A Multiparadigm Approach for Generation Dispatch Optimization in a Regulated Electricity Market towards Clean Energy Transition

Abstract

In Indonesia, the power generation sector is the primary source of carbon emissions, largely due to the heavy reliance on coal-fired power plants, which account for 60% of electricity production. Reducing these emissions is essential to achieve national clean energy transition goals. However, achieving this initiative requires careful consideration, especially regarding the complex interactions among multiple stakeholders in the Indonesian electricity market. The electricity market in Indonesia is characterized by its non-competitive and heavily regulated structure. This market condition often requires the PLN, as the system operator, to address multi-objective and multi-constraint problems, necessitating optimization in the generation dispatch scheduling scheme to ensure a secure, economical, and low-carbon power system operation. This research introduces a multiparadigm approach for GS optimization in a regulated electricity market to support the transition to clean energy. The multiparadigm integrates multi-agent system and system dynamic paradigms to model, simulate, and quantitatively analyze the complex interactions among multiple stakeholders in the Indonesian regulated electricity market. The research was implemented on the Java–Madura–Bali power system using AnyLogic 8 University Researcher Software. The simulation results demonstrate that the carbon policy scheme reduces the system’s carbon emissions while increasing the system’s cost of electricity. A linear regression for sensitivity analysis was conducted to determine the relationship between carbon policies and the system’s cost of electricity. This research offers valuable insights for policymakers to develop an optimal, acceptable, and reasonable power system operation scheme for all stakeholders in the Indonesian electricity market.

1. Introduction

The power generation sector has become the largest carbon emission producer in Indonesia with around 297 million tons of CO₂ emissions (42.6% of national carbon emissions) by 2022 [1]. This issue arises due to the large utilization of coal-fired power plant [2], comprising 60% of the generation share, as indicated in the Indonesian National Electricity Supply Business Plan 2021–2030 document. Therefore, carbon emission reduction in the power generation sector is an essential strategy [3] in achieving the national commitment towards clean energy transition. However, the implementation of this initiative requires attentive consideration, especially in the aspect of multiple stakeholder interactions in Indonesian electricity market.

The National Utility Company (PLN) is a state-owned enterprise that is responsible in generating, transmitting, and distributing the electricity from power producers to consumers. The power producers can be categorized as the PLN-owned power plant and the Independent Power Producer (IPP). For the PLN-owned power plant, the primary cost of electricity production is mainly from the fuel consumption costs, such as coal, gas, and oil price. Meanwhile, the electricity generated from the IPP is acquired by the PLN through a pre-construction bidding price outlined in the Power Purchase Agreement document. To supply the electricity demand, the PLN prioritizes the most economical power plant based on the merit order calculation, thus indicating the non-competitive characteristic of the electricity market in Indonesia. During the operation, the PLN also serves as the system operator, responsible for ensuring the balance of power supply and demand, grid stability to overcome system disturbances, and the reliability of a continuous supply to consumers at all times. On the other hand, the Ministry of State-Owned Enterprises has the objective of maximizing the business profits of the PLN, whereas the Ministry of Energy and Mineral Resources has the objective of minimizing the carbon emission production in the power generation sector. Also, due to the significant interaction between multiple stakeholders and the PLN’s operation, the electricity market in Indonesia can be characterized as a heavily regulated electricity market.

Based on the previously described market conditions, it can be seen that the PLN’s operation faces a complex problem with multiple objectives and constraints; thus, an optimal regulation making strategy becomes necessary to provide an acceptable and reasonable solution for all stakeholders involved in the electricity market. Generation dispatch scheduling (GS) optimization can be considered as a potential solution for the PLN to provide secure (balanced power supply and demand), least-cost (minimum production cost), and environmentally friendly (low carbon emission production) power system operation. GS involves methodical scheduling of electricity production from generating units across daily to weekly timeframes while adhering to different system’s and generator’s constraints [4]. GS primarily comprises unit commitment (UC) and economic dispatch (ED) optimization problems. The UC optimization focuses on deciding the operational state (on/off) of generating units in order to meet the forecasted hourly load demand, while also satisfying the generating unit’s capability and the system’s spinning reserve [5]. Meanwhile, ED optimization is conducted to determine the output power generated by generating units to meet the forecasted hourly load demand, with the objective to minimize the fuel consumption [6].

Multi-objective optimization often deals with complex non-linear problems and involvement from many parties with multiple constraints. This condition sometimes causes disagreements or conflicts among the parties/stakeholders [7]. The formulation in solving this problem needs to be considered as the main concern, in order to obtain a feasible, transparent, economically efficient, and optimal solution [8,9,10,11]. Therefore, this paper proposes the multiparadigm approach for generation dispatch optimization in a regulated electricity market towards clean energy transition. The fundamental idea of the proposed method is to combine the system dynamics (SD) paradigm and multi-agent system (MAS) paradigm with GS optimization. In the MAS model, the dynamic interaction between agents in power system operation is modelled and simulated. The generation company agent (GA) is designed within the MAS to adjust its dispatch according to the hourly instructions provided by the system operator agent (SA). The SA is equipped with GS optimization algorithm in order to generate an optimal GS scheme to supply the forecasted load demand. The consumer agent (CA) is modelled to represent the load curve of the system during 24 h of power system operation. In parallel with the MAS simulation, SD is used to measure the total electricity energy production, total production (fuel) cost, and total carbon emission production resulting from the 24 h of power system operation in the MAS simulation. This process is conducted in several carbon policy scenarios. Therefore, the novelty and innovation of this research is mainly related to the quantification of the multi-agent interactions in a non-competitive and regulated electricity market based on the sensitivity analysis between carbon policy scenarios and the system’s cost of electricity.

The proposed method was implemented in the Indonesian electricity market, specifically in the Java–Madura–Bali power system. The remainder of this paper is organized as follows: Section 2 provides context and background to this paper by discussing the fundamentals of the multiparadigm approach and GS optimization. Section 3 provides a detailed explanation of the research’s modelling, assumptions, simulation scenarios, and methodologies. Section 4 presents the model validation, simulation results, and discussion regarding the findings within the research. Finally, Section 5 presents conclusions from the research, including its limitations and further avenues for work.

2. Literature Review

2.1. Multiparadigm Approach

In engineering studies, the multiparadigm approach has been employed to simulate complex systems [12,13], including system dynamics, agent-based simulation, and discrete-event simulation [14]. The combination of these paradigms is called the multiparadigm approach. This approach allows for the development of models with multiple objectives, multiple levels of aggregation, and multiple perspectives [15]. The combination of multiple paradigms is beneficial for creating a realistic representation of the system under study. However, there are no clear selection mechanism for choosing an appropriate paradigm or combination of paradigms. This process depends on the modeler’s approach in solving the objectives under numerous constraints through the simulation model [16,17].

2.2. System Dynamics Paradigm

The SD paradigm is widely used for understanding complex issues [18,19]. SD can be characterized by stocks and flows [20], which describe the relationships between variables within complex systems [21]. SD-based simulation can be initiated by creating a causal loop diagram (CLD), which is then converted to a stock and flow diagram (SFD) using software designed for SD simulations [22,23,24]. In Figure 1, there are two main components in a SFD diagram: stock and flow. The stock variable has a quantitative value and represents the condition of the system at any given time. A stock’s value can vary due to the flow connected to it. Flow can be defined as the rate of change in the stock’s value over time. There are also auxiliary variables in the SFD diagram that can be expressed as constants or mathematical equations. For quantitative SD modelling, it is necessary to define numbers and mathematical equations for each stock and flow. According to [25], the main assumptions in the quantitative SD model are that flow must be continuous at all times and does not have a random component.

2.3. Multi-Agent System Paradigm

The MAS paradigm is a computational system in which several agents cooperate to achieve some tasks toward interactions, collaborative phenomena, and autonomy [26]. The MAS is based on agent-based simulation modelling, which is the most commonly used paradigm to simulate situations where individual objects can act and adapt on their own [27]. The behavior of agents can be both reactive (e.g., responding to an event/command) and proactive (pursuing a goal/objective) [28]. Unlike a function, an agent can respond to information on its terms and not simply when called. Given their characteristics, the MAS is well-suited for modelling systems in energy optimization, reflecting the dynamic and adaptable nature in handling complex tasks [29].

The MAS paradigm has been used and developed in much research, especially in the field of power system operation. Research [30] describes a simplified structure of an agent-based simulation model, as presented in Figure 2. It is illustrated that agents can receive information from other agents in the form of an input dataset (S_in). The input dataset is then used as a reference for agents in observing system operating conditions. During the observation process, the agent analyzes the input dataset through an embedded functional algorithm as the basis for decision-making. After the agent has finished analyzing the input data, the agent can decide on the next operational status, and then send operational information to other agents in the MAS.

Several studies have explored the utilization and development of the MAS paradigm in the electricity market. Research [31] discusses the application of an MAS to optimize bidding strategies in competitive electricity markets, investigating the impact of varying degrees of negotiation power and information availability on network performance and analyzing profits from social and participant perspectives. The study concludes that an MAS can enhance bidding strategies based on market dynamics, offering valuable insights into market behavior and improving decision-making processes. Research [32] combines an MAS with the experience-weighted attraction reinforcement learning algorithm to provide agents with more intelligent bidding strategies. However, it highlights the difficulty in modelling strategic bidding behavior for both supply and demand sides with elastic demand using reinforcement learning methods. To address this, research [33] introduces an MAS model utilizing a multi-agent deep deterministic policy gradient and a prioritized experience replay mechanism. The findings indicate that this model surpasses state-of-the-art methods under various levels of system uncertainty and dynamic conditions in bidding transactions. Additionally, research [34] explores the use of MAS in a grid-connected microgrid to enhance profit sharing among stakeholders, with promising energy market simulation results demonstrating improvements in sellers’ profit margins.

In research [35], an MAS model is simulated in the wholesale electricity market, the tradable green certificate market, and the carbon emissions trading market to provide effective incentives for green electricity market. The results show that the proposed solution provides significant incentives for all stakeholders while securing the energy production of conventional and renewable power plants, reducing carbon emissions, and promoting the development of renewable energy. Research [36] develops an MAS model of the emission reduction potential of multi-energy power generation, which is based on the core algorithm of the GS approach. The results show that increasing the proportion of renewable energy generation in the system can simultaneously reduce the thermal power generation and the system’s carbon emissions.

2.4. Generation Dispatch Scheduling

Given the large scale of the system, the non-linear input–output characteristics of conventional power generation units, and the high variability in VRE (variable renewable energy) power plants, GS optimization becomes essential. Various methods, such as mixed-integer linear programming, genetic algorithm, and other heuristic or metaheuristic techniques, can be utilized to achieve this optimization. These methods help ensure efficient and reliable power generation that meets demand while minimizing costs and emissions [37,38,39].

Traditional mathematical techniques such as priority list, dynamic programming, branch and bound, linear programming, and Lagrangian relaxation are effective for small- to moderate-scale power systems due to their simplicity and fast computational capabilities. These methods are capable of finding optimal solutions efficiently. However, they face significant challenges when dealing with a large number of constraints, making them less suitable for more complex and larger-scale power systems [40].

In a large-scale system, heuristic techniques such as evolutionary programming, tabu search, simulated annealing, and genetic algorithm are commonly employed. These methods are favored for their ability to produce near-optimal solutions within a practical timeframe [41]. However, due to their iterative nature, an increase in the number of generating units typically results in a higher number of iterations, thereby extending the execution time [42].

Research [43] introduces a bi-level dispatch optimization model for an economic and low-carbon GS scheme with its application in a multi-microgrid system. The upper-level model represents the decisions made by the central authority or microgrid operator, who focuses on maximizing the electricity production from renewable (green) energy sources while minimizing the total system cost. The lower-level model represents the decisions made by individual microgrid operators, which involve the optimization of local operations, including generation scheduling, storage management, and load dispatch, while also considering the willingness of consumers to pay for green electricity.

2.5. Unit Commitment

Due to the fluctuation in load demand over time, the system operator needs to optimize the scheduling of the operational status (on/off) of generating units. This process is known as unit commitment (UC). The objective of UC scheduling is to minimize total costs while satisfying forecasted power demand and other constraints. In this study, UC optimization is conducted using the priority list (PL) method, with several related studies reviewed in the following section.

Research [42] utilized the PL method for UC scheduling, aiming to minimize total costs, including operational, start-up, and shut-down expenses. The optimization process considered various constraints such as load demand, spinning reserve, output power range, ramp rate, minimum up/down time, and the initial status of units. This model was successfully tested on systems with 10, 20, 40, 60, 80, and 100 power generation units, with simulation results confirming the technique’s efficiency and reliability for solving large-scale UC problems. Research [44] introduced a hybrid approach combining the modified priority list and charged system search approaches to tackle UC scheduling issues. This method effectively minimized fuel and start-up costs while adhering to constraints such as power balance, spinning reserve, generation limits, ramp rate limits, and minimum up/down time. The method was successfully applied to a widely recognized test system with up to 100 generator units over 24 h and 168 h periods. Computational results showed that this method performed well in terms of both solution cost and execution time. Research [45] employs the PL method to enhance the evolutionary algorithm for solving UC optimization. By seeding the initial random population with the PL method, the speed of convergence and the algorithm’s efficiency are improved. Subsequently, an evolutionary algorithm, incorporating problem-specific heuristics and genetic operators, is executed to address the optimization problem. Test results demonstrate the superiority of this approach compared to the evolutionary programming and genetic algorithm methods [46,47,48].

2.6. Economic Dispatch

ED optimization involves determining the output power of each available generator to meet the total network demand while minimizing operational costs and/or the carbon dioxide emissions of the generators [49]. ED involves the operation of generators based on their marginal costs, prioritizing those with the lowest costs first. This optimization technique reduces operating expenses, enhances system efficiency, and decreases emissions [14,50]. By precisely adjusting the output of each generator, ED aims to minimize the total fuel cost of electricity production. In this research, ED optimization is carried out using the linear programming (LP) method, with several related studies discussed in the following section.

Research [51] creates a linear ED model using mixed-integer linear programming. The complex non-linear equations of the AC load flow model are simplified with Taylor series expansions and piecewise linear approximation techniques. The model’s performance is tested using IEEE standard test systems, including 14, 30, 39, 57, 118, and 300 bus systems. Results show that this linear ED model effectively finds optimal solutions while considering different operational constraints. Research [52] introduces an improved real-coded genetic algorithm combined with an enhanced mixed-integer linear programming method to manage the unit commitment and economic dispatch of microgrid units. The simulation process takes into account network restrictions such as voltage levels, equipment loadings, and unit constraints. The genetic algorithm employed features a highly flexible set of sub-functions, intelligent convergence behavior, diverse searching approaches, and penalty methods for handling constraint violations.

3. Methodology

3.1. Multi-Agent System

This research uses an MAS to simulate the interaction between multiple stakeholders involved in Indonesia’s electricity market and power system operations. The MAS model includes three types of agents: GA, SA, and CA. Considering N number of generating units and M number of consumers, the MAS architectural model proposed in this research is illustrated in Figure 3.

The diagram shows that GA and CA are represented as multiple agents for each generation and consumer unit in the power system. SA, on the other hand, is a single agent representing the PLN, the system operator. SA acts as a command center, monitoring and managing system operations to keep power supply and demand balanced. It calculates the total power demand of the CA, optimizes the GS scheme for economic and low-carbon efficiency, and sends commands to the GA to meet power needs.

3.1.1. Generation Company Agent

In this research, 327 generation units are modelled as GA with a total capacity of 47,300 MW (47.3 GW). The model is based on the installed power plant data of the Java–Madura–Bali power system in 2023, provided by the PLN [53]. These units are interconnected through a 500 kV extra high transmission network.

Table 1. Overview of installed power plants in Java–Madura–Bali power system (2023).

Generating Unit Category	Number of Unit(s)	Installed Capacity (MW)	Percentage (%)
Geothermal	19	1225	2.6%
Waste-to-energy and biomass	4	34	0.1%
Large-scale hydro	95	2616	5.5%
Small-scale hydro	40	222	0.5%
Coal-fired	62	28,545	60.4%
Combined-cycle gas turbine	87	13,965	29.5%
Open-cycle gas turbine	9	353	0.7%
Gas engine	4	182	0.4%
Diesel	7	152	0.3%
Total	327	47,294	100.0%

shows the number of units and capacity for each type of generating unit in the system. The table indicates that coal-fired power plants dominate with 60.4% of the capacity, followed by combined-cycle gas turbines at 29.5%, large-scale hydro power plants at 5.5%, and geothermal power plants at 2.6%. This condition indicates that the dominance of coal-fired power plants in the system could lead to high carbon emissions during power system operations.

The initial step of GA modelling in an MAS begins with defining the input data. This includes the generation unit’s name, type, loading limits (minimum and maximum), and fuel cost function coefficients. The unit name is used for identification and data retrieval from the database. Loading limits ensure the unit operates within its specified range during optimization, while fuel cost coefficients represent the unit’s non-linear cost function.

The fuel cost function of GA is assumed to be a second-order polynomial (quadratic) equation. This assumption is based on the typical incremental heat rate characteristic of GA, which represents the change in heat input per kilowatt-hour of output at a specific loading point of the generating unit. To obtain the incremental heat rate data for a generating unit, several heat rate tests at different loading points are required.

Table 2. Example of GA input parameters.

Name	Min. Loading (MW)	Max. Loading (MW)	Fuel Cost Function (Cent/Hour)
			Quadratic Coefficient (aP2)	Linear Coefficient (bP)	Constant (c)
CFPP Jawa-4 Tanjung Jati #1	500	1000	1.80	−742.63	1,248,341.14

provides an example of GA input parameters.

The detailed model of a GA is presented in Figure 4. The GA initially starts in a shut-down state and checks for start-up commands from the SA every minute. If the SA sends an ON command, the GA transitions to the start-up state. If the SA sends an OFF command, the GA remains in the shut-down state and continues to check for commands.

After the initial start-up phase, the GA evaluates the downtime variable, which records the duration of its shutdown period. This variable determines whether the GA initiates a hot, warm, or cold start procedure. Each start type dictates the rate at which the GA transitions from zero load to its minimum operating load. Once this start-up period concludes, the GA operates at its designated minimum load level.

Once the GA reaches its minimum loading state, its operations are categorized into two types: frequency-governed (FG) generator and non-FG generator. FG generators are capable of receiving scheduled dispatch commands every hour from the SA and perform power mismatch balancing every minute. Non-FG generators, on the other hand, only receive scheduled dispatch commands every hour from the SA.

Consider K number of FG generators, each with maximum capacity denoted by $P_{k,max}$ in megawatts (MW) and speed droop $\left({SD}_k\right)$ expressed in percentage (%). The primary frequency bias $\left({Kpf}_k\right)$ for each FG generator, measured in megawatts per hertz (MW/Hz), can be calculated using the following mathematical equation:

$${Kpf}_k={\displaystyle \frac{∆P}{∆f}}={\displaystyle \frac{P_{k,max}}{f_{nom}·\left(\raisebox{1ex}{${SD}_k$}\!\left/ \!\raisebox{-1ex}{$100$}\right.\right)}}$$

(1)

In order to determine the adjustment in output power for each FG generator $\left(∆P_k\right)$, expressed in megawatts (MW), in response to variations in system frequency $\left(∆f\right)$, expressed in hertz (Hz), the following equations are utilized:

$$∆P_k={Kpf}_k·∆f$$

(2)

where

$$∆P_{total}=P_{generation}-P_{load}=\sum P_{GA}-\sum P_{CA}$$

(3)

$$∆f={\displaystyle \frac{∆P_{total}}{{\sum }_{k=1}^K{Kpf}_k}}$$

(4)

In addition, certain GAs are assumed to function as FG generators with specific values of speed droop based on data provided by the PLN [54]. Furthermore, some GAs categorized as coal-fired power plants are designated as carbon emission producers, each associated with a specific carbon factor (kWh-to-CO₂ conversion rate) based on data provided by the PLN [55]. These carbon factor data are essential for calculating the total carbon emissions produced by coal-fired power plants based on their total electricity generation.

3.1.2. System Operator Agent

As the system operator, the SA is equipped with the capability to communicate with other agents. This communication allows for the SA to calculate the total power demand from the CA and to access the GA’s input parameter data. Consequently, GS optimization can be conducted to ensure a constant balance between power supply and demand, taking into account both economic and low-carbon considerations. The GS optimization within the SA involves solving UC and ED problems, which are crucial for determining the operational status (on/off) and the dispatch levels of the GA.

The detailed model of the SA is depicted in Figure 5. The SA algorithm includes functionality to access data from the GA and CA, such as the generators’ specifications (name, type, loading limits, and fuel cost function coefficients) and consumers’ electricity demand (load curve). After collecting the necessary data from the GA and CA, the GS optimization process is initiated by establishing the merit order in UC and ED optimization. Once the merit order is established, the SA applies the PL methodology to determine the UC scheme. Subsequently, the output power of the committed GA is calculated using LP methodology. This process is repeated for each hour of the simulation period. A detailed explanation of the PL method for UC optimization and LP method for ED optimization are described in the following section, based on [56].

The PL method is utilized for UC optimization by ranking the GA based on their full-load average production cost [57]. Assume there are N number of GAs with $F_{i,t}\left(P_{i,t}\right)$ representing the fuel cost function of GA i at time t, defined in cents per hour. This function is characterized as a second-order polynomial (quadratic) equation with coefficients $A_i$, $B_i$, and $C_i$ serving as the coefficients. The fuel cost of GA i varies with the output power it generates. This cost relationship is typically non-linear and influenced by the specific characteristics of the generating unit, such as its fuel efficiency at different levels of power output. The full-load average production cost $\left({\mathsf{\Psi }}_i\right)$ is calculated using the following equation:

$${\mathsf{\Psi }}_i={\displaystyle \frac{F_{i,t}\left(P_{i,max}\right)}{P_{i,max}}}$$

(5)

where

$$F_{i,t}\left(P_{i,t}\right)=\left(A_i·P_{i,t}^2\right)+\left(B_i·P_{i,t}\right)+\left(C_i\right)$$

(6)

$$i=\mathrm{0,1},2,\dots ,N$$

(7)

This metric assesses the cost-efficiency of a GA by comparing the fuel cost at full capacity to the output power, thus determining its economic viability. GA with a lower ${\mathsf{\Psi }}_i$ are prioritized for operation, ensuring that the most cost-effective units are committed first [58]. This method supports the goal of optimizing power system operations while maintaining economic and energy efficiency.

Based on the calculation of the full-load average production cost for N number of GAs, the costs can be arranged in ascending order. This ordering allows for the SA to prioritize the GA with the lowest operational costs first, which is essential for optimizing overall system efficiency and reducing operational expenses. The sorted list serves as a guideline for the UC process, ensuring that the most economical generators are activated in response to demand, while maintaining system reliability and cost-effectiveness.

$$\mathsf{\Psi }=[{\mathsf{\Psi }}_1,{\mathsf{\Psi }}_2,\dots ,{\mathsf{\Psi }}_N]$$

(8)

$${\mathsf{\Psi }}_{\mathit{a}\mathit{s}\mathit{c}}=[{\mathsf{\Psi }}_{asc\_1},{\mathsf{\Psi }}_{asc\_2},\dots ,{\mathsf{\Psi }}_{asc\_N}$$

(9)

The PL schemes for UC optimization, aimed at minimizing production costs, are outlined in

Table 3. Priority list scheme for unit commitment.

Priority List Scheme	Committed Generation Unit	Total Minimum Capacity	Total Maximum Capacity
1	${\mathrm{G}\mathrm{A}}_{asc\_1}$	$P_{asc\_1,min}$	$P_{asc\_1,max}$
2	${\mathrm{G}\mathrm{A}}_{asc\_1}$, ${\mathrm{G}\mathrm{A}}_{asc\_2}$	${\displaystyle \sum _{i=1}^2}{P}_{asc\_i,min}$	${\displaystyle \sum _{i=1}^2}{P}_{asc\_i,max}$
…	…	…	…
N	${\mathrm{G}\mathrm{A}}_{asc\_1}$, ${\mathrm{G}\mathrm{A}}_{asc\_2}$, …, ${\mathrm{G}\mathrm{A}}_{asc\_N}$	${\displaystyle \sum _{i=1}^N}{P}_{asc\_i,min}$	${\displaystyle \sum _{i=1}^N}{P}_{asc\_i,max}$

. This table ranks GAs according to their full-load average production costs from the lowest to the highest. This ranking facilitates the implementation of an optimization strategy where the GA with the least costs are committed first, ensuring that the power system operates as economically as possible while meeting the required demand and maintaining system stability. This structured approach allows for system operators to effectively manage and allocate resources, prioritizing cost-efficiency throughout the operational process.

The selection of a priority list scheme for UC optimization must carefully consider the total minimum and maximum power output capacities of GAs, which are necessary to meet specific demands. The following formulations describe the components and constraints of the UC optimization process using the PL method:

• Total maximum output power $\left({\sum }_{i=1}^N{P}_{asc\_i,max,t}\right)$ represents the total maximum output power of N number of GAs at time t, ensuring the system can meet the maximum (peak) load demands.
• Total minimum output power $\left({\sum }_{i=1}^N{P}_{asc\_i,min,t}\right)$ represents the total minimum output power of N number of GAs at time t. This ensures that there is enough generation to meet the base load without violating any operational constraints.
• Total load demand $\left(D_t\right)$ represents the total load demand at time t, wherein the sum of the output powers from the committed GA must match to ensure demand is met.
• Spinning reserve requirement $\left({SR}_t\right)$ represents the system’s spinning reserve requirement at time t, which is a safety margin to accommodate sudden losses of power supply or unexpected increases in demand.

The objective function for UC optimization aims to minimize the total production cost while satisfying the power balance constraints, which can be expressed as follows:

$$Minimize\left(\sum _{i=1}^N{F}_{i,t}\left(P_{i,t}\right)\right)$$

(10)

$$Subject to: \sum _{i=1}^N{P}_{asc\_i,min,t}\le D_t+{SR}_t\le \sum _{i=1}^N{P}_{asc\_i,max,t}$$

(11)

In this research, ED optimization is carried out using the LP method. To effectively solve ED optimization problems using LP, the fuel cost function of the GA needs to be approximated using piecewise linear equations. This approach is necessary because the fuel cost function, typically a second-order polynomial, as illustrated in Figure 6, must be transformed into a linear format compatible with LP techniques.

Consider N number of GAs, each defined by predetermined minimum and maximum loading limits. These limits are crucial for ensuring that each GA operates within its efficient capacity range while adhering to technical and safety standards. By converting the non-linear fuel cost functions into piecewise linear segments, the LP method can efficiently handle and solve the ED problem, aiming to minimize the total fuel cost across all GAs while satisfying the power demand constraints set by the system’s operational requirements. This linearization simplifies the optimization process, allowing for a more straightforward and computationally feasible application of linear programming techniques in managing the dispatch of electric power generation.

From the curve shown in Figure 6, it can be seen that the fuel cost of a GA at a specific loading point can be calculated using Equation (6), expressed in cents per hour. This equation describes how the fuel cost function of GA i, expressed in $F_{i,t}\left(P_{i,t}\right)$, at any given power output, expressed in $P_{i,t}$, can be computed.

The fuel cost for any GA is bounded within a specific range, which is defined by the fuel cost at the minimum loading point, expressed in $F_{i,t}\left(P_{i,min}\right)$, and the fuel cost at the maximum loading point, expressed in $F_{i,t}\left(P_{i,max}\right)$. This ensures that the calculated fuel cost for any output level lies within these limits, reflecting the realistic operating costs of the GA across its operational range. The mathematical expression that defines this relationship is as follows:

$$F_{i,t}\left(P_{i,t}\right)=\left\{\begin{array}{cc}{F}_{i,t}\left(P_{i,min}\right)& if P_{i,t}=P_{i,min}\\ F_{i,t}\left(P_{i,max}\right)& if P_{i,t}=P_{i,max}\\ \left(A_i·P_{i,t}^2\right)+\left(B_i·P_{i,t}\right)+\left(C_i\right)& if P_{i,min}\le P_{i,t}\le P_{i,max}\end{array}\right.$$

(12)

Figure 7 illustrates the approximation of a non-linear fuel cost function using a piece-wise linear approach. In this example, the fuel cost function is divided into three linear segments for simplicity and computational efficiency. Each segment is defined within specific bounds of output power to ensure the approximation aligns with the actual fuel cost curve of a GA.

In the first segment, $P_{i,s1}$ represents the output power for GA i within the first segment $\left(s_1\right)$. The output power $P_{i,s1}$ is restricted to the range between $P_{i,s1\_min}$ and $P_{i,s1\_max}$. If the actual output power of GA i falls below $P_{i,s1\_min}$; then, $P_{i,s1}$ is set to $P_{i,s1\_min}$. Conversely, if it exceeds $P_{i,s1\_max}$, $P_{i,s1}$ is set to $P_{i,s1\_max}$. In the second segment $\left(s_2\right)$, a similar approach is applied to $P_{i,s2}$, where $P_{i,s2}$ is bounded by $P_{i,s2\_min}$ and $P_{i,s2\_max}$. Adjustments are made to ensure $P_{i,s2}$ does not exceed these limits. In the third segment $\left(s_3\right)$, $P_{i,s3}$ is treated in the same method, with bounds set by $P_{i,s3\_min}$ and $P_{i,s3\_max}$. The slopes of each segment can be determined using the following equations:

$$m_{s1}={\displaystyle \frac{F_{i,t}\left(P_{i,s1\_max}\right)-F_{i,t}\left(P_{i,s1\_min}\right)}{P_{i,s1\_max}-P_{i,s1\_min}}}$$

(13)

$$m_{s2}={\displaystyle \frac{F_{i,t}\left(P_{i,s2\_max}\right)-F_{i,t}\left(P_{i,s2\_min}\right)}{P_{i,s2\_max}-P_{i,s2\_min}}}$$

(14)

$$m_{s3}={\displaystyle \frac{F_{i,t}\left(P_{i,s3\_max}\right)-F_{i,t}\left(P_{i,s3\_min}\right)}{P_{i,s3\_max}-P_{i,s3\_min}}}$$

(15)

In the ED optimization, the non-linear fuel cost function of the GA is effectively approximated using piece-wise linear programming. This involves subdividing the function into three linear segments, each characterized by distinct slopes $\left(s_1,s_2, s_3\right)$. These segments approximate the fuel cost curve by linearly interpolating between predefined bounds. This piece-wise linear approximation ensures that the LP method used in ED optimization can effectively address the non-linear nature of fuel cost functions while maintaining close alignment with real-world operational costs of the GA. This method simplifies the complexity of the original function, enabling more tractable optimization calculations. The objective function for ED optimization using piece-wise LP aims to minimize the total fuel cost across all GAs while adhering to power system operational constraints. The objective function can be mathematically expressed as follows:

$$Minimize\left(\sum _{i=1}^N{F}_{i,t}\left(P_{i,t}\right)\right)$$

(16)

where:

$$F_{i,t}\left(P_{i,t}\right)=\left\{\begin{array}{c}\begin{array}{cc}{F}_{i,t}\left(P_{i,s1\_min}\right)& if P_{i,t}\le P_{i,s1\_min}\\ F_{i,t}\left(P_{i,s1\_min}\right)+{\displaystyle \sum _{j=1}^1}\left(m_{sj}·P_{i,sj}\right)& f P_{i,s1\_min}\le P_{i,t}\le P_{i,s1\_max}\end{array}\\ \begin{array}{cc}{F}_{i,t}\left(P_{i,s1\_min}\right)+{\displaystyle \sum _{j=1}^2}\left(m_{sj}·P_{i,sj}\right)& if P_{i,s2\_min}\le P_{i,t}\le P_{i,s2\_max}\\ F_{i,t}\left(P_{i,s1\_min}\right)+{\displaystyle \sum _{j=1}^3}\left(m_{sj}·P_{i,sj}\right)& if P_{i,s3\_min}\le P_{i,t}\le P_{i,s3\_max}\end{array}\end{array}\right.$$

(17)

The objective function in Equation (16) must also satisfy the optimization constraints which consist of the following:

• Power balance constraint, which ensures the total power generated meets the total demand $\left(D_t\right)$ and the system’s fast reserve requirement $\left({FR}_t\right)$.

$${\sum }_{i=1}^N{P}_{i,t}=D_t+{FR}_t$$

(18)

2.

Generator loading limit constraint, which ensures the output power of each GA in any segment can be maintained within its defined bounds.

$$P_{i,min}\le P_{i,t}\le P_{i,max}$$

(19)

Addressing the system’s fast reserve constraint is crucial, particularly considering the role of FG generators. Fast reserve, as defined by the Indonesian Grid Code, pertains specifically to the spinning reserve provided by FG generators. This reserve capacity is critical for immediate response to sudden changes in power demand or generator failures.

Fast reserve can be described as the portion of spinning reserve that is readily available for quick deployment from FG generators. According to the Indonesian Grid Code, the fast reserve available must be equal to or greater than 50% of the largest generator’s capacity installed in the system. This requirement ensures that the system can maintain stability and continue to meet demand in the event of sudden large-scale deviations.

Consider there are K-number of FG generators. The capacity of the largest operating generator at time t, expressed in $\mathrm{m}\mathrm{a}\mathrm{x}\left(P_{k,max}\right)$, indicates that the total fast reserve ${FR}_t$ should at least be half of the capacity of the largest generator to ensure adequate response capability. The fast reserve constraint can be mathematically expressed as follows:

$${FR}_t\ge 50\%·\mathrm{m}\mathrm{a}\mathrm{x}\left(P_{k,max}\right)$$

(20)

This fast reserve requirement must be integrated into the ED optimization process, ensuring that the solution not only minimizes fuel costs but also aligns with grid stability requirements. The optimization model would thus include an additional constraint to ensure that sufficient fast reserve is always available. This can be modelled alongside other constraints such as power balance and generation limit constraints, as previously described. Including fast reserve constraints effectively within the ED optimization ensures that the power system is not only economically efficient but also resilient and capable of handling unexpected disturbances, thus enhancing the overall reliability of the grid.

The allocation of fast reserve capacity among the FG generators is determined based on the relative capacity of each generator. This approach ensures that the responsibility for providing fast reserve is proportionally distributed according to the maximum output power capability of each FG generator.

The proportion of the total system’s fast reserve assigned to each FG generator $\left({FR}_{k,t}\right)$ is calculated by determining the ratio of the maximum output power of the generator $\left(P_{k,max}\right)$ to the total maximum output power of all FG generators in the system $\left({\sum }_{k=1}^K{P}_{k,max}\right)$. The mathematical expression is given as follows:

$${FR}_{k,t}={\displaystyle \frac{P_{k,max}}{{\sum }_{k=1}^K{P}_{k,max}}}·{FR}_t$$

(21)

The optimization model should include constraints that ensure the sum of the individual fast reserve contributions from all FG generators meets or exceeds the required system’s fast reserve $\left({FR}_k\right)$:

$$\sum _{k=1}^K{FR}_{k,t}\ge {FR}_t$$

(22)

This methodical approach to allocating fast reserves ensures that all FG generators contribute fairly and effectively to the stability and reliability of the power system, enhancing the grid’s ability to respond swiftly to changes in demand or supply conditions.

Once the fast reserve proportion for each FG generator $\left({FR}_{k,t}\right)$ has been calculated, the final step in the ED optimization process involves updating the operational limits of these generators to ensure that the system’s fast reserve requirements are met. This update affects the maximum available output power of each FG generator, ensuring that a portion of their capacity is reserved for immediate availability in response to sudden demand spikes or generator outages.

For each FG generator, the adjusted maximum output power $\left(P_{k,max}^{new}\right)$ is computed by subtracting the designated fast reserve proportion $\left({FR}_{k,t}\right)$ from the original maximum output power $\left(P_{k,max}\right)$. This adjustment ensures that the generator retains sufficient capacity to contribute to the fast reserve when needed. The formula for this adjustment is as follows:

$$P_{k,max}^{new}=P_{k,max}-{FR}_{k,t}$$

(23)

3.1.3. Customer Agent

In this research, electricity customers are represented as CS to model the total load demand over a 24 h period of power system operation. The Java–Madura–Bali power system’s electricity customers typically include residential, industrial, public, and social sectors. According to data from the PLN [59], the daily load curve of the system is depicted in Figure 8. This curve shows the lowest demand at 04:00 with a value of 26,759 MW, and the highest (peak) demand at 14:00 with a value of 31,800 MW.

For the purpose of the MAS simulation, each CA is equipped with the capability to calculate the total load demand of the system. This algorithm operates with a time resolution of one hour, providing detailed and timely updates on demand fluctuations. The results of these calculations are crucial, as they are utilized by the SA for GS optimization. This integration ensures that generation resources are allocated efficiently and effectively to meet the dynamic demands of the power system. The detailed diagram of the CA model is presented in Figure 9.

Due to the integration of renewable energy in the system, the Cirata Solar Photovoltaic Power Plant, with a capacity of 192 MWp, is modelled and simulated as having negative demand. This approach reflects the impact of solar power generation on reducing the overall load demand faced by the system. Accordingly, the daily load curve of the system, which is calculated by the CA, is adjusted by subtracting the output power of the Cirata Solar PV power plant across a 24 h period of power system operation.

The adjustment effectively shows the net load that the system needs to meet after accounting for the solar power contribution. The data provided by the PLN (based on the Indonesian Solar Map website, accessed in June 2023) [60], which assumes the daily output power of the Cirata Solar PV power plant in megawatts (MW), is depicted in Figure 10. This illustration helps visualize the fluctuating nature of solar power throughout the day and its significant role in shaping the overall demand profile of the power system.

3.2. System Dynamics

The SD paradigm is employed to model the high-level abstraction of power plant operations. This SD algorithm is embedded within the GAs to simulate their behavior and interactions over time. The primary outputs of the SD model are the quantification of interactions among agents in the MAS, focusing on total electricity energy production, total production (fuel) cost, and carbon emission production over a 24 h period of power system operation. A detailed model of the SD, illustrating these dynamic interactions and their impacts, is presented in Figure 11.

The generator’s ramp rate, fuel cost function coefficients, and carbon factor data are based on the data provided by the PLN. In the SD model, the flows represent the rate of change in the generator’s operational parameters, including dispatch, production cost, electricity energy production, and carbon emission production. The mathematical expressions for these flows are detailed below.

• The dispatch flow represents the change in the generator’s power output over time.

$$Dispatch Rate=\pm Generator Ramp Rate \left[\mathrm{M}\mathrm{W}\right]$$

(24)

2.

The production cost flow is based on the fuel cost function, typically a second-order polynomial with coefficients A, B, and C.

$$Production Cost Rate=A·{Dispatch}^2+B·Dispatch+C \left[\mathrm{U}\mathrm{S}\mathrm{D}\right]$$

(25)

3.

The electricity energy production flow calculates the total energy produced over time.

$$Energy Rate=Generation Dispatch·∆t \left[\mathrm{M}\mathrm{W}\mathrm{h}\right]$$

(26)

4.

The carbon emission production flow uses the carbon factor to determine the emissions based on the energy produced.

$$Emission Rate=Energy Rate·Carbon Factor \left[\mathrm{T}\mathrm{C}\mathrm{O}2\mathrm{e}\right]$$

(27)

These expressions enable the SD model to dynamically simulate the operational parameters of generators, providing insights into their performance and environmental impact over a 24 h period. Based on the calculation of total electricity energy production and total production cost, the system’s cost of electricity [cents/kWh] can be calculated using the following equation:

$$Cost of Electricity={\displaystyle \frac{Total Production Cost·100}{Total Electricity Energy Production ·1000}}\left[{\displaystyle \frac{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}}{\mathrm{k}\mathrm{W}\mathrm{h}}}\right]$$

(28)

3.3. Simulation Scenarios

The Indonesian Ministry of Energy and Mineral Resources set a target to reduce carbon emissions in the power generation sector by 5.36 million TCO2e per year in 2022. This target translates to a daily carbon emission reduction of approximately 15,000 TCO2e. Consequently, the simulation scenarios in this research are divided into three types of emission reduction objectives, as detailed in

Table 4. Simulation scenarios.

Scenario Type	Emission Reduction Objective	Unit
Base	0	TCO2e per day
Carbon policy (low)	5000	TCO2e per day
Carbon policy (moderate)	10,000	TCO2e per day
Carbon policy (high)	15,000	TCO2e per day

. The simulations were conducted using AnyLogic 8 University Researcher Software.

To ensure the validity of the model, the base scenario is simulated first. This initial simulation aims to verify that the GS optimization performs correctly and that all specified constraints, as outlined in

Table 5. Input parameter for simulation model.

Parameter	Constraint	Value	Unit
Power mismatch limit	Less than or equal to (≤)	1.0	%
System spinning reserve	Greater than or equal to (≥)	1000	MW
System fast reserve	Greater than or equal to (≥)	500	MW

, are satisfactorily met. The base scenario serves as a benchmark, providing a reference point against which the outcomes of the carbon policy scenarios can be compared.

4. Discussion

4.1. Base Scenario (Model Validation)

In this scenario, a multiparadigm approach of GS optimization in the Indonesian regulated electricity market and the Jamali power system is performed without considering carbon policy (base scenario). The main goals are to validate the proposed MAS and SD models and to determine the base case operating conditions for the Java–Madura–Bali power system. The validation process involves evaluating system constraints, such as power mismatch limit, spinning reserve, and fast reserve. If all constraints are satisfied, the simulation calculates the total electrical energy production, total production costs, and total carbon emission production over 24 h of simulation time. These results will be used as references to compare the impacts of carbon policy scenarios to the Indonesian power system operation and electricity market.

Figure 12 describes the UC optimization results. It is observed that the model is able to satisfy a system spinning reserve greater than or equal to 1000 MW. Therefore, the simulated model can be considered valid for further simulations regarding the spinning reserve constraint.

For ED optimization results, the evaluation of the power mismatch limit and system’s fast reserve were performed. Figure 13 illustrates that the GS optimization results of the base scenario successfully maintain the power supply–demand balance over the 24 h simulation period. The power mismatch between the load curve (scheduled demand) and the generation curve (GS optimization result) remains below 1.00%. Therefore, the GS optimization model can be considered valid for further simulations, particularly regarding the power mismatch limit constraint.

Figure 14 describes the ED optimization results specifically for FG generators in the system. In the ED optimization algorithm, all FG generators are set to “must-run” during the 24 h of simulation period, resulting in the maximum capacity of all FG generators in the system remaining constant at 7700 MW. The results show that the ED optimization can maintain the system’s fast reserve above 500 MW. Therefore, the simulated model can be considered valid for further simulations regarding the power mismatch limit and system’s fast reserve constraints.

After validating the model from the aspects of UC and ED optimization, the simulation results of the multiparadigm approach for GS optimization in the Indonesian regulated electricity market and Java–Madura–Bali power system are analyzed. Figure 15 and Figure 16 show that the simulated GS scheme for the base scenario results in 716,390 MWh of electricity production over 24 h. The energy mix of the system is dominated by coal (68.8%), followed by gas (21.3%), hydro (9.1%), geothermal (0.5%), solar (0.2%), waste-to-energy/biomass (0.1%), and diesel (0.0%).

In Figure 17, the total production cost of electricity generation based on the simulated GS scheme is USD 21,290,150. This cost arises entirely from the fuel expenses of operating power plants, with no power purchases from independent power producers (IPPs). Given the total electricity production and the total production cost, the system’s cost of electricity under the GS scheme in this scenario is 2.97 cents/kWh. Additionally, the simulated generation scheduling scheme results in total carbon emissions of 478,900 tons of carbon emissions (TCO2e), as shown in Figure 18.

Based on the previous explanation, the proposed multiparadigm approach (MAS and SD) model for GS optimization has been successfully implemented in the Indonesian regulated electricity market and the Jamali power system. The model was validated by evaluating several constraints, including the power mismatch limit, spinning reserve, and fast reserve. The simulation results of this base scenario are compared to those of the carbon policy scenarios, considering carbon emission reductions.

4.2. Carbon Policy Scenarios

In this section, the multiparadigm approach for GS optimization in the Indonesian electricity market and the Jamali power system operation is performed with consideration of carbon policy objectives. The scenarios are categorized into three types: low, moderate, and high carbon emission reduction.

4.2.1. Low Carbon Emission Reduction

In this scenario, the simulation of GS optimization is conducted with the aim of reducing carbon emissions by 5000 TCO2e over a 24 h period. As shown in Figure 19, the simulated GS scheme for the carbon policy scenario with a low carbon emission reduction objective results in 716,390 MWh of electricity production over 24 h. The energy mix is predominantly composed of coal (68.3%), followed by gas (21.8%), hydro (9.1%), geothermal (0.5%), solar (0.2%), waste-to-energy/biomass (0.1%), and diesel (0.0%). Compared to the base scenario, electricity energy production from coal decreases by 3995 MWh to meet the carbon emission reduction target of 5000 TCO2e. Consequently, electricity energy production from gas increases by 3791 MWh, hydro by 40 MWh, and geothermal by 163 MWh.

Figure 20, Figure 21 and Figure 22 show the total energy production, total production cost, and total carbon emissions for the GS scheme under the low carbon emission reduction policy. Compared to the base scenario, the total production cost increases to USD 21,425,290 and the total carbon emission reduces to 473,900 TCO2e. As a result, the system’s cost of electricity rises to 2.99 cents/kWh.

4.2.2. Moderate Carbon Emission Reduction

In this scenario, the simulation of GS optimization is conducted with the aim of reducing carbon emissions by 10,000 TCO2e over a 24 h period. As shown in Figure 23, the simulated GS scheme for the carbon policy scenario with moderate carbon emission reduction objective results in 716,390 MWh of electricity production over 24 h. The energy mix is predominantly composed of coal (67.7%), followed by gas (22.4%), hydro (9.2%), geothermal (0.5%), solar (0.2%), waste-to-energy/biomass (0.1%), and diesel (0.0%). Compared to the base scenario, electricity energy production from coal decreases by 8059 MWh to meet the carbon emission reduction target of 10,000 TCO2e. Consequently, electricity energy production from gas increases by 7534 MWh, hydro by 202 MWh, and geothermal by 323 MWh.

Figure 24, Figure 25 and Figure 26 show the total energy production, total production cost, and total carbon emissions for the GS scheme under the low carbon emission reduction policy. Compared to the base scenario, the total production cost increases to USD 21,563,338 and the total carbon emission reduces to 468,900 TCO2e. As a result, the system’s cost of electricity rises to 3.01 cents/kWh.

4.2.3. High Carbon Emission Reduction

In this scenario, the simulation of GS optimization is conducted with the aim of reducing carbon emissions by 15,000 TCO2e over a 24 h period. As shown in Figure 27, the simulated GS scheme for the carbon policy scenario with a high carbon emission reduction objective results in 716,390 MWh of electricity production over 24 h. The energy mix is predominantly composed of coal (67.1%), followed by gas (23.0%), hydro (9.2%), geothermal (0.5%), solar (0.2%), waste-to-energy/biomass (0.1%), and diesel (0.0%). Compared to the base scenario, electricity energy production from coal decreases by 12,547 MWh to meet the carbon emission reduction target of 15,000 TCO2e. Consequently, electricity energy production from gas increases by 11,773 MWh, hydro by 372 MWh, and geothermal by 402 MWh.

Figure 28, Figure 29 and Figure 30 show the total energy production, total production cost, and total carbon emissions for the GS scheme under the low carbon emission reduction policy. Compared to the base scenario, the total production cost increases to USD 21,624,947 and the total carbon emission reduces to 463,900 TCO2e. As a result, the system’s cost of electricity rises to 3.02 cents/kWh.

4.2.4. Results Overview

In the previous section, several simulations of the proposed multiparadigm approach (MAS and SD) were performed, both on base scenarios and carbon policy scenarios, within the context of the Indonesian regulated electricity market and Java–Madura–Bali power system operation. The simulations were evaluated based on total electricity energy production, total production cost, and total carbon emission production. A summary of the simulation results is presented in

Table 6. Summary of simulation results.

Output Variables	Unit	Base	Carbon Policy (Low)	Carbon Policy (Moderate)	Carbon Policy (High)
Total electricity Energy production	MWh	716,390	716,390	716,390	716,390
Total production (fuel) cost	USD	21,290,150	21,425,290	21,563,338	21,624,947
Total carbon emission production	TCO2e	478,900	473,900	468,900	463,900
Carbon emission reduction	TCO2e	0	5000	10,000	15,000
Cost of electricity	cents/kWh	2.97	2.99	3.01	3.02

.

Linear regression analysis for sensitivity analysis is conducted to observe the dependency of carbon emissions reduction in carbon policy to the system’s cost of electricity. The results are presented in Figure 31. Based on the analysis, there is a positive correlation between emission reduction policy and the system cost of electricity. As emission reductions increase, the system cost of electricity also rises. The slope is calculated to be 0.017, indicating that for each 5000 TCO2e increase in emission reduction, the system cost of electricity increases by 0.017 cents/kWh. This linear equation is particularly beneficial for system operator and policymakers in the Indonesian regulated electricity market and Java–Madura–Bali power system operation.

5. Conclusions

This paper presented a multiparadigm approach for economical and low-carbon generation scheduling optimization in the Indonesian regulated electricity market and Java–Madura–Bali power system operation. The model was validated through UC and ED simulations in the base scenario. The simulation results indicate that the carbon policy scheme reduces the system’s carbon emissions while increasing the system’s cost of electricity. A linear equation for sensitivity analysis was derived to represent the relationship between carbon emission reduction and the incremental of system’s cost of electricity. Therefore, the multiparadigm approach can be considered a valuable tool for policymakers in the Indonesian regulated electricity market and power system operation with consideration to the impact of carbon emission reduction to the system’s cost of electricity. Given that the Java–Madura–Bali power system is undergoing a transformative shift towards renewable energy, further research is recommended to integrate renewable energies, such as in solar photovoltaic and wind power plants. Due to the limitation of this research—that it does not consider the power flow in transmission network and dynamic control of power plants—further studies that consider AC power flow and dynamic control system, such as the automatic voltage regulator (AVR), power system stabilizer (PSS), automatic generation control (AGC), and flexible AC transmission system (FACTS), are suggested to broaden the applicability of these findings and contribute to achieving clean energy transition in Indonesia.