# A novel algorithm for optimizing genset operations to minimize fuel consumption in remote diesel-RES microgrids

Issam Matragi, Alain Maiboom, Xavier Tauzia, Bruno Moricet, Yoann Thevenoux

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Issam Matragi, Alain Maiboom, Xavier Tauzia, Bruno Moricet, Yoann Thevenoux. A novel algorithm for optimizing genset operations to minimize fuel consumption in remote diesel-RES microgrids. Energy Conversion and Management: X, 2024, 24, pp.100728. 10.1016/j.ecmx.2024.100728. hal-05084322

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# A novel algorithm for optimizing genset operations to minimize fuel consumption in remote diesel-RES microgrids

Issam Matragi<sup>a, *</sup>, Alain Maiboom<sup>a</sup>, Xavier Tauzia<sup>a</sup>, Bruno Moricet<sup>b</sup>, Yoann Thevenoux<sup>b</sup>

## ARTICLE INFO

**Keywords:**

Isolated Microgrid

Diesel Gensets

Unit Commitment

Spinning Reserve

Unequal Load Dispatching

Battery Integration

## ABSTRACT

This paper addresses the challenge of reducing fuel consumption in Diesel-RES (Renewable Energy Sources) isolated microgrids, particularly focusing on Diesel Genset's (DG) operation. The study introduces a basic rule based energy management system that serves as a platform to test out various DG operational strategies with a novel approach. Two optimization strategies—load dispatch optimization and unit commitment optimization—are explored to unequally distribute loads among different grid-connected DGs and sequence their start/stop based on predictive demand profiles respectively. Additionally, the integration of a spinning reserve-providing battery is investigated to alleviate DGs from their spinning reserve constraint, resulting in higher operational loads and consequently higher efficiency. The proposed model is applied on a case study of the Tahitian power system, demonstrating reductions in fuel consumption. The combined application of the proposed DG load dispatch and unit commitment optimizations, along with the integration a spinning-reserve-providing battery, yielded a 2.6 % reduction in fuel consumption and 6kt decrease in CO2 emissions over a year compared to a basic DG operation without a battery.

## Introduction

One-sixth of the global land area comprises islands, with a population exceeding 740 million [1]. Many of these islands heavily rely on imported fossil fuels for electricity generation, a vulnerability exacerbated by oil price fluctuations [2]. Notably, transportation fees for islands are considerably higher than conventional rates [3,4]. Beyond the economic challenges, islands face the existential threat of global warming, particularly in the context of rising sea levels that endanger coastal regions and islands [5]. Given the significant role of fossil fuel combustion in CO2 emissions [2], a shift away from fuel dependency and an increased integration of renewable energy can substantially limit CO2 emissions. This, in turn, contributes to mitigating the acceleration of rising sea levels.

As indicated by [6–9], an increase in the penetration of renewable energy in isolated systems can significantly decrease fuel consumption. However, the intermittency and inertia deficiency of renewable sources, pose a challenge, limiting the permissible penetration due to potential system stability issues [10–15]. Day-ahead power management [16] and/or the integration of energy storage [17–19] are solutions to address intermittency. Whether employed for peak shaving, rapid

response, or primary frequency regulation, energy storage systems can substantially enhance system stability and decrease fuel consumption, particularly when appropriately sized [18,20–22]. Nevertheless, it is important to note that energy storage systems are significantly costly, and a sophisticated energy management system is essential to prevent the rapid deterioration of the system’s lifespan [23,24].

While these issues will optimistically not hinder the shift from fossil fuels in the long term, the current state of power systems dictates that traditional energy producers, Diesel Gensets (DGs) in particular for isolated microgrids, still play an important role in ensuring the system’s stability and reliability. Furthermore, replacing diesel fuel with biofuel [25] might as well be a viable solution for reducing fossil fuels dependencies while retaining the internal combustion engine’s functionality. One significant challenge in the operation of Diesel-RES in isolated Microgrids is the energy management system in general, from which, DG’s operation is singled out as the focus of this paper. In [26], Dejamkhooy et al. present a microgrid power dispatching algorithm that ensures that a DG would only be switched on when the ones already connected are operating at their optimal point. In this operation, one of the connected DGs would operate at a variable load, following the power demand, while other connected DGs have fixed power output

<footnote><sup>a</sup> Ecole Centrale de Nantes, France</footnote>

<footnote><sup>b</sup> MAN Energy Solutions, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: issam.matragi@ec-nantes.fr (I. Matragi).</footnote>
corresponding to their optimal operating points. This method was found to reduce fuel cost by 16.6 % compared to a system where all available DGs are switched on and operating at the same load levels. As per the description in this paper, DGs are able to freely start up and shut down at any point without any constraints, and the spinning reserve is not accounted for in the decision-making. A somewhat similar power sharing strategy is discussed by C. Hernandez-Aramburo [27], where a nonlinear power-sharing scheme was applied through an optimization with a fuel consumption objective function. Such an optimization accounted for 20 % fuel savings when power demand was between 30 to 60 % of the total installed power, although no constraints have been presented on the frequency of DG start/stops. M. Lambert et al. in [28], also discuss a nonlinear power-sharing scheme, but report negligible fuel reduction compared to an equal load sharing strategy. This result might be the due to the fact that a penalty cost was introduced in the optimizer's objective function to prevent DGs from operating at loads higher than 70 %.

Other strategies to reduce fuel consumption with a focus on DGs were explored in the literature. Ogunjuyigbe et al. [20] argues that using three small split DGs, which can be aggregated, results in reduced CO2 emissions compared to one big DG. This reduction is more pronounced when the system is hybridized, using a Photovoltaic (PV)/Wind/Battery/DG combination. Lim et al. [29] showed that a variable speed DG with solar PV was found to save nearly 23 % of fuel annually compared to a constant speed diesel generator only system. The main advantage of using a variable speed DG is the wider operation range and lower permissible minimum load. No specific constraints on the DGs were mentioned in [17] or [25]. Rangel et al. [30] propose that DGs' operating limits should be determined based on their specific fuel consumption and brake thermal efficiency. Their developed model suggests that setting the minimal operating point of DGs to 60 % would prevent the selection of oversized DGs in the studied scenario. This approach aims to mitigate low-load operating conditions and thereby reduce the environmental impact of such operations, in small scale (27 kW peak electrical load) isolated microgrids. In [31], Khirennas et al. propose a period ahead operating-scheduling algorithm in a multiunit DG system, where the objective is to study the impact of integrating low level PV penetration on fuel consumption and energy cost. With this operating-scheduling, the optimal DGs ON/OFF status combination is determined at each time step, taking into consideration spinning reserve. Since DGs are available instantaneously when required, the algorithm can shut down and start multiple DGs simultaneously. This assumption might be acceptable for a small system of a few MW, but it would not hold for larger systems with bigger, slower-responding DGs.

On the operational side of a power system, Manandhar et al. [32] tackle the challenge of frequent cycling of DGs with their enhanced energy management and control approach. This method incorporates the integration of a supercapacitor and a new battery state-of-charge control mechanism. While only two potential operating points for the DGs are considered with no start-up delays, their findings demonstrated a decrease in the frequency of DG cycling. Javadi et al [33] outline a system in which both thermal generating units and electrical energy storage systems contribute to spinning reserve. They devise an optimization method to enhance the operation of a system integrated with renewable energy sources (RES), aiming to achieve the optimal spinning reserve margin and subsequently reduce operational costs. Yu Hu et al. [34] explore a stochastic programming model to optimize DG dispatch operation in a wind-diesel hybrid microgrid. In their model, load and wind uncertainties are accounted for, which they consider to provide simulations with closer to reality decision-making. With that, the dispatch strategy can be adjusted dynamically according to the evolution of these uncertainties. This paper's case study is oriented towards small-scale microgrids, with up to one connected DG when needed.

As for system modeling, the thermostatted kinetic theory approach, as presented by Bianca in [35] offers a novel framework for modeling and optimizing energy-multisource networks by applying principles

from nonequilibrium statistical mechanics. This method models energy exchanges among renewable and nonrenewable sources, accounting for system interactions and dynamic behavior, to enhance stability and efficiency. The framework's robustness is ensured by rigorous mathematical analysis, making it a promising tool for addressing environmental and economic challenges in hybrid energy systems. Lu et al. [36] use Hybrid Petri Nets to simulate and study the behavior of microgrids. The paper aims to capture the complexities of microgrid operations, including the integration of renewable energy sources, energy storage systems, and various control strategies. It captures the hybrid nature of microgrids, combining the strengths of both discrete and continuous modeling to offer a comprehensive analysis tool.

The existing literature on reducing fuel consumption in microgrids offers valuable insights, yet it frequently falls short in addressing crucial aspects comprehensively. Few articles explore the specific optimization of fuel consumption through DGs, as the emphasis often leans towards the benefits of increasing RES penetration, with or without integrated batteries, in terms of fuel efficiency. Moreover, studies focusing on DGs often overlook crucial system stability factors, such as spinning reserve, or misapply operational limits, including operational hours, startup delays, frequent start/stop cycles, and permissible load ranges. This oversight occurs because the primary focus tends to be on the electrical aspects rather than the mechanical details. Finally, all the discussed studies were applied to small-scale microgrids (up to a few MW), with limited attention given to larger-scale electrical systems on the order of 100 MW.

In this paper, a basic rule-based energy management algorithm was developed to balance production and consumption by dispatching an adequate amount of thermal power using DGs, based on input demand and renewable energy production profiles. The novelty of this work lies in applying dispatching strategies for the DGs, tailored to these specific inputs, and evaluating their impact on annual fuel consumption while considering a spinning reserve constraint. One study focuses on optimizing fuel consumption by applying unequal load dispatching between gensets using MATLAB's constrained nonlinear optimization. This type of optimization, to the authors' knowledge, has not been done before in a system where DGs have significantly different Specific Fuel Consumption (SFC), highlighting the benefits of such an approach. The second study explores unit commitment optimization, where the decision to start or stop a DG (in a system with multiple types of DGs) is based on forecasted demand profiles, RES profiles, and spinning reserve requirements. Finally, the study investigates the impact of integrating a spinning reserve-providing battery into the system. This addition alleviates DGs from their spinning reserve responsibilities, enabling them to operate at higher and more efficient loads. While the concepts of unequal load dispatching and unit commitment for DGs are not new, as electric grid operators certainly apply these strategies in some form, this paper uniquely quantifies the advantages of such operations in a large-scale isolated power system in terms of fuel consumption. The Tahitian power grid was selected as the case study for this paper due to the availability of 10-minute time-step data on power production from all available sources over several years. With a peak demand of 100 MW, the system features two distinct types of DGs (four of each) in its main power plant, as well as a newly installed spinning reserve-providing battery. These characteristics make it an ideal platform to test the developed algorithm.

The remainder of the paper is structured as follows: In Section 2, the model's architecture is thoroughly examined, including detailed descriptions of its inputs and outputs. Section 3 offers an overview of the power system serving as a case study; this section provides insights into the system's components and unique characteristics. Section 4 elaborates on the optimization strategies utilized in the study, shedding light on the methodologies employed for enhancing system performance. The outcomes of these optimizations are presented in Section 5, where the results of the study are discussed in detail. Finally, the conclusion of this study is presented in Section 6, summarizing the key insights and
implications drawn from the research.

## Model

### Objective

The main objective of the developed model is to identify DG control strategies that will help reduce fuel consumption in Microgrids. A MATLAB code was developed to compute the daily (and up to yearly) fuel consumption of any specific electric system, given the type of the connected generators, their specific fuel consumption and finally, the power demand and RES profiles. This computation could help identify the benefit of different control strategies and potential hardware changes. Neither demand-side management nor distributed generation optimization are considered in this study. As previously mentioned, the sole focus is on the DGs' operational strategy.

### Inputs

The code requires the current configuration of the electric system, including the number and size of available DGs, battery capacity, and renewable energy and demand profiles. These profiles should span from daily to yearly periods with a time-step that can range from 30 s to hours, with a 10-minute time-step used in this study. The renewable energy and demand profiles serve as fixed inputs unaffected by the developed optimizations. Various DG control strategies can be activated, such as load dispatch, unit commitment optimizations, and the configuration of a spinning-reserve battery in terms of availability and size.

### Constraints

It is possible to customize the following parameters: minimum and maximum load constraints for the DGs, time constraints for switching ON/OFF any DG, and the DG start-up time, which introduces a deliberate delay between the decision to start a genset and its contribution to the generated power. Additionally, the model allows for the customization of the forecast horizon for event anticipation, thereby enabling proactive unit commitment.

### Spinning reserve calculation and battery inclusion

To account for power fluctuations in a power system, power plants must maintain a designated amount of dispatchable power to respond to these fluctuations, known as spinning reserve. Traditionally, spinning reserve is provided by connected DGs, often requiring them to operate at sub-optimal loads to reserve a portion of their capacity.

Spinning reserve (SpRes) at any point in the model is calculated as follows:

$$SpRes_{(t)} = \sum_{i=1}^{n} (Cap_{DG(i)} - P_{DG(i,t)}) * \alpha_{(i,t)} \quad (1)$$

with t representing the current time-step that the algorithm is running, n the number of available DGs, CapDG the rated power of the connected DG, PDG the instantaneous power produced by the connected DG at time t, and α the status of the i'th available DG at time t (1 if connected, 0 if not).

As batteries play a pivotal role in modern power grids, especially those with significant renewable energy sources [18], their inclusion in the model became essential. It is important to note that the developed algorithm primarily focuses on DG power dispatch rather than frequency stability monitoring. It includes a spinning reserve-providing battery, which would not inject power unless there is a sudden frequency variation. In Tahiti's power system, a grid-forming battery is installed with an imposed dead-band zone of 200 mHz. This means that under normal operation and for minor frequency fluctuations, the

battery remains passive and does not participate in frequency regulation, unless a significant incident pushes the system's frequency outside the dead-band zone. A similar theoretical approach can be considered in this study. Since no incidents are simulated, a deployment strategy for the battery was not required.

By employing this battery, the burden on the diesel gensets to provide the majority of the spinning reserve is lifted, enabling them to operate at higher loads when needed.

$$SpRes_{(t)} = \sum_{i=1}^{n} (Cap_{DG(i)} - P_{DG(i,t)}) * \alpha_{(i,t)} + P_{BattRes} \quad (2)$$

P BattRes is the maximum power that can be provided by the battery. For the sake of this study, a battery with a large enough capacity to provide its rated power for 30 min can be considered, more than enough time to start a DG if needed and replace the power output of the battery.

To guarantee the necessary spinning reserve (SpResreq) for maintaining grid stability in the event of an incident, it's a common practice to ensure an adequate spinning reserve capable of compensating for the potential loss of power from the largest generator. This principle will be applied within this algorithm.

### Code architecture

The diagrams in Fig. 1 and in Fig. 2 illustrates a simplified code architecture, comprising four key blocks. The initial block handles the DGs' load requirements for the ongoing time-step, while the second block conducts a comparative analysis between the present system status and the anticipated load profile. The third block, informed by data from the preceding blocks, formulates unit commitment decisions, encompassing options such as starting or stopping a DG or maintaining the current system state. The final block, detailed in Fig. 2, carries out the formulated decision and monitors the operational hours of the DGs.

#### First block – Execute current time-step load requirements

For every time-step, the main function in the code pushes in the values for the power demand, available renewable energy power and information regarding the status and operation hours of every DG. This information is then used to calculate the power required to be produced by the connected DGs in order to keep the demand/generated power equilibrium, as depicted by:

$$P_{DG_{total}}(t) = P_{demand}(t) - P_{RES}(t) \quad (3)$$

With P DGtotal the total power of all connected gensets, P demand the power required by the grid and P RES the power available from the RES.

This is where the first optimization algorithm is reached: DGs' load dispatching optimization. If this optimization is active, then the optimizer will run with an objective to minimize fuel consumption by varying the load on each DG individually (in depth explanation of the objective function in section 4.1). If the optimizer is not active, then the load will be equally shared between all connected diesel gensets as follows:

$$LOAD_{DG(t)} = P_{DG_{total}(t)} / \sum_{i=1}^{n} Cap_{DG(i)} * \alpha_{(i,t)} \quad (4)$$

with LOADDG being the load on all connected DG.

A minimum load constraint check will run to verify that the load required on each DG is not below the minimum allowable power output (PDGmin). The minimum permissible load on DGs is a crucial consideration, and it is generally not recommended to operate DGs below a specified load, often around 30 to 40 % (can vary depending on the specific DG model). Operating DGs below this load can lead to issues such as incomplete combustion, resulting in the accumulation of unburnt fuel inside the exhaust system. This can contribute to problems like carbon buildup and unburnt fuel emissions. If this check fails, then
<figure><img src="image_4.png" /><figcaption>Fig. 1. Diagram presenting the layout of the first three blocks of the code: current time-step requirements execution, projected profiles consideration and decision-making.</figcaption></figure>

the RES power has to be curtailed ($P_{RES_{cur}}(t)$), and the DGs are forced to run at their minimum permissible load, whether the optimizer was activated or not. This the only point where the input value of the renewable energy might be modified so that a DG constraint would be respected. Otherwise, as previously mentioned, demand and renewable energy profiles are inputs that are not affected by this energy management algorithm.

$$P_{DG}(t) = P_{DG_{min}}(t) \qquad (5)$$

$$P_{RES_{cur}}(t) = P_{demand}(t) - P_{DG_{min}}(t) \qquad (6)$$

## Second block – Compare current status with projected status

This block is all about preparing for any upcoming predicted event. It examines whether the second optimizer, referred to as the unit commitment optimization, is activated. Whenever a DG is required to start/stop, the next DG in line for the respective action has to be selected.

Either the sequence for starting/stopping available DG is pre-defined or a modifiable list that adapts in line with the optimizer's output. This optimizer can determine the optimal sequence based on forecasted demand and renewable energy profiles (more on this optimization in section 4.2). Once the DG to be switched off is chosen, the potential power that would be required of each genset with n – 1 DG connected is calculated ($P_{DG_{pot}}$).

Moving forward, the model uses prediction profiles to foresee any potential change in the system, for example peaks in demand or declines in renewable energy availability for the upcoming time-steps. This proactive approach readies the system to commit a genset preemptively. Similarly, if the load on the DGs becomes low, and a unit can be disconnected, this function evaluates whether there are any anticipated peaks in demand in the near future. This assessment ensures that a unit is disconnected only if there is no expected increase in demand. The equation for the projected profile comes as follows:
<figure><img src="image_5.png" /><figcaption>Fig. 2. Diagram presenting the layout of the fourth block, responsible the command execution.</figcaption></figure>

$$P_{DG_{proj}}(t') = P_{Demand_{proj}}(t') - P_{RES_{proj}}(t') \quad (7)$$

With $t'$ representing a future time step not reached yet by the main loop, $P_{DG_{proj}}$ the projected power to be produced by the connected DG, $P_{Demand_{proj}}$ the projected power to be required by the consumer and $P_{RES_{proj}}$ the projected power to be available from the RES during the following time-steps.

On one hand, if $P_{DG_{proj}}$ is greater than the maximum available power by all connected DGs or if the projected system spinning reserve ($SpRes_{proj}$) is less than the projected required spinning reserve ($SpRes_{req_{proj}}$), then a DG has to be started.

On the other hand, if the sum of $P_{DG_{proj}}$ (the projected potential power, when 1 DG is switched off) is less than the maximum available power by all connected DGs and the projected potential spinning reserve is greater than $SpRes_{req_{proj}}$, then a DG can potentially be shut down.

If both cases fail, then no change is required in the system based on the predicted profiles.

### Third block – Decision making

After resolving the current time-step requirements and taking into consideration the prediction profiles, the algorithm proceeds to the decision-making phase. The first check is a reactive action, whereby the system detects instances where the maximum permissible load on the gensets is exceeded or when the spinning reserve ($SpRes$) falls below the required threshold ($SpRes_{req}$). In such scenarios, the genset starting procedure is set in motion. Lastly, based on the outcome of the preceding blocks, the algorithm makes decisions to start or stop a DG, or maintain the existing system state. It is important to note that this code has not been configured to operate in a scenario where the renewable energy matches or surpasses the power demand, thus at least 1 DG has to be connected at all times.

### Fourth block – Command execution

This final block executes the command from the third block after performing additional checks. If a genset has to start, the code first verifies whether the starting procedure has been initiated in previous time-steps or not. If it has, and the start-up time delay has been met, the chosen genset's status will switch to 'connected' starting from the next time-step. If the starting procedure has not been initiated yet, the next genset in line, as per the unit commitment optimization, will be set to 'starting procedure' if enough time has passed since its last shutdown. Frequent startups and shutdowns are avoided to prevent wear and tear on the DGs.

If the system is required to stop a DG, the code only checks if the DG chosen by the unit commitment optimization has met the time constraint since the last start-up. If it has, the status of the chosen DG switches to 'disconnected' starting from the next time-step.

Regardless of the outcome discussed above, the algorithm updates the time-on and time-off for all DGs based on their status.

### Outputs

The main output of this model is the total fuel consumption over the chosen simulation period. Alongside that, valuable information can be extracted to analyze the behavior of the system over the whole simulation timeframe:

* Active power of each individual generator

* System's available spinning reserve

* Fuel consumption (per hour)

* Load profile of connected DGs

* The evolution of the number of connected DGs

* Operational hours for each DG

These simulations offer the potential for further data extraction to
cater to specific requirements in future studies.

## Case study

### Power system description

#### Power generators

As a case study, the Tahitian power system was selected for the availability of the power profiles over 8 years and with 10-minute time-steps [37]. In addition, this power system is a great example of an isolated microgrid, with growing renewable energy share. It is worth noting once again that the demand and RES power profiles are extracted and used in the model as they are, with no further energy management.

Table 1 displays the various types of power generators on this island. The thermal power plant includes only two types of DGs, limiting the operator's flexibility in selecting the most suitable DG for power and reserve requirements in various operational scenarios.

It is worth noting that the authorities in Tahiti have fixed the objective to produce 75% of Tahiti's electric demand from RES by 2030 [38]. This underscores the significance of adapting the operational strategy of the currently installed DGs, to be better suited for an increased penetration of RES.

#### Specific fuel consumption (SFC)

In order to calculate fuel consumption over the simulation period, the specific fuel consumption curve used for each DG is illustrated in Fig. 3.

It reveals that each type of DG has its advantages in specific operating conditions. For instance, Type 1 DGs exhibit lower fuel consumption at lower loads and feature a lower minimal power constraint, as specified by the manufacturer. In contrast, Type 2 DGs deliver higher maximum power and have lower specific fuel consumption at higher loads.

#### CO2 emissions

To calculate the CO2 emitted per ton of fuel burned (considering Diesel fuel), two metrics were used:

* Emissions generated by the fuel extraction and transportation to Tahiti, estimated to be 0.1613 t CO2/t of fuel, according to the French Agency for Ecological Transition in the French Polynesia [39].

* Emissions generated by burning the fuel, estimated to be 3.17 t CO2/t of fuel, according to the French Agency for Ecological Transition [40].

Adding these two numbers, 3.33 tons of CO2 are emitted for every ton of fuel consumed.

#### Scenario study

In this section, the output of one-day and one-year simulations are presented.

<caption>**Table 1**</caption>

Power generators considered in the case study and their rated peak power output.

<table><thead><tr><td>Generator type</td><td>Rated Peak Power</td></tr></thead><tbody><tr><td>4 × DG Type 1</td><td>4 × 13.7 MW</td></tr><tr><td>4 × DG Type 2</td><td>4 × 17 MW</td></tr><tr><td>Hydroelectricity Plants</td><td>47 MW</td></tr><tr><td>Solar PV</td><td>22 MW</td></tr><tr><td>Battery System (for Spinning Reserve)</td><td>15 MW</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Specific Fuel Consumption curves of Type 1 and Type 2 DGs in function of their power output.</figcaption></figure>

#### Unit commitment for a one-day simulation

As addressed in the algorithm's architecture, decision-making is either proactive or reactive. Whenever the system spinning reserve drops below the required spinning reserve, a decision has to be made to start a DG. Similarly, by checking the predicted profiles, the algorithm can decide to start or stop a DG preemptively. Fig. 4 shows the energy mix while Fig. 5 shows the evolution of the number of connected DGs and their type over one day.

In the one-day scenario presented in Fig. 4 and Fig. 5, a DG was started at around 14:30.

In Fig. 6, the evolution of the required and available system spinning reserve along with the load output of connected DGs in Fig. 7 for the same day.

When looking at Fig. 6 and Fig. 7, it becomes clear that a DG had to be started following a breach in demand at 14:30. This event is marked by the sudden increase in available system spinning reserve and a lower load percentage on connected DGs at that time.

To mimic real-world predictive behavior in normal conditions,

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Active power generated from Solar PV, Hydroelectricity and Diesel power plant over a one-day simulation.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Evolution of number of connected DGs over a one-day simulation.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. System spinning reserve and spinning reserve threshold evolution over a one-day simulation.</figcaption></figure>

projected profiles are generated from actual measured data by applying small, randomly changing noise at regular intervals as shown in Fig. 8. A similar approach is used by Hu et al. in [31], where Random Gaussian noise is applied to achieve this effect.

This approach takes into account typical predictions in inaccuracies, excluding sudden unpredictable changes due to a fault or an incident.

### Impact of constraints on DG operation for a one-week simulation

A one-week simulation was conducted to highlight the impact of adding operational constraints on the DGs. Spinning reserve requirements were set to zero, DGs were allowed to start/stop as frequently as needed, and the minimum permissible load was set to zero. Fig. 9 and Fig. 10 show the evolution of the number of connected DGs over one week, for a constraint simulation and an unconstraint one respectively.

It is evident that the frequency of starting and stopping DGs is significantly higher, approximately three times more frequent. This strategy can save around 2% of fuel consumption but risks operating the DGs in a manner that could lead to eventual failures and an unstable

<figure><img src="image_10.png" /><figcaption>Fig. 7. Load output of all connected DGs along with the upper/lower load limits, over a one-day simulation.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Comparison between actual and predicted demand and solar PV profiles.</figcaption></figure>

power system, as power fluctuations cannot be absorbed without a spinning reserve margin. As shown in the introduction, many studies do not consider DG operation constraints in their work, which, as pointed out by this section, can have a considerable impact on how a system operates. From this point onward, the simulations presented in this paper will incorporate DG operational constraints.

### Load distribution, operation hours, and spinning reserve over a one-year simulation

For a one-year simulation, the load distribution on both types of DG is presented in Fig. 11 for Type 1 DGs and in Fig. 12 for Type 2 DGs.

Both DGs are operated most of the time around 65 to 75%, which in both cases would be lower than the optimal operating point where specific fuel consumption is at its lowest.

Additionally, the operating hours for each DG are detailed in Fig. 13.

In the default scenario (referred to as 'Default' henceforth), where neither the load dispatch optimization nor the unit commitment optimization is applied, DGs are started in the following order: two Type 2 DGs first, followed by two Type 1 DGs, and this sequence repeats for the remaining four.
<figure><img src="image_12.png" /><figcaption>Fig. 9. Evolution of the number of connected DGs over a one-week simulation with DG operational constraints.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Evolution of the number of connected DGs over a one-week simulation without DG operational constraints.</figcaption></figure>

The spinning reserve histogram Fig. 14 shows that there are extended periods during the simulation where spinning reserve exceeds 17 MW, which is the maximum output of the largest generator.

There is potential to minimize this excess spinning reserve through an optimized spinning reserve requirement, rather than adhering to the fixed rule that it must be at least equal to the power output of the largest producer. This opens up avenues for future investigation.

Observing Fig. 13, it is evident that Type 1.3 and 1.4 are never used and Type 2.3 and Type 2.4 are rarely employed. In practice, operational hours would ideally be evenly distributed among DGs of the same type. Consequently, all four Type 1 DGs should have operated for an equal duration (likewise for Type 2 DGs). Although the model could potentially incorporate this functionality in the future, it would not affect the result of the simulations (in terms of fuel consumption and total operation hours of each type of DGs). The immediate priority is to distinguish between the types of DG used.

<figure><img src="image_14.png" /><figcaption>Fig. 11. Histogram of the load distribution on Type 1 DG for a one-year simulation.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Histogram of the load distribution on Type 2 DG over a one-year simulation.</figcaption></figure>

## Optimizations

### Load dispatch optimization

The objective of this optimization is to minimize fuel consumption in a diesel power plant by optimizing the load distribution among the committed DG units. Specifically, the goal is to find the optimal load output for each DG at each time-step that minimizes the average specific fuel consumption while still meeting the required power demand.

The objective function F represents the average specific fuel consumption weighted by the power output of each DG unit. It is defined as:

$$F = \frac{\sum_{i=1}^{n} (SFC(P_{DG(i,t)}) * P_{DG(i,t)}) * \alpha_{(i,t)}}{\sum_{i=1}^{n} P_{DG(i,t)}} \quad (8)$$

where:

* n is the total number of DG units.

* $P_{DG(i,t)}$ is the power output of the i-th DG unit at time t.
<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Percentage of time that each DG has operated over a one-year simulation.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Histogram of the available spinning reserve over a one-year simulation.</figcaption></figure>

* $SFC(P_{DG(i,t)})$ is the specific fuel consumption of the $i^{th}$ DG unit as a function of its power output $P_{DG(i,t)}$ at time t.

* $\alpha_{(i,t)}$ is a binary indicator that equals 1 if the $i^{th}$ DG unit is committed (i.e., online) at time t, and 0 if it is not.

The function $F$ essentially calculates the weighted average of the specific fuel consumption across all active DG units, where the numerator represents the total instantaneous fuel consumption, and the denominator the instantaneous total power output of all committed DG units. By minimizing $F$, the optimizer aims to find the best load distribution among the DG units that result in the lowest possible average specific fuel consumption, thereby reducing overall fuel consumption.

MATLAB's Constrained Nonlinear Optimization is used to solve this objective function, while adhering to constraints that ensure the total power output meets the demand and other operational limits of the DG units are respected (i.e., minimum and maximum load limits).

Fig. 15 and Fig. 16 show the load evolution on Type 1 and Type 2 DG

<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Load evolution on Type 1 DG with load optimization activated over a one-day simulation.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Load evolution on Type 2 DG with load optimization activated over a one-day simulation.</figcaption></figure>

respectively, when the load dispatch optimization is active.

The optimizer naturally groups similar DGs to operate at the same load levels. DGs with lower specific consumption at higher loads are chosen to operate near their optimal operating points, whereas less efficient DGs are operated at lower and more variable loads following grid variations. This behavior is clearly visible in Fig. 15 and Fig. 16 during the hours from 6 to 18 and then from 21 to 24.

In situations where the power available from the connected DGs significantly exceeds the demand (occurring between hours 0 to 6 and 18 to 21), Type 1 DGs are operated at their minimum load, while Type 2 DGs handle any power fluctuations from the grid at higher loads. The transition between these two operational modes in that specific case is driven by changes in the number of connected DGs.

### Unit commitment optimization

The unit commitment optimization depends on projected profiles of consumer demand and the power generated by RES.

When this optimization is called in the algorithm, multiple parallel simulations are initiated, the quantity depending on the available DG
options. The sole distinction among these parallel simulations lies in the selection of the DG to start or stop. In all other aspects, these simulations operate as if the predicted power profiles were the real profiles. The code calculates fuel consumption after a pre-defined simulation duration (5 h in this study) and subsequently, a comparison is conducted among the fuel consumption results of all these parallel simulations. The DG option with the lowest fuel consumption that meets all operational constraints is selected as the next DG to start or stop, thereby altering the sequence in which DGs are started or stopped. It is worth noting that neither maintenance cost nor start up fuel consumption are considered in this study.

This optimization is called every time a DG has to start/stop, according to the dispatch strategy. The difference in the start/stop sequence can be seen by comparing the 1-week simulation in Fig. 17 where the default case is presented, and Fig. 18 in which the unit commitment optimization is activated.

The algorithm naturally prioritizes higher efficiency DGs. Consequently, as seen in Fig. 18, there is a shift from the initial state, where four Type 1 DGs were running, to only running Type 2 DGs after the fifth day.

## Results and Discussion

In this section, the reductions in fuel consumption achieved separately by the load dispatch optimization, unit commitment optimization, and battery inclusion, are presented. The final subsection highlights a simulation where all three modifications are applied simultaneously.

### Load dispatch optimization

The following graphs depict histograms of load distribution among the connected DGs over a one-year simulation. Fig. 19 displays the results of the default simulation while Fig. 20 illustrates the outcomes of a simulation with the load optimization enabled. In both of these graphs, the blue section represents the load distribution on the Type 2 DGs, the light red section represents the load distribution on Type 1 DGs, and the dark red area indicates the overlap between them. Additionally, SFC curves for both DG types are presented on the right y-axis.

In this optimization strategy, unequal load dispatching among the connected DGs is applied, aiming to minimize the average specific fuel consumption at each time-step. The default simulation, representing a scenario without any optimizations or battery integration, was utilized

<figure><img src="image_20.png" /><figcaption>**Fig. 17.** One-week default simulation with the type and number of DGs connected.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. 18.** One-week simulation with unit commitment optimization activated, with the type and number of DGs connected.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 19.** Load distribution histogram on both types of DGs for a default one-year simulation along with each Type's SFC curve.</figcaption></figure>

as a baseline for comparison. In the default simulation depicted Fig. 19, a subtle disparity in load distribution between the two types of DGs is noted. This distinction arises from the fact that both types of DGs are not necessarily active simultaneously. However, as illustrated in Fig. 20, the divergence in load distribution becomes more pronounced between the two types of DGs. Type 1 DGs consistently operate at minimal permissible load of 30 % for over 60 % of the total simulation duration. In contrast, Type 2 DGs operate around their optimal operating point, typically at 84 %, with a peak of 20 % of the simulation time at this load. The optimization process, which currently does not account for maintenance penalties, strategically allocates higher loads to the more efficient Type 2 DGs, while maintaining the less efficient Type 1 DGs at lower, predominantly minimal loads. The fuel savings achieved with this optimization amount to 1.6 % and the CO2 emitted are reduced by 3.4kt compared to the default simulation.
<figure><img src="image_23.png" /><figcaption>**Fig. 20.** Load distribution histogram on both types of DGs for a simulation with load dispatch optimization activated over a one-year simulation, along with each Type's SFC curve.</figcaption></figure>

## Battery inclusion

In this section, the effect of incorporating a spinning reserve battery into the system (as explained in section 2.4) is illustrated in Fig. 21 by comparing histograms of the load distribution of this simulation on Type 2 DG with the Default simulation (neither of the two cases include the optimization from 5.1). The green section denotes the simulation with batteries, the magenta section represents the Default simulation, and the dark green area indicates the overlap between the two sections. Additionally, SFC of Type 2 DG is displayed on top of the histogram. Although this figure shows Type 2 DG load distribution only, the result for Type 1 DG was similar. Fig. 22 shows a comparison for the same simulations, this time highlighting the percentage of time spent running with a specific number of connected DGs.

The addition of a spinning reserve-providing battery into the system enables the operation of connected DGs at higher loads, as illustrated in Fig. 21 where the green section exhibits significantly higher loads than the magenta section. This effect arises from the mitigation of constraint

<figure><img src="image_24.png" /><figcaption>**Fig. 21.** Type 2 DG load distribution histogram comparing the default one-year simulation to a simulation with included battery, along with Type 2's SFC curve.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>**Fig. 22.** Comparison of the percentage of time spent with a specific number of DGs connected over one-year simulations.</figcaption></figure>

that previously mandated a substantial portion of the DGs' total capacity for spinning reserve purposes. Conveniently, the DGs spend more time at loads that are much closer to their peak efficiency operating points, with a high density of the load distribution approaching the SFC minima.

These higher loads observed on the connected DGs are associated with the system often operating with one fewer DG compared to the default simulation. This phenomenon is illustrated in Fig. 22 where the system significantly reduces the time spent running with five DGs and spends more time running with four, three or two DGs.

Despite the batteries in this algorithm being reserved exclusively for potential incidents (which are not simulated) and unable to inject power, their inclusion still significantly reduces the system's overall fuel consumption by 0.9 % and CO2 emissions by 2kt compared to the default simulation.

## Unit commitment optimization

For this optimization, Fig. 23 compares the percentage of time each DG was active over the course of a year. Similarly, Fig. 24 compares the

<figure><img src="image_26.png" /><figcaption>**Fig. 23.** Comparison of the percentage of time spent with a specific number of DGs connected over one-year simulations.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>**Fig. 24.** Comparison of the percentage of time that each DG has operated between a default one-year simulation and a simulation with order optimization activated.</figcaption></figure>

percentage of time spent using a specific number of DGs between two scenarios. The green bars represent a simulation with unit commitment optimization active, while the magenta bars depict the default simulation.

The aim of this optimization is to refine the decision-making process in this algorithm regarding the selection of DGs to start/stop based on predicted demand and RES profiles. As depicted in Fig. 24, the algorithm consistently favors the use of Type 2 over Type 1. This preference is justified by the fact that DGs are often operated at loads exceeding 50%, making the use of Type 2 more advantageous according to the SFC curves from Fig. 3. The activation of this optimization significantly reduces the percentage of time with five DGs connected, as illustrated in Fig. 23. This reduction is attributed to the higher maximum power capacity of Type 2, resulting in the prioritization of a single Type 2 DG over two Type 1 DGs in many instances. This optimization resulted in a 1.2% reduction in fuel consumption and 2.5kt reduction in CO2 over one year.

### Simulation using both load dispatching and unit commitment optimization with a 15 MW spinning reserve battery

The final simulation incorporates both discussed optimizations along with battery integration, and its output is compared to the default simulation output. The histogram in Fig. 25 illustrates the load distribution between Type 1 and Type 2 DGs in an optimized system. The diagram in Fig. 26 provides a comparison of the number of active DGs between the default and optimized system. Fig. 27 and Fig. 28 zoom in on one specific week in the simulated year to highlight the evolution of connected DGs and the fuel consumption for the default and the optimized system respectively. Finally, Fig. 29 demonstrated the advantage gained by the optimized system in percentage difference of the fuel consumption.

Utilizing both discussed optimizations and introducing the 15 MW spinning reserve battery in the simulation resulted in a 2.6% reduction in fuel consumption and 6kt reduction in CO2 emissions over a year. This simulation demonstrated the combined benefits of all the improvements. As depicted in Fig. 25, the load distribution mirrors that of Section 5.1, but with a notable difference; the Type 2 DGs are allowed to reach higher loads, courtesy of the added spinning reserve-providing battery. Additionally, fewer DGs are connected at all times, illustrating the impact of incorporating a battery and employing the unit

<figure><img src="image_28.png" /><figcaption>**Fig. 25.** Load distribution histogram for both types of DG for a one-year simulation including load dispatch optimization, unit commitment optimization and a 15 MW spinning reserve battery.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Fig. 26.** Comparison of the percentage of time spent with a specific number of connected DGs for a one-year simulation including load dispatch optimization, unit commitment optimization and a 15 MW spinning reserve battery.</figcaption></figure>

commitment optimization (Fig. 26). This can also be seen in Fig. 27 and Fig. 28, where the number of connected DGs tend to be lower at all times for the optimized system. The effect of the unit commitment optimizer is also visible when comparing the fixed starting/stopping sequence of DGs in Fig. 27, to the adaptable starting/stopping sequence according to demand requirements in Fig. 28. All these improvements lead to an overall lower fuel consumption over the presented week, as shown in Fig. 29, with improvements varying between -0.5 and -4% consumption, depending on each time-step's available sources, DG load dispatching and the choice of unit commitment.

## Conclusion and future work

The heart of the study lies in proposing optimized DG operational strategies. Those strategies were implemented in a basic rule-based energy management algorithm, driven by demand and RES yearly profiles, and that considers stability aspects with a spinning reserve constraint
<figure><img src="image_30.png" /><figcaption>**Fig. 27.** Fuel consumption during week 14 along with the number of connected DGs for a defaults simulation.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>**Fig. 28.** Fuel consumption during week 14 along with the number of connected DGs for a simulation with load dispatch and unit commitment optimization, along with an integrated battery.</figcaption></figure>

along with other DG operational constraints. The proposed model allows the examination of the impact of strategy changes on annual fuel consumption.

The paper explores two optimization strategies: load dispatch optimization and unit commitment optimization. The load dispatch optimization seeks to minimize fuel consumption by unequally dispatching loads among DGs. The results demonstrates a 1.6% reduction in fuel consumption and 3.4kt reduction in CO2 emissions compared to the default scenario. The benefits of this optimization are considerable only when the system includes DGs with different specific fuel consumptions.

Unit commitment optimization focuses on optimizing the choice of DG to start/stop based on availability, consumption and predictive demand and RES profiles, achieving a 1.2% reduction in fuel consumption and emitting 2.5kt less of CO2. This optimization is most beneficial with different genset types (different rated powers) and specific fuel consumptions.

The inclusion of a spinning reserve-providing battery also contributes to reducing fuel consumption. By lifting the spinning reserve

<figure><img src="image_32.png" /><figcaption>**Fig. 29.** Percentage reduction in fuel consumption during week 14 between a default and an optimized simulation.</figcaption></figure>

constraint from DGs, the system operated DGs at higher loads, closer to their optimal operating points, and often runs the system with one less connected DG compared to a default scenario. This incorporation results in a 0.9% reduction in fuel consumption and 2kt reduction in CO2 emissions.

The combined application of load dispatch and unit commitment optimizations, along with the integration of a spinning reserve-providing battery, yields the most substantial reduction in fuel consumption and CO2 emissions, reaching 2.6% and 6kt respectively.

Further research is required to explore additional factors, such as maintenance penalties, system reliability, and potential impacts of unforeseen incidents. Additionally, the application of the proposed model to diverse microgrid scenarios and its scalability should be addressed in future studies to validate its robustness and adaptability in various contexts. Possible studies that can be carried out on this model include:

* Quality of the forecasted demand profiles,

* Conducting a sensitivity analysis of the unit commitment scheduling period,

* Adequate dimensioning of DGs and battery according to demand profiles,

* Retrofitting existing DGs for adapted specific fuel consumptions according to the DG's yearly load profiles.

### CRediT authorship contribution statement

**Issam Matragi:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Conceptualization.

**Alain Maiboom:** Writing – review & editing, Supervision, Project administration, Investigation, Conceptualization. **Xavier Tauzia:** Writing – review & editing, Supervision, Project administration, Investigation, Conceptualization. **Bruno Moricet:** Supervision, Resources.

**Yoann Thevenoux:** Writing – review & editing, Supervision, Resources, Project administration.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
# Data availability

The authors do not have permission to share data.

# Acknowledgement

This study was realized within the MAN-ES - Centrale Nantes Industrial Chair. The authors want to acknowledge all people involved in this project, in particular Vivien Leroy from Calculation team, and Nicolas Bulot, head of Engineering at MAN France. The authors also want to thank Jean-Philippe Mangione, Director of Kappenergy for his support and Yann Wolf, Director of Operations at EDT, and his team for kindly sharing information on the Tahitian power grid and hosting Issam Matragi for an observation stay in their power plant.

Issam Matragi's PhD is partially funded by Région Pays de la Loire.

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