A Fuzzy Unit Commitment Model for Enhancing Stability and Sustainability in Renewable Energy-Integrated Power Systems

Abstract

The increasing penetration of renewable energy sources (RESs), particularly solar photovoltaic (PV) sources, has introduced significant uncertainty into power system operations, challenging traditional scheduling models and threatening system reliability. This study proposes a Fuzzy Unit Commitment Model (FUCM) designed to address uncertainty in load demand, solar PV generation, and spinning reserve requirements by applying fuzzy linear programming techniques. The FUCM reformulates uncertain constraints using triangular membership functions and integrates them into a mixed-integer linear programming (MILP) framework. The model’s effectiveness is demonstrated through two case studies: a 30-generator test system and a national-scale power system in Thailand comprising 171 generators across five service zones. Simulation results indicate that the FUCM consistently produces stable scheduling solutions that fall within deterministic upper and lower bounds. The model improves reliability metrics, including reduced loss-of-load probability and minimized load deficiency, while maintaining acceptable computational performance. These results suggest that the proposed approach offers a practical and scalable method for unit commitment planning under uncertainty. By enhancing both operational stability and economic efficiency, the FUCM contributes to the sustainable management of RES-integrated power systems.

1. Introduction and Literature Review

The global transition toward low-carbon energy systems has accelerated the integration of renewable energy sources (RESs), such as solar photovoltaic (PV) sources, into national power grids. While this shift contributes to environmental sustainability, it introduces significant operational uncertainties due to the intermittent and non-dispatchable nature of RES generation. In countries like Thailand, where solar PV capacity exceeded 2300 MW across more than 500 plants as of 2020 [1], the variability in solar output challenges grid stability and complicates generation planning. This challenge is further compounded by the increasing adoption of electric vehicles (EVs) and the strategic integration of energy storage systems (ESSs), both of which introduce new dynamics and uncertainties into grid operations [2,3,4].

Traditionally, deterministic unit commitment (DUC) models have been used to schedule generation units. These models assume precise forecasts for load and generation and fail to capture the stochastic nature of RES output and dynamic reserve requirements, resulting in suboptimal schedules and reliability risks under uncertainty [5]. However, the growing integration of RESs such as wind and solar, combined with the rise in EV charging demand and ESS deployment, has exposed significant limitations in deterministic methods [6,7,8].

To address these limitations, stochastic unit commitment (SUC) models have been developed to incorporate uncertainty through scenario-based optimization. Takriti et al. [6] introduced one of the earliest SUC models using scenario-based load forecasts and Lagrangian relaxation. Building on this foundation, subsequent studies incorporated uncertainties from wind power and price volatility using probabilistic and chance-constrained formulations [9,10,11,12]. Recent work by Doubleday et al. [13] proposed an SUC model supporting high shares of solar PV, while Zhu et al. [14] introduced a security-constrained SUC under extreme wind scenarios. Mena et al. [15] extended SUC frameworks into multi-objective domains, balancing emissions, curtailment, and cost, while Zhang et al. [16] addressed spatiotemporal uncertainty correlation with robust optimization. Notably, a comparative review by Pawar et al [17] highlights the importance of hybrid approaches in modern grids for integrating renewable sources effectively.

While effective, SUC models are often computationally intensive and depend heavily on scenario quality, limiting scalability. Advances in SUC have sought to improve grid resilience through new indices such as the rate of frequency change and demand response programs for extreme events [18,19,20]. Emerging studies are also exploring artificial intelligence techniques, such as large language models (LLMs), to enhance multi-scenario optimization under uncertainty, particularly for wind generation [21]. Further, optimization of reserve exchange between areas through spatial correlation analysis has been shown to strengthen system reliability with high RES penetration [20].

Fuzzy mathematical programming (FMP) offers an alternative that models imprecise variables using fuzzy sets and membership functions. Zimmermann [22] established the foundation for this technique, which has since been applied in energy system optimization. In power systems, Truong and Jeenanunta [23] used fuzzy MILP to address fuel price uncertainty, and Venkatesh et al. [24] applied fuzzy constraints in daily UC with wind power. Prior fuzzy unit commitment studies focused primarily on small-scale systems or a single uncertainty type, leaving a gap in terms of comprehensive models for national-scale systems with multiple uncertainties [25,26,27]. The FUCM differs fundamentally from scenario-based stochastic approaches. A stochastic unit commitment explicitly enumerates uncertainties via a set of scenarios, which leads to very large optimization problems as the system size grows. In contrast, the fuzzy method uses membership bands to represent uncertainty directly in constraints, avoiding scenario enumeration. This tends to reduce the problem size for large systems. However, it represents uncertainty qualitatively through bounds, whereas stochastic models encode explicit probability distributions.

Recent research underscores the critical role of energy storage systems in improving flexibility and minimizing renewable curtailment. Nasab et al. [28] proposed a robust UC model incorporating both pumped-storage hydropower (PSH) and renewable resources, while Naval et al [29] emphasized optimal PSH scheduling under high solar penetration. Wu et al. [30] and Li et al. [31] incorporated battery energy storage systems (BESSs) to mitigate variability in renewables. Fuzzy UC models integrating RESs, EV charging, load uncertainty, and ESSs, including PSH and BESSs, have also been applied to Thailand’s system, demonstrating reductions in Loss-of-Load Probability (LOLP) and expected energy not supplied (EENS) [32,33]. Recent advancements in stochastic UC further show the importance of addressing security constraints in systems with EVs, ESSs, and flexible loads [34].

Despite these advancements, a gap remains in the development of scalable, computationally efficient models that integrate diverse uncertainties and ESS technologies. The FUCM proposed in this research addresses this gap by leveraging fuzzy logic within an MILP framework validated against real-world scenarios. Importantly, Hashem et al. [35] have shown that accurately capturing uncertainty propagation in renewable-dominated systems is critical for operational reliability, further motivating this study’s approach.

This research introduces a Fuzzy Unit Commitment Model (FUCM) that integrates uncertainties in load demand, solar PV generation, and spinning reserve requirements into a unified fuzzy MILP framework. Using triangular membership functions, the FUCM transforms fuzzy constraints into linear forms and incorporates ESS considerations. The model is validated on both a benchmark test system and large-scale national power system, evaluating performance across multiple demand scenarios and 100 stochastic simulations. Evaluation metrics include total production cost, LOLP, and EENS.

This study makes four contributions: (1) the development of a scalable fuzzy MILP model for national-scale unit commitment with high RES penetration; (2) integrated modeling of renewable generation, load demand, and reserve uncertainties using fuzzy logic; (3) demonstration that the fuzzy model improves reliability while maintaining cost efficiency compared to deterministic benchmarks; and (4) provision of a decision-support tool for sustainable power system operation under uncertainty.

The FUCM advances the state of the art in several ways. Unlike previous fuzzy models that typically address a single uncertainty or small test systems, the proposed model simultaneously integrates multiple uncertainties at a national scale. It achieves relatively fast solution times through linear reformulation of fuzzy constraints. The model’s practical relevance is demonstrated through application to Thailand’s grid, where it can guide the setting of spinning reserve requirements in response to variable solar output, a key consideration for operators and policymakers. This combination of broad uncertainty modeling, scalability, and direct operational relevance defines the novelty of the FUCM approach.

2. Mathematical Model Formulation

2.1. Deterministic Unit Commitment Model (DUCM)

The Deterministic Unit Commitment Model (DUCM) addresses a foundational optimization problem in power system operations, wherein the scheduling of generating units is performed over a specified planning horizon to ensure a reliable and cost-effective electricity supply. The primary objective of the DUCM is to determine the on/off status and corresponding power output of each generator at discrete time intervals, subject to a variety of operational and system-wide constraints. The objective function is typically designed to minimize total generation costs, which include startup costs, shutdown costs, and variable production costs [36].

Key constraints embedded in the model include generator operational limits (minimum and maximum output), system-wide power balance requirements to match total generation with demand in each time period, and reserve margin constraints to accommodate unforeseen fluctuations in demand or generation. Decision variables in the DUCM encompass binary variables representing generator commitment status and continuous variables representing generation output levels.

Traditionally, DUCM frameworks have been applied to power systems composed entirely of conventional thermal generators. In this study, the model is extended to incorporate renewable energy sources, specifically solar photovoltaic (PV) systems, alongside conventional units. The integration of RESs introduces additional complexity, particularly in the objective function and power balance equations, due to the variable and non-dispatchable nature of renewable output.

To estimate renewable generation, this study employs forecasted output from installed solar PV systems under the assumption that all available PV generation is utilized within the system. This simplifies the modeling process by excluding curtailment and storage considerations. The resulting DUCM formulation provides a baseline for comparison with the proposed fuzzy-based model, allowing for evaluation of system performance under deterministic versus uncertainty-aware frameworks.

The subsequent section presents the complete mathematical formulation of the deterministic unit commitment model, including all notations, decision variables, and constraints.

2.1.1. Notations

$\begin{array}{cc}T\hfill & \mathrm{is}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{time}\mathrm{periods}\mathrm{of}\mathrm{planning}.\hfill \\ G\hfill & \mathrm{is}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{unit}\mathrm{generators}.\hfill \\ L\hfill & \mathrm{is}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{transmission}\mathrm{lines}\mathrm{in}\mathrm{the}\mathrm{system}.\hfill \\ Z\hfill & \mathrm{is}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{service}\mathrm{zones}.\hfill \\ G_j\hfill & \mathrm{is}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{unit}\mathrm{generators}\mathrm{in}\mathrm{zone}j,\mathrm{where}j\in Z.\hfill \\ s_u\hfill & \mathrm{is}\mathrm{the}\mathrm{startup}\cos \mathrm{t}\mathrm{of}\mathrm{unit}u,\mathrm{where}u\in G.\hfill \\ c_u\hfill & \mathrm{is}\mathrm{the}\mathrm{per}\mathrm{unit}\mathrm{fuel}\cos \mathrm{t}\mathrm{of}\mathrm{unit}u\hfill \\ \phi \hfill & \mathrm{is}\mathrm{the}\mathrm{production}\cos \mathrm{t}\mathrm{of}\mathrm{renewable}\mathrm{energy}.\hfill \\ d_j^t\hfill & \mathrm{is}\mathrm{the}\mathrm{demand}\mathrm{of}\mathrm{zone}j\mathrm{in}\mathrm{time}\mathrm{period}t,\mathrm{where}t\in T.\hfill \\ {\underline{p}}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{minimum}\mathrm{generation}\mathrm{of}\mathrm{unit}u.\hfill \\ {\overline{p}}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{maximum}\mathrm{generation}\mathrm{of}\mathrm{unit}u.\hfill \\ {\overline{TR}}_l^t(i,j)\hfill & \mathrm{is}\mathrm{the}\mathrm{maximum}\mathrm{transportation}\cos \mathrm{t}\mathrm{in}\mathrm{transmission}\mathrm{line}l\hfill \\ & \mathrm{that}\mathrm{connects}\mathrm{zone}i\mathrm{to}\mathrm{zone}j\mathrm{in}\mathrm{time}\mathrm{period}t.\hfill \\ int{u}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{condition}\mathrm{number}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ int{up}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{uptime}\mathrm{number}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ int{down}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{downtime}\mathrm{number}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ R{U}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{ramp}\text{-}\mathrm{up}\mathrm{rate}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ R{D}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{ramp}\text{-}\mathrm{down}\mathrm{rate}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ M{U}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{minimum}\mathrm{uptime}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \\ M{D}_u\hfill & \mathrm{is}\mathrm{the}\mathrm{minimum}\mathrm{downtime}\mathrm{of}\mathrm{unit}u\mathrm{in}\mathrm{the}\mathrm{generator}\mathrm{set}.\hfill \end{array}$

2.1.2. Decision Variables

$\begin{array}{cc}{p}_u^t\hfill & \mathrm{is}\mathrm{the}\mathrm{production}\mathrm{power}\mathrm{from}\mathrm{unit}u\mathrm{in}\mathrm{time}\mathrm{period}t.\hfill \\ T{R}_l^t(i,j)\hfill & \mathrm{is}\mathrm{the}\mathrm{transportation}\cos \mathrm{t}\mathrm{of}\mathrm{transmission}\mathrm{power}\mathrm{line}l\hfill \\ & \mathrm{that}\mathrm{connects}\mathrm{zone}i\mathrm{to}\mathrm{zone}j\mathrm{in}\mathrm{time}\mathrm{period}t.\hfill \end{array}$

$\begin{array}{c}{y}_u^t=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{unit}u\mathrm{is}\mathrm{started}\text{-}\mathrm{up}\mathrm{in}\mathrm{time}\mathrm{period}t,\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \\ u_u^t=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{unit}u\mathrm{in}\mathrm{time}\mathrm{period}t\mathrm{is}\mathrm{turned}\mathrm{on},\hfill \\ 0\hfill & \mathrm{if}\mathrm{unit}u\mathrm{in}\mathrm{time}\mathrm{period}t\mathrm{is}\mathrm{turned}\mathrm{off}.\hfill \end{array}\right.\hfill \\ z_u^t=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{unit}u\mathrm{is}\mathrm{shutdown}\mathrm{in}\mathrm{time}\mathrm{period}t,\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \end{array}$

2.1.3. Extension of Unit Commitment to Include Renewable Energy

Objective: minimize the total cost.

$$z=\sum _{t\in T}\sum _{u\in G}{s}_u{y}_u^t+\sum _{t\in T}\sum _{u\in G}{c}_u{p}_u^t+\sum _{i,j\in Z}\sum _{t\in T}\sum _{l\in L}T{R}_l^t(i,j)+\phi \sum _{j\in Z}\sum _{t\in T}{R}_j^t.$$

(1)

The cost of the power system includes the startup cost, production cost, transmission cost, and renewable cost.

The system is subject to the following constraints.

• Power balance constraint:

  $$\sum _{u\in G_j}{p}_u^t+\sum _{i\in Z,i\ne j}\sum _{l\in L_j,}T{R}_l^t(i,j)-\sum _{i\in Z,i\ne j}\sum _{l\in L_j}T{R}_l^t\left(j,i\right)\ge d_j^t,\forall t\in T,j\in Z.$$

  (2)
    The total of power generation and transmission power must exceed the load demand in each zone and each time period.
• Generator limit constraint:

  $$u_u^t{\underline{p}}_u\le p_u^t\le u_u^t{\overline{p}}_u,\forall u\in G,t\in T.$$

  (3)
    This constraint shows the boundary of the operation for each conventional generator when it operates.
• Spinning reserve constraint:

  $$\sum _{u\in G}({\overline{p}}_u{u}_u^t-p_u^t)\ge \beta ,\forall t\in T.$$

  (4)
    The spinning reserve constraint ensures that the power system maintains sufficient reserve capacity to respond to unexpected fluctuations in load or sudden generation outages during each scheduling period. This constraint establishes a direct relationship between the total scheduled generation and the required minimum reserve margin. Among the various approaches used to define reserve requirements, a widely accepted method is to base the reserve level on the capacity of the single largest generator in the system.
    In this study, the reserve requirement parameter, denoted as $\beta$, is defined as the sum of the maximum capacities of the largest conventional generator and the largest renewable energy generator, specifically a solar photovoltaic (PV) system. This formulation provides a conservative estimate, ensuring that the system can withstand the simultaneous loss of significant generating units while maintaining operational reliability.
• Transportation limit constraint:

  $$T{R}_l^t\left(i,j\right)\le {\overline{TR}}_l^t\left(i,j\right),\forall l\in L,t\in T,i,j\in Z,$$

  (5)

  $$\sum _{i\in Z,i\ne j}\sum _{l\in L_j,}T{R}_l^t(i,j)\le \sum _{u\in G_j}{p}_u^t,\forall j\in Z,t\in T.$$

  (6)
    The first transmission constraint is the limitation of the transmission line. The second constraint shows that the total transmission power into each zone must be less than or equal to the total production in that zone.
• Unit status constraint:

  $$u_u^{t+1}-u_u^t\le y_u^{t+1},\forall u\in G,t\in T,$$

  (7)

  $$z_u^{t+1}=y_u^{t+1}+u_u^t-u_u^{t+1},\forall u\in G,t\in T$$

  (8)
    The unit status constraint defines the relationship between startup, shutdown, and operational status across consecutive time periods. A startup occurs when a unit transitions from offline in the current period to online in the next period, resulting in a startup status value of one. If the unit remains in the same state or shuts down, the startup status is zero, as the objective function minimizes unnecessary startups. The shutdown status reflects the opposite transition, from online to offline, and is calculated based on the difference between the unit status and startup status over adjacent periods.
• Initial condition constraint:

  $$\mathrm{if}int{u}_u>0,\mathrm{then}{y}_u^1=0\mathrm{and}{z}_u^1+u_u^1=1,\forall u\in G,$$

  (9)

  $$\mathrm{if}int{u}_u=0,\mathrm{then}{z}_u^1=0\mathrm{and}{y}_u^1=u_u^1,\forall u\in G.$$

  (10)
    The initial condition constraint connects the unit’s final status from the previous day to its status, startup, and shutdown decisions in the first period of the current day. If the unit was online at the end of the previous day, the startup status for the first period is zero. Conversely, if the unit was offline, the shutdown status for the first period is zero.
• Ramp rate constraint:

  $$p_u^{t+1}-p_u^t\le R{U}_u,\forall u\in G,t\in T,$$

  (11)

  $$p_u^t-p_u^{t+1}\le R{D}_u,\forall u\in G,t\in T.$$

  (12)
    The ramp rate constraint is a limitation on increases and decreases in production in each generator calculated based on the difference between the current period and the next period.
• Minimum uptime/downtime constraint:

  $$\mathrm{if}int{up}_u>0\mathrm{and}int{up}_u<{MU}_u,\mathrm{then}\underset{m=1}{\sum ^{M{U}_u-int{up}_u}}{u}_u^m\le M{U}_u-int{up}_u,\forall u\in G,$$

  (13)

  $$\mathrm{if}int{dw}_u>0\mathrm{and}int{dw}_u<{MD}_u,\mathrm{then}\underset{m=1}{\sum ^{M{D}_u-int{dw}_u}}{u}_u^m=0,\forall u\in G,$$

  (14)

  $$\underset{m=t-M{U}_u+1}{\sum ^t}{y}_u^m\le u_u^t,\forall u\in G,t>M{U}_u,$$

  (15)

  $$\underset{m=t-M{D}_u+1}{\sum ^t}{z}_u^m\le 1-u_u^t,\forall u\in G,t>M{D}_u.$$

  (16)
    The minimum time constraint is a limitation on the number of consecutive operations and shutdown time of each unit, which must be less than or equal to the minimum uptime and minimum downtime, respectively. The cumulative operation and shutdown time of the previous day are also considered by these constraints.

2.2. Mixed-Integer Linear Programming Formulation for Fuzzy Unit Commitment Model (FUCM)

The fuzzy unit commitment model incorporates uncertainty by defining membership functions for constraints involving fuzzy variables. In this study, renewable energy output and reserve requirements are treated as fuzzy parameters. Accordingly, their associated constraints are reformulated as fuzzy constraints with corresponding membership functions.

For each fuzzy constraint, a membership function quantifies the degree of satisfaction on a scale from 0 to 1. Triangular membership functions are selected to represent uncertain ranges. This type of function is defined by a lower bound, a point of full membership at the peak, and an upper bound. Triangular functions are preferred because they are piecewise linear, allowing straightforward reformulation as linear constraints within a mixed-integer linear programming framework. In contrast, trapezoidal functions require additional parameters, and Gaussian functions introduce nonlinear complexity. The triangular form achieves a balance between computational efficiency and sufficient accuracy when modeling bounded uncertainties.

The first such constraint is the power balance constraint. Due to uncertainty in renewable generation, the net load demand is also uncertain. It is assumed that all renewable generation is fully consumed within the system. As a result, the net load demand lies between the total load and the load minus the renewable output. A membership function is defined using ${\mu }_d\left(x_j^t\right)$, and the remaining load not covered by conventional generation. The membership value is 1 when the remaining requirement is less than or equal to the minimum renewable output and 0 when it exceeds the maximum. For values between the minimum and maximum, the membership function decreases linearly from 1 to 0. The formulation of this membership function is presented below.

$$\begin{array}{c}{\mu }_d\left(x_j^t\right)=\left\{\begin{array}{cc}1\hfill & R\left(x_j^t\right)\le R{min}^t,\hfill \\ {\displaystyle \frac{R{max}^t-R\left(x_j^t\right)}{R{max}^t-R{min}^t}}\hfill & R{min}^t<R\left(x_j^t\right)\le R{max}^t,\hfill \\ 0\hfill & R\left(x_j^t\right)>R{max}^t\hfill \end{array}\right.\hfill \end{array}$$

(17)

where $x_j^t$ is the vector of the decision variables at time t for zone j and

$$R\left(x_j^t\right)=d_j^t-\left(\sum _{u\in G_j}{p}_u^t+\sum _{i\in Z,i\ne j}\sum _{l\in L_j,}T{R}_l^t(i,j)-\sum _{i\in Z,i\ne j}\sum _{l\in L_j}T{R}_l^t\left(j,i\right)\right).$$

Similarly, the spinning reserve constraint accounts for the relationship between renewable generation uncertainty and reserve requirements. Higher uncertainty due to renewable penetration necessitates greater reserve capacity to maintain system reliability. In this study, the minimum reserve requirement is set equal to the capacity of the largest conventional generator, denoted as $\beta$, which serves as the lower bound $\left(Remin\right)$. The upper bound $\left(Remax\right)$ is defined by adding the installed renewable capacity to this minimum requirement, thereby covering potential variability in renewable output. The membership function associated with this constraint is presented in the following equation.

$$\begin{array}{c}{\mu }_{Re}\left(x^t\right)=\left\{\begin{array}{cc}0\hfill & Re\left(x^t\right)\le Re{min}^t,\hfill \\ {\displaystyle \frac{Re\left(x^t\right)-Re{min}^t}{Re{max}^t-Re{min}^t}}\hfill & Re{min}^t<Re\left(x^t\right)\le Re{max}^t,\hfill \\ 1\hfill & Re\left(x^t\right)>R{max}^t\hfill \end{array}\right.\hfill \end{array}$$

(18)

where $x^t$ is the vector of the decision variables at time t and

$$Re\left(x^t\right)=\sum _{u\in G}({\overline{p}}_u{u}_u^t-p_u^t).$$

The final fuzzy constraint corresponds to the objective function, which represents the total production and transmission cost. This cost varies with the level of renewable energy penetration. The lowest possible total cost is associated with maximum renewable generation, while the highest cost results from a minimal renewable contribution. Accordingly, the lower bound of the objective function, denoted as $z_{lower}$, is derived from the deterministic unit commitment solution with the highest renewable output. The upper bound, $z_{upper}$, is obtained from the case with the lowest renewable output. Since the fuzzy model aims to minimize total cost, the membership function is defined as a linear decreasing function that equals 0 when the cost exceeds the upper bound.

$$\begin{array}{c}{\mu }_z\left(x\right)=\left\{\begin{array}{cc}1\hfill & z\left(x\right)\le z_{lower},\hfill \\ {\displaystyle \frac{z_{upper}-z\left(x\right)}{z_{upper}-z_{lowwr}}}\hfill & z_{lower}<z\left(x\right)\le z_{upper},\hfill \\ 0\hfill & z\left(x\right)>z_{upper}.\hfill \end{array}\right.\hfill \end{array}$$

(19)

These fuzzy constraints are reformulated as linear inequalities using the max–min fuzzy programming method. The fuzzy unit commitment model solves two deterministic subproblems that represent the extreme cases in order to determine the lower and upper bounds of total system cost. A max–min operator is then applied to compute a compromise solution that balances cost minimization and constraint satisfaction under uncertainty. The formulation of the fuzzy unit commitment model as a mixed-integer linear program is described in the following.

The max–min operator is applied to all fuzzy constraints to obtain the optimal solution. A linear model of the fuzzy unit commitment is shown below.

$$\begin{array}{cc}\mathrm{Maximize}\hfill & \lambda \hfill \\ \mathrm{Subject}\mathrm{to}\hfill & \lambda \le {\mu }_z\left(x\right),\hfill \\ \hfill & \lambda \le {\mu }_d\left(x_j^t\right),\forall t\in T,j\in Z,\hfill \\ \hfill & \lambda \le {\mu }_{Re}\left(x^t\right),\forall t\in T,\hfill \\ \hfill & x\ge 0\hfill \\ \hfill & \mathrm{and}\mathrm{Equations}\left(3\right),\left(5\right)–\left(16\right).\hfill \end{array}$$

(20)

The proposed fuzzy model can be reformulated as a mixed integer linear model as follows. From the membership function of the power balance constraint in (17) and the constraint in the proposed fuzzy model, the following inequalities are obtained.

$$\lambda \le {\displaystyle \frac{R{max}^t-\left(d_j^t-\left({\displaystyle \sum _{u\in G_j}}{p}_u^t+{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j,}}T{R}_l^t(i,j)-{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j}}T{R}_l^t\left(j,i\right)\right)\right)}{R{max}^t-R{min}^t}}$$

$$\left(\sum _{u\in G_j}{p}_u^t+\sum _{i\in Z,i\ne j}\sum _{l\in L_j,}T{R}_l^t(i,j)-\sum _{i\in Z,i\ne j}\sum _{l\in L_j}T{R}_l^t\left(j,i\right)\right)-d_j^t\ge \lambda \left(R{max}^t-R{min}^t\right)-R{max}^t$$

$$\sum _{u\in G_j}{p}_u^t+\sum _{i\in Z,i\ne j}\sum _{l\in L_j,}T{R}_l^t(i,j)-\sum _{i\in Z,i\ne j}\sum _{l\in L_j}T{R}_l^t(j,i)\ge d_j^t-\left[(1-\lambda )R{max}^t+\lambda R{min}^t\right]$$

(21)

Similar to the power balance constraint, the reserve constraints and their membership function in (18) are also transformed into linear constraints:

$$\lambda \le {\displaystyle \frac{{\displaystyle \sum _{u\in G}}({\overline{p}}_u{u}_u^t-p_u^t)-Re{min}^t}{Re{max}^t-Re{min}^t}}$$

$$\sum _{u\in G}({\overline{p}}_u{u}_u^t-p_u^t)-Re{min}^t\ge \lambda \left(Re{max}^t-Re{min}^t\right)$$

$$\sum _{u\in G}({\overline{p}}_u{u}_u^t-p_u^t)\ge \lambda \left(Re{max}^t-Re{min}^t\right)+Re{min}^t$$

$$\sum _{u\in G}({\overline{p}}_u{u}_u^t-p_u^t)\ge (1-\lambda )Re{min}^t+\lambda Re{max}^t$$

(22)

The fuzzy constraint of the objective function and its membership function in (19) are also transformed into a linear constraint as follows:

$$\lambda \le {\displaystyle \frac{z_{upper}-z}{z_{upper}-z_{lower}}}$$

$$\lambda (z_{upper}-z_{lower})\le z_{upper}-z$$

$$z\le (1-\lambda )z_{upper}+\lambda z_{lower}$$

$$\sum _{t\in T}\sum _{u\in G}{s}_u{y}_u^t+\sum _{t\in T}\sum _{u\in G}{c}_u{p}_u^t+\sum _{i,j\in Z}\sum _{t\in T}\sum _{l\in L}T{R}_l^t(i,j)+\phi \sum _{j\in Z}\sum _{t\in T}{R}_j^t\le (1-\lambda )z_{upper}+\lambda z_{lower}$$

(23)

The deterministic problem of the two extreme cases ($\lambda$ is equal to 0 and 1) must be solved to obtain the boundary values of the membership function ($z_{upper}$ and $z_{lower}$).

• Model 1: Lower-Bound Model (case $\lambda =0$)

$$\begin{array}{cc}\hfill \mathrm{Maximize}& z_{lower}={\displaystyle \sum _{t\in T}}{\displaystyle \sum _{u\in G}}{s}_u{y}_u^t+{\displaystyle \sum _{t\in T}}{\displaystyle \sum _{u\in G}}{c}_u{p}_u^t+{\displaystyle \sum _{i,j\in Z}}{\displaystyle \sum _{t\in T}}{\displaystyle \sum _{l\in L}}T{R}_l^t(i,j)+\phi {\displaystyle \sum _{j\in Z}}{\displaystyle \sum _{t\in T}}{R}_j^t.\hfill \\ \hfill \\ \hfill \mathrm{Subject}\mathrm{to}& {\displaystyle \sum _{u\in G_j}}{p}_u^t+{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j,}}T{R}_l^t(i,j)-{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j}}T{R}_l^t\left(j,i\right)+R{max}^t\ge d_j^t\hfill \\ \hfill & \forall t\in T,j\in Z,\hfill \\ \hfill & {\displaystyle \sum _{u\in G}}({\overline{p}}_u{u}_u^t-p_u^t)\ge R{min}^t\hfill \\ \hfill & \mathrm{and}\mathrm{Equations}\left(3\right),\left(5\right)–\left(16\right).\hfill \end{array}$$

(24)

• Model 2: Upper-Bound Model (case $\lambda =1$)

$$\begin{array}{cc}\hfill \mathrm{Maximize}& z_{upper}={\displaystyle \sum _{t\in T}}{\displaystyle \sum _{u\in G}}{s}_u{y}_u^t+{\displaystyle \sum _{t\in T}}{\displaystyle \sum _{u\in G}}{c}_u{p}_u^t+{\displaystyle \sum _{i,j\in Z}}{\displaystyle \sum _{t\in T}}{\displaystyle \sum _{l\in L}}T{R}_l^t(i,j)+\phi {\displaystyle \sum _{j\in Z}}{\displaystyle \sum _{t\in T}}{R}_j^t.\hfill \\ \hfill \\ \hfill \mathrm{Subject}\mathrm{to}& {\displaystyle \sum _{u\in G_j}}{p}_u^t+{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j,}}T{R}_l^t(i,j)-{\displaystyle \sum _{i\in Z,i\ne j}}{\displaystyle \sum _{l\in L_j}}T{R}_l^t\left(j,i\right)+R{min}^t\ge d_j^t\hfill \\ \hfill & \forall t\in T,j\in Z,\hfill \\ \hfill & {\displaystyle \sum _{u\in G}}({\overline{p}}_u{u}_u^t-p_u^t)\ge R{max}^t\hfill \\ \hfill & \mathrm{and}\mathrm{Equations}\left(3\right),\left(5\right)–\left(16\right).\hfill \end{array}$$

(25)

The objective values from Model 1 (lower-bound model) and Model 2 (upper-bound model) are assigned to $z_{lower}$ and $z_{upper}$, respectively, in the fuzzy unit commitment.

• Model 3: Fuzzy Model

$$\begin{array}{cc}\hfill \mathrm{Maximize}& \lambda \hfill \\ \hfill \mathrm{Subject}\mathrm{to}& \mathrm{Equations}\left(3\right),\left(5\right)–\left(16\right)\mathrm{and}\left(21\right)–\left(23\right).\hfill \end{array}$$

(26)

3. Case Study Analysis and Results

To evaluate the effectiveness of the proposed fuzzy unit commitment model (FUCM), two case studies were conducted: one involving a small-scale power system and the other applying the model to Thailand’s national power grid. The small-scale case was designed to test the functionality of the model under controlled conditions using a simplified system, while the large-scale case assesses the scalability and practical applicability of the model in a real-world context, particularly under scenarios of solar PV integration.

3.1. Validation on a Small-Scale Power System

The small-scale test system represents a scaled-down version of Thailand’s power grid. It comprises 30 conventional generators with a total installed capacity of 9475.88 MW. These units are drawn from various regions to reflect a diverse mix of generation technologies. Key operational parameters for each generator, including startup costs, production costs, and maximum output capacity, are summarized in

Table 1. Characteristics of conventional generators in the small-scale system.

Name	Type	Initial Product (MW)	Initial Uptime (Periods)	Initial Down Time (Periods)	Minimum Uptime (Periods)	Minimum Down Time (Periods)	Minimum Generation (MW)	Maximum Generation (MW)	Ramp Rate Uptime (MW/minute)	Ramp Rate Downtime (MW/minute)	Start Cost (THB)	Fuel Cost (THB)
BLCP-T1	Thermal	650	24	0	12	12	161	673.25	450	450	1,484,255	137.9183
BLCP-T2	Thermal	650	24	0	12	12	161	673.25	450	450	1,484,255	137.9183
BPK-T1	Thermal	300	24	0	12	12	300	526.5	150	150	627,676	406.6576
BPK-T2	Thermal	300	24	0	12	12	300	526.5	150	150	627,676	406.6576
BPK-T3	Thermal	300	24	0	12	12	300	576	150	150	627,676	406.6576
BPK-T4	Thermal	0	0	24	12	12	300	576	150	150	627,676	406.6576
RB-T1	Thermal	300	24	0	12	12	300	685	1110	1110	627,676	424.3366
RB-T2	Thermal	0	0	24	12	12	300	685	1110	1110	627,676	424.3366
KA-T1	Thermal	0	0	24	12	12	145	315	204	204	627,676	440.6814
KN-T1	Thermal	70	24	0	12	12	50	75	40.5	25.5	627,676	186.6475
KN-T2	Thermal	0	0	24	12	12	60	75	40.5	24.3	627,676	186.6475
MM-T4	Thermal	140	24	0	6	6	90	150	60	60	627,676	51.16874
MM-T5	Thermal	140	24	0	6	6	90	150	60	60	627,676	51.16874
MM-T6	Thermal	140	24	0	6	6	90	150	60	60	627,676	51.16874
MM-T7	Thermal	140	24	0	6	6	90	150	60	60	627,676	51.16874
MM-T8	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
MM-T9	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
MM-T10	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
MM-T11	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
MM-T12	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
MM-T13	Thermal	285	24	0	6	6	150	300	75	75	627,676	51.16874
SB-T1	GasTur	0	0	24	12	12	110	186	90	90	627,676	409.4488
SB-T2	GasTur	0	0	24	12	12	110	186	90	90	627,676	409.4488
SB-T3	GasTur	0	0	24	12	12	170	265	300	300	627,676	409.4488
SB-T4	GasTur	0	0	24	12	12	170	265	300	300	627,676	409.4488
SB-T5	GasTur	0	0	24	12	12	170	294	300	300	627,676	409.4488
NPO-C11	GasCom	80	24	0	6	6	70	124.96	240	240	3785	272.2742
NPO-C12	GasCom	80	24	0	6	6	70	123.71	240	240	3785	272.2742
NPO-C21	GasCom	80	24	0	6	6	70	120.73	240	240	3785	272.2742
NPO-C22	GasCom	80	24	0	6	6	25	123.98	240	240	3785	272.2742

.

The unit commitment problem is modeled over a 24 h horizon, divided into 48 half-hour intervals. Period 1 begins at 00:00 (midnight), with subsequent periods advancing in 30-minute increments, ending with period 48 at 23:30. Load demand in this system is proportionally scaled from the full-sized national grid while maintaining the original ratio between total demand and installed capacity. To capture temporal and seasonal variability, the demand is categorized into seven representative profiles: winter weekday, winter weekend, summer weekday, summer weekend, rainy weekday, rainy weekend, and long holiday. The maximum peak demand across all profiles is approximately 8100 MW. Daily demand profiles for some groups are illustrated in Figure 1.

Solar PV generation is incorporated into the system with a peak capacity of 550 MW. Generation scenarios for each time period are constructed using a normal distribution based on forecasted solar irradiance data. Two distinct seasonal profiles are considered: the rainy season and the non-rainy season. For each seasonal group, 100 stochastic solar PV generation scenarios are created to reflect variability in solar output. Figure 2 presents sample trajectories from five representative scenarios in both seasonal conditions.

To solve the fuzzy unit commitment model, key fuzzy parameters must be defined. In this study, both fixed and variable production costs of solar energy are assumed to be 0, and all solar photovoltaic (PV) output is considered fully utilized. Consequently, the level of solar PV generation directly influences the total production cost of the system. The minimum and maximum solar PV outputs in each time period (t), denoted as $R{min}^t$ and $R{max}^t$, are presented in

Table 2. Lower and upper bounds of solar PV output (MW) for each time period.

Time Period Starting Time	Solar Min ($\mathit{R}{\mathit{min}}^{\mathit{t}}$)	Solar Max ($\mathit{R}{\mathit{max}}^{\mathit{t}}$)	Time Period Starting Time	Solar Min ($\mathit{R}{\mathit{min}}^{\mathit{t}})$	Solar Max ($\mathit{R}{\mathit{max}}^{\mathit{t}}$)	Time Period Starting Time	Solar Min ($\mathit{R}{\mathit{min}}^{\mathit{t}}$)	Solar Max ($\mathit{R}{\mathit{max}}^{\mathit{t}}$)
12:00 AM	0	0	8:00 AM	30.84	246.69	4:00 PM	25.46	203.65
12:30 AM	0	0	8:30 AM	40.23	321.86	4:30 PM	16.11	128.88
1:00 AM	0	0	9:00 AM	48.55	388.38	5:00 PM	7.96	63.70
1:30 AM	0	0	9:30 AM	55.45	443.63	5:30 PM	2.63	21.04
2:00 AM	0	0	10:00 AM	61.34	490.74	6:00 PM	0.40	3.20
2:30 AM	0	0	10:30 AM	65.13	521.03	6:30 PM	0.01	0.04
3:00 AM	0	0	11:00 AM	67.41	539.24	7:00 PM	0	0
3:30 AM	0	0	11:30 AM	68.41	547.24	7:30 PM	0	0
4:00 AM	0	0	12:00 PM	68.24	545.95	8:00 PM	0	0
4:30 AM	0	0	12:30 PM	66.96	535.70	8:30 PM	0	0
5:00 AM	0	0	1:00 PM	64.84	518.75	9:00 PM	0	0
5:30 AM	0.02	0.18	1:30 PM	61.31	490.48	9:30 PM	0	0
6:00 AM	0.73	5.85	2:00 PM	56.13	449.01	10:00 PM	0	0
6:30 AM	4.48	35.82	2:30 PM	50.00	400.01	10:30 PM	0	0
7:00 AM	11.79	94.29	3:00 PM	42.79	342.29	11:00 PM	0	0
7:30 AM	21.14	169.14	3:30 PM	34.33	274.64	11:30 PM	0	0

.

The minimum spinning reserve requirement, $Remin$, is set at 800 MW, equivalent to the capacity of the largest conventional generator. The maximum spinning reserve for each time period, $Re{max}^t$, is calculated as the sum of $Remin$ and the solar PV output in that period. These boundaries on renewable output and reserve requirements are used to determine the lower and upper bounds of the objective function. The resulting fuzzy cost parameters are denoted as $z_{lower}$ and $z_{upper}$, representing the minimum and maximum possible total system costs, respectively.

Performance of Deterministic and Fuzzy Unit Commitment Solutions

The optimal solutions obtained from the deterministic unit commitment model (DUCM) and the fuzzy unit commitment model (FUCM) across various demand scenarios are presented in

Table 3. Total cost in Thai Baht for the DUCM and FUCM models across demand groups.

Load Demand Groups	DUCM (Upper-Bound Model)	DUCM (Lower-Bound Model)	DUCM with the Mean of Solar Output	FUCM
Winter weekday	366,788,709.45	354,004,140.76	359,659,033.45	359,659,033.45
Winter weekend	223,423,738.00	213,470,077.13	219,100,769.50	217,198,191.26
Summer weekday	331,819,030.25	319,124,664.08	325,389,411.83	325,464,420.50
Summer weekend	284,347,963.06	272,899,916.30	278,078,298.70	278,285,308.57
Rainy weekday	281,868,755.61	270,306,696.95	275,931,547.87	275,849,996.13
Rainy weekend	273,071,257.34	261,078,788.62	266,367,439.64	266,706,435.12
Long Holidays	75,496,148.51	71,910,515.25	73,815,916.13	73,572,939.98

. The results indicate that the FUCM consistently produces cost values within the range defined by the minimum and maximum DUCM solutions based on solar power output assumptions. In scenarios such as winter weekdays, rainy weekdays, and long holidays, the FUCM yields a total cost lower than the DUCM solution based on average solar output. For other demand scenarios, the FUCM cost is equal to or slightly higher than that of the DUCM with average solar generation. However, total cost alone is not sufficient to assess solution quality; system stability must also be evaluated.

To assess system stability, the optimal schedules derived from both the deterministic unit commitment model (DUCM) and the fuzzy unit commitment model were evaluated. For each time period, the total available generation capacity was determined by summing the maximum outputs of all committed units. A Monte Carlo simulation was conducted using 100 randomized scenarios of uncertain variables, including load demand, electric vehicle (EV) charging, and solar photovoltaic generation. These uncertainties were modeled using normal distributions based on empirical datasets. For each scenario and time period, the available capacity was compared with the combined requirement of demand and spinning reserve. A shortage was recorded if the scheduled capacity was insufficient to meet these requirements.

System stability was quantified using four performance metrics based on the loss-of-load probability (LOLP) framework: (1) The first metric is the number of lacked scenarios, defined as the number of scenarios in which the total generation capacity fails to meet the sum of load demand and spinning reserve in at least one period. This metric ranges from 0 to 100 and is computed by counting the scenarios with any occurrence of capacity shortage. (2) The second metric is the number of missing periods, which is the total number of time periods across all scenarios where the available generation is insufficient to cover both load and reserve requirements. This metric ranges from 0 to 4800 and is computed by summing the missing periods across all 100 scenarios. (3) The third metric is the average lack percentage, calculated as the average of the shortage percentages across all missing periods. For each missing period, the shortage percentage is determined by dividing the power deficit by the total requirement of demand plus reserve and expressing it as a percentage. (4) The fourth metric is the maximum lack percentage, which records the highest observed shortage percentage among all missing periods in all scenarios.

As shown in

Table 4. Stability performance metrics for the DUCM and FUCM schedules across demand groups.

Load Demand Groups	The Number of Lacking Scenarios		Total Number of Missing Periods		Average Lack Percentage		Maximum Lack Percentage
	DUCM	FUCM	DUCM	FUCM	DUCM	FUCM	DUCM	FUCM
Winter weekday s	17	17	17	17	0.45%	0.45%	1.1%	1.1%
Winter weekend f	0	21	0	21	0%	0.51%	0.5%	1.38%
Summer weekday d	82	44	147	48	0.6%	0.45%	2.43%	1.17%
Summer weekend d	13	7	13	7	0.36%	0.24%	1.38%	0.62%
Rainy weekday f	6	4	6	4	0.59%	1.27%	2.33%	1.80%
Rainy weekend d	2	9	2	9	1.64%	0.77%	2.42%	2.80%
Long holidays f	93	92	248	247	1.09%	0.8%	4.26%	4.04%

^s Total costs of the DUCM and FUCM are similar. ^f Total cost of the FUCM is lower than that of the DUCM. ^d Total cost of the DUCM is lower than that of the FUCM.

, the fuzzy unit commitment model generally demonstrates superior reliability compared to the DUCM. In most demand profiles, the numbers of lacked scenarios and missing periods were reduced. Even in cases such as winter and rainy weekends, where the fuzzy model exhibited a slightly higher number of lacked scenarios, both the average and maximum lack percentages remained comparable to or lower than those under the DUCM. Notably, the maximum lack percentage under the fuzzy model consistently remains within 5%, confirming that reliability does not deteriorate beyond the most severe outcomes observed under the deterministic approach.

These results confirm that the fuzzy unit commitment model yields more robust and reliable operational schedules under uncertainty. Furthermore, the analysis illustrates a fundamental trade-off between cost and reliability. For example, under rainy weekday and long holiday conditions, the fuzzy model achieved lower operational costs without compromising stability. In contrast, during winter weekends, the DUCM exhibited slightly better stability, although the fuzzy model maintained a cost advantage. Under summer demand profiles, the fuzzy model incurred marginally higher costs while significantly improving reliability metrics.

This trade-off can be effectively managed by adjusting fuzzy logic parameters or spinning reserve requirements. System operators aiming to enhance reliability may adopt higher reserve margins or apply more conservative estimates for renewable generation, whereas those prioritizing cost efficiency may choose to relax these parameters to reduce operational expenses. Thus, the fuzzy unit commitment framework provides a flexible decision-support tool, enabling planners to balance economic performance with operational resilience in uncertain and renewable-integrated power systems.

3.2. Application to National Large-Scale Power System

Following validation on a small-scale system, the proposed fuzzy unit commitment model (FUCM) was applied to Thailand’s national large-scale power system for daily generation scheduling. The system consists of 171 conventional generators, including thermal, gas turbine, combined-cycle, steam-cycle, and hydro units, with a total installed capacity of 24,223 MW. The largest single generator has a capacity of 685 MW. The grid is divided into five regional zones—Metropolitan, Central, North, Northeast, and South—with load demand segmented accordingly. The scheduling horizon covers 48 half-hour periods across a 24 h day.

Solar photovoltaic (PV) is the primary renewable energy source in Thailand, with 501 solar power plants totaling 3514 MW installed across all regions. Due to the variability of solar irradiation, PV output follows a predictable daily pattern, peaking around mid-day and dropping to 0 at night. The minimum and maximum solar outputs for each period (t) are estimated based on installed capacity and forecasted irradiation and are shown in Figure 3 as fuzzy parameters $R{min}^t$ and $R{max}^t$. These parameters are used to compute the lower and upper bounds of the objective function, denoted as $z_{lower}$ and $z_{upper}$, by solving Models 1 and 2 using IBM ILOG CPLEX Optimization Studio version 12.6, executed on a computing platform featuring an Intel Core i5-8300H processor and 16 gigabytes of RAM.

3.2.1. Performance Evaluation for National Large-Scale Power System

This section evaluates the performance of the fuzzy unit commitment model (FUCM) in comparison to the deterministic unit commitment model (DUCM) for Thailand’s national power system. The results, summarized in

Table 5. The results of total operational cost in Thai Baht of the DUCM and FUCM in a large-scale power system.

Demand Groups	DUCM Upper Bound	DUCM Lower Bound	DUCM with Mean Solar Power Output	FUCM
Winter weekday	988,393,514.73	972,570,613.41	977,310,614.65	979,219,219.00
Winter weekend	827,045,401.66	810,586,800.33	816,585,997.99	821,092,464.06
Summer weekday	1,058,328,162.88	1,039,452,661.02	1,045,271,246.00	1,047,922,497.98
Summer weekend	899,683,085.82	884,986,068.41	889,207,314.70	892,447,492.76
Rainy weekday	877,186,680.84	862,265,287.64	867,423,700.54	868,118,138.84
Rainy weekend	1,006,050,776.65	985,791,282.47	992,639,130.93	1,048,041,623.59
Long Holidays	508,277,718.52	507,931,149.07	507,942,510.09	507,517,650.60

,

Table 6. The results of computational time in seconds of the DUCM and FUCM in a large-scale power system.

Load Demand Groups	DUCM Upper Bound		DUCM Lower Bound		DUCM with Mean Solar Power Output		FUCM
	Avg	SD	Avg	SD	Avg	SD	Avg	SD
Winter weekday	182	15	165	20	175	23	2668	73
Winter weekend	111	21	98	18	104	17	3009	50
Summer weekday	92	12	87	15	91	21	842	47
Summer weekend	98	18	102	10	104	25	1844	71
Rainy weekday	57	16	64	22	53	19	2990	57
Rainy weekend	62	20	70	13	65	18	1810	72
Long holidays	55	14	52	11	49	14	603	69

and

Table 7. Comparison of stability performance metrics between the DUCM and FUCM in a large-scale power system.

Load Demand Groups	Number of Lacking Scenarios			Number of Missing Periods
	DUCM *	FUCM	Percent Improvement	DUCM *	FUCM	Percent Improvement
Winter weekday	39	59	−51.28%	42	87	−107.14%
Winter weekend	34	13	61.76%	36	15	58.33%
Summer weekday	44	29	34.09%	50	34	32.00%
Summer weekend	64	36	43.75%	92	46	50.00%
Rainy weekday	46	41	10.87%	62	51	17.74%
Rainy weekend	67	42	37.31%	100	52	48.00%
Long holidays	0	0	0.00%	0	0	0.00%
Load Demand Groups	Average Lack Percentage			Maximum Lack Percentage
	DUCM *	FUCM	Percent Improvement	DUCM *	FUCM	Percent Improvement
Winter weekday	0.87%	0.93%	−6.90%	2.52%	3.54%	−40.48%
Winter weekend	0.94%	1.02%	−8.51%	3.03%	2.90%	4.29%
Summer weekday	0.66%	0.48%	27.27%	1.69%	1.91%	−13.02%
Summer weekend	0.98%	0.90%	8.16%	3.51%	3.09%	11.97%
Rainy weekday	1.19%	0.89%	25.21%	4.01%	2.99%	25.44%
Rainy weekend	0.91%	0.86%	5.49%	3.32%	2.71%	18.37%
Long holidays	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%

* DUCM with mean solar power output.

, provide insights into economic efficiency, computational effort, and system reliability under uncertainty.

The FUCM and DUCM were applied to each load demand group of Thailand’s national power system, and the results are summarized in Table 5. As expected, the FUCM solutions lie within the bounds of the DUCM results for minimum and maximum solar output cases. In most demand groups, the DUCM with mean solar output achieves a slightly lower cost. However, similar to the small-scale case, the FUCM requires a longer computation time, as shown in Table 6. Solver parameters were adjusted to improve efficiency, but the final solution remained consistent. Overall, the FUCM achieved near-optimal solutions within a computation time acceptable for daily planning.

System stability was evaluated by simulating 100 solar photovoltaic output scenarios and computing four performance metrics, namely the number of lacking scenarios, total number of missing periods, average lack percentage, and maximum lack percentage. As summarized in Table 7, the fuzzy unit commitment model consistently demonstrated superior stability compared to the deterministic approach. The improvement percentages in the table were calculated as the relative change from the deterministic unit commitment model to the fuzzy unit commitment model, using the deterministic results as the baseline. A positive percentage indicates that FUCM achieved a better performance, while a negative percentage means FUCM performed slightly worse but other reliability indicators remained acceptable.

The comparison of performance metrics indicates that the FUCM model generally demonstrates superior performance over the DUCM model in most demand profiles. Positive percentage improvements, reflecting reductions in lacking scenarios, missing periods, average lack percentage, and maximum lack percentage, are observed in several cases, such as summer weekday, summer weekend, rainy weekday, and rainy weekend conditions. These results suggest that FUCM enhances reliability and operational stability under variable and uncertain demand conditions.

Conversely, negative percent improvements are seen in winter weekday and winter weekend profiles. This outcome can be attributed to the relatively stable and less fluctuating demand during the winter season, where the advantage of incorporating fuzzy uncertainty diminishes. In these cases, although the FUCM shows more missing periods, the average lack percentages remain low, indicating that the missing events are minor and may represent only slight mismatches in individual periods rather than severe disruptions. This suggests that, while FUCM does not reduce the number of missing events during winter, the overall impact on operational reliability remains limited.

These results indicate that the fuzzy unit commitment model is more effective at capturing operational uncertainty, producing schedules that are more robust under varying demand and solar generation conditions. The percent reductions across multiple performance indicators highlight the advantage of employing a fuzzy modeling approach that accommodates uncertainty through flexible representation rather than fixed point estimates. By balancing computational feasibility with enhanced stability, the FUCM provides power system operators with a practical tool for improving reliability while maintaining acceptable operational costs.

To illustrate the sensitivity of the model, consider a hypothetical variation of key fuzzy bounds. For example, if we increase the upper bound on expected solar output in each period by 10%, the FUCM would assume greater renewable availability. It would likely schedule less conventional generation, lowering costs under optimistic forecasts but potentially increasing risk if actual solar falls short. Conversely, if we increase the minimum spinning reserve requirement, namely the lower fuzzy bound, the model would commit more generation to meet the higher reserve, raising costs but further reducing the probability of shortage. These “what-if” scenarios show that the FUCM’s decisions depend on how the fuzzy parameters are set. In practice, system planners could perform such sensitivity analyses to tune the membership function bounds. They might set more conservative reserve limits when security is paramount or relax them when cost saving is more important.

3.2.2. Generation Scheduling and System Feasibility Assessment

The results for the summer weekday group highlight the significant contributions of thermal and combined-cycle generators to the overall power supply. Figure 4 presents the generation output by generator type, while Figure 5 compares the total available generation capacity with the system’s load demand and reserve requirements across all time periods. The available capacity, calculated from the committed conventional units and solar photovoltaic output, consistently exceeds the total power requirement, which comprises both the net load demand and the spinning reserve.

On average, the generation surplus is 5.93%, with the minimum observed margin at 0.12%. This buffer indicates that the proposed fuzzy unit commitment model (FUCM) can reliably meet both typical and extreme demand conditions, as reflected by the forecast variability shown in the error bars. These findings confirm that the FUCM delivers a feasible and stable operational schedule, ensuring adequate supply and reserve capacity under uncertainty.

Moreover, the reliable scheduling achieved by the FUCM provides a strong foundation for increasing the share of renewable energy in the power system. By effectively managing variability and maintaining system stability, the FUCM supports decisions that promote a transition toward higher renewable penetration. This transition not only enhances energy security but also contributes to a reduction in carbon emissions, aligning operational planning with long-term sustainability goals.

4. Conclusions and Discussion

This research was driven by the increasing challenge of managing uncertainty in power systems characterized by highly integrated renewable energy sources (RESs), particularly solar photovoltaic (PV) energy sources. Conventional deterministic unit commitment models (DUCMs) are inadequate in capturing the intrinsic variability of RESs, load demand, and spinning reserve requirements, which can lead to operational inefficiencies and jeopardize system stability. To mitigate these issues, we introduced a fuzzy unit commitment model (FUCM) that incorporates fuzzy logic within a mixed-integer linear programming (MILP) framework to more accurately represent the multiple sources of uncertainty.

The proposed FUCM employs triangular membership functions to model the uncertainty ranges of net load demand, spinning reserve, and production cost. It transforms these fuzzy constraints into linear formulations, making them tractable within commercial solvers. The model was validated on both a scaled test system and Thailand’s national power grid, comprising 171 conventional generators across five service zones. Results show that FUCM solutions consistently fall within deterministic upper and lower cost bounds, achieving favorable performance in terms of loss-of-load probability, the number of failed scenarios, and energy deficiency metrics.

Key findings reveal that the FUCM enhances system reliability while maintaining cost efficiency, particularly under high-uncertainty conditions. Although computational time is longer than that of the DUCM, the solution remains practical for daily operational use and offers superior performance stability. Notably, the model promotes sustainability by enhancing the system’s ability to reliably accommodate renewable energy integration without compromising grid security.

The fuzzy model offers actionable insights for both operational practice and policy development. For large-scale national power systems, the model can inform the determination of spinning reserve standards that reflect solar generation variability. Where the model indicates elevated shortage risk, operators may respond by increasing reserve procurement, deploying energy storage, or activating demand response measures. Policymakers can also use these insights to justify investments in system flexibility, such as storage capacity, to maintain reliability targets in a renewable-rich grid. In this way, the fuzzy model links methodological advances with practical planning and policy decisions.

This research provides a robust and scalable decision-support instrument for sustainable energy planning, particularly in regions undergoing rapid progress in their transition to renewable energy. Future studies might expand upon this work by investigating alternative or adaptive membership functions, such as trapezoidal or Gaussian types, to more accurately model nonlinearities in renewable energy source (RES) variability. Additionally, integrating electric vehicle demand, battery storage dynamics, and demand response initiatives within a comprehensive fuzzy optimization framework presents a promising avenue for further exploration. Ultimately, this research underpins the development of more resilient and environmentally sustainable energy systems aligned with global sustainability objectives.

The issues raised regarding the consideration of extreme events in renewable energy plants and the quantification of emissions represent important directions for future research. While the present study focused on operational cost and system stability under uncertainty, addressing these additional dimensions would provide a more comprehensive evaluation of power system performance. Specifically, incorporating scenarios that reflect severe solar and hydro variability, as well as grid contingencies, will enable further validation of the model’s robustness under stressed conditions. In parallel, integrating emissions quantification into the unit commitment framework will allow for the assessment of both reliability and environmental sustainability outcomes. These extensions will form the basis of our future research to support more resilient and sustainable power system planning.