NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Resource Planning Model: 

An Integrated Resource 

Planning and Dispatch Tool for 

Regional Electric Systems

Trieu Mai, Easan Drury, Kelly Eurek, 

Natalie Bodington, Anthony Lopez, and 

Andrew Perry

Technical Report

NREL/TP-6A20- 56723

January 2013
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Resource Planning Model: 

An Integrated Resource 

Planning and Dispatch Tool for 

Regional Electric Systems 

Trieu Mai, Easan Drury, Kelly Eurek, 

Natalie Bodington, Anthony Lopez, and 

Andrew Perry 

Prepared under Task No. DRS8.3030

Technical Report

NREL/TP-6A20- 56723

January 2013
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iii

Acknowledgments

We thank Dave Corbus, Donna Heimiller, Walter Short, and Greg Brinkman (National 

Renewable Energy Laboratory) for comments and input. We also thank Rebecca Johnson

(Colorado Public Utility Commission), Mark Dyson (University of California, Berkeley), and 

Eduardo Ibanez, Nate Blair, and Robin Newmark (National Renewable Energy Laboratory) for 

their review and suggestions, and Gil Bindewald (U.S. Department of Energy) for supporting this 

work. This research was funded by the U.S. Department of Energy under contract number DEAC36-08GO28308. 
iv

Abstract

Recent and anticipated trends indicate that renewable resources, particularly wind and solar

energy, will provide a growing contribution to the U.S. and global power systems in the coming 

decades. These resources are variable and uncertain by nature, and their impacts on system 

expansion and operation need to be properly accounted for in electric system models. To this 

end, we introduce a new capacity expansion model, the Resource Planning Model (RPM), with 

high spatial and temporal resolution that can be used for mid- and long-term scenario planning of 

regional power systems. RPM endogenously and dynamically considers grid integration of 

renewable resources, including transmission and interconnection availability and costs, 

renewable resource limits and output characteristics, and dispatch options for conventional 

generators, in its optimal generator and transmission decision-making. As an hourly 

chronological model with a highly discretized regional structure, RPM provides a framework 

where various future scenarios can be explored while ensuring that the scenarios include many 

aspects of grid reliability. Although the structure of RPM was designed to be adaptable to any 

geographic region, here we describe an initial version of the model adapted for the power system 

in Colorado. 

We present example scenario results from this first version of RPM, including an example of a 

30%-by-2020 renewable electricity penetration scenario. Under the assumptions used, the 

preliminary scenario analysis demonstrates that wind technologies are the dominant contributors 

to this 30%-by-2020 renewable electricity scenario and that renewable generation largely 

displaces natural gas. This displacement results in annual carbon dioxide (CO2) emission 

reductions of approximately 12%. We find that under the least-cost deployment solution from the 

model, new wind capacity is largely deployed in the north-central and southeastern regions of 

Colorado and utility-scale solar capacity is largely deployed in the Front Range urban corridor, 

along with northwestern and south-central Colorado regions. Finally, we observe changes to 

fossil generation dispatch, particularly with regard to greater power plant ramping and cycling of 

natural gas combined cycle and coal power plants. In addition to presenting these initial findings, 

this report provides a detailed documentation of RPM as a new analytic tool for regional power 

system planning and dispatch. 
v 

Table of Contents

Acknowledgments ..................................................................................................................................... iii

Abstract....................................................................................................................................................... iv

1 Introduction........................................................................................................................................... 1

2 Brief Model Description ....................................................................................................................... 3

2.1 General Model Framework............................................................................................................... 3

2.2 Model Spatial and Temporal Resolution.......................................................................................... 4

2.2.1 Model Decision Variables .................................................................................................. 8

2.2.2 Objective Function.............................................................................................................. 9

2.2.3 Model Constraints............................................................................................................... 9

3 Model Inputs........................................................................................................................................ 14

3.1 Electricity Demand......................................................................................................................... 14

3.2 Conventional Generation Resources .............................................................................................. 14

3.3 Renewable Resources and Technologies........................................................................................ 16

3.3.1 Hydropower Resources..................................................................................................... 18

3.3.2 Geothermal, Biopower, and Other Renewable Resources................................................ 19

3.4 Electricity Imports and Exports...................................................................................................... 19

3.5 Selection of Model Days................................................................................................................ 20

3.6 Cost Assumptions for Generation Technologies and Fuels............................................................ 21

4 Sample Model Results ....................................................................................................................... 23

4.1 Electric Sector Evolution................................................................................................................ 23

4.2 Electric Sector Emissions and Costs .............................................................................................. 34

5 Conclusions and Future Work .......................................................................................................... 36

References................................................................................................................................................. 37

Appendix. Model Formulation ................................................................................................................. 41

Indicies................................................................................................................................................. 41

Model Data Sets ................................................................................................................................... 41

Model Parameters................................................................................................................................. 42

Complex Sets........................................................................................................................................ 45

Variables .............................................................................................................................................. 45

Objective Function ............................................................................................................................... 46

Constraints............................................................................................................................................ 48
vi 

List of Figures

Figure 1. Regions included in RPM-CO ................................................................................................ 5

Figure 2. Photovoltaic resource quality by model region and technology type: 1-Axis tracking (top) 

and Fixed-tilt (bottom)..................................................................................................................... 6

Figure 3. Wind resource by capacity factor group and model region .................................................... 7

Figure 4. Regions Included in RPM-CO .............................................................................................. 12

Figure 5. Growth in electricity generation (TWh) for the 30% RE scenario and the Baseline

scenario .......................................................................................................................................... 24

Figure 6. Electricity generation fractions for 2010 and for the 2030 30% RE scenario and 

Baseline scenario ........................................................................................................................... 25

Figure 7. Electricity generation fractions for Colorado in-state generation in 2010 for historical

data and modeled results................................................................................................................ 26

Figure 8. Growth in generation capacity (MW) for the 30% RE scenario and the Baseline scenario 

without an RPS .............................................................................................................................. 27

Figure 9. Modeled deployment in the 30% RE scenario...................................................................... 28

Figure 10. Modeled deployment in the Baseline scenario.................................................................... 29

Figure 11. Electric sector dispatch for four days in summer (Sunday-Wednesday) for 2010 and

the 30% RE and Baseline scenarios............................................................................................... 31

Figure 12. Electric sector dispatch for four days in spring (Sunday-Wednesday) ............................... 32

Figure 13. Electric sector dispatch for one day with the peak electricity demand for the year............ 33

Figure 14. Annual electric sector emissions in the Colorado study region for the 30% RE scenario 

(solid lines) and the Baseline scenario (dashed lines).................................................................... 34

Figure 15. Net present value of the 2010–2030 costs of developing and operating generation

resources in the 30% RE scenario and the Baseline scenario ........................................................ 35
vii 

List of Tables

Table 1. Existing Generation Capacity in 2010 by State (MW)........................................................... 15

Table 2. Summary of Xcel Energy’s Pathway to Meeting the Emissions Requirements of the Clean 

Air Clean Jobs Act (PUC Colorado 2010)............................................................................ 16

Table 3. Wind Net Capacity Factors (%) Associated with each Wind Group ..................................... 17

Table 4. Price Projections (2010$/Watt) for Electricity Generating Technologies.............................. 21

Table 5. Fuel Price Projections (2010$/MMBTU)............................................................................... 21

Table 6. Assumed Characteristics for New Thermal Generators......................................................... 22

Table 7. Operating Characteristics for Thermal Generators................................................................. 22

Table 8. Colorado Electricity Generation Capacity (MW) and Annual Generated Energy (TWh) for 

the 30% RE and Baseline Scenarios..................................................................................... 27
1 

1 Introduction

In this report, we introduce a new transparent regional capacity expansion model with high 

spatio-temporal resolution and detailed representation of dispatch. The development of this 

model, referred to as the Resource Planning Model (RPM), is motivated by the lack of a tool in 

the public domain that can be used to characterize optimal regional deployment of resources with 

detailed dispatch modeling. In particular, RPM is designed to evaluate scenarios of renewable 

technology deployment to meet renewable portfolio standard (RPS) and emission-reduction 

goals, and to project possible deployment levels for various projections of future technology and 

fuel prices. 

The model co-optimizes transmission, generation, and storage options. It considers major grid 

operation constraints within its purview as a capacity expansion model. More specifically, 

detailed operational constraints in RPM are used to inform the capacity expansion decisions, i.e., 

the degree to which generation dispatch, ramping, cycling, value of storage, and value of peak 

coincidence affect the amount and location of renewable deployment is inherent within the 

model. The methodologies for treating renewable technologies in RPM can help improve 

commercial models or capacity expansion models with greater geographic scope and more 

limited spatio-temporal resolution. Finally, RPM is designed with a flexible structure to enable 

research into how investment decisions may be affected by the choice of model time periods, 

particularly with high levels of renewable penetration. 

The Resource Planning Model is developed to inform policymakers, academic researchers, and 

electric utility planners. In particular, RPM is a regional capacity expansion model with spatiotemporal resolution and grid operational aspects that approach those of long-term planning tools 

used by utility planners, but with data and model details that are publicly available. Although the 

structure of RPM was designed to be adaptable to any geographic region and any hourly or 

multiple hour time resolution, here we describe the first version of the model adapted for the 

power system in Colorado and henceforth referred to as the RPM-CO model. 

A wide range of power sector models is used by various researchers to evaluate energy policies. 

Although we do not attempt here to provide a comprehensive review of all models used in the 

literature, we provide a brief overview of related models and model types and a description of 

their differences with RPM.

Examples of public sector models that have been used to examine various energy policies 

include the U.S. Energy Information Administration's (EIA's) National Energy Modeling System 

(NEMS) model1

 and Brookhaven National Laboratory's MARKet ALlocation (MARKAL) 

model (Loulou et al. 2004). NEMS and MARKAL model the entire U.S. economy, including all 

energy sectors and, for this reason, have coarse representations of the electricity sector.

2

 In 

particular, NEMS models the power system using 9 time slices per year (three seasons with three 

diurnal periods) and 22 electricity generation regions covering the entire contiguous United 

States. MARKAL includes 12 time slices per year (three seasons with four diurnal periods) and 

10 regions. The resolution of these models requires many simplifications, including 

 

1 Documentation for NEMS can be found at www.eia.gov/analysis/model-documentation.cfm. 2 Multiple versions of MARKAL exist with various geographic scopes. The discussion in this report refers to the 

versions used in the cited references.
2 

approximations of grid operations and aggregation of individual generating units into generalized 

technology categories. Nonetheless, these simplifications are generally adequate to provide 

insights for long-term national scenario analyses, including evaluations of national energy 

policies (EIA 2011, EIA 2012, Alfstad 2008, Mignone et al. 2012). 

Compared with their economy-wide counterparts, electric sector-only capacity expansion models 

can afford to represent the power sector with greater resolution. Examples of such models 

include NREL's Regional Energy Deployment System3

 (ReEDS) model (Short et al. 2011) and 

the University of California, Berkeley's SWITCH model,4 which have coarser spatio-temporal 

resolution. ReEDS is an electric sector-only model that includes 17 time slices per year (four 

seasons with four diurnal periods and one peak time slice) and 134 balancing areas5 in the 

contiguous United States. SWITCH has greater temporal resolution with 144 model hours (12 

months X 2 representative days per month X 6 representative hours per day). The geographic 

scope of SWITCH is limited to the Western Electricity Coordinating Council (WECC), which is 

divided into 50 model regions. These models have been used to examine implications of various 

energy policy options, particularly those related to the electric sector (Logan et al. 2009; 

Mignone et al. 2012; Nelson et al. 2012). The detailed grid representation in these types of model 

has become increasingly necessary with recent historical and potential trends in the power sector, 

particularly with increasing renewable technology deployment. ReEDS has also been used to 

evaluate technical grid integration challenges of renewable generation technologies (DOE 2012; 

Mai et al. 2012).6

Although ReEDS and SWITCH were developed to capture many of the major grid integration 

challenges of future expansion scenarios, their large geographic scopes, technology aggregations, 

and other necessary simplifications limit their applicability for regional utility or service area 

planning. For example, ReEDS and SWITCH represent Colorado with two and four regions,7

respectively, which is likely insufficient to inform generation siting and planning for the local 

utilities within Colorado. 

Because utilities typically use internal or proprietary tools for long-term capacity planning, we 

are unable to easily evaluate them or compare them with public or academic models.8 However, 

we believe these models generally lack certain important characteristics. We identify some of 

these deficiencies here. These tools typically do not simultaneously co-optimize transmission and 

generation. In addition, renewable technologies and their integration challenges and 

opportunities are not dynamically treated in these tools. For example, the contributions from 

variable (wind and solar photovoltaics) generators for planning reserves may be exogenously 

considered even though they may vary depending on the penetration level and the locations 

where they are deployed. More generally, the overall options for grid flexibility, including 

 

3 Documentation for ReEDS can be found at www.nrel.gov/analysis/reeds. 4 Documentation for the SWITCH model can be found at rael.berkeley.edu/sites/default/files/

SWITCH_Model_Documentation_December_2011.pdf. 5 ReEDS also includes 356 wind and CSP resource regions. 6 These technical studies also relied on commercial production cost models described below.

7 ReEDS includes 13 wind and CSP resource regions within Colorado and 2 "balancing areas" where all other 

technologies and load are treated. 8 Mills and Wiser (2012b) reviews methods and models used in utility planning and procurement processes, with a 

focus on solar valuation.
3 

changes to how plants are dispatched, may not be fully represented when renewable integration 

is considered in the models. 

Utility planners and system operators also use production cost models to inform their generation 

and transmission planning.9

 Examples of production cost models include PLEXOS (CAISO 

2010), GridView (Feng et al. 2002), and GE MAPS (GE Energy 2010). As with the utility 

planning tools described above, this suite of commercial models are also often proprietary. 

Commercial production cost models are security-constrained unit-commitment (SCUC) and 

security-constrained economic dispatch (SCED) models that typically model the hourly or 

subhourly operation of all individual generator units in the model system for a given period. 

They typically represent energy transfers through DC optimal powerflow models. Although the 

size of the model system can range widely, the number of model generators, load buses, and 

transmission lines can exceed ten thousand. Although the level of operational detail contained in 

these models far exceeds the models described above, this suite of models is not designed to 

directly address the capacity expansion problem. In short, production cost models have detailed 

representation of system dispatch but rely on other models or tools for the generation capacity 

and transmission available for dispatch. Capacity expansion models and production cost models 

can be used in tandem for planning purposes, but this process may require several iterations to 

identify optimal generation portfolios. 

Section 2 provides a brief description of the model with more details provided in the appendix. 

Section 3 describes the input data used in the models. Section 4 provides a sample of model 

outputs based on preliminary scenario analysis conducted. We list conclusions and next steps in 

Section 5. 

2 Brief Model Description 

This section provides a qualitative description of RPM-CO. We provide a more complete listing 

of the major model sets, parameters, variables, and equations in the appendix. 

2.1 General Model Framework 

RPM-CO is a mixed-integer linear program that minimizes overall system cost, including capital 

costs, operations and maintenance (O&M) costs, fuel costs, and start-up costs during each 

optimization period. The objective function (see the appendix) includes annual operating costs 

(fuel and variable O&M) and annual fixed costs (amortized cost of capital assets including 

generation and transmission infrastructure resources, and fixed O&M). All costs and input data 

are user-defined, and we describe sample data inputs in Section 3. As in many other electric 

sector optimization models, cost optimization is subject to several constraints to characterize

power plant operation, transmission dispatch, grid reliability, and capacity expansion. We 

qualitatively describe model constraints here, and we provide more-detailed descriptions, 

including constraint equations, in the appendix. 

RPM-CO is a sequential optimization model with five optimization periods separated by five 

years from 2010 to 2030. Sequential optimization allows non-linear calculations to be made 

 

9 Other models with greater detail than the ones described here are also used, and they include AC transmission, 

voltage stability, and other models. We consider these models to be outside the long-term planning domain.
4 

between optimizations. These calculations are necessary to update parameters, including capacity 

value of wind and solar technologies, for the next linear optimization period. In addition, the 

five-year separation provides an appropriate planning timeframe for many generation-types10. 

We represent all major commercial generation technologies in RPM-CO, including: two types of 

pulverized coal, three types of natural gas combined cycle (NG-CC), three types of natural gas 

combustion turbines (NG-CT), oil and gas steam (OGS), nuclear, biopower, geothermal, 

hydropower, five classes of onshore wind, and utility-scale fixed-tilt (PV-fixed) and 1-axis 

tracking photovoltaics (PV-track). The multiple types of fossil technologies reflect the range of 

efficiencies and emission controls that are present in the existing fleet of fossil generators in 

Colorado. Differentiation between fossil types is based on plant size and is described in 

Section 3. The main parameters that characterize each generation technology include nameplate 

capacity, heat rate, fuel type and costs, O&M costs, outage rates, start-up costs, minimum 

generation levels, and minimum on and off periods. In addition, generation profiles for wind and 

solar technologies are also exogenously defined, as are limits to hydropower dispatch. For new 

technology options, cost and performance projections and minimum plant sizes are considered in 

the model. The technologies currently considered in RPM-CO are motivated by the existing 

system and recent and anticipated trends in deployment. The flexible model structure of RPM

allows for the inclusion of additional technologies.

2.2 Model Spatial and Temporal Resolution

One of the distinguishing features of RPM-CO is the high spatial resolution of the model. 

Figure 1 shows the 27 regions within Colorado and the 4 boundary regions representing 

Wyoming (two regions), Utah, and New Mexico.11 The Colorado regions are based on 

aggregations of one or more counties, where aggregations were guided by the spatial 

distributions of load, existing large generators, and renewable resources. The combination of 

multiple regions, multiple fossil technologies, and the mixed-integer programming structure of 

RPM-CO allow it to model large individual fossil power plants. For example, in the current 

implementation, the largest coal (>250 megawatts (MW)) and NG-CC (>250 MW) technology 

types (see Section 3.2) represent individual existing power plants.12 By modeling individual 

plants, as opposed to aggregations of plants, the dispatch characteristics for each plant can be 

accurately represented in the model. In addition, power plant retirements can be assessed at the 

individual plant level. 

 

10 We do not model construction lead times explicitly; new power plants are immediately available for dispatch 

during the same year that they are built. Technology-specific fixed charge rates (see Section 2.3.2) are based on 

differing construction periods for different technology types.

11 Nebraska, Kansas, and Oklahoma also neighbor Colorado; however, they are excluded from the model because

they are not in WECC. Limited capacity of DC lines connecting Colorado to the Eastern Interconnection exist; 

however, these are ignored in RPM-CO. 12 Several power plants consist of multiple generating units and these are treated in aggregate. This aggregate 

treatment of individual units effectively lowers the operational flexibility of modeled generation resources. 
5 

Figure 1. Regions included in RPM-CO

The highly discretized regional structure of the model also allows us to more accurately represent 

the locational differences in renewable resource quality. Figure 2 shows the model regions 

overlaid with PV resource quality and Figure 3 shows wind resource quality for Colorado and 

surrounding regions. The data sources for renewable resources are described in Section 3. In 

addition, high spatial resolution allows us to model transmission limits within Colorado (and 

between Colorado and neighboring states) to better identify locations with accessible high 

quality renewable resources. The model inherently considers the limits and costs of transmission 

between resource regions in its capacity expansion optimization. 
6 

Figure 2. Photovoltaic resource quality by model region and technology type: 1-Axis tracking (top) 

and Fixed-tilt (bottom) 
7 

Figure 3. Wind resource by capacity factor group and model region

RPM-CO is an hourly chronological model. Because meteorological conditions play the primary 

role in determining (1) electricity demand, (2) wind speeds, and (3) solar PV output, the input 

hourly data rely on the data from the same year for all three. In the current implementation, data 

for 2005 are used (see Section 3). Certain parameters (e.g., capacity value) rely on the full vector 

of 8,760 hours. The dispatch modeling within the optimization relies on a subset of these hours. 

In particular, we divide the year into four seasons (summer, fall, winter, spring) and represent 

each season with a set of user-selected consecutive days. Although any number of days can be 

modeled, runtime and other constraints limit our analyses to one week of dispatch per season; 

however, we typically limit our model runs to four days per season (see Section 3.6). 

The chronological nature of the model enables it to capture plant cycling limits and costs, and 

minimum on and off periods.13 Thus, the choice of model days or hours can affect overall model 

results related to dispatch and capacity expansion. In particular, intra- and inter-day variations in 

load, wind, and solar are present throughout the year, and these variations change with renewable 

 

13 Ramp rate limits can also be represented in the model; however, these limits are generally not binding under 

hourly time steps. For this reason, they are currently not modeled in RPM for fossil units. Ramping limits would be 

necessary for subhourly modeling. 
8 

penetration levels.

14 Section 3 describes some preliminary analysis we have conducted to select 

the representative model days. However, more work is needed to evaluate how the selection of 

model days impacts overall modeling results. RPM-CO provides a framework in which these 

types of research questions can be answered. 

2.3 Qualitative Model Description

We designed many of the model equations and variables in RPM-CO based loosely on a 

combination of the ReEDS model (Short et al. 2011) and a dispatch model by Sioshansi and 

Denholm (2010). The primary decision variables in RPM-CO include capacity expansion 

variables as well as detailed dispatch variables. The equations in the model are designed to 

capture both of these aspects while maintaining the linearity of the problem. The major model 

equations and variables are qualitatively described in this section. A more complete list of model 

equations and variables is provided in the appendix. 

2.3.1 Model Decision Variables

We categorize the model decision variables into the following: generation, transmission, and 

storage. Each of these categories is subdivided into capacity expansion and dispatch, and solved 

concurrently. For generator variables, the model decides the types and sizes of generators to 

build in each model region (capacity expansion), concurrently with the hourly dispatch status for 

each existing generator, start-up/shut-down events, spinning reserve provisions, and nonspinning reserve provisions (dispatch). For transmission variables, the model decides the sizes 

and locations of new transmission capacity to build (capacity expansion), concurrently with the 

hourly power flow between regions (dispatch). For storage variables, the model decides the types 

and sizes of storage resources to build in each region (capacity expansion), while solving for the

hourly charging, discharging and spinning reserve provisions (dispatch). 

Included in the decision variables listed above is a subset of binary decision variables that serve 

two major functions. The first functional group of binary variables helps enforce minimum plant 

size requirements for new generator capacity expansion of large fossil and nuclear technologies 

to capture the economies of scale relevant for these plant types. With these variables, the model 

captures the value of modularity of certain technologies over others. The second functional group 

of binary variables helps enforce operation constraints of existing generators, including 

minimum generation requirements, minimum on and off periods, start-up and shut-down event 

logic, and the ability of a generator to provide energy and reserves. With these variables, the 

model captures the on or off status of plants and whether or not a plant start-up or shut-down 

event has occurred. 

Note that the second functional group of binary decision variables applies only to existing 

capacity. More stringent operational limits are applied to new capacity for certain technology 

types. In particular, all new coal, NG-CC, and nuclear plants are required to operate above their 

minimum generation points for all model hours, whereas existing plants of the same type only 

operate above their minimum generation points if the plant is up and running. These stringent 

operational limits on new capacity is relaxed during the next five-year optimization period as the 

 

14 For each set of days chosen, we scale the overall load, wind, and solar profiles so that the overall energy required 

(for load) and energy available (for wind and solar) matches that of the seasonal average. This is necessary to 

capture the annual plant economics for capacity expansion decision-making. 
9 

"new" capacity is rolled into the "existing" capacity representation during the next solve. This 

different treatment of "new" versus "existing" capacity is necessary to maintain linearity in the 

problem15. However, it also loosely represents the fact that newer and more efficient large plants 

are likely to be dispatched prior to inefficient plants and are therefore less likely to be cycled. 

2.3.2 Objective Function

The objective function of RPM-CO represents the one-year cost of all new capital investments16

and the annual cost to operate the model system. Capital investments include the cost of new 

generation, storage, grid interconnection, and transmission capacity. Operational costs include 

fixed and variable O&M costs, fuel costs, start-up costs, and shut-down costs. Other costs, 

including a carbon price, can also be included in the objective function. The model minimizes 

this objective function during each solve subject to the constraints described in Section 2.3.3. 

2.3.3 Model Constraints

Major constraints in RPM-CO include load balance, planning and operating reserve 

requirements, renewable resource limits, exogenously defined wind and solar generation profiles, 

thermal power plant constraints, transmission constraints, and policy constraints. 

2.3.3.1 Load Balance Constraints

The load balance constraint requires that for each of the 31 model regions and each hour, 

generation within the region and power imports into the region exactly equals the sum of the 

local demand, exports out of the region, and curtailments. Curtailment by region is a variable in 

the model. Power imports include an estimate of transmission losses from the source regions. In 

addition, because RPM-CO does not explicitly represent the distribution network and any losses 

within the distribution network, the demand that must be met represents the bus-bar demand, 

which is assumed to be 4% higher than the end-use electricity demand (CEC 2011). 

2.3.3.2 Planning Reserve Constraints

Planning reserve requirements ensure sufficient firm capacity is available to at least exceed the

peak demand by a reserve margin. The required reserve margin for the Rocky Mountain Power 

Pool region is set by the North American Electric Reliability Corporation (NERC) to be 12.5% 

(NERC 2011). We model the Rocky Mountain Power Pool to include all Colorado regions and 

the two Wyoming regions. For dispatchable generators (i.e., all generator types excluding wind 

and solar PV), full nameplate capacity is counted toward the planning reserve requirement, i.e., 

the capacity value of these plants is one. Variable generators, including solar PV and wind, have 

a lower capacity value that is endogenously calculated between optimization periods. 

Capacity values for PV and wind can be estimated in several ways (Milligan and Porter 2006; 

Madaeni et al. 2012; Mills and Wiser 2012a). Here, we use a simplified net-load approach. 

 

15 Since "new" capacity is a decision variable, it cannot be combined with other decision variables, including the 

binary decision variables used to represent start-up and shut-down events, while maintain model linearity. This is 

not an issue for "existing" capacity since generation resources become parameters and not a decision variables after 

they are built.

16 More precisely, the overnight capital cost is multiplied by technology-specific fixed charge rate. For the 

preliminary scenario analysis presented in Section 4, fixed charge rates ranging from 0.10 to 0.15 are used based on 

financing assumptions from (Mai et al. 2012). The objective function is defined in the appendix.
10 

Separate capacity value estimates are calculated for existing installed variable generators and 

potential new installations. In particular, the capacity value of total existing wind and solar 

capacity is estimated by the ratio of the difference between the peak load and net peak load to the 

installed nameplate capacity. Net load is defined as the load minus wind and solar PV 

generation. Marginal capacity values are applied to potential new installation and are calculated 

for each region and technology separately.17 The marginal capacity value of each technology in 

each region is estimated as the ratio of the reduction in net peak load to an assumed increment of 

new nameplate capacity. The contribution to the capacity reserve requirement for wind and solar 

PV is reduced accordingly, based on the estimated capacity values for all new and existing 

variable generators. All else being equal (e.g. capacity factor, access to transmission, etc), the 

optimization routine would deploy variable generation technologies in regions with the highest 

capacity values. In general, capacity value declines with increasing renewable penetration level, 

particularly if the deployment is concentrated in small spatial regions. This representation of 

planning reserves and capacity value allows RPM-CO to endogenously value geospatial and 

technological diversity. In addition, the capacity value calculations are dynamic and they depend 

on the specific deployment and load scenario modeled. 

2.3.3.3 Operating Reserve Constraints

Operating reserve constraints ensure sufficient contingency and frequency regulation reserves are 

available for each model hour in RPM-CO. Requirements for operating reserves are imposed for 

two balancing authorities within the model system: Public Service Company of Colorado 

(PSCO) and Western Area Colorado Missouri (WACM).

18 For each balancing authority, 

contingency reserve requirements at each hour are based on the maximum between 6% of the 

hourly demand and an absolute contingency requirement based on the single largest contingency 

within the system (i.e., the 810-MW Comanche Generating Station coal plant).

19 At least half of 

the contingency reserves are required to be spinning reserves. In addition, we require additional 

spinning reserves (1% of demand) to be available during each hour to represent frequency 

regulation reserves. RPM-CO provides a framework for increasing operating reserve 

requirements with increasing renewable energy penetration levels; however, that is not 

considered in the preliminary scenario analysis. Future work will focus on quantifying the 

potential need for additional reserves, and how to model them in dispatch models. 

2.3.3.4 Renewable Resource Limits and Wind and Solar Generation Profiles

Based on the resource data described in Section 3, the model also limits deployment and output 

characteristics of wind, solar, and hydropower technologies. 

In particular, wind supply curves are calculated for each model region and five wind power 

classes20 to (1) limit the amount of wind capacity that could be installed based on the available 

 

17 For wind, a distinct capacity value is calculated for each wind power class in each region. 18 Each model region in Colorado is associated with one of these two balancing authorities; however, the generators 

and load within the region boundaries do not perfectly align with actual boundaries for the PSCO and WACM 

service areas. Modeled operating reserves requirements were based on current requirements in PSCO and WACM, 

but may not capture the full set of reserve requirements. 19 We require PSCO to hold at least 451 MW of contingency reserves and WACM to hold at least 359 MW of 

contingency reserves.

20 Five wind power classes are defined based on average wind generation characteristics from AWS Truepower

(AWS 2012), as described in Section 3.3.
11 

land area and resource quality, and (2) incorporate grid interconnection costs (which depend on 

the proximity to, and availability of, the regional transmission infrastructure) for new wind 

installations. Furthermore, we apply regional hourly wind and PV generation profiles. For PV, 

we use distinct profiles for fixed-tilt and 1-axis tracking systems based on results from NREL’s 

System Advisor Model (see Section 3). Due to the large solar resource and less restrictive siting 

challenges (relative to wind), we do not characterize regional PV resource limits, or additional 

grid interconnection costs in the model.21 

We currently do not allow new builds for other renewable technologies, including biopower, 

geothermal, or hydropower; however, RPM-CO can be easily modified to include these options. 

We limit hydropower dispatch with maximum and minimum hourly generation constraints, 

hourly ramping constraints and a seasonal energy constraint. These limits are derived from 

historical hydropower generation, and they loosely represent water and other stream-flow 

constraints. Constraints to biopower and geothermal dispatch are characterized in a similar 

manner as other thermal power plants. 

2.3.3.5 Thermal Power Plant Constraints

Unlike wind and solar generation, thermal power plant dispatch is endogenously determined 

within the optimization routine. However, modeled thermal power plant dispatch is constrained 

based on the physical flexibility of the technology types. Plant flexibility is modeled based on 

parameters that characterize each technology type, including minimum generation points, ramp 

rates, start-up and shut-down issues, minimum on and off times and outage rates. 

We apply multiple constraints to thermal power plant dispatch to help inform the flexibility 

limits (and options) for future deployment scenarios, particularly for those scenarios with higher 

levels of renewable penetration. The major constraints to thermal power plant dispatch consider 

generator capacity allocation, minimum generation requirements, and start-up and shut-down 

event logic. Many of these constraints require binary variables as described in Section 2.3.1 as 

well as in the appendix. 

Generator capacity allocation constraints limit the sum of thermal power plant generation and the 

amount of capacity allocated to provide operating reserves to be less than the nameplate capacity 

of the plant for each hour. The ability to provide spinning and non-spinning reserves depends on 

the state of the plant. Specifically, only plants that are on, synchronized, and generating 

electricity can provide spinning reserves if they have sufficient available capacity to provide 

reserves. The ability to provide different services also depends on technology type. For example, 

we allow NG-CT plants to provide non-spin (or quick-start) reserves when they are not 

generating because of their ability to start quickly from a cold start. However, we limit the ability 

of all other technology types to provide such services. 

Minimum generation requirements ensure that generators must either produce at a technologyspecific minimum level or be shut down by the model. New coal, NG-CC, and nuclear plants are 

required to operate at or above their minimum generation level during the model period in which 

 

21 A base grid interconnection cost is applied to all technologies, including PV.
12 

they are built, whereas existing generators are constrained to operate at or above their minimum 

generation levels only if the plant is up and running. 

Start-up and shut-down event logic constraints govern plant transitions from generating to idle, 

and vice versa, as well as minimum on and off periods, which are technology-specific. Plant 

start-up costs are also characterized in the model based on Lew et al. (2012), and they capture the 

relative economics of cycling in the dispatch (and expansion) decision-making of the model. 

2.3.3.6 Transmission Constraints 

We model transmission in RPM-CO based on a simple transport model. In other words, full flow 

control is allowed within the model along each transmission path and power flow is only 

constrained by the line capacity. Figure 4 shows the model representation of the existing 

transmission network based on the assumptions described in Section 3. New transmission lines 

are allowed within the model as well; however, these new lines are restricted to neighboring 

regions or locations where current connections exist.

22 Future work will improve the simple 

transport model to more accurately reflect electric flow in the system.

Figure 4. Transmission representation in RPM-CO

kV = kilovolt

 

22 For the preliminary scenario analysis described in Section 4, we disallowed any new transmission capacity for 

simplicity.
13 

Inter-state transfer capacities are defined using data from the WECC Loads and Resources 

Subcommittee. Intra-state transfer capacities were estimated using existing transmission line 

spatial data from Ventyx Velocity Suite (Ventyx 2012) and geographic information systems 

(GIS) analysis. Though the spatial data are detailed, they lack the existing capacity of each line. 

The voltage and length of each line is used to translate to capacity using the approximate power 

carrying capability of an uncompensated AC transmission line (National Regulatory Research 

Institute 1987). Defining the existing transfer network relied on GIS, by first determining the 

start and end vertices of each transmission line and then associating them with a region, 

producing region pairings. Capacities of regions with multiple pairings are aggregated producing 

distinct transfer capacities.

RPM-CO is designed to evaluate long-term planning scenarios for a small area; however, this 

area is electrically connected to a larger synchronous grid (WECC). For this reason, treatment of 

the boundary conditions can play a significant role in overall model results. Currently, we 

assume hard boundary conditions around the model system, which includes Colorado and parts 

of three surrounding states. Inter-state transfer of power within this model system is treated in a 

similar manner as intra-state transfers. In other words, we allow transfer of power between model 

regions based on the simple transmission treatment described above, irrespective of the state to 

which the source and destination regions belong. Future work will be needed to evaluate 

different boundary conditions and their effect on model results. 

2.3.3.7 Policy Constraints 

Options for policy-related constraints are available in RPM-CO and include renewable portfolio 

standards (RPS) and annual emission limits. The RPS in Colorado imposes an annual 

requirement for renewable generation. Current legislation23 dictates that 30% of electricity sales 

must come from renewable resources by 2020. The legislation includes an in-state multiplier of 

1.25 for in-state renewable generation. In addition, there is a 3%-by-2020 solar rooftop PV 

requirement. Any of these parameters can be changed to model different RPS scenarios. RPMCO tracks power sector emissions for CO2, sulfur dioxide (SO2), nitrogen oxides (NOx), and 

mercury (Hg), and constraints can be applied to limit the annual emissions of any of these 

pollutants. 

 

23 See www.dsireusa.org. 
14 

3 Model Inputs

The Resource Planning Model is a tool for exploring efficient development of electricity 

generation and transmission resources for a wide range of market dynamics, including different

technology and fuel costs, generator retirement schedules, RPS, emissions constraints, and so on. 

RPM was designed to allow users to set key market parameters and simulate a diverse range of 

electric sector growth scenarios. In this section, we describe several model inputs chosen in the 

preliminary scenario analysis (Section 4) to demonstrate model functionality. Both the input 

parameters and preliminary scenario analysis results are intended to highlight model capabilities; 

they should not be interpreted as projections of future technology costs, market trends, or 

renewable and conventional market potential. 

3.1 Electricity Demand

We characterize electricity demand for each model region using hourly electricity demand 

profiles for 2005 from the Ventyx Velocity Suite (Ventyx 2012). Electricity demand in Ventyx is 

characterized for "transmission zones," which are larger than model regions considered (six in 

Colorado, and nine in the full study region, including Wyoming, Utah, and New Mexico). To 

associate transmission zones with more spatially resolved model regions, we assume that 

electricity demand scales directly with population. We use LandScan nighttime population data 

(ORNL 2012) with approximately 1-kilometer (km) x 1-km resolution to calculate populationweighted scaling factors, and we use these to associate Ventyx demand to model regions. This 

methodology is applied to the Colorado study region, but it could be adapted to any U.S. region. 

We focus on 2005 electricity demand data because 2005 is the most recent year with coincident 

hourly wind and solar generation data (Section 3.3), and electricity demand data. RPM is 

designed to simulate capacity expansion from 2010 to 2030, and we scale 2005 electricity 

demand to approximate total 2010 demand, while maintaining 2005 hourly demand profiles. 

Electricity demand is assumed to increase additionally from 2010 through 2030 by 1% per year, 

based loosely on AEO 2011 (EIA 2011). For all years, we assume that the temporal shape of 

hourly electricity demand remains unchanged (represented by 2005 data), and we scale hourly 

electricity demand to be consistent with annual growth rate assumptions. 

RPM provides a framework for exploring the impact of varying hourly load profiles, which 

could result from several factors, including wide-scale adoption of electric vehicles, smart grid 

appliances, and so on. Efficient capacity expansion under different, and potentially uncertain, 

demand profiles will be the focus of subsequent research.

3.2 Conventional Generation Resources

Plant-specific generator characteristics are calculated using three datasets: Ventyx Velocity Suite 

(Ventyx 2012), the Environmental Protection Agency’s (EPA’s) National Electric Energy Data 

System (NEEDS) (EPA 2010) and Form EIA-923 (EIA 2010a) for generator capacity24; and 

EPA’s Continuous Emission Monitoring System (CEMS)25 (EPA 2012b) for plant-specific 

operating characteristics. We use a statistical characterization of hourly CEMS data from 2008 

 

24 Several data sources archive generator characteristics for some, but not all, of the generators within the study 

region. Three data sources were used to develop a complete data set of generator capacity and plant characteristics. 

25 See www.epa.gov/ttn/emc/cem.html.
15 

(Lew et al. 2012) to inform plant-specific heat rates, minimum generation levels, ramping and 

cycling characteristics, and emissions levels for generation resources within the study region. 

Similarly, we obtained oil and gas steam (OGS) generator characteristics from the Ventyx 

Velocity Suite. We associate each generator with a model region, and we use a capacityweighted average of plant-level generation characteristics to represent existing generators within 

each model region. 2010 generation capacity is listed for each state in Table 1. 

Table 1. Existing Generation Capacity in 2010 by State (MW)

Colorado Wyoming Utah New Mexico

Coal 5,702b 6,262c 4,771c 3,970c

Natural Gas—Combined Cycle 2,579b -

c 1,195c -c

Natural Gas—Combustion Turbine 2,350b 68c 390c 574c

Oil / Gas Steama 184 6 25 2 

Hydropowera 680 306 281 85 

Winda 1,306 1,415 224 292 

Utility PVa 85 - - 54 

CSPa - - - - 

Biopowera 13 - 9 6 

Geothermala 3 - 44 - 

Pumped-Hydropower Storagea 563 0 - - 

Total 13,465 8,057 6,938 4,983 a Ventyx 2012

b EIA 2010a

c EPA 2010

RPM uses a mixed-integer optimization structure that deploys discrete plants with specific sizes, 

heat rates, minimum generation characteristics, and emission rates. In the preliminary scenario 

analysis (Section 4), we allow only new natural gas generation resources (CCs and CTs) to be 

developed, consistent with recent trends and industry projections for the Colorado study region 

(GEO 2010).

Currently, RPM does not endogenously model the decision to retire electric generating capacity. 

However, the model exogenously considers planned retirement and fuel conversion activities 

based on Xcel Energy’s pathway to meet emission requirements defined in Colorado’s Clean 

Air, Clean Jobs Act (PUC Colorado 2010). This emission reduction pathway includes retiring 

596 MW of the existing coal capacity, converting 463 MW of coal to natural gas26, and 

implementing emissions controls to 742 MW of coal capacity27. Table 2 summarizes the 

expected timeline for these actions. Additionally, Xcel Energy has plans to install 569 MW of 

natural gas combined cycle capacity at the Cherokee site (Denver, Colorado) in 2015 to 

supplement the retired coal generation. These 569 MW are exogenously forced into RPM as new 

combined cycle construction in 2015. 

 

26 The 463 MW of fuel conversions from coal to natural gas are exogenously forced into RPM based on scheduled 

retirements of coal capacity, and the development of new combined cycle generation capacity.

27 Included in the 596 MW of retirements are 551 MW of coal capacity that will be decommissioned and a 45-MW 

coal plant that will be converted to a synchronous condenser. The retirements and fuel conversions are modeled in 

RPM; however, we currently do not model emission control retrofits in RPM.
16 

Table 2. Summary of Xcel Energy’s Pathway to Meeting the Emissions Requirements of the

Clean Air Clean Jobs Act (PUC Colorado 2010) 

Coal Unit Capacity (MW) Action Completion Date (Estimated)

Cherokee 1 107 Retirement 2011

Cherokee 2 106 Retirement 2011

Cherokee 3 152 Retirement 2015

Cherokee 4 352 Conversion To Natural Gas 2017

Arapahoe 3 45 Retirementa 2013

Arapahoe 4 111 Conversion To Natural Gas 2014

Valmont 5 186 Retirement 2017

Hayden 1 139 Emissions Controls 2015

Hayden 2 98 Emissions Controls 2016

Pawnee 505 Emissions Controls 2014 a Arapahoe 3 will be converted to a synchronous condenser by decoupling the turbine from the generator. 

Synchronous generators do not provide real power, but they regulate reactive power for system stability. 

Although the turbine and generator can be recoupled whereby restoring the synchronous generating 

capabilities, as we do not model reactive power in RPM, we simply assume that the 45 MW of generating 

capacity are no longer available at Arapahoe 3.

3.3 Renewable Resources and Technologies

We obtained the characteristics of existing renewable energy resources (i.e., installed by 2010) 

from the Ventyx Velocity Suite. In this section, we describe the methodology used to simulate 

hourly generation profiles for wind and solar resources, and generation constraints for semidispatchable renewable resources such as hydropower (run-of-river and pumped storage), 

geothermal, and biopower generators. 

Wind Resources

We use two data sources to characterize wind generation characteristics at high temporal 

resolution (3Tier 2010) and high spatial resolution (AWS Truepower 2012). First, we simulate 

hourly wind generation profiles for each model region and five wind groups (defined based on 

annual average wind capacity factors; see Table 3), and these hourly profiles are used to capture 

the different temporal generation patterns for wind resources with different capacity factors.

28 To 

do this, we use detailed simulations of wind generation at specific locations for 2005 (3Tier 

2010). These potential wind generation sites were chosen for the Western Wind and Solar 

Integration Study (GE Energy 2010); we use site locations to associate each site with a model 

region. We then characterize “aggregate” hourly wind generation profiles for each wind group by 

averaging the hourly generation from six wind sites within each of the five wind groups. This 

results in 30 wind sites for each model region. If model regions do not have a sufficient number 

of wind sites within each group to satisfy the selection criteria, we use the closest unselected 

wind sites from nearby regions to approximate hourly generation patterns. We use “aggregate” 

wind generation profiles from six wind sites to represent the inherent smoothing of variable wind 

 

28 Capacity factors represent the amount of electricity generated over a given period divided by the amount of 

electricity that could have been produced if the generator produced electricity at nameplate capacity for the full 

period. For example, if a 1-MW wind turbine generates 8 megawatt-hour (MWh) of electricity over the course of 

one day, it would have a capacity factor equal to 8 MWh/24MWh or 33% for that day.
17 

generation by developing wind resources in spatially dispersed locations. This methodology may 

underestimate the frequency and magnitude of wind ramping at low levels of wind penetration

and overestimate ramping at higher levels of penetration. 

Next, we calculate wind resource supply curves for the five wind groups in each model region. 

The resource supply curves represent the marginal cost of developing new wind resources per 

unit of additional capacity developed, based on the quality of undeveloped wind resources and 

access to existing transmission resources. We characterize the amount of new wind capacity that 

could be developed in each model region and wind group, using AWS Truepower (AWS 2012) 

simulations of wind gross capacity factors (based on simulated 80 meter wind velocities from 

2003 to 2010) at 200-meter x 200-meter horizontal spatial resolution.

29 We then filter this dataset 

to remove land area deemed unsuitable for wind development, such as urban areas, developed 

land, protected areas (local, state and national parks), and slopes greater than 20% (Lopez et al. 

2012). We convert the remaining land area into wind capacity by assuming that 5 MW of wind 

capacity could be sited on one square kilometer of land (DOE EERE 2008). Lastly, we estimate 

the potential need for, and cost of, new transmission and interconnection resources to develop 

each potential wind location based on the proximity of each location to existing transmission 

corridors and the dynamic utilization of these transmission resources.

30 This results in 155 wind 

resource supply curves (5 wind groups for 31 model regions) that represent the incremental cost 

of developing an additional unit of wind capacity. Model regions frequently do not have any 

resources associated with a given wind group (Figure 3), and the wind resource supply curves 

will show zero capacity. 

Table 3. Wind Net Capacity Factors (%) Associated with each Wind Groupa 

Capacity Factor Group 1 Group 2 Group 3 Group 4 Group 5

Mean Annual Capacity Factor (%) 28 33 38 42 48

Range in Annual Capacity Factors (%) 25–31 31–36 36–41 41–46 >46 a Wind resource characterizations from AWS Truepower (AWS 2012), based on simulated 80-m wind 

speeds from 2003 to 2010 and proprietary relationships between wind speed and generation profiles 

(wind power curves). 

Photovoltaics Resources

We simulate hourly PV generation profiles for two utility-scale31 PV technologies: (1) fixed 

mount PV systems that are south-facing with a 25-degree tilt, based on a common utility-scale 

system orientation (Ong et al. 2012), and (2) 1-axis tracking PV systems that are mounted flat 

(no tilt) and rotate from east-to-west with a maximum tracking angle of ±45 degrees.32 Hourly 

PV generation profiles are calculated for fixed and tracking PV systems at 10-km x 10-km 

resolution using the PVWatts module (Marion et al. 2001) in System Advisor Model (SAM).

33

We simulate PV generation for 2005 using hourly solar radiation data from the National Solar 

 

29 We assume an 85% availability factor to convert gross capacity factor to net capacity factor. The model uses net 

capacity factor to account for outages and other effects that limit availability of wind power plants.

30 Short et al. 2011 describes the same methodology used in the ReEDS model. 31 The RPM framework characterizes optimal capacity expansion of wholesale generation technologies, and does not 

characterize the potential evolution of distributed generation technologies like rooftop photovoltaics.

32This orientation was chosen to represent flat-mounted, ganged tracking systems that are common for large utilityscale PV projects in the United States (Ong et al. 2012) 33 See sam.nrel.gov.
18 

Radiation Database (NREL 2007), meteorological data from the North American Regional 

Reanalysis (Mesinger et al. 2006), and an 85% derate factor (based on inverter losses, panel 

soiling, system wiring, and module mismatch). 

We characterize aggregate hourly PV generation profiles for each system type and model region 

using three steps: (1) identify the 10 resource areas (10-km x 10-km) with the highest PV 

capacity factors in each model region; (2) remove the 3 resource areas with the highest PV 

capacity factors to conservatively estimate PV resources in areas that could be developed; and 

(3) use the remaining seven resource areas to calculate aggregate hourly generation profiles for 

each model region. We use aggregate PV generation profiles to estimate the impact of 

developing spatially dispersed solar resources.

We do not calculate transmission-based resource supply curves for PV as we do for wind. This is 

because solar resources are very large compared to the amount deployed in the model (Lopez et 

al. 2012), and there is less spatial diversity within the resource (Figures 2 and 3). Based on this, 

we assume that solar resources will be developed near existing transmission corridors for the 

levels of PV penetration explored in the preliminary scenario analysis. We apply the same grid 

interconnection cost for PV as other non-wind generation types. 

3.3.1 Hydropower Resources

A significant amount of hydropower capacity—680 MW—exists in the Colorado study region 

(Ventyx Velocity Suite). We characterize hydropower generation using hourly generation 

profiles from specific hydropower units within the study region34 (WECC 2012a) to statistically 

represent dispatch characteristics. From these data, we calibrate hydropower dispatch using three

operational constraints: (1) minimum and maximum hydropower generation, determined for each 

season; (2) total seasonal hydropower generation; and (3) hourly ramp rate limits (±15%). The 

first two constraints are informed by the hourly hydropower generation data, but the last 

constraint is developed to limit the dispatchability of these resources.

35

Colorado also has 563 MW of pumped-storage hydropower resources (Ventyx Velocity Suite). 

Pumped-storage hydropower units store electrical energy by pumping water from a low- to highelevation reservoir, and then later re-generate electricity, subject to about a 20% energy loss, by 

sending water back down to the low-elevation reservoir. We allow the model to economically 

dispatch these storage resources. In the current implementation, we do not explicitly model 

energy storage (megawatt-hours [MWh]) levels for the pumped-storage hydropower plants. 

However, we require a balance between the total energy discharged and the amount charged 

minus efficiency losses over each season.

 

34 Hydropower data were available from 2006, while other system characteristics (hourly electricity demand, PV 

generation, and wind generation) are based on 2005. It is important to match hourly electricity generation with 

demand to characterize the optimal dispatch of conventional generators to integrate renewable. However, we assume 

that hydropower resources are somewhat dispatchable, and we use the hourly generation statistics to calibrate basic 

generation characteristics. For this purpose, it is not as important to match generation years for hydropower as it is 

for wind and solar.

35 There are large ranges of hydropower resource types and dispatch characteristics. Defining general operational 

constraints to approximate both historical generation characteristics and potential future dispatch strategies can be 

challenging. We use this constraint to limit hydropower ramping to conservatively estimate the dispatchability of 

hydropower resources.
19 

In the preliminary model simulations described in Section 4, we did not allow new hydropower 

or pumped-storage hydropower resources to be developed. However, we do allow hydropower 

resources (and pumped-storage hydropower) to be dispatched differently, within the operational 

constraints described above, to add flexibility to the electric sector. Additionally, RPM provides 

a framework for evaluating the economic deployment of new hydropower resources and we 

anticipate using the model in this capacity in future work. 

3.3.2 Geothermal, Biopower, and Other Renewable Resources

Limited deployment of geothermal (3 MW) and biopower (13 MW) capacity has occurred in the 

Colorado study region (Ventyx Velocity Suite). Geothermal plants are modeled as dispatchable 

generators, and they are dispatched as baseload generation because they have no fuel costs.

Biopower resources are similarly modeled as dispatchable resources, and they will also generate 

as baseload units if biomass feedstock costs are lower than the costs of other fuels in a given 

scenario. In the preliminary model analysis, we did not allow new geothermal or biopower 

capacity to be developed; however, the economic development and dispatch of these 

technologies could be explored within the RPM framework. 

3.4 Electricity Imports and Exports

One challenge in optimizing capacity expansion for distinct regions within an electricity

interconnect is characterizing electricity imports and exports between the study region and 

boundary areas. In the preliminary scenario analysis, we approximate current and future imports 

and exports using historical power flows from WECC transmission path data (WECC 2012b). 

Colorado has historically exported electricity to Utah (WECC path 30), imported electricity from 

Wyoming (WECC path 36), and either imported or exported a small amount of electricity to 

New Mexico (WECC path 31). We calibrate seasonal import and export constraints using hourly 

power flow between regions from 2009, which is the most recent year with power-flow data 

(WECC 2012b). Based on these data, we constrain seasonal imports into Colorado to less than 

10.3% to 12.4% of electricity demand (depending on the season), and we limit seasonal exports 

to less than 2.0% to 5.1% of demand. No other restrictions or costs are placed on inter-state 

energy transfers. Future works is needed to better account for power transfers across regions. In 

the preliminary model runs, we find that the electricity import constraint is frequently binding, 

but the export constraint is typically not binding, as discussed in Section 4. 

RPM can be used to explore optimal capacity expansion in scenarios with very different 

electricity import/export dynamics, which can be essential to efficiently integrating large 

amounts of renewable electricity (DOE 2012, Mai et al. 2012). To do this, electricity generation 

and demand in boundary regions must be modeled in appropriate detail. We intend to expand the 

representation of boundary regions in future work to explore interregional power-flow dynamics. 
20 

3.5 Selection of Model Days

The RPM framework is unique in that it combines multi-year capacity expansion with hourly 

dispatch dynamics. Given the computationally intensive nature of capacity expansion models,

36

simulating dispatch for all hours of the year would require very long model run times. Instead, 

we select several representative days from each season to run. In the preliminary scenario 

analysis (Section 4), we simulate hourly dispatch for 17 days per year, including four 

consecutive days (Sunday-Wednesday) for each calendar season and one peak electricity demand

day to ensure sufficient generation/transmission capacity. This represents 408 dispatch hours,37

with chronological dispatch within each season. 

We choose a representative week for each season by finding a period that is most representative 

of “typical” seasonal electricity demand, using 3 steps: (1) we calculate seasonal average

electricity demand for each day of the week at hourly resolution38; (2) we then calculate the rootmean-square error (RMSE) difference between hourly electricity demand for each week and the 

seasonally averaged electricity demand; and (3) we choose the week with the lowest RMSE 

deviation from mean electricity demand for each season. We then choose four consecutive days 

(Sunday-Wednesday) from this representative week to model. 

After identifying representative weeks for each season, we scale electricity demand, and solar 

and wind generation profiles, to ensure that the scaled four-day electricity demand and 

generation represent total seasonal load, and wind and solar generation.39 This scaling is 

necessary to properly capture plant economics for the capacity expansion decision-making. By 

minimizing the deviation between weekly and seasonal electricity demand, we choose days that 

require the least amount of scaling to represent total seasonal electricity demand, but these weeks 

may require more scaling to represent seasonal wind and solar generation than other weeks that 

could have been chosen. 

The methodology for choosing representative times to characterize the value of variable (wind 

and solar) and dispatchable resources in capacity expansion models is an area of active research. 

We have designed the RPM framework to be run at various time resolutions (hourly to multiple 

hour temporal resolution) and to use different methodologies for choosing representative days. 

We explored a few different methods for choosing representative days while developing the 

model, including minimizing the RMSE deviation between daily and seasonal mean wind and 

 

36 Capacity expansion problems are computationally intensive because of the large number of combinations of 

generation resources that could be developed, including: different types and sizes of generation capacity, different 

generator locations, trade-offs between adding new generation or transmission capacity, among others. This limits 

the spatial and temporal resolution of capacity expansion models.

37 The number of optimization periods equals (4 days/season * 4 seasons + 1 peak day) * 24 hours/day = 408 hours. 38 This is to capture different electricity use trends for weekdays versus weekends. 39 For example, if a season has 90 days, we calculate the following scaling factor, C, to apply to hourly PV 

generation: 

Seasonal PV Generation C =

90 Model PV Generation

4

      . 

We calculate similar scaling factors for electricity demand and wind generation.
21 

solar generation profiles. However, we have not systematically assessed how these different 

selection methods would impact capacity expansion decisions. Developing optimal methods for 

selecting representative periods will be the focus of future work.

3.6 Cost Assumptions for Generation Technologies and Fuels

The cost of electricity generated by different technologies is driven by several factors including 

capital costs, fuel prices, O&M costs, planned and forced outage rates, emissions costs in various 

policy scenarios, and other factors. Future capital costs and fuel costs are inherently uncertain, 

and RPM allows users to set these prices to facilitate scenario analysis. The cost projections used 

here are intended to demonstrate model capabilities and features, and they do not represent 

forecasts of future price and performance potential. 

Table 4 outlines the capital cost assumptions used in the preliminary scenario analysis in Section 

4. All conventional and renewable technology prices are based on Black and Veatch, Inc. (2012), 

and they represent a relatively conservative projection of future price and performance 

improvements for all technologies. Other cost and performance factors, including technologyspecific O&M costs, can be found in Black and Veatch (2012). Fixed charge rates are also 

assumed to differ by technology and are based on the financing and lifetime assumptions from 

Mai et al. (2012). Here and elsewhere in this report, all technology and system costs are shown in 

2010 US dollars (2010$).

Table 4. Price Projections (2010$/Watta

) for Electricity Generating Technologies

Technology 2010 2015 2020 2025 2030

Coal 2.94 2.94 2.94 2.94 2.94

Natural Gas—Combined Cycle 1.25 1.25 1.25 1.25 1.25

Natural Gas—Combustion Turbine 0.66 0.66 0.66 0.66 0.66

Wind—All Wind Classes 2.01 2.01 2.01 2.01 2.01

PV—Fixed Tilt 2.88 2.59 2.45 2.32 2.22

PV—1-xis Tracking 3.98 2.66 2.55 2.45 2.35 a All prices are converted from 2009 to 2010 US dollars using the consumer price index 

(www.bls.gov/data/inflation_calculator.htm). 

Table 5 shows the fuel price projections used in the preliminary scenario analysis, and are based 

on the AEO 2011 reference scenario (EIA 2011). As with other system characteristics, these 

prices are intended only to demonstrate model capabilities, and RPM provides a framework for 

exploring the impact of various future price scenarios on capacity expansion and dispatch. 

Table 5. Fuel Price Projections (2010$/MMBTUa) 

2010 2015 2020 2025 2030

Coal 2.30 2.14 2.19 2.28 2.36

Natural Gas 5.15 4.75 5.09 5.85 6.31

Biomass 5.08 5.08 5.08 5.08 5.08 a All prices are converted from 2009 to 2010 US dollars using the consumer price index 

(www.bls.gov/data/inflation_calculator.htm). 
22 

Table 6 summarizes the assumed operating characteristics for new fossil generators developed by 

the model. RPM uses mixed-integer optimization, allowing generation units of distinct sizes to 

be built. In the preliminary model scenarios, we assume minimum generator sizes for coal and 

natural gas resources, as shown in Table 6, along with technology-specific operational 

characteristics (heat rates, emissions rates, and minimum generation) from Black and Veatch 

(2012). For fossil generators built before 2010, we use historical plant operation from the EPA 

CEMS data (EPA 2012, Lew et al. 2012) to inform plant-specific heat rates, emission rates and 

minimum generation levels. These are included as capacity-weighted operating characteristics 

for each generator type in all model regions. For fossil generators built after 2010, we estimate

NOx emission rates using average emission rates from existing Colorado generators based on the 

EPA CEMS data, and we estimate CO2, SO2 and mercury emission rates based on national 

averages used in the ReEDS model (Short et al. 2011).40 

Table 7 summarizes additional operating characteristics assumed for existing fossil generation 

resources. These include the planned and forced outage rates (Black and Veatch 2012), the 

maximum amount of capacity that can be used for spinning reserves, as well as the time and 

costs associated with starting up and shutting down fossil generators (Lew et al. 2012). 

Table 6. Assumed Characteristics for New Thermal Generators

Minimum

Size (MW)

Heat Rate 

(MMBTU/MWh)

CO2 Rate

(metric 

tons/MMBTU)

NOx Rate

(short 

tons/MMBTU)

SO2 Rate

(short 

tons/MMBTU)

Minimum 

Generation

(% of 

nameplate)

Coal 606 9.4 9.3E-02 1.4E-04 3.1E-05 40%

NG CC 580 6.7 5.4E-02 3.6E-06 1.7E-06 50%

NG CT 211 10.4 5.4E-02 1.7E-05 4.9E-06 50%

Table 7. Operating Characteristics for Thermal Generators 

Forced 

Outage 

Rate (%)

Planned

Outage 

Rate (%)

Maximum 

Spinning 

Fraction 

(% of total)

Fixed 

Start-Up 

Cost 

($/MW)

Start-Up Fuel 

Usage

(MMBTU/MW)

Minimum 

On Time 

(hr)

Minimum 

Off Time 

(hr)

Coal 6% 10% 10% 129 14.5 12 12

NG CC 4% 3% 10% 79 0.24 4 4

NG CT 3% 5% 50% 34 1.53 0 0

 

40 NOx and SO2 emissions rates depend on site-dependent generator characteristics, combustion controls and postcombustion controls. We estimate NOx and SO2 emissions rates for new generators based on historical averages 

which may may overestimate future emissions. However, these emissions factors can be modified in different 

scenarios to explore the regional costs of complying with future regulation standards, such as the EPA New Source 

Performance Standards (NSPS).
23 

4 Sample Model Results

To demonstrate the RPM capabilities, we explore two capacity expansion scenarios in the 

Colorado study region: (1) a 30% renewable portfolio standard (RPS) to be met by 2020 and 

sustained for all subsequent periods applied to Colorado (referred to as “30% RE” throughout), 

and (2) a Baseline scenario with no RPS requirement (referred to as “Baseline” throughout). The 

first scenario is similar to the current Colorado RPS41, with a few modifications.42 We do include 

a 3% solar carve-out43 to the 30% RPS, similar to the current Colorado RPS. For years preceding 

2020, we apply intermediate RPS targets based on linearly scaling from current RE penetration 

to the 30% target by 2020. The Baseline scenario is identical in all ways except that it does not 

include a RPS requirement or the solar carve-out. 

The amount and location of wind and solar deployment is sensitive to several assumptions, 

including renewable energy targets and new and existing transmission capacity. RPM provides a 

framework for exploring the impact of these and other factors on the deployment of renewable 

and fossil-based generators. The scenarios explored here are intended to demonstrate model 

capabilities and should not be interpreted as projections of future market trends, technology 

costs, or renewable and conventional market potential. In addition, these scenarios are not 

intended to represent a policy analysis of the existing Colorado RPS.

4.1 Electric Sector Evolution 

Figure 5 shows the progression in annual Colorado generation in terawatt-hours (TWh) and netimports of electricity from surrounding states (including Wyoming, Utah and New Mexico), and 

Figure 6 shows generation fractions for each technology in 2010 and 2030. Colorado end-use 

electricity demand is assumed to increase from about 60 to 73 TWh from 2010 to 2030. This 

increase in demand is met by increased wind, solar and natural gas generation in the 30% RE

scenario, and almost entirely by increased natural gas generation in the Baseline scenario. 

 

41 See www.dsireusa.org. 42 The modeled RPS was used to explore the costs and benefits of reaching 30% renewable energy generation in 

Colorado, and it differs from the existing CO RPS in several key ways, including: (1) we apply the renewable 

requirement to all Colorado electricity demand, not just the demand served by investor owned utilities; (2) we 

constrain the RPS to be met with renewable resources developed within Colorado state boundaries, and we do not 

consider interstate trading of renewable electricity credits; (3) we remove the 1.25 multiplier for renewable energy 

generated within Colorado; (4) we model the 3% solar carve-out to apply to all Colorado electricity demand and 

require the carve-out to be met by utility-scale PV; and (5) we allow existing hydropower generation to contribute to 

the RPS requirement.

43 The modeled solar carve-out requires 3% of electricity demand in Colorado to be generated by solar technologies 

by 2020, and the 3% generation level to be maintained after 2020 as electricity demand increases. Since RPM-CO 

does not include a representation of rooftop PV markets, we require the 3% solar carve-out to be met by utility-scale 

PV projects.
 

 

 

Figure 5. Growth in electricity generation (TWh) for the 30% RE scenario and the 

Baseline scenario
 

Figure 6 shows the fractional breakdown of modeled 2010 and 2030 electricity generation from 

different technologies. In the Baseline scenario, no new wind or solar capacity is developed after 

2015,44 and the relative generation fractions of wind and solar decrease based on increasing 

electricity demand. In the 30% RE scenario, wind increases from 5.5% of electricity generation 

in 2010 to about 22% by 2030, and solar generation increases from 0.23% to about 4.3%. The 

30% RE scenario included a 3% solar carve-out, and we see additional PV capacity developed to 

reach the renewables target. The renewable energy fraction is stipulated to meet 30% of end-use 

electricity demand, but based on energy losses in the transmission and distribution systems,45 we 

model the renewables target as reaching 28.3% of total electricity generation. 

Figures 5 and 6 show natural gas combined cycle (CC) generation increases in both scenarios, 

from 14.9% in 2010 to about 16.8% in the 30% RE scenario and 33.6% in the Baseline scenario. 

We find that natural gas combustion turbine (CT) generation increases slightly, and that existing 

CT capacity is sufficient to meet these small increases. Coal generation is projected to decrease 

in both scenarios, from about 65.9% in 2010 to 46.4% by 2030 in the 30% RE scenario and 

47.5% by 2030 for the Baseline scenario. Coal generation declines over the study period as coal 

capacity is retired based on planned retirement schedules (Section 3.2), and because the model is 

constrained to restrict new coal development in these scenarios.46 

44 We exogenously force 497 MW of new wind builds in the 2015 optimization to account for historical wind
 

capacity additions between 2010 and 2012. 

45 We do not explicitly model the distribution system; we simply assume 4% distribution losses (CEC 2011). 46 New coal capacity is limited in the sample model results to limit the model from exogenously retiring and then rebuilding coal generation resources. 

24 
 

 

Figure 6. Electricity generation fractions for 2010 and for the 2030 30% RE scenario and 

Baseline scenario
 

Figure 7 compares 2010 Colorado in-state generation fractions from the RPM model with 

historical generation data from EIA form 923 (EIA 2010b). Electricity demand and generation 

capacity are calibrated for 2010 using historical data (see Section 3), but the RPM model 

determines optimal dispatch for all years.47 The EIA data does not include generators less than 

1 MW, and only captures about 90% of in-state CO generators and electricity demand,48 

however, the comparison suggests that the RPM optimal dispatch algorithm is largely in line 

with the historical data. The RPM model shows a larger fraction of in-state coal generation, as 

compared to historical trends, and a correspondingly smaller natural gas generation fraction. 

Reasons for these differences may include differences in plant- or utility-specific fuel price 

contracts, congestion issues that RPM does not capture, as well as various real-world dispatch 

considerations such as additional regional reserve requirements that are not captured within the 

least-cost dispatch algorithm. Further work is needed to understand differences between model 

dispatch and historical data. 

47 The Comanche 3 coal unit came online mid-year of 2010, therefore, we only allow it to generate electricity or 

provide reserve services during the summer and fall model seasons for the 2010 model year. 48 EIA form 923 contains generation data for some, but not all, U.S. electric service providers. As such, the 

generation fractions in Figure 7 represent a subset of the generation resources and end-use demand included in the 

RPM model. 

25 
Figure 7. Electricity generation fractions for Colorado in-state generation in 2010 for historical 

data and modeled results 

Note: The 2010 generation fractions in Figure 7 represent the relative contribution from each generation 

technology to total in-state generation in Colorado. Figure 7 differs from Figure 6 which represents the 

contribution from each generation technology to serving Colorado electricity demand, which is met using 

a combination of in-state generation and electricity imports. 

Figure 8 shows the development of new generation capacity within the Colorado study region, 

for both the 30% RE scenario and the Baseline scenario. In the 30% RE scenario, 3,632 MW of 

new wind capacity and 1,722 MW of solar capacity are developed to meet the renewables target. 

In the Baseline scenario, no new wind or solar capacity is developed after 2015 in the absence of 

a renewables target. In both scenarios, new natural gas generators are developed to meet 

increasing electricity demand and replace retired coal generators. In sum, new natural gas 

capacity totals 2,428 MW by 2030 in the 30% RE scenario and 3,426 MW in the Baseline 

scenario. Planned coal retirements and fuel conversion to natural gas (Section 3.2) decrease coal 

capacity from 5,702 MW in 2010 to 4,648 MW by 2020. We assume that no new geothermal or 

biopower resources will be developed, and their contribution to Colorado generation capacity 

remains marginal (represented by the “Other RE” category). Table 8 summarizes 2010 and 2030 

capacity and generation shown in Figures 6–8. 

26 
 

 

Figure 8. Growth in generation capacity (MW) for the 30% RE scenario and the Baseline scenario 

without an RPS 

Table 8. Colorado Electricity Generation Capacity (MW) and Annual Generated Energy (TWh) for 

the 30% RE and Baseline Scenarios 

Capacity Generation 

Technology (MW) (TWh / % total generation)a 

2010 2030 2030 2010 2030 2030 

30% RE Baseline 30% RE Baseline 

Coal 5,702 4,648 4,648 41.5 / 65.9% 35.7 / 46.4% 36.3 / 47.5% 

Natural Gas–CC 2,579 5,008 6,005 9.36 / 14.9% 12.9 / 16.8% 25.7 / 33.6% 

Natural Gas–CT 2,350 2,350 2,350 <1 / <1% <1 / <1% <1 / <1% 

Oil / Gas Steam 184 184 184 <1 / <1% <1 / <1% <1 / <1% 

Hydropower 680 680 680 1.85 / 2.93% 1.85 / 2.4% 1.85 / 2.42% 

Wind 1,306 4,938 1,803 3.48 / 5.52% 16.6 / 21.6% 5.14 / 6.72% 

Photovoltaics 85 1,807 85 <1 / <1% 3.33 / 4.33% <1 / <1% 

Other RE 16 16 16 <1 / <1% <1 / <1% <1 / <1% 

Electricity Imports - - - 6.59 / 10.5% 6.5 / 8.45% 7.3 / 9.55% a The RPS target is based on the fraction of end-use electricity demand, which is about 4% less than total 

generation because of transmission and distribution losses. As such, the fraction of total generation from renewable 

electricity is slightly less than 30% in the RPS scenario. 

27 
Figure 9 shows the geographic location of modeled wind, solar, natural gas (CC and CT), and 

coal generators deployed in the 30% RE scenario by 2030; and Figure 10 similarly shows 

modeled deployment in the Baseline scenario by 2030. After 2015, no new wind and solar 

resources are developed in the Baseline scenario, and the 2030 geographic distribution represents 

systems built by 2015. Also, both scenarios use the same coal retirement and fuel conversion 

schedule (Section 3.2) and do not allow new coal generation to be built. 

Figures 9 and 10 show that new wind resources are developed in several regions to meet the 30% 

RE target. Strong development is modeled in southeastern and north-central Colorado, 

corresponding to regions with Class 4 wind resources (Figure 3) and proximity to existing 

transmission capacity. Solar resources are primarily developed in central, southern (San Luis 

Valley) and northwestern Colorado, which correspond to regions with access to good solar 

resources (Figure 2) and access to existing transmission capacity. PV is also deployed in and 

around load centers in the Front Range, by Denver, Colorado Springs, and Fort Collins. In the 

preliminary scenario analysis, we do not allow new transmission resources to be developed, and 

the modeled deployment of wind and solar projects are based, in part, on using existing 

transmission capacity. 

Figure 9. Modeled deployment in the 30% RE scenario 

28 
 

Figure 10. Modeled deployment in the Baseline scenario 

Figures 9 and 10 show the geographic location of natural gas generators built in the 30% RE and 

Baseline scenarios. Colorado had more than 2,300 MW of CT capacity by 2010, and RPM 

optimizes the Colorado system without additional CT builds in either scenario by 2030. This is a 

direct result that the planning reserve constraint is not found to be binding under any scenario or 

year. One reason for this is that the Rocky Mountain Power Pool region (to which Colorado and 

Wyoming belong) currently exceeds the NERC-directed 12.5% capacity reserve margin 

requirement and continues to exceed this requirement based on our load growth and retirement 

assumptions. 

We do find significant new CC capacity built in both the 30% RE scenario (2,428 MW by 2030) 

and the Baseline scenario (3,426 MW by 2030). Combined cycle capacity is primarily deployed 

near load centers in the Front Range urban corridor in both scenarios, including a large amount 

of new capacity near Denver in the Baseline scenario that is not seen in the 30% RE scenario 

because of a combination of locally sited PV capacity and remotely sited wind and PV projects. 

29 
Figures 11–13 show the optimal hourly dispatch of generation resources within Colorado for 

2010 and the 2030 30% RE scenario. In all seasons, coal generators are run as baseload resources 

but are ramped down during hours when natural gas CCs reach minimum generation limits. 

Natural gas CTs, CCs, and hydropower resources are used to provide operational flexibility to 

follow variations in electricity demand, and wind and solar generation. Since we only apply 

seasonal constraints to imports from out of state, they are also used as an additional source of 

flexibility. Further work is needed to improve the constraints on inter-regional power transfers. 

Figure 11 shows the dispatch of electricity generation resources during four representative days 

(Sunday-Wednesday) during summer. In 2010, summer afternoon electricity demand is met 

using natural gas CCs, pumped-hydropower storage, and electricity imports. In the 2030 30% RE 

scenario, wind generation is relatively consistent during all hours, and PV generates strongly 

midday with natural gas and pumped storage ramping up to meet strong afternoon and evening 

load. In the 2030 Baseline scenario, natural gas CCs generate much more significantly and 

provide the majority of load following. 

Figure 12 shows a similar dispatch of generation resources for four days in spring. Spring 

dispatch profiles are primarily different to summer dispatch characteristics because electricity 

demand is significantly lower (peaking at about 9,500 MW rather than 12,000 MW in summer in 

2030), while both wind and solar generation are relatively high. This leads to significantly less 

natural gas CC generation in all scenarios and a small amount of coal ramping. We do not find 

significant curtailment in any season or model scenario. 

Lastly, Figure 13 shows model dispatch for one day in mid-July with the highest electricity 

demand. Electricity demand peaks at about 11,500 MW in 2010, and is projected to peak at 

about 14,000 MW in 2030. As with during other times of year, ramping is provided by gas CCs, 

CTs, and pumped-hydropower storage (as shown by the difference between solid and dashed 

black lines). In the 30% RE scenario, wind generates most strongly during the night and morning 

preceding peak demand. PV generation peaks during the middle of the day and begins to decline 

during the early afternoon peak hours. Wind and PV primarily displace natural gas CC 

generation on the peak day and shift the timing of natural gas ramping from midday to the 

afternoon and early evening. Wind and PV generation do not significantly decrease the amount 

of natural gas CT capacity dispatched to meet peak demand. All scenarios show a small amount 

of coal ramping in the early morning before the peak based on the assumed minimum generation 

limits for natural gas CC units. 

30 
 

Figure 11. Electric sector dispatch for four days (Sunday-Wednesday) in summer for 2010 and the 

30% RE and Baseline scenarios 

Pumped-hydropower storage charging is shown during times when the retail load (dashed line) is 

below the storage-shifted load (solid line) during the night, and vice-versa for storage discharging 

during the day. 

31 
Figure 12. Electric sector dispatch for four days in spring (Sunday-Wednesday) 

Pumped-hydropower storage charging is shown during times when the retail load (dashed line) is 

below the storage-shifted load (solid line) during the night, and vice-versa for storage discharging 

during the day. 

32 
 

Figure 13. Electric sector dispatch for one day with the peak electricity demand for the year 

Pumped-hydropower storage charging is shown during times when the retail load (dashed line) is 

below the storage-shifted load (solid line) during the night, and vice-versa for storage discharging 

during the day. 

33 
 

4.2 Electric Sector Emissions and Costs 

RPM is designed to characterize electric sector costs, emissions rates, transmission utilization, 

and other parameters for various deployment scenarios. In doing so, RPM can be used as a tool 

by policymakers to understand the costs and benefits associated with various policy scenarios, 

such as the potential costs and impacts on emissions associated of reaching a RPS target. 

Figure 14 shows the electric sector emissions49 of CO2, NOx, and SO2 for the 30% RE scenario 

and the Baseline scenario. Emissions decrease significantly in all scenarios from 2010 to 2020 

based on assumed coal retirements (Section 3.2). In the 30% RE scenario, electric sector carbon 

emissions decrease 12% below the Baseline scenario. Carbon reductions (12%) are less than the 

increase in renewable generation (about 12% to 28% of CO generation) because renewable 

electricity primarily offsets natural gas CC generation, which has lower carbon emission rates, 

per unit of generated electricity, than coal generation. The 30% RE scenario also reduces 

electric-sector NOx emissions (2%–3% below the Baseline scenario for 2020–2030) and SO2 

emissions (1%–2% below the Baseline), but by far less than the RE generation fraction because 

RE primarily displaces natural gas CC generation and not coal generation. SO2 emissions are 

reduced more significantly from 2010 to 2020 than NOx because SO2 are primarily emitted by 

coal generation, while NOx are emitted by all fossil generators. 

Figure 14. Annual electric sector emissions in the Colorado study region for the 30% RE scenario 

(solid lines) and the Baseline scenario (dashed lines) 

49 Emissions rates were calculated using average historical emissions factors (Colorado average for NOx and national 

averages for CO2 and SO2). As such, the emissions in Figure 14 represent possible emissions trends based on the 

evolution of the Colorado electric sector, but may not represent actual electric sector emissions for any given year. 

34 
35 

Figure 15 shows the net present value (NPV) of the 2010 through 2030 costs of developing and 

operating the generation resources in the 30% RE and Baseline scenarios. NPVs are calculated 

by linearly interpolating annual capital and operating costs between the five-year model intervals

and discounting at a 3% discount rate (real dollars).50 Capital costs are assumed to be paid over a 

20-year loan term extending beyond the model’s time horizon at a uniform fixed charge rate, 

based on those used in Mai et al. (2012). 

 

Figure 15. Net present value of the 2010–2030 costs of developing and operating generation 

resources in the 30% RE scenario and the Baseline scenario

 

50 Representing a social discount rate.
36 

Figure 15 shows that discounted electric sector costs vary from about $77.3 to 85.4 billion 

dollars for the Colorado study region from 2010–2030. The primary difference between the 30% 

RE scenario and the Baseline scenario is the significant deployment of wind and solar capacity. 

This additional capacity costs an additional $15.3 billion dollars but offset about $7.1 billion 

dollars in building and operating natural gas CC resources. In total, we find that the modeled 

30% RE scenario cost an additional $8.1 billion dollars for the 2010–2030 period. The cost 

results presented here strongly depend on assumed fossil fuel and capital costs and sensitivity 

analyses are needed to bound the cost implications represented here. We find that the cost of 

reaching the modeled 30% RE scenario represents about a 0.82 cents/kWh average increase in 

electricity costs,

51 based on the cost assumptions listed in Section 3.6.52 

5 Conclusions and Future Work

In this report, we present a new capacity expansion model, the Resource Planning Model (RPM) 

that uniquely combines hourly dispatch with multi-year generator and transmission planning. 

The high resolution of the model allows it to represent the flexibility limits of a power system in 

its capacity expansion decision-making, including physical limits on thermal generator dispatch, 

coincidence of variable generation and load, hourly transmission availability and congestion, and 

reserve requirements. RPM is ideally suited for regional electric system planning with increasing 

levels of variable generation as it considers the simultaneous and chronological hourly variations 

in load, wind, and solar resources across a geospatial region. It can be used to explore a variety 

of future scenarios with varying levels of renewable deployment and evaluate the emissions and 

cost impacts of such scenarios, while ensuring many aspects of power resource adequacy across 

all scenarios.

In addition, RPM provides a framework to answer questions that are of interest to the modeling 

and analysis communities. RPM can be used to research the selection of optimal "representative" 

model time slices and the importance of time resolution in reduced-form models. The flexible 

model structure of RPM also enables us to evaluate the impacts on deployment and dispatch of 

simplifications to a representative physical system. RPM provides a test-bed to explore how 

representations of boundary conditions on a small region within a larger electric system impact 

results. These and related research areas would be of value to the broader energy modeling 

community. 

We present preliminary scenario analysis results for an initial version of RPM representing the 

power system in Colorado. These preliminary results indicate that achieving 30% renewable 

electricity by 2020 and sustained through 2030 is possible for this system and would result in 

12% reduction in annual CO2 emissions. The increased renewable capacity and reduced fossil 

capacity and fuel use result in a 10% increase in NPV costs over 20 years (2010-2030, 3% real 

discount rate). Most of the new renewable capacity is comprised of wind capacity, located in 

 

51 Total electric sector costs were related to a variable cost per kWh by linearly interpolating annual load projections 

between 2010 and 2030, and discounting at a 3% (real) rate (same as used in the NPV calculation). This resulted in 

995.1 million MWh for 2010 to 2030. The possible increase in electricity prices ($/kWh) was calculated by dividing 

the additional cost of reaching the 30% RE target by the discounted electricity demand. 52 The future costs of each model scenario, and cost differences between scenarios, are highly dependent on several 

assumptions, including future fuel prices, technology-specific price and performance characteristics, and other 

system parameters. We plan to explore these sensitivities in future work. 
37 

north-central and southeastern Colorado. New solar PV capacity is also observed and is found to 

be located in south-central and northwestern Colorado and the Front Range urban corridor. RPM 

finds that electricity supply-demand balance (and reserve provision) is possible with this level of 

renewables, even without new inter-regional transmission capacity, through greater fossil power 

plant ramping and cycling. More research is needed to confirm these results.

Future work will focus on improving the boundary-condition representations of the focus region. 

A more accurate representation of boundary regions could help improve our estimate of emission 

reductions that renewable technologies provide and allow for more realistic conditions for power 

plant dispatch in Colorado. Another area of model improvement is in the transmission 

representation, such as through DC optimal power-flow methods. We also plan to include 

representation of demand-side options, such as demand response or distributed generation, in 

RPM. Future research with the model will focus on the sensitivity of model results to the 

selection of model days and hours. We plan to work with various stakeholders to improve the 

model representations in the areas described.

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Energy Laboratory. 

“LandScan.” (2012). Oak Ridge National Laboratory (ORNL). http://www.ornl.gov/sci/ 

landscan/. Accessed April 2012. 

Ong, S.; Campbell, C.; Denholm, P.; Margolis, R. (forthcoming). Land Use Requirements for 

Solar Power Plants in the United States. Golden: CO. National Renewable Energy Laboratory. 
40 

PSCO (Public Service Company of Colorado). (2011). 2012 Renewable Energy Standard 

Compliance Plan, Volumes 1 and 2. Denver, CO: Xcel Energy, Inc. http://www.xcelenergy.com/ 

About_Us/Rates_&_Regulations/Regulatory_Filings/CO_2012_Renewable_Energy_Standard 

_Compliance_Plan

PUC Colorado. (2010). Final Order Addressing Emission Reduction Plan, Decision No. C10-

1328, issued December 15, 2011. http://www.ferc.gov/EventCalendar/Files/20111208072455-

Colorado%20PUC%20HB10-1365,%20Final%20Order%20Addressing%20Emission 

%20Reduction%20Plan.pdf. Accessed November 8, 2012. 

Short, W.; Sullivan P.; Mai T.; Mowers M.; Uriarte C.; Blair N.; Heimiller, D.; Martinez A. 

(2011). Regional Energy Deployment System (ReEDS). NREL/TP-6A20-46534. Golden, CO: 

National Renewable Energy Laboratory. 

Sioshansi, R.; Denholm, P. (2010). “Value of Plug-In Hybrid Electric Vehicles as Grid 

Resources.” Energy Journal (31:3); pp. 1–23. 

U.S. Department of Energy (DOE). (2008). 20% Wind Energy by 2030: Increasing Wind 

Energy’s Contribution to U.S. Electricity Supply. DOE/GO-102008-2567. 

U.S. Department of Energy (DOE). (2012). SunShot Vision Study. DOE/GO-102012-3037. 

Ventyx Velocity Suite (Ventyx) (2012). Ventyx Velocity 

Suite, www.ventyx.com/en/enterprise/business-operations/business-products/velocity-suite. 

Accessed February 2012. 

Western Electricity Coordinating Council (WECC) (2012a). Assumptions Matrix for the 2020 

Transmission Expansion Planning Policy Committee (TEPCC) Dataset. http://www.wecc.biz/ 

library/StudyReport/Documents/Assumptions%20Matrix%20for%20the%202020%20TEPPC 

%20Dataset.pdf

Western Electricity Coordinating Council (WECC). (2012b). Historical path 

data. http://www.wecc.biz/library/.
41 

Appendix. Model Formulation

This appendix describes the formulation of RPM-CO, which was written in the General 

Algebraic Modeling System (GAMS) platform. All major sets, parameters, variables, and 

equations are listed and defined. 

Indices

• bin : wind supply curve bin 

• c : wind power class 

• d : dispatch period

• h,h’ : hour 

• n,p : region 

• pol : pollutant type 

• q : electricity generating technology

• st : storage technology 

Model Data Sets

Temporal Sets

• D : set of dispatch periods {summer, fall, winter, spring, peak} 

• NONPEAK ⊂ DR : set of nonpeak dispatch periods where NONPEAK is a proper subset 

of D {summer, fall, winter, spring} 

• Hd : set of hours for each dispatch period d

Spatial Sets

• N : set of all regions {1..31} 

• CO ⊂ N : set of Colorado regions where CO is a proper subset of N {1..27} 

• NONCO ⊂ N : set of non-Colorado regions where NONCO is a proper subset of N

{28..31} 

• PSCO ⊂ N : set of PSCO regions where PSCO is a proper subset of N 

• WACM ⊂ N : set of WACM regions where WACM is a proper subset of N

• WY ⊂ N : set of Wyoming regions where WY is a proper subset of N 

• TCONNECT : set of all arcs (n,p) that connect regions n and p

Technology Sets

• Q : set of all electricity generating technologies

• DG ⊂ Q : set of distributed generation technologies where DG is a proper subset of Q 

• DISPATCH ⊂ Q : set of dispatchable technologies where DISPATCH is a proper 

subset of Q

• HYDRO ⊂ Q : set of hydro-based technologies where HYDRO is a proper subset of Q

• NONMOD ⊂ Q : set of generating technologies that are non-modular53 where 

NONMOD is a proper subset of Q 

• NONSPIN ⊂ Q : set of generating technologies that can provide non-spinning reserves 

where NONSPIN is a proper subset of Q 

 

53 Non-modular refers to plants that must be built in bulk capacity, such as nuclear, coal and natural gas.
42 

• PV ⊂ Q : set of photovoltaic-based technologies where PV is a proper subset of Q 

• RE ⊂ Q : set of renewable energy technologies where RE is a proper subset of Q {wind, 

fixed-axis pv, 1-axis pv, hydropower, geothermal, biopower} 

• SPIN ⊂ Q : set of generating technologies that can provide spinning reserves where 

SPIN is a proper subset of Q 

• THERMAL ⊂ Q : set of thermal technologies where THERMAL is a proper subset of Q 

• VG ⊂ Q : set of variable generation technologies where VG is a proper subset of Q 

{wind, fixed-axis pv, 1-axis pv}

• WIND ⊂ Q : set of wind-based technologies where WIND is a proper subset of Q 

• ST : set of storage technologies 

Wind Technology Sets

• B : set of wind supply curve bins. Five (5) bins define the wind resource supply curves.

• C : set of wind classes. There are five (5) wind power classes.

Emissions Data Sets

• POL : set of emissions types {CO2, SO2, NOx, Hg} 

• CO2 ⊂ POL : set of carbon dioxide emissions types where CO2 is a proper subset of 

POL {CO2} 

Model Parameters

Generation Technology Cost Data

• capcostq --$ per MW-- overnight capital cost for technology q

• fcrq --unitless-- fixed charge rate for technology q

• fomNq --$ per MW-year-- fixed O&M costs for new plant technology q

• fomOn,q --$ per MW-year-- fixed O&M costs for region n and existing technology q

• fuelpriceq --$ per MMBtu-- fuel price for technology q

• regmultn,q --unitless-- overnight capital cost multiplier for region n and technology q

• shutdowncostq --$ per MW-- cost per shutdown for thermal generator q

• startupcostq --$ per MW-- cost per startup for thermal generator q

• vomNq --$ per MWh-- variable O&M costs for new plant technology q

• vomOn,q --$ per MWh-- variable O&M costs for region n and existing technology q

Generation Technology Performance Data

• capacityOn,q --MW-- installed capacity for region n and technology q

• capacityWOc,n --MW-- installed wind capacity for wind power class c and region n

• cfd,h,n,q --unitless-- PV profile during dispatch period d, hour h, in region n

• cfprofileWc,d,h,n --unitless-- normalization factor for the wind power profile by power 

class c, dispatch period d, hour h, in region n

• cfWNc --unitless-- annual capacity factor for wind power class c

• cfWOc,n --unitless-- annual capacity factor for existing wind power class c in region n

• foq --unitless-- forced outage rate for thermal generator q

• heatrateNq --MMBtu per MWh-- heat rate for new thermal generator q

• heatrateOn,q --MMBtu per MWh-- heat rate for region n and existing thermal generator q
43 

• hydromaxcfd,n --unitless-- maximum run-of-river hydropower capacity factor during 

dispatch period d, in region n

• hydromaxgend,n --MWh-- maximum seasonal generation for run-of-river hydropower 

during dispatch period d, in region n

• hydromincfd,n --unitless-- minimum run-of-river hydropower capacity factor during 

dispatch period d, in region n

• maxplantsizeq --MW-- maximum plant size for new thermal generator q

• mingenNq --unitless-- minimum generation level for new thermal generator q

• mingenOn,q --unitless-- minimum generation level in region n for existing thermal 

generator q

• minoffq --hours-- minimum off time for thermal generator q

• minonq --hours-- minimum on time for thermal generator q

• minplantsizeq --MW-- minimum plant size for new thermal generator q

• pod,q --unitless-- planned outage rate during dispatch period d thermal generator q

• spinfracq --unitless-- fraction of nameplate that can contribute to spinning reserves for 

technology q based on 10 min ramp rates 

Storage Technology Cost Data

• stcapcostst --$ per MW-- overnight capital costs for storage technology st

• stfcrst --unitless-- fixed charge rate for storage technology st

• stfomNst --$ per MW-year-- fixed O&M costs for new storage technology st

• stfomOn,st --$ per MW-year-- fixed O&M costs for existing storage technology st

• stfuelpricest --$ per MMBtu-- fuel prices for storage technology st

• stvomNst --$ per MWh-- variable O&M costs for storage technology st

• stvomOn,st --$ per MWh-- variable O&M costs in region n for storage technology st

Storage Technology Performance Data

• stcapacityOn,st --MW-- installed storage capacity for region n and existing storage 

technology st

• stfost --unitless-- forced outage rate for storage technology st

• stheatrateNst --MMBtu per MWh-- heat rate for new storage technology st

• stheatrateOn,st --MMBtu per MWh-- heat rate for region n and existing storage 

technology st

• stmaxplantsizest --MW-- maximum size for new storage technology st

• stminplantsizest --MW-- minimize size for new storage technology st

• stpod,st --unitless-- planned outage rate during dispatch period d for storage technology 

st

• strtest --unitless-- round trip efficiency for storage technology st

• stsupplyn,st --MW-- available storage resource for region n and existing storage 

technology st

Grid Interconnection Data

• gridconnectq --$ per MW-- grid interconnection costs for generator q

• stgridconnectst --$ per MW-- grid interconnection costs for storage technology st
44 

• windbinObin,c,n --MW-- wind resources already installed for each wind supply curve bin 

bin, wind power class c, in region n

• windgridconnectbin,c,n --$ per MW-- grid interconnection costs for wind supply curve bin 

bin, wind power class c, in region n

• windsupplybin,c,n --MW-- wind resource available for each wind supply curve bin bin, 

wind power class c, in region n 

Transmission Data

• distancen,p --miles-- distance between region n and p

• max_exportsd --MWh-- maximum energy flows exported out of Colorado in dispatch 

period d

• max_importsd --MWh-- maximum energy flows imported into Colorado in dispatch 

period d

• tcapacityOn,p --MW-- existing transfer capacity between region n and p

• tcapcost --$ per MW-mile-- new transmission costs

• tfcr --unitless-- fixed charge rate for transmission

• tloss --% per mile-- fractional transmission losses per mile

Policy Data

• 2010_nonCO_ReGen --MWh-- total generation from renewables outside of Colorado in 

2010 

• dgfrac --unitless-- fraction of generation from distributed generation (i.e., fixed-axis pv) 

• emissioncappol --tons-- emission cap by pollutant pol

• instate_mult --unitless-- multiplier for in-state generation to meet the RPS

• pollutefactorpol,q --tons per MMBtu-- emission factor for pollutant pol and technology q

• rpsfrac --unitless-- fraction of annual generation from renewables 

• stpollutefactorpol,st --tons per MMBtu-- emission factor for pollutant pol and storage 

technology st

Reserves Data

• cvNn,q --unitless-- marginal capacity value for pv in region n (fixed tilt is separate from 1 

axis tracking)

• cvO --unitless-- average capacity value of all variable generation capacity {wind and pv} 

• cvWNc,n --unitless-- marginal capacity value for wind of power class c in region n

• orspin_pscod,h --MW-- spinning reserve requirement for PSCO during dispatch period d, 

in hour h

• orspin_wacmd,h --MW-- spinning reserve requirement for WACM during dispatch period 

d, in hour h

• ortot_pscod,h --MW-- total reserve requirement for PSCO during dispatch period d, in 

hour h

• ortot_wacmd,h --MW-- total reserve requirement for WACM during dispatch period d, in 

hour h

• reservemargin --unitless-- reserve margin requirement for planning reserves 

Load Data

• distributionloss -- unitless-- fractional losses in the distribution network (5%) 
45 

• loadd,h,n --unitless-- demand during dispatch period d, in hour h, of region n

• season_scaled --unitless-- ratio of days per season to days per week for dispatch period d

(used to scale the selected week days to a full season) 

Complex Sets

• Hd,h,q: max �ord(h) − minonq , |Hd| − �minonq − ord(h)�� ≤ ord(h′) ≤ ord(h) 

∋ h′ ∈ Hd , h ∈ Hd, q ∈ THERMAL

Set of valid time periods in dispatch period d, hour h of thermal technology q where each 

element of the set, i.e., h’, is greater than the maximum of (h – minonq) and (the 

cardinality of set Hd) – (minonq – h ) and where h’ is less than h. Simplified, the 

elements of the set include all hours from h-minonq to h with time wrapping 

considered.

54 Hd,h,q is the set of consecutive time periods that are used to enforce 

minimum on periods. 

• Hd,h,q: max �ord(h) − minoffq , |Hd| − �minoffq − ord(h)�� ≤ ord(h′) ≤ ord(h) 

∋ h′ ∈ Hd , h ∈ Hd, q ∈ THERMAL

Set of valid time periods in dispatch period d, hour h of thermal technology q where each 

element of the set, i.e., h’, is greater than the maximum of (h – minoffq) and (the 

cardinality of set Hd) – (minoffq – h ) and where h’ is less than h. Simplified, the 

elements of the set include all hours from h-minoffq to h with time wrapping considered. 

Hd,h,q is the set of consecutive time periods that are used to enforce minimum off periods. 

Variables

Binary Variables 

• Shutdownd,h,n,q : 1 if existing thermal technology q is shutdown during dispatch period d, 

in hour h, in region n; 0 otherwise

• Startupd,h,n,q : 1 if existing thermal technology q is started up during dispatch period d, in 

hour h, in region n; 0 otherwise 

• StUnitNn,st : 1 if storage technology st is built in region n; 0 otherwise 

• UnitNn,q : 1 if non-modular technology q is built in region n; 0 otherwise 

• Upd,h,n,q : 1 if existing thermal technology q is on during dispatch period d, in hour h, in 

region n; 0 otherwise

Generation Variables

• CapacityNn,q --MW-- new generating capacity of technology q in region n

• CapacityWNc,n --MW-- new wind generating capacity of wind power class c in region n

• Curtailmentd,h,n --MW-- amount of power curtailed during dispatch period d, hour h, in 

region n

• GenerationNd,h,n,q --MW-- generation from new technology q during dispatch period d, in 

hour h, in region n

 

54 As an example of time wrapping, let h ∊ Hd ∊ {1..10}. If h = 1, then h-1 = 10.
46 

• GenerationOd,h,n,q --MW-- generation from existing technology q during dispatch period 

d, in hour h, in region n

• NonspincapNd,h,n,q --MW-- non-spinning capacity reserved from new technology q during 

dispatch period d, in hour h, in region n

• NonspincapOd,h,n,q --MW-- non-spinning capacity reserved from existing technology q

during dispatch period d, in hour h, in region n

• SpincapNd,h,n,q --MW-- spinning capacity reserved from new technology q during 

dispatch period d, in hour h, in region n

• SpincapOd,h,n,q --MW-- spinning capacity reserved from existing technology q during 

dispatch period d, in hour h, in region n

• WindBinNbin,c,n --MW-- new wind resources installed for each wind supply curve bin bin, 

wind power class c, in region n

Transmission Variables

• TCapacityNn,p --MW-- new transfer capacity between region n and p

• TFlowd,h,n,p --MW-- power transferred during dispatch period d, in hour h between 

region n and p

Storage Variables

• StCapacityNn,st --MW-- new storage capacity of storage technology st in region n

• StChargeNd,h,n,st --MW-- amount charging for new storage capacity during dispatch 

period d, in hour h, in region n from storage technology st

• StChargeOd,h,n,st --MW-- amount charging for existing storage during dispatch period d, 

in hour h, in region n from storage technology st

• StGenerationNd,h,n,st --MW-- generation from new storage capacity during dispatch 

period d, in hour h, in region n from storage technology st

• StGenerationOd,h,n,st --MW-- generation from existing storage capacity during dispatch 

period d, in hour h, in region n from storage technology st

• StSpincapNd,h,n,st --MW-- spinning capacity reserved during dispatch period d, in hour h, 

in region n from storage technology st

• StSpincapOd,h,n,st --MW-- spinning capacity reserved during dispatch period d, in hour h, 

in region n from storage technology st

Objective Function

The objective function minimizes the annualized system cost. This annual system cost includes 

the annualized capital cost, grid connection cost, fixed and variable O&M cost, fuel cost, startup55 and shut-down costs and emission costs for conventional and storage technologies. 

Minimize Total Annual Cost

Total capital, grid connection, and fixed O&M costs for all new technologies and all regions 

� CapacityNn,q ∗ �fcrq ∗ �regmultn,q ∗ capcostq + gridconnectq� + fomNq�

n∊N,

q∊Q

 

55 Startup costs include costs associated with the fuel requirement for plant startups.
47 

+ Total grid connection cost for new wind used from all resource supply curve bin, all wind 

power classes, and all regions 

+ � WindBinNbin,c,n ∗ windgridconnectbin,c,n

bin∊B,

c∊C,

n∊N,

q∊ WIND

∗ fcrq

+ Total fuel and variable O&M costs for all new and existing technologies in all hours of all 

dispatch periods and all regions 

+ � GenerationNd,h,n,q ∗ season_scaled ∗ (vomNq + heatrateNq ∗ fuelpriceq)

d∊D,

h∊Hd,

n∊N,

q∊Q

+ � GenerationOd,h,n,q ∗ season_scaled ∗ (vomOn,q + heatrateOn,q ∗ fuelpriceq)

d∊D,

h∊Hd,

n∊N,

q∊Q

+ Total storage capital, grid connection, and fixed O&M costs for all storage technologies in all 

regions 

+ � StCapacityNn,st ∗ (stfcrst ∗ (stcapcostst + stgridconnectst) + stfomNst) 

n∊N,

st∊ST

+ Total storage fuel and variable O&M costs for all new and existing storage technologies in all 

hours of all dispatch periods and all regions 

+ � StGenerationNd,h,n,st ∗ season_scaled ∗ (stvomNst + stheatrateNst

d∊D,

h∊Hd,

n∊N,

st∊ST

∗ stfuelpricest) 

+ � StGenerationOd,h,n,st ∗ season_scaled ∗ (stvomOn,st + stheatrateOn,st

d∊D,

h∊Hd,

n∊N,

st∊ST

∗ stfuelpricest) 

+ Total new transmission line costs

+ � TCapacityNn,p ∗ distancen,p ∗ tcapcost ∗ tfcr

n∊N,

p∊N ∍

(n,p) ∊ TCONNECT

+ Total start-up and shut-down costs for all existing thermal technologies in all hours of all 

dispatch periods and all regions 

+ � Startupd,h,n,q ∗ startupcostq ∗ capacityOn,q ∗ season_scaled

d∊D,

h∊Hd,

n∊N,

q ∊ THERMAL
48 

+ � Shutdownd,h,n,q ∗ shutdowncostq ∗ capacityOn,q ∗ season_scaled

d∊D,

h∊Hd,

n∊N,

q ∊ THERMAL

+ Total cost of carbon for all new and existing technologies in all hours of all dispatch periods 

and all regions 

+ � (GenerationNd,h,n,q ∗ heatrateNq ∗ season_scaled ∗ pollutefactorpol,q) ∗ carbon_price

d∊D,

h∊Hd,

n∊N,

q ∊ Q,

pol∊CO2

+ � �GenerationOd,h,n,q ∗ heatrateOn,q ∗ season_scaled ∗ pollutefactorpol,q� ∗ carbon_price

d∊D,

h∊Hd,

n∊N,

q ∊ Q,

pol∊CO2

Constraints

Load Constraints

The load constraints ensure that generation less curtailments plus net power imports is equal to 

load in each region and time period. 

load_balanced,h,n

Total generation from all technologies

��GenerationNd,h,n,q + GenerationOd,h,n,q�

q∊Q

+ Total discharge from all storage technologies

+ � �StGenerationNd,h,n,st + StGenerationOd,h,n,st�

st∊ST

+ Total imports into region n minus transmission line losses

+ � TFlowd,h,p,n ∗ (1 − tloss ∗ distancen,p)

p∊N ∍

(n,p) ∊ TCONNECT

= load in that region, plus total charge into all storage technologies, plus total exports out of 

region n + curtailments in region n

= loadd,h,n + � �StChargeNd,h,n,st + StChargeOd,h,n,st�

st∊ST

+ � �TFlowd,h,n,p�

p∊N ∍

(n,p) ∊ TCONNECT

+ Curtailmentd,h,n

These constraints hold for every hour h in each dispatch period d and for all regions n.

∀ d ∊ D, h ∊ Hd, n ∊ N
49 

Transmission Constraints 

The transmission constraints ensure that transmission line flows do not exceed the transmission 

line capacity between two regions in each time period. 

transfer_limitd,h,n,p

Power flowing from region n to region p must be less than the total transmission line capacity 

from n to p. These constraints hold for every hour h in each dispatch period d and for all regions 

n and p where n and p are grid connected.

TFlowd,h,n,p ≤ TCapacityNn,p + TCapacityNp,n + tcapacityOn,p

∀ d ∊ D, h ∊ Hd, n ∊ N, p ∊ N ∍ (n, p) ∊ TCONNECT

CO_import_limitd,h,n,p

Total transmission into Colorado in each dispatch period d must be less than the dispatch period 

import limits. These constraints hold for every dispatch period d. 

� TFlowd,h,n,p

h∊Hd

n∊NONCO

p∊CO∍

(n,p)∊TCONNECT

∗ season_scaled ≤ max_importd ∀ d ∊ D

CO_export_limitd,h,n,p

Total transmission flows out of Colorado in each dispatch period d must be less than the 

dispatch period export limits. These constraints hold for every dispatch period d. 

� TFlowd,h,n,p ∗ season_scaled

h∊Hd

n∊CO

p∊NONCO∍

(n,p)∊TCONNECT

≤ max_exportd ∀ d ∊ D

Long-Term Planning Reserve Constraints

The following constraints ensure that sufficient infrastructure exists to meet long-term planning 

and operating reserve requirements.

planning_reservesd,h

The North American Electric Reliability Corporation requires a 12.5% reserve margin for the 

Rocky Mountain Power Area (RMPA), which includes Colorado and Wyoming regions. 

Therefore, the total firm capacity in the RMPA must be exceed the peak demand in the RMPA 

by 12.5%. 

Total capacity of all dispatchable generators in CO and WY 

� �CapacityNn,q + capacityOn,q�

q∊DISPATCH

n∊CO ∪ n∊WY

+ Total capacity value of existing variable generators in CO and WY 

+ � capacityOn,q ∗ cvO

q∊VG

n∊CO ∪ n∊WY
50 

+ Total capacity value of new wind in CO and WY 

+ � CapacityWNc,n ∗ cvWNc,n

c∊C n∊CO ∪ n∊WY

 

+ Total capacity value of new PV in CO and WY 

+ � CapacityNn,q ∗ cvNn,q

q∊PV

n∊CO ∪ n∊WY

+ Total capacity of all storage units in CO and WY 

+ � �StCapacityNn,st + stcapacityOn,st�

st∊ST n∊CO ∪ n∊WY

≥ Reserve margin requirement for CO and WY 

≥ � loadd,h,n ∗ (1 + reservemargin)

n∊CO ∪ n∊WY

 

These constraints hold for every hour h in each dispatch period d.

∀ d ∊ D, h ∊ Hd

Operating Reserve Constraints

For both PSCO and WACM,56 contingency reserve requirements in each hour are based on the 

maximum between 6% of the hourly demand and an absolute contingency requirement based on 

the single largest contingency within the system (i.e., 451 MW for PSCO and 359 for WACM). 

At least half of the contingency reserves are required to be spinning reserves. In addition, we 

require additional spinning reserves (1% of demand) to be available during each hour to 

represent frequency regulation reserves. 

tot_or_requirement_pscod,h

Total spin capacity in PSCO 

� �SpinCapNd,h,n,q + SpinCapOd,h,n,q�

q∊SPIN

n∊PSCO

+ Total non-spin capacity in PSCO 

+ � �NonspinCapNd,h,n,q + NonspinCapOd,h,n,q�

q∊NONSPIN

n∊PSCO

+Total storage spin capacity in PSCO 

+ � �StSpinCapNd,h,n,st + StSpinCapOd,h,n,st�

st∊ST n∊PSCO

≥ Total operating reserve requirement for PSCO, i.e., contingency reserve (max{0.06*loadpsco , 

451}) + frequency reserve (0.01*loadpsco).

≥ ortot_pscod,h 

 

56 Each model region within Colorado is associated with one of these two balancing authorities; however, the 

generators and load within the region boundaries do not perfectly align with actual boundaries for the PSCO and 

WACM service areas. We also associate the two Wyoming regions with the WACM balancing authority.
51 

These constraints hold for every hour h in each dispatch period d. 

∀ d ∊ D, h ∊ Hd

spin_or_requirement_pscod,h

Total spin capacity in PSCO

� �SpinCapNd,h,n,q + SpinCapOd,h,n,q�

q∊SPIN

n∊PSCO

+Total storage spin capacity in PSCO

+ � �StSpinCapNd,h,n,st + StSpinCapOd,h,n,st�

st∊ST n∊PSCO

≥ Total spinning operating reserve requirement for PSCO, i.e., half of contingency reserve 

(0.5*max{0.06*loadpsco ,451}) + frequency reserve (0.01*loadpsco ).

≥ orspin_pscod,h

These constraints hold for every hour h in each dispatch period d.

∀ d ∊ D, h ∊ Hd

tot_or_requirement_wacmd,h

Total spin capacity in WACM

� �SpinCapNd,h,n,q + SpinCapOd,h,n,q�

q∊SPIN

n∊WACM

+ Total non-spin capacity in WACM

+ � �NonspinCapNd,h,n,q + NonspinCapOd,h,n,q�

q∊NONSPIN

n∊WACM

+Total storage spin capacity in WACM

+ � �StSpinCapNd,h,n,st + StSpinCapOd,h,n,st�

st∊ST n∊WACM

≥ Total operating reserve requirement for WACM, i.e., contingency reserve (max{0.06*loadwacm , 

359}) + frequency reserve (0.01*loadwacm).

≥ ortot_wacmd,h 

These constraints hold for every hour h in each dispatch period d.

∀ d ∊ D, h ∊ Hd

spin_or_requirement_wacmd,h

Total spin capacity in WACM

� �SpinCapNd,h,n,q + SpinCapOd,h,n,q�

q∊SPIN

n∊WACM

+Total storage spin capacity in WACM 

+ � �StSpinCapNd,h,n,st + StSpinCapOd,h,n,st�

st∊ST n∊WACM
52 

≥ Total spinning reserve requirement for WACM, i.e., half of contingency reserve 

(0.5*max{0.06*loadwacm , 359}) + frequency reserve (0.01*loadwacm).

≥ orspin_wacmd,h 

These constraints hold for every hour h in each dispatch period d.

∀ d ∊ D, h ∊ Hd

Wind Constraints

The wind constraints track wind resource supply curve usage and resource limits as well as

enforce wind generation levels. Wind generation follows an hourly profile. 

wind_resourcec,n

Total new and existing wind capacity builds of wind power class c in region n must be less than 

the total wind resource supply for wind power class c in region n. These constraints hold for 

every wind power class c and every region n.

CapacityWNc,n + capacityWOc,n ≤ � windsupplybin,c,n

bin∊B

 ∀ c ∊ C, n ∊ N

wind_interconnectionc,n

Total new wind resource usage for wind power class c in region n must be equal to the new wind 

capacity builds for wind power class c in region n. These constraints hold for every wind power 

class c and every region n.

� WindBinNbin,c,n

bin ∊B

= CapacityWNc,n ∀ c ∊ C, n ∊ N

wind_interconnection2bin,c,n

Total new and existing wind resource usage for wind supply curve bin bin of wind power class c

in region n must be less than or equal to the wind resource supply in supply curve bin bin of 

wind power class c in region n. These constraints hold for all wind supply curve bins bin every 

wind class c and every region n.

WindBinNbin,c,n + windbinObin,c,n ≤ windsupplybin,c,n ∀ bin ∊ B, c ∊ C, n ∊ N

wind_capacity_newn,q

New wind capacity in region n must be equal to the total new wind capacity from all wind power 

classes c. These constraints hold for every region n.

CapacityNn,q = �CapacityWNc,n

c∊C

 ∀ n ∊ N, q ∊ WIND

wind_generation_newd,h,n

Generation from new wind in hour h of dispatch period d in region n must be equal to the total 

new wind generation from all wind classes c in hour h of dispatch period d in region n. Wind 

generation is defined by a seasonal/diurnal profile specific to each wind power class and region. 

These constraints hold for every hour h in each dispatch period d in every region n.

GenerationNd,h,n,q = � CapacityWNc,n ∗ cfWNc ∗ cfprofileWc,d,h,n

c∊C 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ WIND
53 

wind_generation_oldd,h,n

Generation from existing wind in hour h of dispatch period d in region n must be equal to the 

total existing wind generation from all wind classes c in hour h of dispatch period d in region n. 

Wind generation is defined by a seasonal/diurnal profile specific to each wind power class and 

region. These constraints hold for every hour h in each dispatch period d in every region n.

GenerationOd,h,n,q = � capacityWOc,n ∗ cfWOc,n ∗ cfprofileWc,d,h,n

c∊C 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ WIND

PV Constraints

PV constraints enforce generation levels according to hourly profiles. 

pv_generation_newd,h,n,q

Generation from new PV in hour h of dispatch period d in region n must be equal to new PV 

capacity in region n times the seasonal/diurnal capacity factor for new PV in hour h of dispatch 

period d in region n. These constraints hold for each PV technology q, for every hour h in each 

dispatch period d in every region n.

GenerationNd,h,n,q = CapacityNn,q ∗ cfd,h,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ PV

pv_generation_oldd,h,n,q

Generation from existing PV in hour h of dispatch period d in region n must be equal to existing 

PV capacity in region n times the seasonal/diurnal capacity factor for existing PV in hour h of 

dispatch period d in region n. These constraints hold for each PV technology q, for every hour h

in each dispatch period d in every region n.

GenerationOd,h,n,q = capacityOn,q ∗ cfd,h,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ PV

Hydropower Constraints

The hydropower constraints enforce minimum and maximum generation in each hour as well as 

seasonal generation limits for hydropower. Note that HYDRO exists in DISPATCH. Therefore, 

hydropower generation is also constrained with the “DispTech_capacity_bound” suite of 

constraints for DISPATCH technologies (below). 

We do not allow new capacity expansion of run-of-river hydropower, so constraints on new runof-river hydropower generation are not included here. Furthermore, the model does not include 

any reservoir hydropower capacity. Therefore, we have excluded the reservoir hydropower

constraints here. 

hydro_generation_rord,n,q

Total generation from existing run-of-river hydropower generation for dispatch period d in 

region n must be less than or equal to the maximum allowed generation for dispatch period d in 

region n. Seasonal generation limits are based on historical data. These constraints hold for every 

non-peak dispatch period d in every region n.

� GenerationOd,h,n,q

h∊Hd

∗ season_scaled ≤ hydromaxgend,n 

∀ d ∊ NONPEAK, n ∊ N, q ∊ HYDRO
54 

hydro_gen_min_max_rord,h,n,q

Generation from existing run-of-river hydropower in hour h of dispatch period d in region n

must be between the minimum and maximum allowed generation for any hour h of dispatch 

period d in region n. These constraints hold for every hour h in each non-peak dispatch period d 

in every region n.

capacityOn,q ∗ hydromincfd,n ≤ GenerationOd,h,n,q 

≤ capacityOn,q ∗ hydromaxcfd,n 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ HYDRO

hydro_ramp_rord,h,n,q

Generation from existing run-of-river hydropower in hour h of dispatch period d in region n

cannot ramp up or down more than the hydropower ramping rate with respect to the generation 

in hour h-1. These constraints hold for every hour h in each non-peak dispatch period d in every 

region n.

 GenerationOd,h−1,n,q − GenerationOd,h,n,q ≤ hydroramp ∗ GenerationOd,h,n,q 

− GenerationOd,h−1,n,q + GenerationOd,h,n,q ≤ hydroramp ∗ GenerationOd,h,n,q

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ HYDRO

Required Plant Size Constraints

The following constraints enforce a size range for new capacity builds of certain technologies.

minimum_maximum_buildn,q

New plant capacity of non-modular technology q in region n must be between the minimum and

maximum non-modular plant sizes for technology q. These constraints hold for every region n 

and every non-modular technology q.

UnitNn,q ∗ minplantsizeq ≤ CapacityNn,q ≤ UnitNn,q ∗ maxplantsizeq 

∀ n ∊ N, q ∊ NONMOD 

Generation Capacity and Operating Reserve Capacity Constraints

The following operation constraints enforce how generating capacity can be allocated to help 

meet load and system reliability. Generators can provide combinations energy, spinning reserves 

and non-spinning reserves. Only thermal generators can provide spinning reserves and nonspinning reserves. 

ThermTech_capacity_bound_new_energy_spind,h,n,q

New generation and spin capacity for thermal technology q in hour h of dispatch period d in 

region n must be less than the new capacity for thermal technology q in region n. Because all 

elements of THERMAL exist in DISPATCH, these constraints are not as tight as the 

“DispTech_capacity_bound_new_energy_spin_nonspin” constraints for DISPATCH

technologies (below). These constraints hold for every hour h in each dispatch period d in every 

region n and for all thermal technologies q.

GenerationNd,h,n,q + SpinCapNd,h,n,q ≤ CapacityNn,q

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL
55 

ThermTech_capacity_bound_old_energy_spind,h,n,q

Existing generation and spin capacity for thermal technology q in hour h of dispatch period d in 

region n must be less than the existing capacity for thermal technology q in region n. Note that 

these constraints require that a thermal plant is ‘up’ to provide energy and spinning reserves. 

These constraints hold for every hour h in each dispatch period d in every region n and for all 

thermal technologies q.

GenerationOd,h,n,q + SpinCapOd,h,n,q ≤ Upd,h,n,q ∗ capacityOn,q

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

DispTech_capacity_bound_new_energyd,h,n,q

New generation for thermal technology q in hour h of dispatch period d in region n must be less 

than the new capacity for thermal technology q in region n derated by forced and planned 

outages. These constraints hold for every hour h in each dispatch period d in every region n and 

for all dispatchable technologies q.

GenerationNd,h,n,q ≤ CapacityNn,q ∗ �1 − foq� ∗ �1 − pod,q�

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ DISPATCH

DispTech_capacity_bound_old_energyd,h,n,q

Existing generation for thermal technology q in hour h of dispatch period d in region n must be 

less than the existing capacity for thermal technology q in region n derated by forced and 

planned outages. Even though all elements of THERMAL exists in DISPATCH, thermal 

technologies do not need capacityO multiplied by ‘Up’ in these constraints. The requirement that 

thermal generators must be ‘up’ to produce energy is embedded in the 

“ThermTech_capacity_bound_old_energy_spin” constraints (above). These constraints hold 

for every hour h in each dispatch period d in every region n and for all dispatchable technologies 

q.

GenerationOd,h,n,q ≤ capacityOn,q ∗ �1 − foq� ∗ �1 − pod,q� 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ DISPATCH

DispTech_capacity_bound_new_energy_spin_nonspind,h,n,q

New generation, spin capacity and non-spin capacity for dispatch technology q in hour h of 

dispatch period d in region n must be less than the new capacity for dispatch technology q in 

region n. Because all elements of THERMAL exist in DISPATCH, these constraints are tighter 

than the “ThermTech_capacity_bound_new_energy_spin” constraints for THERMAL

technologies (above). These constraints hold for every hour h in each dispatch period d in every 

region n and for all dispatchable technologies q.

GenerationNd,h,n,q + SpinCapNd,h,n,q + NonspinCapNd,h,n,q ≤ CapacityNn,q 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ DISPATCH

DispTech_capacity_bound_old_energy_spin_nonspind,h,n,q

Existing generation, spin capacity and non-spin capacity for dispatch technology q in hour h of 

dispatch period d in region n must be less than the existing capacity for dispatch technology q in 

region n. Even though all elements of THERMAL exist in DISPATCH, thermal technologies 

do not need capacityO multiplied by ‘Up’ in these constraints. The requirement that thermal 

generators must be ‘up’ to produce energy and provide spinning reserves is embedded in the 
56 

“ThermTech_capacity_bound_old_energy_spin” constraints (above). These constraints hold 

for every hour h in each dispatch period d in every region n and for all dispatchable technologies 

q.

GenerationOd,h,n,q + SpinCapOd,h,n,q + NonspinCapOd,h,n,q ≤ capacityOn,q 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ DISPATCH

SpinTech_capacity_bound_new_spind,h,n,q

New spin capacity for technology q in hour h of dispatch period d in region n must be less than 

the maximum allowed spin capacity for new spin technology q in region n. These constraints 

hold for every hour h in each dispatch period d in every region n and for all spin technologies q.

SpinCapNd,h,n,q ≤ CapacityNn,q ∗ spinfracq

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ SPIN

SpinTech_capacity_bound_old_spind,h,n,q

Existing spin capacity for technology q in hour h of dispatch period d in region n must be less 

than the maximum allowed spin capacity for existing spin technology q in region n. Even though 

all elements of SPIN exists in THERMAL, thermal technologies that can provide spin do not 

need capacityO multiplied by ‘Up’ in these constraints. The requirement that thermal generators 

must be ‘up’ to provide spinning reserves is embedded in the 

“ThermTech_capacity_bound_old_energy_spin” constraints (above). These constraints hold 

for every hour h in each dispatch period d in every region n and for all spin technologies q.

SpinCapOd,h,n,q ≤ capacityOn,q ∗ spinfracq

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ SPIN

Minimum Generation for Thermal Plants

minimum_generation_newd,h,n,q

New generation for technology q in hour h of dispatch period d in region n must be greater than 

or equal to the minimum generation requirement for new plants of technology q in region n. 

These constraints hold for every hour h in each dispatch period d in every region n and for all 

thermal technologies q.

GenerationNd,h,n,q ≥ CapacityNn,q ∗ mingenNq

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

minimum_generation_oldd,h,n,q

Existing generation for technology q in hour h of dispatch period d in region n must be greater 

than or equal to the minimum generation requirement for existing plants of technology q in 

region n if the existing plant is ‘up’. These constraints hold for every hour h in each dispatch 

period d in every region n and for all thermal technologies q.

GenerationOd,h,n,q ≥ Upd,h,n,q ∗ capacityOn,q ∗ mingenOn,q

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

Thermal Plant Start-up and Shut-down Constraints

The following start-up and shut-down constraints provide the logic for thermal generator start-up 

and shut-down operations in each time period. 
57 

minimum_ond,h,n,q

If a plant of thermal technology q is up in hour h, the plant could have started up in at most one 

hour from h-minon to h (with time wrapping considered).57. If a plant is not up in hour h, the 

plant cannot have started up in any hour from h-minon to h (with time wrapping considered). 

These constraints hold for every hour h in each dispatch period d in every region n and for all 

thermal technologies q.

� Startupd,h′,n,q

h′ ∊ Hd,h,q 

 ≤ Upd,h,n,q 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

minimum_offd,h,n,q

If a plant of thermal technology q is up in hour h, the plant cannot have shut down in any hour 

from h-minon to h (with time wrapping considered). If a plant is not up in hour h, the 

plant could have shut down in at most one hour from h-minon to h (with time wrapping 

considered). These constraints hold for every hour h in each dispatch period d in every region n

and for all thermal technologies q. 

� Shutdownd,h′,n,q

h′ ∊ Hd,h,q 

 ≤ 1 − Upd,h,n,q 

∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

startup_transitiond,h,n,q

If a plant of thermal technology q starts up in hour h, the plant must be up in h, having 

previously not been up in h-1 (with time wrapping considered). These constraints hold for every 

hour h in each dispatch period d in every region n and for all thermal technologies q. 

Startupd,h,n,q ≥ Upd,h,n,q − Upd,h−1,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

shutdown_transitiond,h,n,q

If a plant of thermal technology q shuts down in hour h, the plant must not be up in h, having 

previously been up in h-1 (with time wrapping considered). These constraints hold for every 

hour h in each dispatch period d in every region n and for all thermal technologies q.

Shutdownd,h,n,q ≥ Upd,h−1,n,q − Upd,h,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

startup_transition2d,h,n,q

If a plant of thermal technology q starts up in hour h, the plant cannot have been up in h-1 (with 

time wrapping considered). These constraints hold for every hour h in each dispatch period d in 

every region n and for all thermal technologies q.

Startupd,h,n,q ≤ 1 − Upd,h−1,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

 

57 As an example of time wrapping, let h ∊ Hd ∊ {1..10}. If h = 1, then h-1 = 10.
58 

startup_transition2d,h,n,q

If a plant of thermal technology q shuts down in hour h, the plant must have been up in h-1 (with 

time wrapping considered). These constraints hold for every hour h in each dispatch period d in 

every region n and for all thermal technologies q.

Shutdownd,h,n,q ≤ Upd,h−1,n,q ∀ d ∊ D, h ∊ Hd, n ∊ N, q ∊ THERMAL

Storage Build Constraints

The storage build constraints track storage resource supply curve usage and enforce a size range 

for new storage capacity builds. 

storage_resourcen,st

Total new and existing storage capacity in region n of storage technology st must be less than the

storage supply in region n of storage technology st. These constraints hold for every region n

and for all storage technologies st.

StCapacityNn,st + stcapacityOn,st ≤ stsupplyn,st ∀ n ∊ N, st ∊ ST

storage_minimum_maximum_buildn,st 

New storage capacity in region n of storage technology st must be between the minimum and 

maximum storage size for storage technology st. These constraints hold for every region n and 

for all storage technologies st.

StUnitNn,st ∗ stminplantsizest ≤ StCapacityNn,st ≤ StUnitNn,st ∗ stmaxplantsizest 

∀ n ∊ N, st ∊ ST

Storage Operations Constraints

The storage operation constraints define the round trip efficiency for a storage plant and how 

storage capacity can be allocated to help meet load and contribute to system reliability. 

storage_balance_newd,n,st

The ratio of the total new storage generation to total new storage charging for all hours in 

dispatch period d of storage technology st must be equal to the round trip efficiency of storage 

technology st. These constraints hold for every dispatch period d every region n and for all 

storage technologies st. 

� StGenerationNd,h,n,st

h∊Hd

= � StChargeNd,h,n,st

h∊Hd

∗ strtest ∀ d ∊ D, n ∊ N, st ∊ ST

storage_balance_oldd,n,st

The ratio of the total existing storage generation to total exiting storage charge for all hours in 

dispatch period d of storage technology st must be equal to the round trip efficiency of storage 

technology st. These constraints hold for every dispatch period d every region n and for all 

storage technologies st. 

� StGenerationOd,h,n,st

h∊Hd

= � StChargeOd,h,n,st

h∊Hd

∗ strtest ∀ d ∊ D, n ∊ N, st ∊ ST
59 

storage_capacity_bound_newd,h,n,st

New storage generation and new storage charging in hour h of dispatch period d, in region n for 

storage technology st must be less than the new storage capacity in region n for storage 

technology st derated by forced and planned outages. These constraints hold for every hour h in 

each dispatch period d in every region n and for all storage technologies st.

 StGenerationNd,h,n,st + StChargeNd,h,n,st

≤ StCapacityNn,st ∗ (1 − stfost) ∗ �1 − stpod,st� 

∀ d ∊ D, h ∊ Hd, n ∊ N, st ∊ ST

storage_capacity_bound_oldd,h,n,st

Existing storage generation and existing storage charging in hour h of dispatch period d, in 

region n for storage technology st must be less than the existing storage capacity in region n for 

storage technology st derated by forced and planned outages. These constraints hold for every 

hour h in each dispatch period d in every region n and for all storage technologies st.

 StGenerationOd,h,n,st + StChargeOd,h,n,st

≤ stcapacityOn,st ∗ (1 − stfost) ∗ �1 − stpod,st� 

∀ d ∊ D, h ∊ Hd, n ∊ N, st ∊ ST

storage_spin_bound_newd,h,n,st

New storage spin capacity in hour h of dispatch period d, in region n for storage technology st 

must be less than or equal to the new storage capacity that is not used for storage generation or 

storage charging in hour h of dispatch period d, in region n for storage technology st. These 

constraints hold for every hour h in each dispatch period d in every region n and for all storage 

technologies st.

 StSpinCapNd,h,n,st

≤ StCapacityNn,st − StGenerationN(d, h, n, st) − StChargeNd,h,n,st 

∀ d ∊ D, h ∊ Hd, n ∊ N, st ∊ ST

storage_spin_bound_oldd,h,n,st

Existing storage spin capacity in hour h of dispatch period d, in region n for storage technology 

st must be less than or equal to the existing storage capacity that is not used for storage 

generation or storage charging in hour h of dispatch period d, in region n for storage technology 

st. These constraints hold for every hour h in each dispatch period d in every region n and for all 

storage technologies st.

 StSpinCapOd,h,n,st ≤ stcapacityOn,st − StGenerationO(d, h, n, st) − StChargeOd,h,n,st 

∀ d ∊ D, h ∊ Hd, n ∊ N, st ∊ ST

Policy Constraints

Policy constraints enforce annual renewable portfolio standard and emission requirements.

state_rps

Total annual renewable Colorado generation – Total Colorado curtailments
60 

� �GenerationNd,h,n,q + GenerationOd,h,n,q�

d∊D, 

h∊Hd,

n∊CO,

q∊RE

∗ season_scaled

− � Curtailmentd,h,n ∗

d ∊ D, 

h ∊ Hd,

n ∊ CO

season_scaled

≥ rps fraction * total annual end-use demand in Colorado 

≥ rpsfrac ∗� 1

1 + distributionloss ∗ loadd,h,n ∗ season_scaled

d∊D, 

h∊Hd,

n∊COn

dg_carveout 

Total annual distributed generation in Colorado must be greater than or equal to the distributed 

generation requirement (i.e., distributed generation fraction times the annual end-use demand in 

Colorado). 

� �GenerationNd,h,n,q + GenerationOd,h,n,q�

d∊D, 

h∊Hd,

n∊CO,

q∊DG

∗ season_scaled

≥ dgfrac ∗� 1

1 + distributionloss ∗ loadd,h,n ∗ season_scaled

d∊D, 

h∊Hd,

n∊CO

emission_limitpol

Total annual emissions of pollutant type pol emitted from all technologies q and all storage 

technologies st must be less than or equal to the emissions cap for pollutant type pol. These 

constraints hold for every pollutant pol.

� �GenerationNd,h,n,q ∗ heatrateNq� ∗ season_scaled ∗ pollutefactorpol,q 

d ∊ D, 

h ∊ Hd,

n ∊ N,

q ∊ Q

+ � �GenerationOd,h,n,q ∗ heatrateOn,q� ∗ season_scaled ∗ pollutefactorpol,q 

d ∊ D, 

h ∊ Hd,

n ∊ N,

q ∊ Q

+ � �StGenerationNd,h,n,st ∗ stheatrateNst� ∗ season_scaled ∗ stpollutefactorpol,st

d ∊ D, 

h ∊ Hd,

n ∊ N,

st ∊ ST
61 

+ � �StGenerationOd,h,n,st ∗ stheatrateOn,st� ∗ season_scaled ∗ stpollutefactorpol,st

d ∊ D, 

h ∊ Hd,

n ∊ N,

st ∊ ST

≤ emissioncappol ∀ pol ∊ POL

Binary and Non-Negativity Constraints

UnitNn,q , StUnitNn,st , Upd,h,n,q , Startupd,h,n,q , Shutdownd,h,n,q ∊ {0,1}

All other variables ≥ 0