technologies and including water consuming energy-sector technologies.

Secondly, the transition from a fossil-based to a renewable-based energy system presents some challenges that traditional ESOMs are currently not able to address (Aryanpur et al. 2021). First, the location of suitable sites to place energy plants (considering the physical and atmospheric parameters determining its performance) may not coincide with the availability of electrical infrastructure. Then, the land use of a specific site may be constrained by many factors (e.g., administrative, technical, economic). In addition, optimal land allocation should consider all of the different multi-sectoral options for that specific site, ranging from agricultural to energy use (Ramos et al. 2022). Lastly, Variable Renewable Energy Sources (VRESs) are characterized by intensive land-use and variable production (Wang et al. 2020). In existing optimization models that minimize the total cost of the energy system, location-specific production profiles are often used to estimate VRES potential, but land-use and land cover aspects have been largely ignored (Wang et al. 2020). In the Italian context, these challenges are particularly relevant due to the significant landscape heritage and the economic relevance of the agricultural sector (ISTAT 2023), each imposing distinct constraints and tradeoffs in terms of land utilization. Consequently, to investigate how the integration of these aspects into ESOM could impact the proposed decarbonization pathways, the authors are in the process of developing a TEMOA-Italy land-specific model instance. Properly understanding
the interconnection between land use and the energy sector is of pivotal importance, especially in the context of the Water-Energy-Food Nexus (Liu et al. 2018) and realization of the SDG 15.

Eventually, the energy-material nexus is the latest extension of the TEMOA modeling framework: in particular, the problem is currently being addressed from an energy security perspective. Indeed, the spread of clean energy technologies can increase the energy independence of countries that presently have a high fossil fuel import reliance. However, the production of many so-called “clean” energy technologies (e.g., solar panels, wind turbines, battery electric vehicles) present high geographical concentration (mainly in China (IEA 2023)) along all the supply chain steps, from raw material extraction to component manufacturing and system assembly, thereby increasing the risk of possible supply bottlenecks (Carrara et al. 2023). Hence, the massive penetration of renewable energy stated by the worldwide energy policies could lead to new energy security issues, that must be strategically addressed (Hache 2018). Energy security, and in particular import dependence, is only one of the several aspects to consider when addressing the energy-material nexus. Indeed, future developments have already been identified regarding the environmental, social, and governance practices in the clean energy technology supply chain (Colucci et al. 2023), allowing for the transversal consideration of several SDGs such as the 7, 8, 9, and 12.

**Data Availability** The release 3.0 of the TEMOA-Italy database is available at https://github.com/MAHTEP/TEMOA-Italy/releases/tag/3.0, and the TEMOA version developed by MAHTEP Group is available at https://github.com/MAHTEP/TEMOA.

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Part II

# Using Energy System Modelling to Support the Transition to Renewable Energy
# Assessing the Impact of Climate Variability on Wind Energy Potential in Decarbonization Scenarios in Energy Systems Models

<figure><img src="image_45.png" /></figure>

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Bryn Stecher, Taiba Jafari, Lewis Wu, Olexandr Balyk, Áine Greene, and James Glynn

**Abstract** Anticipated changes in wind patterns and magnitudes due to climate change pose potential challenges to future wind energy potential. Using three shared socioeconomic pathways (SSP) across five global climate models, the impacts of climate variability on wind energy potential were assessed, utilizing the wind capacity factor as a comparable value. The evaluation includes all operating onshore and offshore wind farms globally over the remainder of the century. Adopting global statistical analysis methods and the TIMES United States model (TUSM), the influence of climate variability on wind energy is modeled, providing insights into how specific decarbonization scenarios impact the achievement of Sustainable Development Goals (SDGs), particularly SDG 7 (Affordable and Clean Energy) and SDG 11 (Sustainable Cities and Communities). Results reveal minimal variation in capacity factor values among the SSP scenarios, indicating that wind energy is likely to remain a robust power generation source, regardless of the chosen decarbonization scenario. These findings hold important implications for wind turbine design, deployment strategies, and regional energy planning and policy. The study underscores the need to consider climate variability in decarbonization strategies, emphasizing the role of wind energy in aligning with the objectives of SDG 7 and SDG 11.

## Key Messages

* The global path to decarbonization will shape wind generation patterns and strength, affirming wind as a reliable and robust source of energy, with variations in global wind capacity factors being mostly negligible compared to historical values.

B. Stecher (✉) · T. Jafari · L. Wu · O. Balyk · Á. Greene · J. Glynn
Center on Global Energy Policy, SIPA, Columbia University, New York, NY, USA
e-mail: bs3157@columbia.edu; tj2528@columbia.edu; zw2783@columbia.edu;
o.balyk@columbia.edu; ag4679@columbia.edu; james.glynn@columbia.edu
* Using TIMES, scenarios based on user-imposed economic and environmental constraints were analyzed, revealing increases in wind energy generation and new capacity installation in alignment with the goals of attaining SDGs 7, 11 and 13; onshore projects underscore sensitivity to climate impacts.

* Future annual wind energy potential (2015–2100), on average, is expected to remain relatively consistent with historical values (1981–2014).

* Policymakers should consider focusing on developing wind farms in high-potential regions, enhancing electricity infrastructure, and energy storage and mix diversification.

# 1 Introduction

Rapid global expansion of wind energy capacity is a core component of the future zero-carbon power system globally (IEA 2023; Intergovernmental Panel on Climate Change (IPCC) 2023). A remarkable surge in wind energy installed capacity, in response to climate change mitigation and improving energy security has occurred in the past two decades. However, there is minimal knowledge about how climate change may affect wind energy potential by the end of this century globally. Climate change will impact various climate variables such as surface wind speeds, wind patterns and intensity and thereby directly affect wind energy production in certain regions. In anticipation of additional new wind farm developments, planning wind turbine deployment in areas of projected high wind energy potential is beneficial.

Previous studies assessing the impact of climate variability on wind energy potential have concentrated on individual countries or specific geographic regions (Fournier et al. 2023; Miao et al. 2023; Soares et al. 2019; Tobin et al. 2016; Viviescas et al. 2019), specific decarbonization scenarios (Lobeto et al. 2021), did not include energy modeling (Jung and Schindler 2022; Pryor et al. 2020), and or a shorter timeline (Devis et al. 2018) which are often constrained by a limited spatial and temporal scope. This study overlooks the intricate spatial and temporal fluctuations in wind patterns and their consequential impact on wind energy. Additionally, previous studies have shown a decrease in wind energy in the Northern Hemisphere and the mid-latitudes, while an increase in the Southern Hemisphere and the tropics. This southward wind shift is linked to the consequences of polar amplification and enhanced land-sea thermal gradients (Karnauskas et al. 2018). Tropical processes and changes in subtropical static stability potentially also play a role in this southward shift in wind (Mbengue and Schneider 2013). However, some found that wind speeds decrease in the tropics (30°N – 30°S) but increase in the extratropics (30°–90° in both hemispheres) due to the intensification and poleward shift of the midlatitude storm tracks (Gastineau and Soden 2009). Additionally, wind speeds have decreased over the past several decades due to anthropogenic climate change, defined as ‘global stilling.’ Global stilling occurs since the arctic is warming at a faster rate compared to the tropics, which is causing a decrease in the temperature gradient between poles and equator, resulting in weaker atmospheric circulation patterns and wind speeds globally (Tian et al. 2019; Zeng et al. 2019).
This research investigates how climate variability and decarbonization scenarios could simultaneously affect the capacity factor of current operating wind farms globally. Decarbonization scenarios are future insights into how the world may respond to climate change mitigation and adaptation. By using historical data and five global circulation model simulations of daily wind from 2015 through 2100, a new analysis is presented on how changes in wind speeds from different SSPs affect wind energy production. As temperatures increase, the air becomes less dense, which reduces the speed of the wind and therefore the energy output of turbines. Additionally, under various SSPs, the weather conditions undergo diverse changes that impact wind patterns, influencing factors such as wind speed, direction, and overall atmospheric dynamics, thereby shaping the performance of wind energy systems. The results highlight areas where wind energy production is expected to fluctuate depending on the decarbonization scenario and global climate model. The findings can inform decision-making processes related to deploying wind turbines under various decarbonization scenarios within specific communities and regions and add to the larger conversation on the switch to more renewable energy sources in order to meet various infrastructural and climate goals.

An approach of maximizing wind energy production aligns with SDG 7: Affordable and Clean Energy, by examining the impact of climate variability and decarbonization scenarios on the capacity factor of wind farms globally. The capacity factor is a crucial metric for assessing wind energy operation and availability. The capacity factor of a wind turbine measures the actual power output of a wind turbine relative to its maximum power potential under ideal conditions and for a given wind speed is dependent on the International Electrotechnical Commission (IEC) classification of that turbine. Strategic development of wind farms in regions with projected high wind energy potential correlates to ensuring access to affordable, reliable and clean energy. Additionally, as climate change can lead to extreme weather events, including wind-related events, this research further aligns with SDG 11: Sustainable Cities and Communities, as it has implications for planning sustainable energy solutions in urban and rural communities. Improving the resilience of cities and human settlements by implementing informed planning and infrastructure development can help mitigate the impacts of climate-induced changes in wind patterns.

## 2 Methods

An in-depth statistical analysis of how wind farm capacity changes on a global scale over an 85-year period at a daily resolution was conducted. This novel approach, incorporating decarbonization scenarios and global climate models, aims to mitigate bias and enhance the robustness of the results for future projected scenario analysis. Subsequently, a TIMES United States energy system model (TUSM) was developed, and used to compare power sector scenarios with and without climate impacts and the corresponding projected effects on wind energy generation, electricity
supply and new capacity installation. Analyzing the TUSM results enabled discussion on the alignment of SDGs 7 and 11 to the energy transition. The overall objective was to compile a comprehensive outlook on the potential trajectories of wind speeds and their associated impacts on wind energy production, ultimately providing insights into the resilience and adaptability of wind farms in different decarbonization pathways.

## 2.1 Definition of the Decarbonization Scenarios

Three decarbonization scenarios, SSP 1-2.6, SSP 3-7.0, and SSP 5-8.5, run by five different global climate models, GFDL-ESM 4, IPSL-CM6A-LR, MPI-ESM 1-2-HR, MRI-ESM 2-0, and UKESM1-0-LL (Boucher et al. 2020; Dunne et al. 2020; Müller et al. 2018; Tang et al. 2019; Yukimoto et al. 2019) were used to assess the impact of climate variability on wind energy potential:

1. SSP 1-2.6: Represents a low-emission pathway, characterised by rapid and comprehensive decarbonization of the global economy. It involves a significant shift towards renewable energy sources, energy efficiency, and sustainable practices. Emissions are reduced substantially to limit global warming to well below 2 °C in line with the Paris Agreement;

2. SSP 3-7.0: Portrays a high-emission pathway, where emissions continue to rise due to limited efforts to reduce greenhouse gas (GHG) emissions. The global economy relies heavily on fossil fuels, and there is limited international cooperation to address climate change. Consequently, this scenario does not comply with the Paris Agreement and would lead to a projection of a 3.0 °C global mean temperature increase by 2084;

3. SSP 5-8.5: Emissions continue to increase at a high rate, primarily driven by a fossil fuel-dependent global economy. There is a lack of effective climate policies and little effort to mitigate GHG emissions. This scenario is highly incompatible with the Paris Agreement and would lead to a projection of a 3.0 °C global mean temperature increase by 2076.

The GFDL-ESM 4, IPSL-CM6A-LR, MPI-ESM 1-2-HR, MRI-ESM 2-0, and UKESM1-0-LL global climate models manifest distinctions in their portrayal of temperature changes, stemming from unique structural attributes and modeling methodologies. GFDL-ESM 4 stands out for its advanced representation of atmospheric, chemistry, carbon, and ecosystem dynamics utilizing the National Oceanic and Atmospheric Administration's (NOAA) coupled carbon-chemistry-climate model (Dunne et al. 2020). IPSL-CM6A-LR is recognized for its comprehensive and sensitive Earth system components and robust simulation of biogeochemical processes. However, IPSL-CM6A-LR has certain biases including the double Intertropical Convergence Zone, frequency of midlatitude wintertime blockings, and El Nino-Southern Oscillation dynamics (Boucher et al. 2020). MPI-ESM 1-2-HR
specifically examines oceanic and atmospheric conditions, including the El Nino-
Southern Oscillation climate phenomena and the North Atlantic Oscillation. This
yields a decreased bias of upper-level zonal wind and atmospheric jet stream position
in the northern extratropics (Müller et al. 2018). MRI-ESM 2-0 distinguishes itself
with its emphasis on cloud processes and improved representation of aerosols as it
has 80 atmospheric layers (Yukimoto et al. 2019). UKESM1-0-LL, the first United
Kingdom Earth System Model that uses climate model HadGEM3-GC31-LL as its
base, is notable for its high climate sensitivity and complex ocean, land, atmo-
spheric, and biochemical cycles that are unprecedented compared to other Earth
system models (Sellar et al. 2019). The models range in latitude-longitude grid
resolution from 1.0 to 2.0° with IPSL-CM6A-LR and UKESM 1-0-LL having the
lower resolution. Among the models, GFDL-ESM 4, MPI-ESM1-2-HR, and
MRI-ESM 2-0 exhibit similar projections of future temperature increases across
SSP scenarios, with annual temperatures anticipated to range from 15 to 18 °C by the
end of the century, where the annual average temperature in 2022 was 13.3 °C
(National Weather Service n.d.). Contrarily, IPSL-CM6A-LR and UKESM1-0-LL
project larger temperature increases as they account for larger climate sensitivities,
spanning 15.5–21 °C. Notably, under these latter two global climate models, the
temperature disparities between SSP 1-2.6 and the higher SSPs are more pronounced
than in the other three models. Across all five global climate models, SSP 5-8.5
demonstrates the highest temperature increase over time, closely followed by SSP
3-7.0, and then SSP 1-2.6. These variations emphasize the significance of consider-
ing specific modeling characteristics when interpreting temperature change projec-
tions derived from these models in the context of climate research.

## 2.2 Data Pipeline Process

The global climate data was accessed through The Inter-Sectoral Impact Model Intercomparison Project (ISIMIP), which provided access to surface wind speed historical and future data under each decarbonization scenario and global climate model (Lange et al. 2023). For the location of the wind turbines, the Global Energy Monitors’ (GEM) Wind Power Tracker data provided comprehensive information regarding the state of the geographical distribution of operational wind farms globally as of May 2023 (“Global Wind Power Tracker,” 2023). Using the nearest neighbor search technique without any tolerance level, the surface wind speeds were extracted at each operating turbine location. The data pipeline developed for this study, as depicted in Fig. 1 is a significant innovative aspect of the research work.

To convert the wind speeds to an 80 m hub height level, as this is the typical
height for onshore wind (Lee and Kang 2019), from a 10 m level, the empirical
power law (Hueging et al. 2013; Miao et al. 2023) was used, where S<sub>80</sub> is wind speed
(m/s) at an 80 m hub height and S is the near-surface wind speed (m/s):
<figure><img src="image_46.png" /><figcaption>**Fig. 1** Workflow used to generate capacity factors from surface wind speed data</figcaption></figure>
$$S_{80} = S \cdot \left(\frac{80}{10}\right)^{0.143} \qquad (1)$$

Having a 80 m hub height for all wind turbines, both onshore and offshore, is a broad assumption. However, this uniform assumption serves as a baseline to analyze changes in wind speeds at the most typical height. This approach promotes a reasonably tractable analysis within data limitations of the impact of decarbonization scenarios on wind energy at large, ensuring a fair assessment across different turbine types and locations.

An industry standard from the IEC was used to classify wind turbines based on their ability to withstand wind speeds and conditions and calculate the corresponding capacity factors. The IEC classification is determined based on the 80 m floored surface wind speed value of the individual turbine over its average lifespan, typically 25 years (Alsaleh and Sattler 2019). Within the scope of this study, three IEC classifications were used, ranging from Class I for turbines that can withstand the lowest wind speeds to Class III for turbines designed to withstand the highest ones. The wind profiles are based on normalized power curves for a 1 MW turbine for each of the three IEC classifications (Table 1).

## 2.3 Global Statistical Analysis

To examine the temporal evolution of wind capacity factors, this study involved a comparative assessment of future capacity factors with their historical counterparts. The investigation was initiated by calculating the average performance of individual wind turbines from 1981 to 2014 using ISIMIP's historical wind speed data. Subsequently, the daily and yearly differences between future and past wind speeds were quantified.

## 2.4 Overview of the TIMES United States (TUSM) Energy System Model Framework

This study builds on previous work using a TIMES United States model (TUSM) from Columbia University's Center on Global Energy Policy. While data is analyzed on a global scale, TUSM is used as an illustrative example of the comprehensive

<table><caption>**Table 1** IEC classifications</caption><thead><tr><th>25-year average surface wind speed 80 m floor value (m/s)</th><th>IEC classifications</th></tr></thead><tbody><tr><td>&lt;7.5</td><td>Class I</td></tr><tr><td>7.5 ≤ X ≤ 8.5</td><td>Class II</td></tr><tr><td>&gt;8.5</td><td>Class III</td></tr></tbody></table>
modeling capabilities available for examining and optimizing energy systems. TUSM is a model that stems from the International Energy Agency's (IEA) Energy Technology Systems Analysis Program's (ETSAP) Integrated MARKAL-EFOM System (TIMES) (IEA-ETSAP 2024), a bottom-up energy system optimization model. TIMES uses linear programming to determine the least-cost optimal energy system configuration based on various technical and economic constraints set by the user on medium to long-term timescales. TUSM, which is under ongoing development, currently models the United States' power sector using open source datasets including National Renewable Energy Laboratory (NREL) Annual Technology Baseline, Energy Information Administration (EIA) Form 860 and demand forecasts, and United States Environmental Protection Agency's (EPA) National Electric Energy Data System (NEEDS). The model studies the power sector on an annual, seasonal, weekly, daily, and hourly level to best capture the dynamics of the power sector from 2020 to 2050. The results shown are those using 40 time slices which means that the data is averaged by season and weekday type for each of the lower 48 states each as an aggregated node, such as weekdays in Fall 2020 in New York. TUSM computes the least-cost configuration of energy technologies that meet energy demands while adhering to technical, economic, and policy limitations as specified within a scenario analysis. To illustrate the interconnectedness of energy and climate change, TUSM provides a technology-rich basis for representing the power sector dynamics incorporating decarbonization scenarios. TUSM has operational constraints, including commodity prices, and the role of storage. The model offers a way to analyze the effect of a changing wind capacity factor on electricity supply and new capacity installations. The capacity or growth constraint of new wind annually cannot grow more than 11% year-over-year for 2024 onwards for onshore wind and 2023 for offshore wind. The 11% is derived from the United States' average annual increase in wind capacity (Hoen et al. 2018). Additionally, the years 2024 and 2023 were chosen as the data up until those years was exogenously specified in terms of installed capacity. For the years before 2024 for onshore wind and 2023 for offshore wind, the capacity or growth constraint is defined by the Energy Information Agency data.

Four scenarios were developed as shown in Table 2. The BASE (Reference) scenarios and Net-Zero 2035 (NZE35) scenarios represent the pathways with and

<table><caption>**Table 2** Scenario matrix</caption><thead><tr><td>Scenario name</td><td>Decarbonization scenario used for climate impacts</td><td>Description</td></tr></thead><tbody><tr><td>BASE (reference) with climate impacts</td><td>SSP 3-7.0</td><td>Wind capacity factor is changing from 2020 to 2100</td></tr><tr><td>BASE (reference) without climate impacts</td><td>—</td><td>Wind capacity factor locked at 2020 levels</td></tr><tr><td>NZE35 with climate impacts</td><td>SSP 1-2.6</td><td>Wind capacity factor is changing from 2020 to 2100</td></tr><tr><td>NZE35 without climate impacts</td><td>—</td><td>Wind capacity factor locked at 2020 levels</td></tr></tbody></table>
without wind related climate impacts and provide a benchmark of comparison for wind energy generation, electricity supply and new capacity installation. Climate impacts on solar photovoltaic operation or temperature impacts upon energy service demands are not included in the model at this stage. The capacity factors for the climate impact scenarios are derived from GFDL-ESM 4.

* **BASE scenario with Climate Impacts:** The Base scenario is the least cost optimal pathway that delivers energy service demands. This scenario includes the current macroeconomic outlook, but does not explicitly include any emissions or policy constraints. It further includes climate impacts upon wind energy capacity factors, aligns with the decarbonization scenario SSP 3-7.0 and the wind capacity factors are changing from 2020 to 2100.

* **BASE scenario without Climate Impacts:** The Base scenario in this instance is modeled without climate impacts considered upon wind capacity factors. As such, instead of having a capacity factor specified by SSP 3-7.0, the data is based on the actual state-level capacity factor from the year 2020.

* **NZE35 scenario with Climate Impacts:** The Net-Zero scenario is the least cost optimal pathway that delivers energy service demands based on net zero carbon dioxide emissions by 2035 in the power sector. It includes climate impacts, aligns with the decarbonization scenario SSP 1-2.6 and the wind capacity factors are changing from 2020 to 2100.

* **NZE35 scenario without Climate Impacts:** The Net-Zero scenario in this instance is modeled without climate impacts considered. As such, instead of having a capacity factor specified by SSP 1-2.6, the data is based on the actual state-level capacity factor from the year 2020.

# 3 Results

In this section, the results are compared across the decarbonization scenarios and the global climate models using both statistical analyses and energy system optimization scenario analysis in TUSM.

## 3.1 Global Statistical Analysis

The following are the results of analyzing onshore wind separated by region, followed by an analysis of offshore wind. The section for offshore wind includes all of the countries that have operating offshore wind as of May 2023.
### 3.1.1 Africa

Under SSP 3-7.0, there is a significant and widespread increase in wind capacity factors for the majority of African countries, indicating a substantial improvement in wind energy potential across the continent (Fig. 2). Additionally, South Africa and Cabo Verde show consistent increases in wind capacity factors over time, underscoring a positive trend in wind energy development in these nations. Contrarily, Tunisia and Western Sahara experience a decrease in wind capacity factors over time, indicating a decline in wind energy potential.

### 3.1.2 Oceania

Australia and New Caledonia experience a slight decrease in wind capacity factors, indicating a minor decline in wind energy potential in these regions. Alternatively, Fiji and New Zealand largely maintain stable wind capacity factors, with Fiji showing a slight increase, particularly during peaks associated with SSP 3-7.0 (Fig. 3).

### 3.1.3 Americas

A notable decrease in wind capacity factors is observed in the United States, Canada, Bonaire, Sint Eustatius and Saba, Aruba, Argentina, and Colombia, reflecting a decline in wind energy potential in these regions (Fig. 4). Nonetheless, there is an increase in wind capacity factors in Martinique, Brazil, and Bolivia, suggesting a positive trend in wind energy potential. Under SSP 3-7.0, a notable increase in wind capacity factors is recorded in Guadeloupe and Guatemala. Additionally, under both SSP 3-7.0 and SSP 5-8.5, Honduras, Costa Rica, and Nicaragua experience an increase in wind capacity factors, indicating a promising outlook for wind energy development.

### 3.1.4 Asia

There is an overall increase in wind capacity factors in Thailand, Turkey, and the Philippines, signifying a positive trend in wind energy potential. Conversely, a decrease in wind capacity factors is observed in China, Cyprus, Jordan, Kazakhstan, Mongolia, and Kuwait, indicating a reduction in wind energy potential in these regions. Other countries show relatively stable wind capacity factors, suggesting a more neutral trend. Notably, SSP 1-2.6 and SSP 5-8.5 exhibit the most extreme fluctuations, both positive and negative, in wind capacity factors compared to the baseline values from 1981 to 2014, underlining the significance of how these decarbonization scenarios are shaping wind energy prospects (Fig. 5).
<figure><img src="image_47.png" /><figcaption>**Fig. 2** Change in capacity factor for individual onshore wind turbines by the year 2100, relative to their 1981–2014 average in Africa under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>
<figure><img src="image_48.png" /><figcaption>**Fig. 3** Change in capacity factor for individual onshore wind turbines by the year 2100, relative to their 1981–2014 average in Oceania under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>
<figure><img src="image_49.png" /><figcaption>**Fig. 4** Change in capacity factor for individual onshore wind turbines by the year 2100, relative to their 1981–2014 average in American countries under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>
<figure><img src="image_50.png" /><figcaption>**Fig. 5** Change in capacity factor for individual onshore wind turbines by the year 2100, relative to their 1981–2014 average in Asia under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>
### 3.1.5 Europe

Consistently, every country experiences a decrease in capacity factor, with the notable exception of Finland, where capacity factors grew over the remainder of the century. There were notably larger decreases in capacity factors under SSP 3-7.0. Several countries, including Poland, Romania, Ukraine, Aland Islands, Ireland, Italy, Luxembourg, Lithuania, Kosovo, Netherlands, Belgium, and France, experience the largest decreases in Europe (Fig. 6).

### 3.1.6 Offshore

Over time, there is a notable increase in wind capacity factors in the United States, Belgium, and Finland, indicating a positive trajectory for wind energy potential offshore these countries (Fig. 7). In contrast, offshore wind in Japan is the only country that experiences a consistent decrease in wind capacity factors over time under all three decarbonization scenarios. Under SSP 3-7.0, both Mexico and Vietnam show a decrease in wind capacity factors, suggesting a decline in their wind energy prospects. China, on the other hand, experiences a decrease in wind capacity factors across different scenarios, except for SSP 5-8.5, where there is a slight positive trend, highlighting the variability in wind energy trends across different scenarios. SSP 3-7.0 and to a lesser extent SSP 1-2.6 are responsible for the majority of the peaks and troughs, except in the United States where SSP 5-8.5 is responsible for the most extreme outliers.

## 3.2 Decarbonizing the Electricity Generation

To analyze how wind generation changes under the scenarios outlined in 2.4 involved the utilization of TUSM. Over time, a discernible upward trend is observed in onshore wind generation, with scenario NZE35—No Climate Impacts standing out as the leader in terms of the highest generation additions followed by NZE35—With Climate Impacts. Contrarily, scenarios that do not align with the NZE35 goals depict a relatively constant level of generation, akin to the present-day. However, over time, the BASE scenarios generation gradually converges to approximately half of what is seen under NZE35 scenarios. This stagnant trend underscores the significant shift and scaling required in energy generation to meet net-zero targets under a least-cost optimal energy system configuration (Fig. 8). In summary, the temporal evolution in onshore wind generation emphasizes the pivotal role of scenarios aligned with NZE35, particularly without climate impacts, in driving substantial increases in generation.
<figure><img src="image_51.png" /><figcaption>**Fig. 6** Change in capacity factor for individual onshore wind turbines by the year 2100, relative to their 1981–2014 average in European countries under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>
<figure><img src="image_52.png" /><figcaption>**Fig. 7** Change in capacity factor for individual offshore wind turbines by the year 2100, relative to their 1981–2014 average under the SSP 1-2.6, 3-7.0, and 5-8.5 scenarios (Color figure online)</figcaption></figure>

The minimal addition of new capacity offshore wind energy (Fig. 9) is attributed to the development of onshore wind and solar energy, given their status as the least-cost optimal solution, as delineated by TUSM. Unlike onshore wind energy, there is no difference in offshore wind generation by decarbonization scenario. However, there is a slight increase in the amount of offshore wind energy overtime.
<figure><img src="image_53.png" /><figcaption>**Fig. 8** Onshore wind generation (TWh) by decarbonization scenario in the United States 2020–2050</figcaption></figure>

<figure><img src="image_54.png" /><figcaption>**Fig. 9** Offshore wind generation (TWh) by decarbonization scenario in the United States 2020–2050</figcaption></figure>
## 3.3 Decarbonizing New Capacity Installation

The capacity factor influences the new capacity installation of wind energy. In any given region, final energy demands fluctuate, particularly under net-zero scenarios where the energy mix is altered to favor renewable energy, based on the least cost optimal solution. Regions with higher capacity factors can meet energy demands more efficiently, necessitating fewer new capacity installations. Conversely, regions with lower capacity factors require more new capacity installations to fulfill the final energy demand. This underscores the role of capacity factors in shaping the deployment dynamics of wind energy infrastructure under various decarbonization scenarios.

NZE35 scenarios emerge as having the highest new capacity installation increases, whereas the BASE scenarios appear to lack any significant new capacity installation. Specifically, the NZE35—No Climate Impacts scenario exhibits the most substantial new capacity installation increases in the United States (Fig. 10). Consequently, TUSM depicts investment in wind energy to achieve net-zero goals by 2035, irrespective of climate impacts as the least cost optimal solution in this case. The installed capacity in the Base—Climate Impacts surpasses that of the Base—No Climate Impacts scenario, primarily attributed to variations in data inputs. The discrepancy arises from the fact that one set of inputs leads to a higher new installed capacity than the other. This divergence in trends is discernible due to the distinctive nature of the input sources. The NZE35 scenarios derive their inputs from SSP 1-2.6, while the Base scenarios are from SSP 3-7.0.

<figure><img src="image_55.png" /><figcaption>**Fig. 10** Onshore wind new installed capacity (GW) by decarbonization scenario in the United States 2020–2050</figcaption></figure>
# 4 Conclusion

An innovative data pipeline methodology was developed to examine wind speeds at the sites of all operational onshore and offshore wind farms globally, utilizing five distinct global climate models and three decarbonization scenarios, SSP 1-2.6, 3-7.0 and 5-8.5.

From the results of the global statistical analysis, over time, there were notable increases in capacity factors observed in various regions, including the United States offshore, offshore and onshore Finland, offshore Norway, Thailand, Vietnam, Martinique, Honduras, Costa Rica, Dominican Republic, and Bolivia. These regions experienced growth in their capacity factors, reflecting improved efficiency or expanded capabilities in renewable energy generation potential. Conversely, some areas may witness decreases in their capacity factors. These regions include Aruba, Cyprus, Bonaire, Sint Eustatius, and Saba, Curacao, Mongolia, Spain offshore, Vietnam offshore, Macao offshore, Japan offshore, Portugal offshore, Kosovo, Lithuania, Luxembourg, Ireland, Bulgaria, Belgium, Poland, Portugal, Romania, Russia, and Serbia. In developing countries, such as Thailand, Vietnam, Honduras, Costa Rica, Dominican Republic, and Bolivia, a substantial shift in capacity factor has a direct influence on the accessibility and reliability of wind energy in these countries. In turn, this has implications for the attainment of SDG 7 as these countries may experience new changes in wind generation.

Utilizing TUSM, it was found that net-zero scenarios have the highest capacity increases. Additionally, scenarios run with no climate impacts considered have a larger positive impact on generation of wind energy. Climate impacts from SSP1-2.6 on the NZE35 scenario have relatively positive impacts on future capacity factors, whereas the climate impacts from SSP3-7 on the base scenario have relatively negative impacts on future capacity factors. As such, there will be more wind generation and new installation capacity, specifically onshore wind, under net-zero scenarios and particularly those coupled without climate change impacts.

The results indicate that variations in wind capacity factors were mostly negligible among the examined scenarios. This implies that despite the potential influence of various social, economic, and climatic factors within the decarbonization scenarios, future wind energy potential (2015–2100), on average, is expected to remain relatively consistent with historical values (1981–2014). When comparing the different decarbonization scenarios, all three scenarios were found to be mostly similar and primarily followed suit of the changes in surface wind speeds. There is a pronounced impact of regional aggregation on capacity factor changes. While specific locations exhibit larger volatility, observing capacity factors at the national level reflects a more stable trend, emphasizing the importance of considering regional nuances in renewable energy planning and policymaking.

In terms of data limitations and potential shortcomings, it is noteworthy that the wind speed data utilized in this study was on a daily basis, thus lacking the granularity to capture hourly nuances in wind speed variations. This is a key consideration given the variable intermittent nature of wind energy over the course
of 24 hours. Although the available data was sufficient for this study within the context of integration into TUSM, future studies may consider analyzing the capacity factors in a global TIMES energy system optimization model. Assessing and interpreting the impact of capacity factors on a global scale would significantly enhance the findings. Expanding the geographical scope of generation and new installed capacity would lead to a better understanding of energy trade and mix in regions where decarbonization scenarios may impact wind capacity factors differently.

Conclusively, the world's path to decarbonization will determine the extent of changes in wind generation patterns, such as where wind will gain or lose speed and thereby generation potential. The present energy system is for several reasons not sustainable, with a need to transition to a more sustainable energy system. These changes have a direct impact on the fulfilment of SDG 7 and SDG 11 in particular. The findings overall suggest that wind energy is a robust and reliable source of renewable energy that can contribute significantly to achieving SDG 7 and 11. However, it's imperative to recognize that the projections indicating decreases pose a challenge, while those indicating increases present an advantage in the pursuit of achieving the SDG 7 target for affordable and clean energy. This can be achieved through strategic development of new wind farms in regions with projected high wind energy potential. The locations expected to increase their wind energy capacity factors compared to historical values are further poised to have an additional advantage in achieving SDG 11. The reduction in carbon emissions, improved air quality, and enhanced energy security that come with increased wind capacity factors holds the potential to transform environments into cleaner, more sustainable spaces. Furthermore, wind energy improves energy resilience, which is crucial for SDG 11's commitment to constructing sustainable and resilient communities. Alongside these environmental and energy-related benefits, wind energy development stimulates economic growth and job creation, promoting inclusive and economically prosperous urban communities, a key component of SDG 11.

Finally, the potential shifts in transmission demands as a result of new wind energy capacity installations will likely require governments to reevaluate their electricity grid transmission infrastructure. They may need to invest in upgrading or expanding transmission networks to ensure efficient energy distribution in areas with changing wind behavior. In particular, proactive transmission planning lowers offshore wind costs, accelerates deployment timelines and decreases environmental impacts. Essentially, informed planning and infrastructure development can help mitigate the impacts of climate induced changes in wind patterns. Additionally, the amount of wind energy being generated in some areas will be different depending on the decarbonization scenario, ultimately affecting a reliable energy supply. As a result, some policies that could be implemented as a result of this research include strategic development of new wind farm locations and electricity infrastructure in regions with projected high wind energy potential, incorporating energy storage solutions and/or diversifying the energy mix.
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# Clean and Affordable Norwegian Offshore Wind to Facilitate the Low-Carbon Transition

<figure><img src="image_56.png" /></figure>

Check for
updates

Kristina Haaskjold and Pernille Seljom

**Abstract** Norwegian offshore wind power can be a significant electricity supply contributor to facilitate the Norwegian and European green transition. The Norwegian government aim to grant concessions of 30 GW offshore wind within 2040, however, the realisation of this target depends on numerous uncertainties, related to e.g., future development in technology, national energy demand, the European power market, as well as social acceptance of energy production and grid expansion. This chapter analyses the role and cost-competitiveness of offshore wind to facilitate the low-carbon transition towards 2050. The energy system model, IFE-TIMES-Norway, is used to quantify the techno-economic capacity and distribution of offshore wind towards 2050, along with its impact on the overall energy system. Our results demonstrate that the ambitions of the Norwegian government can be economically viable without the necessity of subsidies, however, the outcome depends on the future development of the European power market. Moreover, the correlation of the Norwegian offshore wind resources is relatively weak between the northern and southern regions, as well as with Northern European countries. Less simultaneity enables an overall smoother production across Europe, which can enhance energy security. Further, results show that Norwegian offshore wind can play a central role in the decarbonization of end-use sectors by enabling greater hydrogen production from electrolysis.

## Key Messages

* The Norwegian target of 30 GW offshore wind by 2040 is economically viable under certain market conditions.

* Norwegian offshore wind enhances the security of electricity supply in Norway and Europe (SDG 7).

* Offshore wind facilitates green hydrogen production and lower greenhouse gas emissions (SDG 13) and could contribute to new industry development (SDG 9).

<footnote>K. Haaskjold (✉) · P. Seljom
Institute for Energy Technology (IFE), Kjeller, Norway
e-mail: kristina.haaskjold@ife.no; pernille seljom@ife.no</footnote>
* Energy system models capture how offshore wind enables emission cuts in end-use.

# 1 Introduction

Norwegian offshore wind power can support the achievement of both Norwegian and European climate targets by providing new green electricity supply, as well as contributing to the political ambition to transform the Norwegian petroleum-based economy to be a value-creating and cost-competitive low-emission economy (Energi 21 2022). Consequently, offshore wind in Norway can contribute to the United Nations (UN) Sustainability Goals on “Affordable and Clean Energy” (SDG 7), “Climate action” (SDG 13) and on “Industries, Innovation and Infrastructure” (SDG 9). The role of offshore wind power in the transition of the Norwegian energy system is however highly uncertain. It depends inter alia on the future development of technology, the onshore Norwegian energy demand, the European power market, and the impact of climate change on renewable production. Further, a national market for offshore wind power is considered a prerequisite for the Norwegian industry to succeed in the international market (Afewerki et al. 2019). This chapter analyses under what conditions Norwegian offshore wind power is cost-competitive and can contribute to reaching the sustainability goals.

## 1.1 Motivation

Norway has a climate policy goal of reaching a low emission society in 2050 (Miljødirektoratet 2023). The largest sources of greenhouse gas emissions are the transport sector at 34%, with 16.4 million CO₂-equivalent, followed by the oil and gas production at 25%, with 12.2 million CO₂-equivalent in 2022 (Environment Norway 2022). As opposed to many other countries, there are negligible emissions from Norwegian electricity generation, which is primarily based on hydro- and onshore wind power. Consequently, offshore wind power will not directly contribute to lowering the emissions in the electricity sector but can facilitate the electrification of end-use sectors and the establishment of new green industries. For example, offshore wind can contribute to lowering emissions from oil and gas production in Norway, by replacing offshore gas turbines with electricity from offshore wind (Voldsund et al. 2023).

This study uses the long-term energy system model IFE-TIMES-Norway (Haaskjold et al. 2023), to analyse the role of offshore wind power in the decarbonisation of the Norwegian energy system. The cost-competitiveness of offshore wind power in 20 identified areas (Norwegian Water Resources and Energy Directorate 2023b) is analysed, taking into consideration the future uncertainty of demand and technology development. The future Norwegian energy demand is
highly uncertain (Malka et al. 2023), where the electricity demand depends both on future activity and the degree of electrification in end-use sectors. However, the Norwegian Transmission System Operator (TSO), Statnett, expect a negative electricity balance from 2027 due to a projected increase in electricity consumption, without a corresponding increase in power production (Statnett 2022). One action that can reduce Norway's dependency on electricity imports is the ambition of the Norwegian government to grant concessions of 30 GW offshore wind by 2040 (Regjeringen 2022b). As a response, the Norwegian Water and Energy Directorate (NVE) (Norwegian Water Resources and Energy Directorate 2023b) identified 20 areas on the Norwegian continental shelf that have the potential to accommodate the 30 GW offshore wind power. However, as offshore wind power, particularly floating installations, is a technology that is under development, there are high uncertainties regarding the future costs and technology development (Shields et al. 2022).

The Norwegian government further stated that a significant share of the electricity from the 30 GW offshore wind power needs to be exported to other countries as it is too large for the Norwegian grid to accommodate (Regjeringen 2022a). At the same time, the Member States of the offshore grid corridor Northern Seas Offshore Grid (NSOG) have recently increased their targets for offshore renewable energy generation, with 60 GW by 2030 and up to 218 GW by 2050 (European Commission 2023). In this regard, it is important to understand the correlation between offshore wind power production in Norway and Northern Europe. A strong correlation makes it more profitable to use Norwegian offshore wind power to meet national electricity demand, store for future use, or produce other energy, such as hydrogen, rather than being exported or curtailed. On the other hand, a weaker correlation fosters higher offshore wind exports, reinforcing the energy security of northern European countries. Understanding the correlation between offshore wind areas within Norway is also important as it influences the need for other electricity generation and transmission to ensure the security of electricity supply.

The role of offshore wind power is also influenced by public acceptance, political preferences and legal and regulatory frameworks. (Linnerud et al. 2022), through a nationwide choice experiment with over 1612 individuals, examined how the general public's preferences for wind energy developments in Norway are affected by a shift from onshore to nearshore or offshore locations. The study concludes that respondents prefer offshore and nearshore locations to onshore ones. The social acceptance of new domestic transmission can also affect the offshore wind expansion, as transmission capacity expansion can be needed to match the offshore wind resources with Norwegian demand in various locations. According to a survey presented in (Aas et al. 2014), local acceptance of high voltage power lines in Norway was below the mid-point average. To proactively address the risk of public opposition of offshore wind, akin to the challenges faced by onshore wind (Korsnes et al. 2023), NVE has recently proposed several amendments to the administrative process for offshore wind, in particular to the Offshore Energy Act (Andersson et al. 2023). The amendments relate to the knowledge base and clarifications needed for the opening and allocation of areas for energy production at sea, the distribution of
responsibility and tasks, and the content and structure of the concession process of energy production with associated grid infrastructure. The main goal of the proposal is to ensure (1) sufficient decision-making foundation, (2) efficient management processes that actively involve and consider public interest, and (3) increased predictability for project owners, which all aim to avert significant impediments to project progression. NVE also highlights the importance of harmonizing grid connection process with the licencing process for offshore wind.

## 1.2 Energy Modelling Literature

Numerous recent analyses have used power market models to address the cost-efficient integration of offshore wind power from a North Sea and Northern European perspective. For example, (Durakovic et al. 2023) use EMPIRE (Backe et al. 2022), a capacity expansion model of the European power market, to analyse how large-scale deployment of green hydrogen production affects the investments in transmission and generation in the North Sea area towards 2060. The analysis includes investment options in two of the 20 identified regions for offshore wind in Norway (Norwegian Water Resources and Energy Directorate 2023b). The chapter concludes that a high demand for green hydrogen will increase investments in offshore wind power, and that the North Sea will have a significant share of the total European electrolyser capacity, due to the favourable wind conditions. The authors suggest that further work should look more closely at national and regional analysis, to better incorporate national energy policies and strategies.

Another example is (Jåstad and Bolkesjø 2023) that uses the BALMOREL model (Wiese et al. 2018) to analyse the market value and economic potential of offshore wind developments for various grid connection strategies using the Norwegian continental shelf as a case. The analysis covers the Northern European power and heat market and includes offshore regions that are connected to four of the five spot price regions in Norway. By using Monte Carlo simulations, covering uncertainty in economic and political developments, 0–8.1 GW installed capacity can be economically attractive in Norway without any subsidy, when assuming a radial connection. Another result is that the market value is highest for offshore wind power when a plant has a hybrid grid connection to several markets compared to a radial connection to only one market. (Koivisto et al. 2020) also used the BALMOREL model to analyse the development of the electricity sector towards 2050 for the North Sea region with a focus on offshore wind power. Similarly to (Durakovic et al. 2023), the authors conclude that an increased electricity consumption, through sector coupling, is a more important driver for increasing offshore wind power installations.

(Reulein et al. 2023) uses the European energy system model, GENeSYS-MOD (Löffler et al. 2017), to address the influence of the introduction of 30 GW offshore wind in one of the 20 identified Norwegian offshore wind areas. The chapter concludes that the introduction of offshore wind capacity results in less capacity expansion of onshore wind and solar power. Note that in (Reulein et al. 2023),
30 GW offshore wind is a model assumption, whereas in our chapter we endogenize investments in offshore wind power and analyse under what conditions investments in Norwegian offshore wind is a techno-economic solution.

Compared to the described literature above, our analysis has a Norwegian perspective, providing a high detail level of the Norwegian energy system that includes interactions within the framework of sector coupling. In addition, we have identified three novelty contributions of our study.

* First, according to our knowledge, this is the first study that examines all the 20 identified offshore wind areas on the Norwegian continental shelf to analyse the cost-competitiveness of offshore wind. Thus, in contrast to the literature described above, we include a more detailed spatial representation of e.g., wind conditions, grid connections and onshore energy system integration. Moreover, this chapter quantifies the correlation of offshore wind resources between the 20 Norwegian regions and other Northern European countries.

* Second, we analyse the effect of offshore wind on Norwegian end-use sectors and emissions. By using a holistic energy system model that endogenizes sector coupling and electricity demand, we quantify how offshore wind can contribute to electrifying and lowering emissions in end-use sectors. Although (Reulein et al. 2023) also used an energy system model, the results presented only focused on the electricity sector.

* Third, we analyse under what conditions Norwegian offshore wind power is cost-competitive, considering relevant uncertain parameters. In addition to the uncertainty on acceptance of onshore wind power technology development that is also included in (Jåstad and Bolkesjø 2023), we also include uncertainty on technology development of offshore wind, expansion of new transmission capacity and national demand under various development pathways of the European electricity market.

## 1.3 Research Questions

The overall objective of the chapter is to analyse the role of offshore wind power in the transition of the Norwegian energy system. In the conducted analysis, we address the following research questions:

* How is wind production from the 20 identified Norwegian offshore areas correlated, and how does this production align with offshore wind in the Northern European region?

* How does the cost-optimal investments in Norwegian offshore wind power depend on the development of future national demand, technology learning and subsidies, and on the European power market?

* How does Norwegian offshore wind power contribute to the Sustainable Development Goals (SDGs) on energy and climate, economy, and industry?
The outline of this chapter is as follows: Section 2 is devoted to the applied methodology, including a description of the TIMES model and model assumptions. Section 3 presents the corresponding results, whereas the conclusions are given in Sect. 4.

## 2 Methodology

First, this section presents the model structure and assumptions of the IFE-TIMES-Norway energy system model, including a detailed description of modelling of offshore wind. Second, we describe the analysed case studies and sensitivities and how they are quantified.

### 2.1 Energy System Model

The TIMES modelling framework is developed within ETSAP (the Energy Technology Systems Analysis Program), an implementing agreement of the International Energy Agency (IEA) during several decades (IEA-ETSAP 2023). TIMES is a bottom-up framework that provides a detailed techno-economic description of resources, energy carriers, conversion technologies and energy demand. TIMES models minimise the total discounted cost of the energy system to meet the demand for energy services for the analysed model horizon.

IFE-TIMES-Norway (Haaskjold et al. 2023) is a technology-rich model of the Norwegian energy system and is split into five regions corresponding to the current electricity spot price regions, NO1 to NO5. The model provides operational and investment decisions from the starting year, 2018, towards 2050, with model periods for every fifth year from 2020 to 2050. To capture operational variations in energy generation and end use, each model period is divided into 96 sub-annual time slices, where four seasons (winter, spring, summer, and fall) are represented by one day of 24 hours in each season. The model has a detailed description of end-use of energy, and the demand for energy services is represented by numerous end-use categories within industry, buildings, and transport. Each energy service demand category can be met by existing and new technologies using different energy carriers such as electricity, biofuel, hydrogen, and fossil fuels. Other input data include fuel prices, electricity prices in countries with interconnections to Norway, renewable resources, and technology characteristics such as costs, efficiencies, and availabilities.

Existing transmission capacity, both domestically and to European countries, is modelled exogenously and based on current capacity and ongoing capacity expansion. Moreover, the model allows for new investment capacity, both on existing and new connections. First year of investment is fixed to 2030 due to the long planning and construction process of building new transmission lines. The Norwegian electricity prices in the five spot regions are endogenous, as they are the dual values of
the electricity balance equation. The electricity prices in countries with interconnections to Norway, including Denmark, Sweden, United Kingdom, Finland, Netherlands, and Germany, are a model input. Furthermore, these electricity trade prices are assumed to be independent of the traded quantities with Norway.

## 2.2 Modelling of Offshore Wind

The offshore wind modelling is based on the 20 identified offshore wind areas of NVE, that is illustrated in Fig. 1. The colour coding reflects the variations in wind conditions, in which green colour indicates the highest capacity factors (52–56%) and red indicates the lowest (46–47%). The power production potential for each area is provided by NVE as an hourly capacity factor for the period from 1951 to 2022 (Norwegian Water Resources and Energy Directorate 2023a). To adjust to the sub-annual temporal resolution of the model, we generate one normalized production profile for each offshore wind region consistent of four representative days (one for each season). The four days are chosen based on random selection of a subset of days, falling within a 50% span in standard deviation from the daily mean across all days within the period (1951 to 2022). The same days are used for all offshore wind regions to ensure consistency in production. The resulting profiles are shown in Fig. 4. These profiles are further scaled to hourly capacity factors by adopting the average capacity factor provided by NVE (Norwegian Water Resources and Energy Directorate 2023a), given in Table 1. Maximum expansion potential for each offshore wind area is assumed to be 2 GW by 2050 (40 GW in total). By 2030, 3 GW capacity is available for investments, corresponding to the two opened areas (Utsira Nord, located in Vestavind F, and Sørlige Nordsjø II, located in Sørvest F).

We assume that the areas that are located closest to Europe in the Southern North Sea, Sørvest A-E and Sønnavind A, can export electricity to Europe. For these connections, export to the United Kingdom (UK), Western Denmark, Germany and the Netherlands are included. These connections are hybrid, meaning that the cables can be used also for electricity trade between countries whenever offshore wind production does not exceed the cable capacity. Noteworthy, the invested capacity to European countries are limited by the invested capacity to Norway, meaning that radial connections to Norway need to be realized before investments in cables to Europe are made. This is reasoned by the Norwegian government's decision to only grant radial connections in the first development phase (Regjeringen 2022c). For the remaining offshore areas, the model can only invest in a unilateral connection to the adjacent spot region in Norway, as presented in Table 1. The investment costs for export cables are calculated based on the estimated kilometer distance to the various connection points.
<figure><img src="image_57.png" /><figcaption>**Fig. 1** Map of the 20 identified new areas for offshore wind development in Norway (Norwegian Water Resources and Energy Directorate 2023d). *Note*: Added color-coding to represent average wind conditions (Color figure online)</figcaption></figure>

## 2.3 Case Studies and Sensitivity Analysis

To develop a robust analysis, different case studies and sensitivities have been examined to identify the parameters that have the largest influence on the investment
in offshore wind power in Norway. All case studies assume a low-carbon society by 2050, with CO₂ price assumptions of 200 €/tCO₂ in 2030 and 438 €/tCO₂ in 2050, assuming a currency rate of 10 NOK/€. Three main parameters are chosen for the case studies:

1. **Investment cost of offshore wind:** For this study, a high (denoted “High”) and a low (denoted “Low”) cost case is used based on data provided by NVE (Norwegian Water Resources and Energy Directorate 2023c). The data differ depending on the foundation type and whether the connection to shore is alternating current (AC) or direct current (DC). Information for each area can be found in Table 1, with costs summarized in Table 2. Technology learning towards 2050 is assumed to be 15% (International Renewable Energy Agency (IRENA) 2019). In the

<table><caption>**Table 1** Capacity factor, type of foundation and grid connection point for each offshore wind area (Norwegian Water Resources and Energy Directorate 2023b)</caption><thead><tr><th>Offshore Area</th><th>Capacity factor (%)</th><th>Foundation</th><th>Grid connection point</th></tr></thead><tbody><tr><td>Nordavind A</td><td>49.6</td><td>Floating</td><td>NO4</td></tr><tr><td>Nordavind B</td><td>50.2</td><td>Floating</td><td>NO4</td></tr><tr><td>Nordavind C</td><td>48.8</td><td>Floating</td><td>NO4</td></tr><tr><td>Nordavind D</td><td>48.8</td><td>Floating</td><td>NO4</td></tr><tr><td>Nordvest A</td><td>49.5</td><td>Floating</td><td>NO4</td></tr><tr><td>Nordvest B</td><td>48.3</td><td>Floating</td><td>NO3</td></tr><tr><td>Nordvest C</td><td>47.0</td><td>Floating</td><td>NO3</td></tr><tr><td>Vestavind A</td><td>51.3</td><td>Floating</td><td>NO3</td></tr><tr><td>Vestavind B</td><td>49.6</td><td>Floating</td><td>NO3</td></tr><tr><td>Vestavind C</td><td>48.9</td><td>Floating</td><td>NO5</td></tr><tr><td>Vestavind D</td><td>45.8</td><td>Floating</td><td>NO5</td></tr><tr><td>Vestavind E</td><td>52.3</td><td>Floating</td><td>NO2</td></tr><tr><td>Vestavind F</td><td>50.1</td><td>Floating</td><td>NO2</td></tr><tr><td>Sørvest A</td><td>54.5</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sørvest B</td><td>54.3</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sørvest C</td><td>55.1</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sørvest D</td><td>54.5</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sørvest E</td><td>56.1</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sørvest F</td><td>55.9</td><td>Bottom-fixed</td><td>NO2, DK1, DE, NL, UK</td></tr><tr><td>Sønnavind A</td><td>56.5</td><td>Floating</td><td>NO2, DK1, DE, NL, UK</td></tr></tbody></table>

<table><caption>**Table 2** High and low investment cost projections used for the case studies (€/GW) (Norwegian Water Resources and Energy Directorate 2023c)</caption><thead><tr><th rowspan="2">Type + connection</th><th colspan="2">Low price projection</th><th colspan="2">High price projection</th></tr><tr><th>2030</th><th>2050</th><th>2030</th><th>2050</th></tr></thead><tbody><tr><td>Floating DC</td><td>3037</td><td>2581</td><td>4181</td><td>3554</td></tr><tr><td>Floating AC</td><td>3034</td><td>2579</td><td>4178</td><td>3551</td></tr><tr><td>Bottom-fixed DC</td><td>2140</td><td>1819</td><td>2756</td><td>2343</td></tr></tbody></table>
following, high technology learning refers to low investment costs, while low
technology learning refers to high investment costs.

2. **Energy demand for industry and transport:** Two projections for future development in industry and transport demand is assumed based on (Aamodt Espegren et al. 2023). The high projection assumes an increase in industry demand of 69%, road transport demand of 37% and other transport demand of 14%. The low projection assumes a 1% increase in industry demand, while individual transport demand decreases by 10%.

3. **Electricity price in Europe:** Four price sets for European countries have been applied: (1) Reference prices based on linking with the European power market model EMPIRE (Haaskjold and Pedrero 2023), (2) high price set, with average price and volatility adjusted by 2, (3) low price set with average price and volatility adjusted by 0.8, (4) halved price set with average price and volatility adjusted by 0.5. The change in variability is computed by applying a square power transformation at each hour, resulting in lower lows and higher peak values.<fnref n="1" /> The price profiles for a winter and a summer day in Sweden in 2050 for each price set are illustrated in Figs. 2 and 3.

The combination of parameters used in the case studies are presented in Table 3.
In total, 10 cases have been analysed.

If not specified, investments in new land-based wind power and transmission
capacity are a modelling option. To account for uncertainties related to social
acceptance of such large infrastructure, a sensitivity analysis is also performed for
each case combination in which no new land-based wind or domestic transmission
cables can be built.

<figure><img src="image_58.png" /><figcaption>**Fig. 2** Four price projections for electricity price development on a winter day in Sweden in 2050</figcaption></figure>

<footnote n="1">¹The squared values for each hour were normalized by the mean value of the transformed time series. These normalized profiles were then scaled by multiplying the mean value of the original price profile and a scaling factor corresponding to the desired increase/decrease in average electricity prices.</footnote>
<figure><img src="image_59.png" /><figcaption>**Table 3** Combination of parameters for the case analysis</figcaption></figure>

<table><thead><tr><td>Name</td><td>Investment cost</td><td>Energy demand</td><td>Electricity price Europe</td></tr></thead><tbody><tr><td>HH-Ref</td><td>High</td><td>High</td><td>Ref</td></tr><tr><td>LH-Ref</td><td>Low</td><td>High</td><td>Ref</td></tr><tr><td>HH-High</td><td>High</td><td>High</td><td>High</td></tr><tr><td>LH-High</td><td>Low</td><td>High</td><td>High</td></tr><tr><td>HH-Low</td><td>High</td><td>High</td><td>Low</td></tr><tr><td>LH-Low</td><td>Low</td><td>High</td><td>Low</td></tr><tr><td>HH-Half</td><td>High</td><td>High</td><td>Half</td></tr><tr><td>LH-Half</td><td>Low</td><td>High</td><td>Half</td></tr><tr><td>HL-Low</td><td>High</td><td>Low</td><td>Low</td></tr><tr><td>HL-High</td><td>High</td><td>Low</td><td>High</td></tr></tbody></table>

# 3 Results

First, this section presents the results of the Norwegian offshore wind resources used as input to the model, along with the correlation between offshore wind resources in Norway and neighbouring European countries. Second, the main results from the sensitivity analysis will be presented with focus on offshore wind investments and its impact on the Norwegian energy system.

## 3.1 Norwegian Offshore Wind Resources

As illustrated in Fig. 1, the average annual capacity factors for Norwegian offshore wind areas range between 46% and 57%. The areas located furthest south in Norway have the greatest wind conditions, with average annual capacity factors of 54–57%. Besides Sønnnavind A, the areas in the south are also the ones mainly suitable for bottom-fixed foundation, entailing a significantly lower cost of investment. In addition to differences in annual production potential, the wind conditions across regions can also vary largely within a day and within seasons, as shown in Fig. 4.
<figure><img src="image_60.png" /><figcaption>**Fig. 4** Normalized capacity factors for five of the offshore wind areas, representing the hourly differences along the Norwegian coastline</figcaption></figure>
While "Sørvest A", "Vestavind A" and "Nordvest A" obtain maximum capacity factors during the winter, "Nordavind A" and "Sønnavind A" have almost no production in this period. This indicates that there is a smoothing effect among the areas that provide a more stable overall production.

Figure 5 illustrates the correlation between offshore wind areas in Norway and Northern Europe based on hourly resolution of wind data from 1951 to 2022. The results demonstrate that there is a low correlation in wind speeds between the various offshore areas in Norway. The correlation is below 0.5 for all instances, and in 7 out of 10 cases, the correlation is below 0.2. The highest correlation can be found between Sørvest A and Sønnavind A (0.5), which are located closer compared to the other areas.

Moreover, Fig. 5 also shows a weak correlation in offshore wind conditions between Norway and Europe. This applies especially for those located on the western and Northern part of Norway, in which correlation is below 0.25 for all instances. For Sørvest A and Sønnavind A, the correlation is slightly stronger, but still significantly lower compared to the correlation between the European countries. For example, correlation between Sønnavind A and Germany is 0.45, while that between Denmark and Germany is 0.81.

In further results, the offshore wind areas will be grouped according to their location, referred to as Nordavind (incl. A-D), Nordvest (incl. A-C), Vestavind (incl. A-F), Sørvest (incl. A-E) and Sønnavind (incl. A).

<figure><img src="image_61.png" /><figcaption>**Fig. 5** Statistical correlation matrix with hourly time resolution for offshore wind areas in Norway and Northern European countries</figcaption></figure>
## 3.2 Offshore Wind Investments

The results demonstrate that investments in offshore wind is highly dependent on the development of European electricity prices. Figure 6 shows the invested capacity for each offshore wind area for each of the ten case studies. With high electricity prices, the offshore wind capacity in 2040 ranges from 23 to 33 GW, whereas for the low price cases the capacity ranges from 12 to 28 GW. The case with highest capacity at 33 GW, has a production of 168 TWh, and occurs when the investment cost of offshore wind is low, and the national electricity demand is high.

The results indicate that the future technology learning and investment cost of offshore wind has a great impact on the invested capacity in 2040. Further, the impact of investment costs is more significant in the cases featuring lower electricity price levels in Europe. As shown in Fig. 6, compared to the low technology learning cases (HH-Ref and HH-Low), a higher technology learning gives additional 18 GW capacity in the reference price case (LH-Ref) and 16 GW capacity in the low price case (LH-Low). The significance of technology learning is further highlighted by the case with high investment costs and very low prices in Europe (HH-Half), in which no investments are made in offshore wind power.

Among the Norwegian offshore areas, the ones located in southern and western Norway are the most cost-competitive for offshore wind. These areas have the best wind conditions and are also located close to onshore regions with high demand and connections to the European power market. In the cases with low energy demand, investments are mainly concentrated in these areas, whereas investments are more

<figure><img src="image_62.png" /><figcaption>**Fig. 6** Investments in offshore wind across all sensitivity cases and regions by 2040 (GW). Notes: HH High investment cost and High demand, LH Low investment cost and High demand, HL High investment cost and Low demand</figcaption></figure>
widely distributed across areas in cases with high energy demand. Consequently, the future electricity demand in Norway influences the offshore wind deployment.

## 3.3 Electricity Production and Use

Among the electricity generation technologies, offshore wind investments have the largest impact on investments in building applied PV (BAPV) and hydropower. This is illustrated in Fig. 7 that shows electricity generation by technology from new investments by 2050, comparing cases with high and low investment cost of offshore wind across different European price levels. Note that utility PV is not included as an investment option. The impact on hydropower is largest in high price cases (LH-High), with an 8% reduction in production compared to the high investment cost case (HH-High). Moreover, the flexible hydropower shifts production from winter to summer months to accommodate offshore wind production. The impact on PV investments is reduced the most in the low-price case (LH-Low), with a 40% reduction compared to the high investment cost case (HH-Low). This can be explained by the correlation between PV production and periods of low electricity prices in Europe. With zero prices during mid-day hours (as illustrated in Fig. 3), the market value of offshore wind becomes relatively higher compared to that of PV. Finally, since onshore wind is a highly cost-optimal solution in Norway, the production is identical for all cases, and is thus independent of the offshore wind investments.

<figure><img src="image_63.png" /><figcaption>**Fig. 7** New renewable production by energy source for 2050. *Notes:* HH High investment cost and High demand, LH Low investment cost and High demand</figcaption></figure>
The electricity generation mix influences the long-term marginal cost of electric-
ity in Norway. The results indicate that higher technology learning for offshore wind
power, which lowers the investment costs and increases offshore wind investments,
lowers the average electricity price in Norway. The cases with low investment costs
have 5–8% lower average Norwegian electricity prices in 2050 compared to the
cases with higher investment costs. Further, the impact on electricity prices varies
between the Norwegian spot price regions. With low European prices, the price
impact is highest in the spot price regions of Oslo and Bergen, NO1 and NO5,
decreasing with 6–8%, whereas with high European prices, the electricity price is
reduced most in the spot price regions of Trondheim and Tromsø, NO3 and NO4,
with a 28% reduction.

For end-use, offshore wind primarily affects the use of electricity for hydrogen
production. Figure 8 illustrates the electricity use per sector in 2050, comparing
cases with high and low investment cost of offshore wind. The impact is largest in
high price cases, where lower investment cost of offshore wind (LH-High) results in
a 40% increase in hydrogen production compared to the high investment cost case
(HH-High). With low electricity prices, the total electricity use is the same indepen-
dent on investment cost of offshore wind. For the other sectors- building, district
heat, industry and transport- offshore wind investments have negligible impact on
electricity use.

The increased hydrogen production, resulting from offshore wind power,
decreases the Norwegian CO2 emissions. Lower investment costs of offshore wind
result in a 3% decrease in emissions compared to higher investment costs in the high
price case. In the latter, the hydrogen production from electrolysis is mainly
substituted by blue hydrogen (92%), however the overall production level is still
reduced. The reduction can be found in mainly sea transport. Higher investment

<figure><img src="image_64.png" /><figcaption>**Fig. 8** Electricity use per sector for 2050. *Notes*: HH High investment cost and High demand, LH Low investment cost and High demand</figcaption></figure>