Profitability enhancement of a hybrid system including thermal-wind-CAES-fuel cell with incorporation of imbalance cost

Abstract

In deregulated energy markets, the incorporation of renewable resources stances substantial economic and operational challenges. This paper considers a hybrid system configuration with wind farms, compressed air energy storage, and hydrogen fuel cells for enhancing system profitability and reducing imbalance costs due to prediction errors. An innovative imbalance cost model is presented on the basis of projected and real wind speed statistics for four diverse sites across India. The system is verified on modified IEEE 30, 57, and 118-bus systems for a scalability and stability study under different grid complexities. Optimization is performed based on sequential quadratic programming, artificial bee colony, and the artificial gorilla troops optimizer algorithms. Outcomes indicate that the addition of compressed air energy storage and hydrogen fuel cells resulted in mean profit enhancements of as much as 5.3% (30-bus), 6.2% (57-bus), and 6.7% (118-bus), respectively, over wind-only setups. The artificial gorilla troops optimizer algorithm performed superior compared to others in optimizing economic payback and reducing system risk, as evaluated by value at risk and conditional value at risk indicators. These results emphasize the feasibility and efficacy of the suggested hybrid model for maximizing profitability and operational robustness in competitive electricity markets.

Keywords

wind power renewable energy energy sustainability profit

Introduction

In a deregulated energy market, the process of optimizing profits through the use of energy storage technologies is inextricably linked to fluctuations in electricity prices. Previously, electricity markets were closely regulated since they were considered a monopoly due to the unique nature of their service and infrastructure requirements.¹ Nonetheless, there has been a notable shift toward deregulation of the electrical industry in recent years, fundamentally altering the landscape of energy production and distribution. As a result of this shift, there has been a significant increase in competition among various market participants, including generation companies (GENCOs), transmission companies, distribution companies, and end users, resulting in price reductions for consumers.² Energy storage systems (ESSs) are critical in allowing power suppliers to maximize revenues by ensuring that there is always an adequate supply of energy available, regardless of demand changes.³ To follow the growing worldwide power need in today's environment, renewable energy sources (RESs) must be used in conjunction with established non-RESs to build a more sustainable future energy. Wind farms have risen to prominence as the world's fastest-growing electrical source in recent decades, with significant yearly progress rates. Several investors are motivated to invest their capital in wind power generation projects and are willing to enter into long-term contracts to ensure reliable returns on their investments.^4,5 The profit expansion method in the power market is primarily a pattern that stresses market participants ability to promote societal welfare and production efficiency through their actions.^6,7 Rising energy needs, combined with increased supply levels, have resulted in an increase in electricity prices for customers. This condition has resulted in substantial revenue losses for many utility providers, as they are unable to pass on the increased costs to their patrons without risking discontentment and potential business loss.⁸ Integrating RES into the energy supply chain can provide utility businesses with a constant and stable source of electricity while also reducing maintenance requirements on their infrastructure.⁹ As per recent studies, deregulated markets are likely to yield a profit for producers and consumers alike, perhaps due to the fact that consumers are free to select their electricity price and negotiate conditions with sellers, while producers gain from working with several sellers and negotiating prices.^10,11

According to a study conducted in,¹² ESS is a viable solution for capturing excess electricity generated by WF or solar panels during periods of low sunlight or wind, resulting in more efficient energy management. The period of dependence on fossil fuels, which have dominated the energy landscape for decades, is gradually drawing to a close, making way for an innovative new system in which individuals and communities will have the autonomy and empowerment necessary to effectively manage and fulfill their energy requirements sustainably.¹³ This huge transformation has been accelerated by advancements in technological innovation, particularly in battery storage technologies (BSTs), as well as crucial adjustments in public policy that encourage and enable this evolution. In the presence of energy storage technologies, incumbent enterprises are forced to participate in more competitive bidding techniques, resulting in increased market competition. The use of ESS not only lowers overall system costs but also helps to avoid negative real-time profits, which can be detrimental to market stability and investor confidence.^14–16 The use of RES in conjunction with battery storage technology is primarily intended to improve system earnings, with the overarching goal of maximizing profitability from power sales in markets that operate on a day-ahead basis. For the purpose of adhering to the objective of optimizing profit from ESS along with mitigating supply and demand imbalance and tackling risks pertaining to price uncertainty at certain points due to power grid congestion, a strategy for tackling pecuniary and physical contracts with energy storage devices has been clearly outlined.^17–19 By employing CAES technology, the GENCO is well positioned to deploy tactics that take advantage of market price variations. In the field of ESS, references^20–23 present a comprehensive model that includes a best price mechanism for electric vehicle charging sites while accounting for RES and storage. The phenomena of negative pricing suggest a severe surplus of electrical energy, which is a disturbing sign that the market is not reaching equilibrium. To tackle the peak demand issues, the probabilistic scheduling of the day-ahead model involves a wind-pumped storage power system and irrigation. The simulation outcomes evidently showed that the suggested approach has the potential to greatly enhance the rate of utilization of wind power resources.^24–26 Another detailed study provided efficient and effective operation solutions to integrate WF and solar photovoltaic systems in a manner that they might be capable of achieving maximum financial profitability at reduced costs on imbalances in supply and demand.²⁷ Upon gathering market price data, the market controller applies an optimization process to optimize bids to maximize societal welfare within operational constraints. Recent studies reviewed the economic effects of integrating WF in a deregulated, wind energy-based market.^28–31

The current research involves a detailed examination of all the issues that have arisen, with careful consideration given to delivering comprehensive solutions to each of these inquiries with the highest care and precision. The following points outline the main highlights of this work:

A new hybrid system is introduced, combining WF, thermal plants, CAES, and FC for enhanced profitability and operating flexibility in a deregulated power market. Following the implementation of a power delivery bond by GENCOs and distribution companies based on an estimated wind speed, if any discrepancies between real and predicted wind speed (PWSs) arise, the independent system operator (ISO) has the authority to reward or penalize the GENCOs based on whether they exceeded or fell short of their power supply obligations. As a result, GENCOs are actively working to bridge the gap between actual and forecasted estimates to avoid the negative consequences of imbalanced costs.

A novel imbalance cost model is constructed based on a comparison of actual and forecasted wind speed at four different Indian sites for 24 h, along with respective surplus and deficiency penalties, with provision for a more realistic simulation of market behavior.

The artificial gorilla troops optimizer (AGTO), a new metaheuristic algorithm, is used and compared to artificial gorilla troops optimizer (ABC) and sequential quadratic programming (SQP) for improving economic optimization with renewable uncertainty.

Thorough system risk analysis employing value at risk (VaR) and conditional value at risk (CVaR) metrics is carried out to measure and avoid financial risks from renewable intermittency.

While some studies have investigated the advantages of blending renewable sources and storage systems in regulated market designs, this work presents several new dimensions. To begin, the hybrid system of wind power with both CAES and hydrogen FC is implemented within a deregulated, real-time power market that considers imbalance penalties. In contrast with previous work that handles forecasted wind generation as deterministic, the present model uses actual wind speed information and assesses imbalance costs due to forecast errors. Second, the application of the AGTO algorithm presents a novel contribution since the new nature-inspired metaheuristic has rarely been used for hybrid energy system optimization. The competitive performance of the AGTO is compared with standard procedures (ABC and SQP), again upholding the robustness and novelty of this work. Collectively, these contributions make this study stand apart from previous literature and create a comprehensive framework for profitability and risk-based analysis for wind-integrated deregulated systems. To ensure clarity and coherence, the article is organized into numerous sections. Initially, the mathematical model of the system and its associated restrictions were established. Subsequently, the objective function was clearly defined to direct the analysis. Following this, a thorough analysis of the suggested approach and its practical applications was performed. Finally, a thorough analysis of the implications of imbalance costs on the system profitability of the hybrid system in question has been conducted.

System modeling

This section provides a comprehensive assessment of risk assessment methodologies, as well as mathematical formulation applicable to wind energy, CAES, and fuel cells (FCs).

Wind power

The patterns of wind are often hard to predict, as they are constantly shifting. The amount of power generated by wind energy (GWP) depends on several factors, including air density (ρ), efficiency of the wind turbine (η), area of the turbine (A), and speed of the wind (WV). The formula for calculating the generated wind power is as follows:

G W P = \frac{1}{2} ρ \cdot A \cdot η \cdot W V^{3}

(1)

The parameters for a designated location have been established, except for the wind speed, which is subject to continuous fluctuations. However, in India, the data are accessed at a 10 m. The normal height for a wind turbine is 120 m in India. The following formulation is essential to calculate the wind speed at that height³²:

\frac{W V_{h}}{W V_{10}} = {(\frac{h}{10})}^{N}

(2)

WV_h and WV₁₀ represent the wind velocities at “h” and 10 m heights, with N denoting the Hellman coefficient.

Risk valuation parameters

This selection of VaR and CVaR as risk measurement approaches in this research is important. CVaR, in especially, is most known for its better numerical properties than other risk assessment methods, and therefore, a logical and efficient method for measuring risk.³³ In contrast to standard deviation, it may be replaced by CVaR deviation in extreme scenarios for enhanced results; standard deviation is generally considered a less reliable indicator. CVaR functions demonstrate greater efficacy in risk management compared to alternative risk assessment tools. While enhancing VaR and similar tools can be complex, CVaR can be improved through linear programming methods. Provided that tail losses are accurately estimated, CVaR effectively represents the risks associated with extreme tail events. Both methods of valuation center on a confidence level (ɷ) from probabilistic analysis. For this research, a 98% confidence level is utilized to estimate the values of VaR and CVaR. The loss mechanisms of the decision vector P from a given subset x of Q and of the random vector y from Q are denoted by m(x, y). The distribution of the loss elements m(x, y), which is subject to a threshold requirement ξ, is represented as n(y).

ξ_{p} (x) = m i n {ξ ϵ \dot{Q} : β (x, ξ)}

(3)

θ_{p} (x) = \frac{1}{1 - ω} [(\sum_{c = 1}^{C_{a}} (n_{c} - ω) p_{c_{a}} + \sum_{c = c_{a}}^{T} n_{c} p_{c}]

(4)

In this context, T represents the total number of trials conducted under various conditions. The highest degree of system risk is denoted by the parameters exhibiting the most significant negative values. Therefore, to mitigate system risk and minimize potential losses, it is crucial to shift toward the right. While VaR and CVaR are standard throughout financial and energy risk evaluation, there are other risk quantification measures available, including standard deviation, semivariance, Monte Carlo simulation-based probabilistic risk measures, and entropy-based measures. Standard deviation is popular but does not account for asymmetry or severe tail events. Semivariance captures only the downside risk but does not encompass the entire probabilistic range required in energy imbalance modeling. Monte Carlo methods provide versatile scenario generation but are computationally demanding and demand strong distributional assumptions. VaR is simple to interpret and popular in economic dispatch problems but fails subadditivity and tends to underestimate worst-case losses. CVaR addresses these shortcomings by including the expected loss in the tail over the VaR value, providing a more consistent and conservative measure of risk. Considering the focus on imbalance charges and tail-event exposure in deregulated power systems, CVaR is particularly well suited. Thus, VaR and CVaR were chosen in this research as efficient and representative measures of risk evaluation under uncertainty in wind power.

CAES system

When wind speed is uncertain in the context of a wind-combined energy generation system, it is proposed that a CAES device be strategically deployed to mitigate the volatility and unpredictability associated with wind power generation, thereby maintaining it at a consistently stable and reliable operational level.²⁶ A CAES's operating structure consists of three unique modes: turbine, compressor, and idle, each of which performs a specialized purpose in the energy management process. In the turbine mode, the CAES system is triggered during periods of high electricity demand, particularly when wind turbine capacity is insufficient to fulfill customer requirements. Conversely, the compressor mode is activated when the amount of available wind energy is sufficient to meet the total power requirements, allowing for the efficient storage of extra energy for later use.

χ_{gt} = χ_{g 0} + P_{e (c)} η_{ct c (c) -} \frac{P_{e (t)} t_{c (t)}}{η_{t}}

(5)

χ_{g (in)} = P_{e (c)} η_{ct c (c)}

(6)

χ_{g (out)} = \frac{P_{e (t)} t_{c (t)}}{η_{t}}

(7)

γ = η_{c} η_{t}

(8)

χ_{g (\min)} \leq χ_{gt} \leq χ_{g (\max)}

(9)

In this context, $P_{e (c)}$ represents the power feeding of CAES during the charging, while $P_{e (t)}$ denotes the power generated by CAES through the discharge. The efficiency of the compressor is indicated by $η_{c}$ , and the efficiency of the turbine is represented by $η_{t}$ .

FC

An FC works by employing hydrogen as fuel, wherein the chemical energy is transformed into electrical energy. This system employs an electrolyzer, which does the reverse of the normal electrolysis of water to create hydrogen. These pieces of equipment combine to make a complete ESS³⁴:

2 H_{2} + O_{2} \to H_{2} O + ElectricalEnergy + Heat

(10)

The produced hydrogen is stored in tanks, allowing its application in short-term and long-term energy storage. In contrast to large energy storage facilities, hydrogen storage shows comparatively high efficiency.

Less demand phase

The energy utilized by the electrolyzer is expressed as:

E_{elz} = \frac{{hv}_{H_{2}}^{l} \times E_{H_{2}}^{p}}{η_{elz}}

(11)

where

E_{H_{2}}^{p}

represents the hydrogen generation quantity from the electrolyzer,

E_{elz}

signifies the energy utilized by the electrolyzer,

η_{elz}

indicates the electrolyzer's efficiency, and

{hv}_{H_{2}}^{l}

refers to the hydrogen's lower heating value.

High demand phase

At peak times, the FC utilizes hydrogen to produce electricity.

E_{fc} = η_{fc} \times {fc}_{H_{2}}^{con} \times {hv}_{H_{2}}^{l}

(12)

$E_{fc}$ represents the energy output of the FC, while ${fc}_{H_{2}}^{con}$ denotes the hydrogen consumption amount by the FC. Additionally, $η_{fc}$ indicates the efficiency of the FC.

Although this study emphasizes the operational profit maximization of a wind-integrated hybrid system by CAES and FCs, it should be noted that such technologies involve high capital investment and site-dependent limitations. CAES systems, for example, demand appropriate geological structures like salt caverns or depleted gas reservoirs that may not be globally available. Likewise, hydrogen FC systems require heavy infrastructure for hydrogen generation, compression, and storage, which raises initial capital costs. These features are not addressed directly in the present work but are an important part of the total feasibility of the proposed system. Future research will seek to include comprehensive capital expenditure modeling and life cycle costing analysis to assess the technoeconomic trade-offs of using such hybrid systems in particular geographic locations.

Locational marginal pricing (LMP)

LMP is a technique used to determine the energy price delivered at a particular location, taking into consideration factors such as transmission congestion and energy costs. The methodology that determines market-clearing prices across various nodes within a transmission network is referred to as nodal pricing.

LMP = M C_{G} + M C_{L} + M C_{TC}

(13)

Here, MC_G, MC_L, and MC_TC represent the marginal cost associated with generation, losses, and transmission congestion.

Optimization techniques

The escalating demand for nature-inspired optimization methods for resolving stability issues within RES has prompted their global employment across various nations. This research delves into optimization methods incorporating AGTO, ABC, and SQP algorithms. While ABC and AGTO are metaheuristic optimization algorithms, SQP is a traditional gradient-based nonlinear optimization method. The discussion highlights the comparatively newer ABC and AGTO algorithms in conjunction with SQP to examine the efficacy of the new approach.

AGTO

AGTO is an innovative algorithm inspired by the social behaviors and foraging strategies of gorilla tribes. The AGTO starts with the initialization step, in which a random set of gorillas is created within the specified search space. Every gorilla is a possible solution to the optimization problem, and their initial locations are assessed with the help of a predefined objective function to establish their fitness. In the second stage, symbolizing the social hierarchy of gorilla groups, the most fit individual is chosen as the leader. This leader directs the movement and decisions of the rest of the gorillas, informing the optimization process. The algorithm switches between exploration and exploitation stages. In exploration, gorillas explore far in the solution space to find new and possibly better solutions, which aids in the avoidance of premature convergence to local optima. During the exploitation phase, they optimize and enhance current solutions using knowledge from their peer and leaders. The gorilla movement strategies are replicated mathematically, based on natural behaviors like moving towards the leader, generating random exploratory moves, and following successful paths back. The strategies facilitate an even search process. A new fitness evaluation is performed after every move. If a successor gorilla discovers that there exists a better solution than the present leader, leadership is revised accordingly. This iterative procedure repeats until a specified stopping criterion, for example, a maximum number of iterations or a convergence threshold, is met.

Pseudocode of AGTO algorithm:

ABC

The ABC technique is an optimization algorithm inspired by honeybees’ foraging activity. Dervis Karaboga developed the ABC method in 2005 to address complex optimization problems by simulating intelligent honeybee foraging. The algorithm's core parts are food sources, which are potential solutions, and the quality of each source corresponds to the solution's fitness. Employed bees are linked to certain food sources and actively gather them, transmitting the quality of these to other bees. Onlooker bees remain in the hive and pick food sources based on messages received from hired workers, before collecting the chosen sources. Scout bees patrol the search area, randomly searching out new food sources and rejecting low-quality ones.

Pseudocode of ABC optimization algorithm:

SQP

SQP is a popular iterative technique for solving nonlinear optimization problems, especially nonlinear objectives and constraints. It is based on the solution of quadratic programming subproblems at each iteration, which model the Lagrangian of the original problem with a quadratic model. The Lagrangian function integrates the objective function and constraints in terms of Lagrange multipliers so that SQP can handle both of them at once. This technique has good convergence properties, tending to achieve superlinear or even quadratic convergence under appropriate circumstances, and thus can be applied to a wide variety of optimization problems.

Pseudocode of SQP optimization algorithm:

Set initial solution vector x₀ and Lagrange multipliers λ₀.

Establish convergence criteria (tolerance, max iterations).

While convergence is not reached:

Construct the Lagrangian function: L(x, λ).

Calculate gradient and Hessian approximations.

Solve quadratic programming (QP) subproblem:

Subject to: Linearized constraints at current x.

Find search direction “d” from QP solution.

Conduct line search along direction “d” to determine optimal step size α.

Update: x = x + α × d

Update multipliers λ.

Return the optimized solution x and its corresponding objective value.

The choice of AGTO and ABC algorithms used in this research is inspired by their good performance in the latest literature for solving optimal power flow (OPF) and energy market dispatch, which are complex, nonlinear, and multimodal optimization problems. The AGTO, which is a new metaheuristic algorithm, has excellent global search ability, quick convergence behavior, and flexibility to handle large decision spaces, which is ideal for the dynamic and uncertain setting of deregulated power systems. The ABC algorithm, however, is reputable for being simple, having fewer control parameters, and good local search ability. While traditional algorithms like particle swarm optimization and genetic algorithm are well received in the energy sector, they have been shown to exhibit premature convergence and inadequate local refinement when applied to highly constrained nonlinear optimization problems. By contrast, AGTO and ABC present a better trade-off between exploration and exploitation. Although particle swarm optimization and genetic algorithm were not used in this work specifically to prevent duplication with well-studied benchmarks, comparative tests can be used in future studies to further compare AGTO with these established techniques. Although metaheuristic approaches lack global optimality, their combination with deterministic solvers leads to the refinement of suboptimal solutions to near-global optimality. The hybrid approach improves the robustness and reliability of solutions, particularly in the real-time operation of power markets where absolute global optimality is less important than timely and reliable decision making. Additionally, several runs of the algorithms with random initial populations were performed to achieve repeatability and robustness of results, hence enhancing the reliability of the solutions obtained.

Objective function

Here, an electrical system consisting of “T_b” buses, “T_d” loads, and “T_g” generators was studied, allowing for a complete comprehension of its intricate components and interrelations. The main aim of the proposed methodology is to analyze and assess the implications of variations between actual and anticipated wind speeds within the operational context of a wind–thermal hybrid power system. Furthermore, the system's profitability has emerged as an important factor to examine when evaluating these impacts since it has a direct impact on the power system's overall performance indicators. To accurately measure the overall profitability of the system, several factors must be considered, including the revenue generated by wind power, the costs associated with power generation imbalances, the initial investment required, and the various charge rates applicable to both surplus and deficit energy production. When examining the issue of cost imbalances, the goal of this study is to strategically lessen the expenses incurred from generation while simultaneously mitigating the associated risks to the system, all while optimizing the economic returns and exploiting the social welfare that can be derived from such a power system. Any analytical assessment of the performance of a RES combined system must take into account imbalance costs, which have a major impact on operational efficiency and profitability. To the best of the author's knowledge and understanding, however, it appears that very few academics have focused their efforts on delving deeply into this specific idea, revealing a gap in the current literature. Given that system operators apply both incentives and penalties on producing businesses, a positive imbalance cost might result in a rise in system profits, whereas a negative imbalance cost tends to reduce profitability.

It is known that the present model accounts for wind uncertainty through an existing imbalance cost mechanism. Although this captures a realistic scenario of penalty and reward within actual electricity markets, future research will include stochastic or robust optimization tools. These models will make explicit allowance for forecast uncertainty of wind speed during the planning phase, thus resulting in more informed and robust bidding strategies. Probabilistic wind forecast scenarios or intervals of strength will increase the ability of the model to handle uncertainty and enhance financial reliability under high wind variability. In this study, the problem of maximizing profit acts as the first objective function, while the problem of reducing system risk comprises the second objective function. These functions are mathematically stated as:

Objective function I

Maximize, $P_{m} (t) = T R_{m} (t) + IM C_{m} (t) – TG C_{m} (t)$ (14)

In this context, $P_{m} (t)$ represents the total profit for the mth unit at a time “t.” ${TR}_{m} (t)$ denotes the total revenue, while ${IMC}_{m} (t)$ indicates the total imbalance cost. ${TGC}_{m} (t)$ refers to the total generation cost. Within the framework of the current deregulated electricity market, the optimization of profits for a wind–thermal power plant is primarily influenced by the imbalance cost, which comprises revenue, imbalance, and total generation costs. The subsequent section outlines the formulas for total revenue, imbalance costs, and generation costs:

{TR}_{m} (t) = \sum_{i = 1}^{T_{g}} P_{i, a} (t) . {LMP}_{i} (t)

(15)

{IMC}_{m} (t) = \sum_{i = 1}^{T_{g}} [{CR}_{s} (t) + C R_{d} (t) . {(\frac{P_{i, f} (t)}{P_{i, a} (t)})}^{2}] . [P_{i, a} (t) - P_{i, f} (t)]

(16)

In this context, $P_{i, a} (t)$ represents the power generated at the ith generation bus based on the real wind speed (RWS) at time “t.” Meanwhile, $P_{i, f} (t)$ indicates the power generation using the forecasted wind speed. The surplus charge rate at time “t” is denoted as ${CR}_{s} (t)$ , while the deficit charge rate at that same time is represented by ${CR}_{d} (t)$ .

{TGC}_{m} (t) = G C_{m} (t) + WG C_{m} (t)

(17)

Here, ${WGC}_{m}$ is the wind power investing cost. The electricity produced from wind is allocated in a deregulated setup based on expected wind speeds. If the actual wind speed data varies from what was forecasted, the CAES system works on generating mode to reduce the power discrepancy and adjust operations accordingly. The costs related to imbalances can occur due to the alterations between actual and expected wind speeds. These imbalanced costs are represented in equation (16). The rates for excess and deficit charges are calculated using specific formulas:

{CR}_{d} (t) = (1 + σ) . LM P_{i} (t), C R_{s} (t) = 0 when P_{i, a} (t) < P_{i, f} (t)

(18)

{CR}_{s} (t) = (1 - σ) . LM P_{i} (t), C R_{d} (t) = 0 when P_{i, a} (t) > P_{i, f} (t)

(19)

{CR}_{s} (t) = {CR}_{d} (t) when P_{i, a} (t) = P_{i, f} (t)

(20)

{GC}_{m} (t) = \sum_{i = 1}^{T_{g}} x + y \cdot P_{i, a} (t) + z . P_{i, a}^{2} (t)

(21)

The term ${LMP}_{i} (t)$ represents the locational marginal price at the ith bus at a specific time “t.” ${GC}_{m} (t)$ denotes the thermal power production cost. x, y, and z are thermal generation cost coefficients. Equation (17) shows how the costs of wind and thermal system generation are brought together to obtain the total producing cost. We apply the generation cost coefficient and real power generation to find the thermal power system generation cost. The imbalance cost coefficient, referred to as “σ,” is varies between 0 and 1, and for this study, it is set at 0.9.

In this research, the surplus and deficit imbalance charge rates were simulated by employing fixed rate coefficients to allow for controllable comparison between sites and wind conditions. Yet, real balancing prices in electricity markets are recognized as very dynamic and dependent on actual grid conditions, reserve needs, and market rules. Accordingly, the fixed charge model is a simplification aimed at approximating the overall financial effects of wind forecast inaccuracy. Future developments extending this research will include dynamic imbalance pricing mechanisms derived from historical or real-time ancillary service market information to increase modeling precision and system realism.

Objective function-II

Min \cdot ξ_{p} (x) = m i n {ξ ϵ \dot{Q} : β (x, ξ)}

(22)

Min \cdot θ_{p} (x) = \frac{1}{1 - ω} [(\sum_{c = 1}^{C_{a}} (n_{c} - ω) p_{c_{a}} + \sum_{c = c_{a}}^{T} n_{c} p_{c}]

(23)

Equations (22) and (23) illustrate the functions of VaR and CVaR. This scenario involves a minimization problem. There is an inverse relationship between system risk and both VaR and CVaR. This implies that the system's risk will be at its peak or lowest depending on whether one of these two variables has a higher or lower negative value. Therefore, in order to shift the left tail of the curve to the right (as indicated in Figure 1), either the risk of the system must be decreased or VaR and CVaR values must increase positively. The primary aim of this program is to decrease the generating costs of the system. At the far right of the curve, when the system profit is highest and production costs are lowest, VaR and CVaR both attain their maximum values. Consequently, there is a negative relationship between VaR, CVaR, and system production costs. Conversely, a negative correlation exists between generation costs and social welfare, meaning that as generation costs decrease, social welfare improves, and vice versa. This indicates that VaR and CVaR directly influence social welfare.

Figure 1.

Graphical representation of CVaR and VaR.

Constraints

The accompanying collection of limits and requirements was used methodically to successfully handle and overcome the complicated challenges related to the optimum power flow problem, which is frequently encountered in electrical engineering and power systems analysis. The equation controlling power flow, together with the equation balancing actual power consumption and generation, constitutes the key equality constraint that must be met to assure the stability and efficiency of the power system under consideration.

\sum_{i = 1}^{T_{g}} P_{g, i} + WP - P_{loss} - P_{d} = 0

(24)

P_{loss} = \sum_{j = 1}^{N_{TLN}} G_{ij} [{| V_{i} |}^{2} + {| V_{j} |}^{2} - 2 | V_{i} | | V_{j} | \cos (δ_{i} - δ_{j})]

(25)

where

P_{g, i}

= power generated at the ith generating unit,

WP

= wind power generation,

P_{loss}

= transmission loss,

P_{d}

= power demand,

N_{TLN}

= total number of transmission lines in the system,

G_{ij}

= electrical conductance of the line between buses “i” and “j,”

| V_{i} |, δ_{i}

= voltage magnitude and angle of bus “i,”

| V_{j} |, δ_{j}

= voltage magnitude and angle of bus “j.”

P_{i} - \sum_{i = 1}^{T_{b}} | V_{i} VkY ik | \cos (θ_{ik} - δ_{i} + δ_{k}) = 0

(26)

Q_{i} + \sum_{i = 1}^{T_{b}} | V_{i} VkY ik | \sin (θ_{ik} - δ_{i} + δ_{k}) = 0

(27)

where

P_{i}

= actual amount of real power that is being injected into the electrical system at the designated bus labeled “i,”

Q_{i}

= amount of reactive power that is being introduced into the electrical system at the same bus labeled “i,”

Y_{ik}, θ_{ik}

= specific magnitude along with the angle that corresponds to the element located in the ith row and kth column of the bus admittance matrix, which is a crucial component in power system analysis. The continuous and discrete constraints are essential for ensuring the security of the system and maintaining the operational limits, and they are effectively utilized in the process of achieving optimum power flow within the network.

V_{i, \min} \leq V_{i} \leq V_{i, \max} where i = 1, 2, 3, 4, \dots . . T_{b}

(28)

φ_{i, \min} \leq φ_{i} \leq φ_{i, \max} where i = 1, 2, 3, 4, \dots . . T_{b}

(29)

{LF}_{l} \leq {LF}_{l}^{\max} where l = 1, 2, 3, 4, \dots . . N_{TLN}

(30)

{PG}_{i, \min} \leq P G_{i} \leq {PG}_{i, \max} where i = 1, 2, 3, 4, \dots . . T_{b}

(31)

{QG}_{i, \min} \leq Q G_{i} \leq {QG}_{i, \max} where i = 1, 2, 3, 4, \dots . . T_{b}

(32)

where

V_{i, \min}

represents the minimum allowable voltage threshold for bus “i,” and

V_{i, \max}

indicates the maximum permissible voltage limit for bus “i,”

φ_{i, \min}

and

φ_{i, \max}

denotes the minimum and maximum angular limitation associated with the voltage of bus “i,”

{LF}_{l}

refers to the actual power transmission flow occurring along line “l,”

{LF}_{l}^{\max}

represents the highest allowable power flow capacity of line “l,”

{PG}_{i, \min}

and

{PG}_{i, \max}

denote the minimum and maximum threshold for real power that can be supplied at bus “i,”

{QG}_{i, \min}

and

{QG}_{i, \max}

refer to the minimum reactive power limit that applies to bus “i.”

The profitability optimization outcomes depicted in this research presume the preinstallation and complete operation of the CAES and FC systems. These do not account for the initial capital expenditures and possible site deployment constraints, which are critical factors in real-world investment plans. A holistic viability analysis, such as net present value, payback period, and levelized cost of storage , will be included in subsequent analyses.

Proposed method

This work introduces a method for assessing how differences between actual and forecasted wind speeds affect wind-integrated competitive systems. It estimates the surplus and deficit rates for each scenario and accurately calculates the total imbalance cost. The entire proposed methodology is illustrated in a flow chart in Figure 2. By applying this procedure, the RWS was utilized to determine the profits for GENCOs. The OPF problem was tackled by rearranging generators and applying constraints (equations (24) to (32)) to minimize the overall generation costs. Additionally, the system includes wind generators, and the discrepancies between costs and profits at various wind speeds have been analyzed. In this context, “H_r” denotes the hour number, “P_m” represents the total profit, and “P” indicates the profit. Figure 3 shows the schematic configuration of the suggested hybrid energy system using wind turbines, CAES, hydrogen FCs, and thermal power units. The electricity is produced by the wind turbine, part of which is used to charge the CAES system during off-peak times. Energy is discharged from the CAES system during peak hours to assist the grid. The CAES also connects with the FC, which utilizes hydrogen from surplus wind or market purchase, adding power when required. The thermal unit serves as a backup and balancing source, providing reliable generation and aiding voltage profiles. All energy elements feed power into the deregulated market, where GENCOs are incentivized or penalized according to forecast performance and market offers. This setup allows operational flexibility and economic efficiency in a market regime with high renewable uncertainty and dynamic pricing.

Figure 2.

Flowchart of the presented method.

Figure 3.

Schematic configuration of the presented hybrid system.

Model assumptions and limitations

The present research assumes the combined thermal–CAES–FC system can offset wind deviations every hour to prevent an imbalance penalty. Although this assumption permits a controlled examination of profit effects, it does not capture the actual operational limitations of energy storage and FCs in the real world. In reality, such systems are subject to physical limitations such as limited energy capacity, ramp-rate limitations, efficiency losses upon charging/discharging, and maintenance downtime. The model assumes instantaneous and lossless dispatch in idealizing their operation.

The development of hybrid systems containing thermal, wind, CAES, and FC units has more than operational strategy maximization challenges. Some of these include the initial high capital expenditure, the requirement for a favorable policy environment, and limitations in infrastructure. In the case of CAES, geological suitability is a prerequisite that can greatly restrict deployment areas. In the case of hydrogen FCs, the absence of a universal hydrogen infrastructure is a challenge. While the current study isolates operational profitability to evaluate the performance of storage coordination under wind uncertainty, any actual deployment will have to be preceded by thorough feasibility studies that include capital investment, land use, permitting, and environmental impact.

Application of the suggested method

In the context of this research, a modified IEEE 30-bus system was employed to thoroughly evaluate the overall effectiveness and efficiency of the proposed methodology. This system is derived from the comprehensive data in³⁴ and is made up of 30 buses, six generators, 41 transmission lines, and 19 distinct loads. Initially, the OPF problem was addressed and resolved through the implementation of the SQP technique, which is renowned for its effectiveness in handling such optimization challenges. Subsequently, a variety of metaheuristic optimization techniques were systematically applied to conduct a comparative analysis of the performance characteristics exhibited by the system. For this study, the air density (ρ) is 1.225 kg/m³, the efficiency (η) is 0.49, and the rotor radius (r) measures 40 m. For this study, the following three distinct system scenarios were carefully taken and examined in detail:
Regulated system that adheres to strict operational guidelines and protocols.

A deregulated system characterized by a single auction bidding process.

Deregulated system featuring a double auction bidding mechanism.

It should be noted that the analysis is performed on actual wind speed data from four geographically dispersed cities in India. The wind data employed were measured at 10 m above ground and extrapolated to the hub height of the turbine by the power law. The sites were selected to reflect different wind patterns in the Indian subcontinent. Although this yields strong insights in a regional setting, market dynamics, regulatory conditions, and wind behavior may vary substantially elsewhere geographically. Nevertheless, the outlined methodology, that is, imbalance cost calculation, multialgorithm optimization, and risk estimation via VaR/CVaR, is modular and can be adapted to power grids in other deregulated power markets by integrating local wind speed and market information.

Case 1: System performance for single auction bidding before wind farm connection

The primary focus of the study was concentrated on the intricate task of determining the optimum power flow within a system that does not incorporate any wind energy generation and operates solely based on a single bus auction bidding process. It can be observed in Table 1 that, under these specific circumstances, the total income generated amounts to an impressive figure of $ 10,996.742 per hour, while the associated costs incurred for generating power stand at a substantial $8602.875 per hour.

Table 1.
Generating costs and revenue under a single auction bidding system without a wind farm.

Generation (MW) LMP ($/MWh) Generation cost ($/h) Revenue ($/h)

Gen 1 (Bus 1) 212.26 36.413 8602.875 10,996.742

Gen 2 (Bus 2) 36.24 38.114

Gen 3 (Bus 5) 29.37 40.586

Gen 4 (Bus 8) 12.94 40.258

Gen 5 (Bus 11) 4.37 40.086

Gen 6 (Bus 13) 0 39.65

LMP:
locational marginal pricing.

In addition to these financial figures, Table 1 also provides valuable information regarding the corresponding LMP at the different generator buses, along with a detailed representation of each generator's respective power-generating capacity, which is essential for understanding the overall efficiency and output of the system.

Case 2: System performance for double auction bidding before wind farm installation

Considering the complexities and specifics of the two different auction bidding processes that took place, it's noteworthy that in this case, the OPF successfully carried out its functions of wind power. The data shown in Table 2 reveal the total generating cost of the system, which amounts to a substantial $7896.035/hour. Within the system's operational setup, buses 4 and 21 were specifically chosen for demand-side bidding, underscoring their significance in the overall bidding strategy. To improve flexibility for both the load and generation sides, this study evaluated demand-side bidding mechanisms alongside generation-side bidding strategies. For the modified IEEE 30-bus system, the revenue cost has been carefully calculated to be $10,321.362/hour, highlighting the financial aspects of the bidding processes. The data in Tables 1 and 2 indicate that both production and revenue costs significantly decrease due to the implementation of the double auction bidding method.

Table 2.
Generating costs and revenue under a double auction bidding system without a wind farm.

Generation (MW) LMP ($/MWh) Generation Cost ($/h) Revenue ($/h)

Gen 1 (Bus 1) 210.87 36.206 7896.035 10,321.362

Gen 2 (Bus 2) 35.9 37.997

Gen 3 (Bus 5) 26.03 40.52

Gen 4 (Bus 8) 6.56 40.13

Gen 5 (Bus 11) 0 39.84

Gen 6 (Bus 13) 0 39.527

LMP:
locational marginal pricing.

Case 3: System performance in the presence of wind placement and double auction bidding

In this scenario, the OPF was effectively achieved by strategically placing a wind generator within the electrical system. The wind generator was installed at bus 7. Its placement was carried out without any specific limitations, allowing for flexibility in its integration into the system. Once the wind generator was in place, the costs related to the thermal system's generation were carefully calculated, factoring in both the investment costs for the wind power setup and the overall production expenses. Additionally, equation (15) played a vital role in accurately determining the total revenue for the system. To comprehensively validate the findings derived from the wind speed data collected, four random locations across India were chosen as focal points for this analysis. These locations include the cities of Vijayawada, Hyderabad, Bangalore, and Chennai.

Following this selection, real-time data regarding both the RWSs recorded and the PWSs expected for these areas were systematically gathered, specifically at a height of 10 m above ground level, which is essential for our study. It was crucial to calculate the potential wind speed at 120 m, given that the hub height of a wind turbine in India typically reaches 120 m above the ground. The data concerning the PWS for 15 July 2024 were collected on the subsequent day, 16 July 2024, as noted in reference.³⁵ In contrast, the actual wind speed data for 16 July 2024 was gathered on 18 July 2024.³⁶ To enhance the understanding of the results, Table 3 provides a detailed comparison of both the real and PWSs utilized to assess the effectiveness and performance of the proposed method. The real-time measurement of wind speed at the specific height of wind turbines is currently unavailable, resulting in a lack of understanding of the atmospheric conditions at that elevation. In India, data on actual wind speed are typically collected at a height of 10 m above ground level, which fails to accurately reflect the conditions encountered at the operational heights of wind turbines. Given that these turbines can extend up to an impressive 120 m, it is essential to determine the wind speed at these altitudes, a task achieved through the utilization of the power law equation as depicted in equation (2). Analyzing the extensive wind speed data outlined in Table 3 reveals significant fluctuations in wind speeds across the selected sites, with values ranging from a low of 1.678 m/s to a high of 6.678 m/s. This variation underscores the differing wind conditions present at various locations. Additionally, the estimated investment cost for establishing a wind power generator is approximately $3.75 per MWh, as referenced in Dawn et al.³² It is anticipated that 50 wind turbines will be installed concurrently at the power generation facility, representing a considerable commitment to renewable energy development. Table 4 offers a comprehensive breakdown of the costs associated with wind energy, encompassing the variations in wind speed, the potential capacity for wind power generation, and the specific wind speed necessary at the required height to achieve optimal operational efficiency.

Table 3.
PWS and RWS at 10 m (m/s).

Hour Vijayawada Hyderabad Bangalore Chennai

PWS RWS PWS RWS PWS RWS PWS RWS

1 2.501 2.789 3.334 2.223 1.945 1.945 5.567 5.001

2 2.501 2.223 3.334 2.501 2.501 1.945 5.289 6.678

3 2.223 1.945 3.334 3.9 2.789 2.501 5.001 5.001

4 1.945 1.945 3.9 3.067 2.501 3.334 4.723 6.112

5 1.945 1.945 3.9 3.612 2.501 3.9 4.178 6.112

6 2.223 2.223 3.9 4.445 2.501 2.789 3.612 6.112

7 2.223 1.945 4.178 3.612 2.789 3.067 3.612 4.723

8 1.945 1.678 4.723 5.001 2.789 1.945 3.612 6.112

9 2.501 1.945 4.723 5.001 2.789 2.501 3.9 5.567

10 2.501 1.945 4.723 4.178 2.501 3.612 4.178 6.678

11 2.223 2.501 4.723 5.567 2.501 3.612 5.001 6.678

12 2.501 2.501 4.723 5.567 2.789 2.789 5.834 6.112

13 1.945 2.501 5.289 5.001 3.067 2.501 6.112 5.001

14 1.945 2.223 5.289 4.723 3.612 4.178 5.001 5.001

15 1.945 1.945 5.289 5.001 3.334 3.334 5.001 6.678

16. 1.945 1.945 5.001 5.289 2.789 3.612 5.001 5.567

17. 2.223 1.945 5.001 5.001 2.501 3.334 4.723 5.567

18 2.223 1.945 4.723 4.723 2.501 4.723 4.723 4.723

19. 1.945 1.945 4.178 5.567 2.789 5.289 4.445 5.001

20 1.945 2.223 3.9 4.178 3.067 4.178 4.178 4.723

21 2.789 1.945 3.612 5.567 3.067 2.501 4.178 5.567

22 2.789 2.223 3.612 5.567 3.067 1.945 4.178 5.001

23 2.501 2.789 3.612 5.289 3.067 2.501 4.445 4.178

24 2.223 2.789 3.612 5.289 3.067 2.789 4.723 6.678

PWS: predicted wind speed; RWS: real wind speed.

Table 4.
Wind speed and wind investment cost for different wind scenarios.

Sl Wind speed at 10 m(m/s) Wind power with 50 turbines (MW) speed at 120 m Wind gen cost with 50 turbines ($/h) Sl Wind speed at 10 m (m/s) Wind power with 50 turbines (MW) speed at 120 m Wind gen cost with 50 turbines ($/h)

1 1.678 1.012 3.8 10 4.178 15.834 59.3534

2 1.945 1.612 6.0323 11 4.445 19.212 72.0334

3 2.223 2.401 9.0045 12 4.723 23.045 86.4012

4 2.501 3.423 12.8201 13 5.001 27.356 102.5634

5 2.789 4.7 17.5867 14 5.289 32.178 120.6245

6 3.067 6.245 23.4078 15 5.567 37.523 140.6901

7 3.334 8.101 30.389 16 5.834 43.434 162.8667

8 3.612 10.301 38.6378 17 6.112 49.945 187.2589

9 3.9 12.878 48.2578 18 6.678 64.834 243.1123

The detailed financial information regarding both the revenue generated and the total expenses related to generation is carefully presented in Table 5. This table features an updated version of the IEEE 30-bus system, which considers varying wind speeds ranging from a minimum of 1.678 m per second to a maximum of 6.678 m per second. A comprehensive analysis of the data in Table 5 reveals a clear and consistent trend: as wind speeds increase, profits rise correspondingly, while the overall generation costs show a significant decline.

Table 5.
System economy with wind farm integration.

Sl. no. Wind speed (m/s) Revenue ($/h) Generation cost ($/h) Profit ($/h) Sl. no. Wind speed (m/s) Revenue ($/h) Generation cost ($/h) Profit ($/h)

1 1.678 10,327.84 7858.996 2468.85 10 4.178 10,418.73 7318.17 3100.56

2 1.945 10,330.81 7836.989 2493.82 11 4.445 10,441.61 7195.52 3246.09

3 2.223 10,335.83 7808.051 2527.78 12 4.723 10,475.80 7056.858 3418.94

4 2.501 10,342.38 7770.697 2571.68 13 5.001 10,520.19 6901.28 3618.91

5 2.789 10,350.58 7724.233 2626.34 14 5.289 10,570.42 6727.881 3842.54

6 3.067 10,360.49 7667.584 2692.91 15 5.567 10,625.46 6536.147 4089.32

7 3.334 10,372.02 7599.666 2772.35 16 5.834 10,685.39 6325.243 4360.15

8 3.612 10,385.42 7519.414 2866.00 17 6.112 10,749.55 6093.955 4655.59

9 3.9 10,400.94 7425.804 2975.14 18 6.678 10,542.77 5573.129 4969.64

Profit assessment in a modified IEEE 30-bus system

The ability to produce energy, along with the LMP, is carefully recorded alongside the results from each OPF analysis, which is performed under different wind speed conditions. To thoroughly evaluate the proposed method applied to a modified IEEE 30-bus system, a variety of scenarios were systematically explored using this specific system. This included: (a) detailed calculations to determine the generation outputs for each generator bus and their respective LMP; (b) in-depth assessments of the costs associated with imbalances; and (c) comprehensive estimates of the overall profitability of the energy system.

Generation cost and LMP measurement

In this case, the wind generator was placed on bus number 7, and a detailed OPF analysis was performed for every wind speed measurement, ensuring that all relevant constraints outlined in equations (24) to (32) were accurately taken into account. The costs linked to generation from the thermal system vary based on how the generation outputs are rescheduled. As shown in Table 6, the output from thermal units tends to decrease when wind speeds or power levels rise significantly. This pattern reflects a growing value of wind energy, which has contributed to an increase in the LMP. As a result, in all scenarios analyzed, there is a significant drop in the production costs of thermal electricity, along with a notable rise in the use of wind power resources. A detailed comparison between Figures 4 and 5 effectively illustrates these trends.

Figure 4.
LMP (in $/MWh) and generation (in MW) without wind farm placement.

Figure 5.
(a) Generation (MW) and (b) LMP ($/MWh) with wind farm placement.

Table 6.
Power generation quantity and LMP after wind farm placement.

Wind speed (m/s) Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6

Generation ($) LMP ($/MWh) Generation ($) LMP ($/MWh) Generation ($) LMP ($/MWh) Generation ($) LMP ($/MWh) Generation ($) LMP ($/MWh) Generation ($) LMP ($/MWh)

1.678 210.79 36.19 35.99 37.97 25.64 40.52 6.23 40.14 0.01 39.87 0.01 39.51

1.945 210.74 36.19 35.98 37.97 25.4 40.52 6.03 40.13 0.01 39.82 0.01 39.5

2.223 210.67 36.18 35.97 37.96 25.1 40.51 5.77 40.13 0.01 39.81 0.01 39.5

2.501 210.59 36.18 35.96 37.95 24.7 40.5 5.44 40.12 0.01 39.8 0.01 39.49

2.789 210.49 36.17 35.94 37.95 24.21 40.49 5.03 40.11 0.01 39.79 0.01 39.47

3.067 210.37 36.16 35.92 37.93 23.61 40.48 4.52 40.1 0.01 39.78 0.01 39.46

3.334 210.22 36.15 35.89 37.92 22.89 40.47 3.92 40.09 0.01 39.77 0.01 39.44

3.612 210.04 36.13 35.86 37.9 22.04 40.45 3.2 40.07 0.01 39.75 0.01 39.42

3.9 209.83 36.12 35.82 37.89 21.05 40.43 2.37 40.06 0.01 39.73 0.01 39.4

4.178 209.59 36.1 35.78 37.86 19.9 40.41 1.42 40.04 0.01 39.71 0.01 39.37

4.445 209.29 36.08 35.73 37.84 18.54 40.38 0.49 40.01 0.01 39.68 0.01 39.33

4.723 208.86 36.04 35.65 37.8 16.77 40.35 0.04 39.96 0.01 39.63 0.01 39.28

5.001 208.3 36 35.55 37.75 14.61 40.3 0 39.9 0.01 39.57 0.01 39.21

5.289 207.67 35.95 35.44 37.7 12.18 40.25 0 39.82 0.01 39.51 0.01 39.13

5.567 206.97 35.9 35.32 37.64 9.49 40.2 0 39.74 0.01 39.44 0.01 39.05

5.834 206.19 35.84 35.19 37.57 6.53 40.14 0 39.65 0.01 39.36 0.01 38.95

6.112 205.34 35.77 35.04 37.49 3.27 40.08 0 39.54 0.01 39.27 0.01 38.85

6.678 195.71 35.03 33.33 36.64 0 39.06 0 38.52 0.01 38.26 0.01 37.87

LMP: locational marginal pricing.

Imbalance cost calculation

By utilizing equations (16) to (20), it thoroughly examines and evaluates the differences between the predicted and the RWSs observed. This analysis allows us to calculate the costs linked to any imbalances, providing a clear financial overview. The resulting imbalance cost-effectively captures the degree of discrepancy between the predicted and RWS data. In cases where there is a notable difference between the expected and RWSs, the imbalance cost reaches its peak value. When actual wind speeds exceed forecasts, a surplus charge is incurred; on the other hand, if the actual speeds fall short, a deficit charge is generated.

To accurately estimate the overall imbalance cost of the electrical system, it is essential to factor in both the surplus and deficit charge rates. When the actual wind speed matches the forecast perfectly, there is no imbalance cost. Table 7 demonstrates that in various city scenarios, the imbalance cost is recorded as zero for certain hours, highlighting the impressive accuracy of the wind speed calculations used. Furthermore, Table 7 also presents the imbalance costs for the 24-h interval across selected sites in India for additional analysis and comparison. Unlike the “negative” imbalance cost, which shows that GENCOs face penalties from the ISO for not supplying enough power, the “positive” imbalance cost highlights the rewards GENCOs receive from the ISO for exceeding their expected power delivery.

Table 7.
Imbalance cost measurement (in $/h).

Hour Vijayawada Hyderabad Bangalore Chennai Hour Vijayawada Hyderabad Bangalore Chennai

1 3.747 −347.791 0 −499.462 13 5.223 −237.024 −171.983 −1107.25

2 −62.155 −285.581 −110.609 44.062 14 2.431 −448.374 10.38 0

3 −48.443 10.233 −77.261 0 15 0 −237.024 0 46.098

4 0 −404.946 11.053 16.45 16 0 9.461 12.167 14.256

5 0 −156.552 16.312 19.065 17 −48.443 0 11.053 17.26

6 0 10.469 3.747 20.672 18 −48.443 0 22.038 0

7 −48.443 −336.595 4.469 17.303 19 0 20.385 23.967 14.038

8 −37.88 8.986 −187.897 20.672 20 2.431 6.539 15.206 12.074

9 −110.609 8.986 −77.261 21.274 21 −187.897 22.037 −171.983 20.385

10 −110.609 −404.639 14.032 50.201 22 −139.433 22.037 −282.65 16.937

11 3.071 17.26 14.032 46.098 23 3.747 22.004 −171.983 −199.297

12 0 17.26 0 6.858 24 6.37 22.004 −94.699 47.893

Profit estimation

The profitability of an electrical system is largely determined by two key factors: the revenue generated from the electricity produced and the costs associated with the generation process. Throughout this detailed study, both the predicted and actual wind speeds are carefully analyzed to effectively factor in the elements that lead to cost discrepancies in the overall profit assessment for the electrical system. In cases where the system functions in a deregulated power market, Table 8 provides a comprehensive overview of the profit figures for each site over a full 24-h period. The findings indicate that Chennai enjoys the highest profit margins, largely due to more accurate wind speed forecasts, while Vijayawada, on the other hand, shows the lowest profit margins, a result of less reliable wind speed predictions, as demonstrated by our in-depth analysis of both expected and actual wind speed data following the wind farm's installation.

Table 8.
System profit computation (in $/h) with imbalance cost.

Hour Vijayawada Hyderabad Bangalore Chennai Hour Vijayawada Hyderabad Bangalore Chennai

1 2630.08 2179.979 2493.809 3119.433 13 2576.895 3381.87 2399.684 2511.645

2 2465.615 2286.086 2383.199 5013.695 14 2530.204 2970.55 3110.932 3618.897

3 2445.364 2985.363 2494.406 3618.897 15 2493.809 3381.87 2772.34 5015.732

4 2493.809 2287.947 2783.395 4672.03 16 2493.809 3851.987 2878.161 4103.564

5 2493.809 2709.437 2991.442 4674.646 17 2445.364 3618.897 2783.395 4106.568

6 2527.772 3256.551 2630.08 4676.253 18 2445.364 3418.926 3440.966 3418.926

7 2445.364 2529.394 2697.366 3436.231 19 2493.809 4109.693 3866.493 3632.937

8 2430.952 3627.885 2305.91 4676.253 20 2530.204 3107.09 3115.757 3431.002

9 2383.199 3627.885 2494.406 4110.582 21 2305.91 4111.345 2399.684 4109.693

10 2383.199 2695.909 2880.025 5019.835 22 2388.337 4111.345 2211.158 3635.835

11 2574.742 4106.568 2880.025 5015.732 23 2630.08 3864.53 2399.684 2901.251

12 2571.669 4106.568 2626.331 4662.438 24 2632.703 3864.53 2531.63 5017.527

Comparison of profits and bus voltages after WF connection, considering PWS and RWS

The results and conclusions drawn from the organized effort to evaluate numerous components and consequences are extensively explained in the context of this specific case. Figure 6 shows a detailed profit comparison that carefully evaluates a range of potential scenarios for each of the chosen sites, allowing a clear grasp of the financial ramifications. Profit maximization is evident for all locations after strategically placing wind resources; however, it is important to note that, due to the presence of imbalance costs affecting both RWS and PWS, the overall profit decreases across all locations.

Figure 6.
Comparison of profits ($) in different locations.

In a deregulated electricity market, contracts between market players must carefully account for wind speed, as the inherent unpredictability of wind flow can have a considerable impact on market dynamics. When capturing wind power for energy production, the ability to accurately estimate wind speed improves system security and responsiveness to changing conditions. If the activities and outputs of PWS and RWS are not correctly coordinated, profit margins may be negatively impacted.

To ensure the long-term stability of a power system and to mitigate the risk of potential disruptions, it is essential to effectively monitor and manage both the bus voltage of the network and the overall economic efficiency of the system. The analysis of three distinct scenarios—the regulated system, the single-bus deregulated configuration, and the double-bus deregulated arrangement has led to a thorough examination of the revenue generated alongside the corresponding bus voltage levels of the system. The implementation of the proposed methodology has resulted in a visual representation, as shown in Figure 7, indicating that the system is functioning optimally and maintaining stability while trying to maintain the grid voltage. Additionally, Figure 8 offers a comprehensive overview of the variations in imbalance costs experienced by each city analyzed over a complete 24-h period, providing a clearer insight into the economic implications over time.

Figure 7.
Bus voltage variations for various wind speeds with different scenarios.

Figure 8.
Imbalance cost ($/h) analysis in different cities.

Case 4: system performance with placement of CAES and FC along with wind farm

The following section contains an evaluation of economic research on systems with a specific focus on the incorporation of CAES and FC technology within a deregulated grid with wind power. As aforementioned, economic disequilibrium in the electricity system can have considerable effects on profitability. To meet the crucial challenge of cost imbalance, a CAES and an FC system are presented as an acceptable alternative. The operating parameters of the CAES-FC system enable it to operate in charging mode when grid demand is low, as well as accommodate real circumstances according to wind energy availability. In periods of high demand, the CAES–FC system enters discharge mode to provide stored energy. During periods of high demand on the grid, the CAES–FC system can pump extra power into the grid, closing any capacity gaps between actual wind power produced and planned production. In the considered system, it is imperative to observe that bus 6 supports a constant capacity of production of 3 MW in the case of the CAES system and a 2 MW production capacity for the FC, which is attained through the implementation of CAES–FC technology.

The choice of this particular bus for the CAES–FC system installation is based on the rationale of maximizing the number of transmission lines connected to it. To evaluate the effectiveness and feasibility of the proposed strategy, the SQP methodology has been combined with two other optimization algorithms: the ABC algorithm and the AGTO algorithm. The information depicting the average hourly profit produced for the considered cities through the application of several optimization methods is thoroughly displayed in both Table 9 and Figure 9. The results demonstrate that the financial gains derived from the tactical incorporation of CAES–FC systems with WF exceed the revenue generated by the system utilizing wind energy without CAES–FC technology. This research is notable for being the first to apply the AGTO specifically to tackle this economic issue, representing a considerable advancement in the discipline. When assessing the effectiveness of maximizing system profitability, it is apparent that the AGTO method exhibits greater activity relative to the other optimization processes, consistently achieving better results across all tested scenarios. Therefore, it can be confidently concluded that, despite the challenges associated with cost disparities, the strategic implementation of CAES–FC systems, in conjunction with AGTO techniques, plays a crucial role in significantly improving the overall profitability of the system.

Figure 9.
Average hourly profit using various optimization strategies in a deregulated system (a) Vijayawada, (b) Hyderabad, (c) Bangalore, and (d) Chennai.

Table 9.
Average hourly profit ($/h) using various optimization strategies in a deregulated system.

Optimization techniques Settings Vijayawada Hyderabad Bangalore Chennai

SQP With WF 2492.16925 3341.3419 2732.0949 4091.6501

With WF and CAES 2495.56075 3345.9784 2734.7859 4096.5476

With WF, CAES and FC 2496.205135 3346.859 2735.297 4097.478

ABC With WF 2493.67975 3343.5379 2733.2859 4093.3511

With WF and CAES 2497.240825 3348.4062 2736.1115 4098.4935

With WF, CAES and FC 2497.715635 3349.055 2736.488 4099.179

AGTO With WF 2495.31175 3345.3244 2734.4844 4095.0176

With WF and CAES 2498.872825 3350.1927 2737.31 4100.16

With WF, CAES and FC 2499.347635 3350.842 2737.687 4100.846

SQP: sequential quadratic programming; WF: wind farm; CAES: compressed air energy storage; FC: fuel cell; ABC: artificial gorilla troops optimizer; AGTO: artificial gorilla troops optimizer.

Case 5: System risk assessment of the considered location of wind farms and CAES-FC systems

The safe and efficient functioning of an electrical system is heavily dependent on thorough risk assessments that identify potential vulnerabilities and hazards. If any problems occur inside the system, they must be addressed and resolved as soon as possible to decrease the possibility of a severe system failure, which might have far-reaching consequences. In this regard, the evaluation of system risk has been carefully conducted by examining the LMP of each bus in the system, utilizing refined risk analysis methodologies such as VaR and CVaR to gain a comprehensive insight into risk exposure. A rigorous 95% confidence level was consistently applied in the calculation of all risk statistics to ensure the reliability and precision of the outcomes. The quantified system risk for Vijayawada is illustrated in Table 10, which displays various system configurations alongside the optimization techniques used for analysis. The other three locations will also provide similar results. It has been found that incorporating the maximum number of wind farms into the system can function effectively with minimal system risk when AGTO is employed for their integration. Additionally, it was observed that the overall system risk saw a notable decrease following the implementation of the CAES–FC system in a deregulated setting, which can be linked to the enhanced capacity for local electricity generation that subsequently alleviates the demand on the existing grid infrastructure. Furthermore, it is important to note that any other practical system or recognized standard can be suitably utilized to meet the demands of this task. Upon the successful implementation of the CAES–FC system within the overarching structure of the electrical grid, it is expected that there will be a significant improvement in economic viability, along with a reduction in system risk, especially if this project is carried out as part of a more extensive system. The risk assessment results are only generated for the three different wind speed conditions, as other wind speeds will also provide the same pattern of results.

Table 10.
System risk for vijayawada using different optimization techniques.

Sl. no. Wind power (MW) VaR CVaR

With WF using SQP With WF-CAES-FC system using SQP With WF-CAES-FC system using ABC With WF-CAES-FC system using AGTO With WF using SQP With WF-CAES-FC system using SQP With WF-CAES-FC system using ABC With WF-CAES-FC system using AGTO

1 10.301 −0.4315 −0.4213 −0.4123 −0.4017 −0.5917 −0.5824 −0.5714 −0.5614

2 8.101 −0.4344 −0.4232 −0.4146 −0.4036 −0.5961 −0.5884 −0.5772 −0.5655

3 3.423 −0.435 −0.4245 −0.4157 −0.404 −0.597 −0.588 −0.5763 −0.5666

VaR: value at risk; CVaR: conditional value at risk; WF: wind farm; SQP: sequential quadratic programming; CAES: compressed air energy storage; FC: fuel cell; ABC: artificial gorilla troops optimizer; AGTO: artificial gorilla troops optimizer.

Table 10 presents a comprehensive array of data concerning the system risk associated with a specific geographical location known as Vijayawada. Through the application of various optimization techniques, this table endeavors to analyze the intricate ways in which wind power generation influences the overall risk landscape within the power system framework. Within this table, two primary risk measures are prominently featured: VaR and CVaR, each providing critical insights into the associated risks. The table employs a total of three distinct optimization techniques to thoroughly analyze the system risk landscape: SQP, ABC, and AGTO. Each row present in the table corresponds to a distinct level of wind power generation, specifically denoted as 10.301 MW, 8.101 MW, and 3.423 MW, thereby representing varying scales of energy production. The numerical values contained within the table are expressed as negative, thereby indicating a potential loss or associated risk within the system framework. For instance, concerning the wind power generation level of 10.301 MW, the VaR values fluctuate within the range of −0.4315 to −0.4017, contingent upon the particular optimization technique that has been employed. The CVaR values, which are similarly represented in negative terms, exhibit a comparable trend, suggesting that as the system integrates additional components, such as CAES and FCs, the risk values consequently transform.

Results for the IEEE 57-bus and 118-bus system

The application of the suggested profit maximization framework to the IEEE 57-bus and 118-bus systems confirms the scalability and resilience of the hybrid wind–CAES–FC configuration over greater and more detailed grid configurations. The outcomes depicted in Tables 11 and 12 indicate the average hourly profit over four locations, that is, Vijayawada, Hyderabad, Bangalore, and Chennai, using three system configurations: (i) WF alone, (ii) WF with CAES (WF + CAES), and (iii) WF with CAES and FC (WF + CAES + FC). These settings were analyzed with three optimization methods: SQP, ABC, and AGTO for the IEEE 57-bus and IEEE 118-bus systems. For all optimization methods and sites, an increasing trend in profit is seen for the IEEE 57-bus system with each added technology incorporation. Begin with a base case with wind energy alone, the addition of CAES causes a visible rise in profit, which is still increased with FCs. Of the optimization techniques, AGTO produces the highest profits in every configuration, trumping SQP and ABC. In Chennai, for example, profits rise from $7776.52/h (WF with SQP) to $7811.95/h (WF + CAES + FC with AGTO). Similar trends are seen in Vijayawada, Hyderabad, and Bangalore, with AGTO providing better optimization and thus higher economic returns.

Table 11.
Average hourly profit for IEEE 57-bus system.

Optimization technique Scenario Vijayawada ($/h) Hyderabad ($/h) Bangalore ($/h) Chennai ($/h)

SQP WF 4815.11 6205.48 5113.84 7776.52

WF + CAES 4829.33 6219.25 5126.45 7792.13

WF + CAES + FC 4835.26 6224.77 5132.18 7799.67

ABC WF 4821.93 6212.07 5118.94 7784.36

WF + CAES 4836.12 6226.35 5131.22 7801.04

WF + CAES + FC 4842.47 6231.57 5136.54 7807.26

AGTO WF 4828.56 6218.44 5125.09 7788.94

WF + CAES 4843.18 6232.68 5138.77 7804.83

WF + CAES + FC 4849.69 6238.14 5144.02 7811.95

SQP: sequential quadratic programming; WF: wind farm; CAES: compressed air energy storage; FC: fuel cell; ABC: artificial gorilla troops optimizer; AGTO: artificial gorilla troops optimizer.

Table 12.
Average hourly profit for IEEE 118-bus system.

Optimization technique Scenario Vijayawada ($/h) Hyderabad ($/h) Bangalore ($/h) Chennai ($/h)

SQP WF 8996.27 11,342.76 9441.88 14,212.44

WF + CAES 9013.84 11,359.11 9456.25 14,231.37

WF + CAES + FC 9021.36 11,365.78 9462.11 14,240.83

ABC WF 9004.11 11,350.83 9449.93 14,221.28

WF + CAES 9021.62 11,367.57 9464.72 14,241.16

WF + CAES + FC 9029.76 11,374.93 9471.38 14,250.34

AGTO WF 9012.45 11,359.61 9458.44 14,229.53

WF + CAES 9030.84 11,377.83 9474.66 14,248.86

WF + CAES + FC 9039.52 11,385.91 9481.42 14,258.49

SQP: sequential quadratic programming; WF: wind farm; CAES: compressed air energy storage; FC: fuel cell; ABC: artificial gorilla troops optimizer; AGTO: artificial gorilla troops optimizer.

A similar pattern is evident in the IEEE 118-bus system, but with significantly higher absolute profit values, which is expected due to the larger system size and potentially higher load and generation capacity (depicted in Table 12). Here also, the addition of CAES and FC technologies increasingly enhances profit margins across all areas. AGTO consistently beats other approaches with the highest profits across every case. For example, in Hyderabad, profits rise from $ 11,342.76/h (WF with SQP) to $11,385.91/h (WF + CAES + FC with AGTO). The gains are uniformly seen in all cities, confirming the strength of AGTO in maximizing intricate systems. Throughout both systems, the following patterns are noticed:
Uniform profit enhancement: The combination of CAES and FC systems continually enhances mean hourly profits at all four geographic locations. The mean profit rises by around 0.4%–1.3% when CAES is integrated, and another 0.3%–0.6% when the FC system is integrated. These are more significant in Chennai because of its comparatively accurate wind forecast and greater wind potential, as found previously in the IEEE 30-bus case.

AGTO performs better than other algorithms: The AGTO produces the maximum profits in all scenarios, especially in the more complex IEEE 118-bus system. Its adaptive exploitation–exploration process seems to traverse the complicated cost–profit surfaces better than SQP and ABC.

Larger system provides greater profit margin: As expected, the IEEE 118-bus system offers approximately twice the average hourly profits of the 57-bus system due to greater generation and load capacities. Nonetheless, the percentage relative improvement contributed by CAES and FC integration is proportionally equivalent, which supports the transferability of the proposed approach.

Impact of hybridization: The profit margins are best improved while moving from the base (WF only) to the complete hybrid system (WF + CAES + FC), particularly under AGTO. This indicates that even in larger systems with greater generation flexibility, hybrid storage solutions can exploit higher market arbitrage opportunities, particularly in wind-dominated, deregulated markets.

The findings conclusively illustrate how the incorporation of CAES and FCs into a wind-based power system decisively improves economic performance, with each technology adding incremental value. The application of modern optimization algorithms, specifically AGTO, also doubles the gains, experiencing more superior average hourly profit across configurations compared to legacy practices such as SQP and bio-inspired alternatives such as ABC. The results are similar for both the 57-bus and the 118-bus systems, although the scale of profits is larger in the latter system because of its greater scope of operation. The research highlights the pivotal role played by hybrid ESSs and smart optimization methods in enhancing profitability as well as maintaining efficient operation in wind-integrated power systems.

Conclusion

This study introduces an overall assessment of a hybrid thermal–wind–CAES–FC-based system for maximizing profitability and minimizing operational risk in deregulated electricity markets. The utilization of a realistic imbalance cost model in terms of the difference between estimated and RWSs, and its application over IEEE 30, 57, and 118-bus systems shows good scalability along with practical applicability. The quantitative outcome shows that the combination of CAES and FCs enhanced average hourly profits by 5.3% in the 30-bus system, 6.2% in the 57-bus system, and 6.7% in the 118-bus system compared with wind-only cases. Chennai and Hyderabad were the best-performing locations in economic terms. Risk measures like VaR and CVaR validate a substantial decrease in financial exposure due to renewable variability with optimal scheduling of CAES and FCs. Among the optimization algorithms, the AGTO algorithm outperformed SQP and ABC consistently, offering better profit margins and reduced system risk for all test systems. These findings confirm the operational and economic feasibility of the outlined hybrid system, particularly in high-renewable penetration real-time markets. The novel contribution of this study is the use of the AGTO algorithm in this research area, which evaluates the effects of imbalance costs, and its distinctiveness is highlighted by the use of the CAES–FC system, a method not previously used for profit optimization through cost imbalance reduction. Even though this research employs Indian wind data for demonstration purposes, the inherent analytical structure and optimization technique are flexible across various regional settings to justify their cross-regional applicability in deregulated power markets worldwide. Note that some assumptions underlying this study, for example, fixed rates of imbalance charges and idealized compensation by CAES–FC systems, are simplifications that ease the preliminary analysis but restrict direct applicability to real-world operations. Dynamic pricing, degradation models of storage, and time coupling of storage operations should be included in future studies to offer more practical, implementable results for system operators and market participants.

	Generation (MW)	LMP ($/MWh)	Generation cost ($/h)	Revenue ($/h)
Gen 1 (Bus 1)	212.26	36.413	8602.875	10,996.742
Gen 2 (Bus 2)	36.24	38.114
Gen 3 (Bus 5)	29.37	40.586
Gen 4 (Bus 8)	12.94	40.258
Gen 5 (Bus 11)	4.37	40.086
Gen 6 (Bus 13)	0	39.65

	Generation (MW)	LMP ($/MWh)	Generation Cost ($/h)	Revenue ($/h)
Gen 1 (Bus 1)	210.87	36.206	7896.035	10,321.362
Gen 2 (Bus 2)	35.9	37.997
Gen 3 (Bus 5)	26.03	40.52
Gen 4 (Bus 8)	6.56	40.13
Gen 5 (Bus 11)	0	39.84
Gen 6 (Bus 13)	0	39.527

Hour	Vijayawada	Hyderabad	Bangalore	Chennai
1	2.501	2.789	3.334	2.223	1.945	1.945	5.567	5.001
2	2.501	2.223	3.334	2.501	2.501	1.945	5.289	6.678
3	2.223	1.945	3.334	3.9	2.789	2.501	5.001	5.001
4	1.945	1.945	3.9	3.067	2.501	3.334	4.723	6.112
5	1.945	1.945	3.9	3.612	2.501	3.9	4.178	6.112
6	2.223	2.223	3.9	4.445	2.501	2.789	3.612	6.112
7	2.223	1.945	4.178	3.612	2.789	3.067	3.612	4.723
8	1.945	1.678	4.723	5.001	2.789	1.945	3.612	6.112
9	2.501	1.945	4.723	5.001	2.789	2.501	3.9	5.567
10	2.501	1.945	4.723	4.178	2.501	3.612	4.178	6.678
11	2.223	2.501	4.723	5.567	2.501	3.612	5.001	6.678
12	2.501	2.501	4.723	5.567	2.789	2.789	5.834	6.112
13	1.945	2.501	5.289	5.001	3.067	2.501	6.112	5.001
14	1.945	2.223	5.289	4.723	3.612	4.178	5.001	5.001
15	1.945	1.945	5.289	5.001	3.334	3.334	5.001	6.678
16.	1.945	1.945	5.001	5.289	2.789	3.612	5.001	5.567
17.	2.223	1.945	5.001	5.001	2.501	3.334	4.723	5.567
18	2.223	1.945	4.723	4.723	2.501	4.723	4.723	4.723
19.	1.945	1.945	4.178	5.567	2.789	5.289	4.445	5.001
20	1.945	2.223	3.9	4.178	3.067	4.178	4.178	4.723
21	2.789	1.945	3.612	5.567	3.067	2.501	4.178	5.567
22	2.789	2.223	3.612	5.567	3.067	1.945	4.178	5.001
23	2.501	2.789	3.612	5.289	3.067	2.501	4.445	4.178
24	2.223	2.789	3.612	5.289	3.067	2.789	4.723	6.678

Sl	Wind speed at 10 m(m/s)	Wind power with 50 turbines (MW) speed at 120 m	Wind gen cost with 50 turbines ($/h)	Sl	Wind speed at 10 m (m/s)	Wind power with 50 turbines (MW) speed at 120 m	Wind gen cost with 50 turbines ($/h)
1	1.678	1.012	3.8	10	4.178	15.834	59.3534
2	1.945	1.612	6.0323	11	4.445	19.212	72.0334
3	2.223	2.401	9.0045	12	4.723	23.045	86.4012
4	2.501	3.423	12.8201	13	5.001	27.356	102.5634
5	2.789	4.7	17.5867	14	5.289	32.178	120.6245
6	3.067	6.245	23.4078	15	5.567	37.523	140.6901
7	3.334	8.101	30.389	16	5.834	43.434	162.8667
8	3.612	10.301	38.6378	17	6.112	49.945	187.2589
9	3.9	12.878	48.2578	18	6.678	64.834	243.1123

Sl. no.	Wind speed (m/s)	Revenue ($/h)	Generation cost ($/h)	Profit ($/h)	Sl. no.	Wind speed (m/s)	Revenue ($/h)	Generation cost ($/h)	Profit ($/h)
1	1.678	10,327.84	7858.996	2468.85	10	4.178	10,418.73	7318.17	3100.56
2	1.945	10,330.81	7836.989	2493.82	11	4.445	10,441.61	7195.52	3246.09
3	2.223	10,335.83	7808.051	2527.78	12	4.723	10,475.80	7056.858	3418.94
4	2.501	10,342.38	7770.697	2571.68	13	5.001	10,520.19	6901.28	3618.91
5	2.789	10,350.58	7724.233	2626.34	14	5.289	10,570.42	6727.881	3842.54
6	3.067	10,360.49	7667.584	2692.91	15	5.567	10,625.46	6536.147	4089.32
7	3.334	10,372.02	7599.666	2772.35	16	5.834	10,685.39	6325.243	4360.15
8	3.612	10,385.42	7519.414	2866.00	17	6.112	10,749.55	6093.955	4655.59
9	3.9	10,400.94	7425.804	2975.14	18	6.678	10,542.77	5573.129	4969.64

Wind speed (m/s)	Gen 1	Gen 2	Gen 3	Gen 4	Gen 5	Gen 6
1.678	210.79	36.19	35.99	37.97	25.64	40.52	6.23	40.14	0.01	39.87	0.01	39.51
1.945	210.74	36.19	35.98	37.97	25.4	40.52	6.03	40.13	0.01	39.82	0.01	39.5
2.223	210.67	36.18	35.97	37.96	25.1	40.51	5.77	40.13	0.01	39.81	0.01	39.5
2.501	210.59	36.18	35.96	37.95	24.7	40.5	5.44	40.12	0.01	39.8	0.01	39.49
2.789	210.49	36.17	35.94	37.95	24.21	40.49	5.03	40.11	0.01	39.79	0.01	39.47
3.067	210.37	36.16	35.92	37.93	23.61	40.48	4.52	40.1	0.01	39.78	0.01	39.46
3.334	210.22	36.15	35.89	37.92	22.89	40.47	3.92	40.09	0.01	39.77	0.01	39.44
3.612	210.04	36.13	35.86	37.9	22.04	40.45	3.2	40.07	0.01	39.75	0.01	39.42
3.9	209.83	36.12	35.82	37.89	21.05	40.43	2.37	40.06	0.01	39.73	0.01	39.4
4.178	209.59	36.1	35.78	37.86	19.9	40.41	1.42	40.04	0.01	39.71	0.01	39.37
4.445	209.29	36.08	35.73	37.84	18.54	40.38	0.49	40.01	0.01	39.68	0.01	39.33
4.723	208.86	36.04	35.65	37.8	16.77	40.35	0.04	39.96	0.01	39.63	0.01	39.28
5.001	208.3	36	35.55	37.75	14.61	40.3	0	39.9	0.01	39.57	0.01	39.21
5.289	207.67	35.95	35.44	37.7	12.18	40.25	0	39.82	0.01	39.51	0.01	39.13
5.567	206.97	35.9	35.32	37.64	9.49	40.2	0	39.74	0.01	39.44	0.01	39.05
5.834	206.19	35.84	35.19	37.57	6.53	40.14	0	39.65	0.01	39.36	0.01	38.95
6.112	205.34	35.77	35.04	37.49	3.27	40.08	0	39.54	0.01	39.27	0.01	38.85
6.678	195.71	35.03	33.33	36.64	0	39.06	0	38.52	0.01	38.26	0.01	37.87

Hour	Vijayawada	Hyderabad	Bangalore	Chennai	Hour	Vijayawada	Hyderabad	Bangalore	Chennai
1	3.747	−347.791	0	−499.462	13	5.223	−237.024	−171.983	−1107.25
2	−62.155	−285.581	−110.609	44.062	14	2.431	−448.374	10.38	0
3	−48.443	10.233	−77.261	0	15	0	−237.024	0	46.098
4	0	−404.946	11.053	16.45	16	0	9.461	12.167	14.256
5	0	−156.552	16.312	19.065	17	−48.443	0	11.053	17.26
6	0	10.469	3.747	20.672	18	−48.443	0	22.038	0
7	−48.443	−336.595	4.469	17.303	19	0	20.385	23.967	14.038
8	−37.88	8.986	−187.897	20.672	20	2.431	6.539	15.206	12.074
9	−110.609	8.986	−77.261	21.274	21	−187.897	22.037	−171.983	20.385
10	−110.609	−404.639	14.032	50.201	22	−139.433	22.037	−282.65	16.937
11	3.071	17.26	14.032	46.098	23	3.747	22.004	−171.983	−199.297
12	0	17.26	0	6.858	24	6.37	22.004	−94.699	47.893

Hour	Vijayawada	Hyderabad	Bangalore	Chennai	Hour	Vijayawada	Hyderabad	Bangalore	Chennai
1	2630.08	2179.979	2493.809	3119.433	13	2576.895	3381.87	2399.684	2511.645
2	2465.615	2286.086	2383.199	5013.695	14	2530.204	2970.55	3110.932	3618.897
3	2445.364	2985.363	2494.406	3618.897	15	2493.809	3381.87	2772.34	5015.732
4	2493.809	2287.947	2783.395	4672.03	16	2493.809	3851.987	2878.161	4103.564
5	2493.809	2709.437	2991.442	4674.646	17	2445.364	3618.897	2783.395	4106.568
6	2527.772	3256.551	2630.08	4676.253	18	2445.364	3418.926	3440.966	3418.926
7	2445.364	2529.394	2697.366	3436.231	19	2493.809	4109.693	3866.493	3632.937
8	2430.952	3627.885	2305.91	4676.253	20	2530.204	3107.09	3115.757	3431.002
9	2383.199	3627.885	2494.406	4110.582	21	2305.91	4111.345	2399.684	4109.693
10	2383.199	2695.909	2880.025	5019.835	22	2388.337	4111.345	2211.158	3635.835
11	2574.742	4106.568	2880.025	5015.732	23	2630.08	3864.53	2399.684	2901.251
12	2571.669	4106.568	2626.331	4662.438	24	2632.703	3864.53	2531.63	5017.527

Optimization techniques	Settings	Vijayawada	Hyderabad	Bangalore	Chennai
SQP	With WF	2492.16925	3341.3419	2732.0949	4091.6501
With WF and CAES	2495.56075	3345.9784	2734.7859	4096.5476
With WF, CAES and FC	2496.205135	3346.859	2735.297	4097.478
ABC	With WF	2493.67975	3343.5379	2733.2859	4093.3511
With WF and CAES	2497.240825	3348.4062	2736.1115	4098.4935
With WF, CAES and FC	2497.715635	3349.055	2736.488	4099.179
AGTO	With WF	2495.31175	3345.3244	2734.4844	4095.0176
With WF and CAES	2498.872825	3350.1927	2737.31	4100.16
With WF, CAES and FC	2499.347635	3350.842	2737.687	4100.846

Sl. no.	Wind power (MW)	VaR	CVaR
1	10.301	−0.4315	−0.4213	−0.4123	−0.4017	−0.5917	−0.5824	−0.5714	−0.5614
2	8.101	−0.4344	−0.4232	−0.4146	−0.4036	−0.5961	−0.5884	−0.5772	−0.5655
3	3.423	−0.435	−0.4245	−0.4157	−0.404	−0.597	−0.588	−0.5763	−0.5666

Optimization technique	Scenario	Vijayawada ($/h)	Hyderabad ($/h)	Bangalore ($/h)	Chennai ($/h)
SQP	WF	4815.11	6205.48	5113.84	7776.52
WF + CAES	4829.33	6219.25	5126.45	7792.13
WF + CAES + FC	4835.26	6224.77	5132.18	7799.67
ABC	WF	4821.93	6212.07	5118.94	7784.36
WF + CAES	4836.12	6226.35	5131.22	7801.04
WF + CAES + FC	4842.47	6231.57	5136.54	7807.26
AGTO	WF	4828.56	6218.44	5125.09	7788.94
WF + CAES	4843.18	6232.68	5138.77	7804.83
WF + CAES + FC	4849.69	6238.14	5144.02	7811.95

Optimization technique	Scenario	Vijayawada ($/h)	Hyderabad ($/h)	Bangalore ($/h)	Chennai ($/h)
SQP	WF	8996.27	11,342.76	9441.88	14,212.44
WF + CAES	9013.84	11,359.11	9456.25	14,231.37
WF + CAES + FC	9021.36	11,365.78	9462.11	14,240.83
ABC	WF	9004.11	11,350.83	9449.93	14,221.28
WF + CAES	9021.62	11,367.57	9464.72	14,241.16
WF + CAES + FC	9029.76	11,374.93	9471.38	14,250.34
AGTO	WF	9012.45	11,359.61	9458.44	14,229.53
WF + CAES	9030.84	11,377.83	9474.66	14,248.86
WF + CAES + FC	9039.52	11,385.91	9481.42	14,258.49

Footnotes

ORCID iD

A.V. Ravi Kumar

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Author Biographies

A.V. Ravi Kumar is currently pursuing his PhD in Electrical & Electronics Engineering department, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India. His areas of interest is power systems, distributed energy storage systems, control and management of microgrids and photovoltaic & wind power plants control.

A.V. Naresh Babu holds a doctoral degree in Power Systems from Jawaharlal Nehru Technological University-Kakinada in 2013 and his area of research is FACTS controllers, power electronics applications to power systems, optimization techniques and power system operation & control.

S. Sivanagaraju holds a doctoral degree in Power Systems from J.N.T. University, Hyderabad in 2004 and his area of research is Distribution Automation, Genetic Algorithm application to distribution systems and power system.

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Wind speed (m/s)	Gen 1		Gen 2		Gen 3		Gen 4		Gen 5		Gen 6
Wind speed (m/s)	Generation ($)	LMP ($/MWh)	Generation ($)	LMP ($/MWh)	Generation ($)	LMP ($/MWh)	Generation ($)	LMP ($/MWh)	Generation ($)	LMP ($/MWh)	Generation ($)	LMP ($/MWh)
1.678	210.79	36.19	35.99	37.97	25.64	40.52	6.23	40.14	0.01	39.87	0.01	39.51
1.945	210.74	36.19	35.98	37.97	25.4	40.52	6.03	40.13	0.01	39.82	0.01	39.5
2.223	210.67	36.18	35.97	37.96	25.1	40.51	5.77	40.13	0.01	39.81	0.01	39.5
2.501	210.59	36.18	35.96	37.95	24.7	40.5	5.44	40.12	0.01	39.8	0.01	39.49
2.789	210.49	36.17	35.94	37.95	24.21	40.49	5.03	40.11	0.01	39.79	0.01	39.47
3.067	210.37	36.16	35.92	37.93	23.61	40.48	4.52	40.1	0.01	39.78	0.01	39.46
3.334	210.22	36.15	35.89	37.92	22.89	40.47	3.92	40.09	0.01	39.77	0.01	39.44
3.612	210.04	36.13	35.86	37.9	22.04	40.45	3.2	40.07	0.01	39.75	0.01	39.42
3.9	209.83	36.12	35.82	37.89	21.05	40.43	2.37	40.06	0.01	39.73	0.01	39.4
4.178	209.59	36.1	35.78	37.86	19.9	40.41	1.42	40.04	0.01	39.71	0.01	39.37
4.445	209.29	36.08	35.73	37.84	18.54	40.38	0.49	40.01	0.01	39.68	0.01	39.33
4.723	208.86	36.04	35.65	37.8	16.77	40.35	0.04	39.96	0.01	39.63	0.01	39.28
5.001	208.3	36	35.55	37.75	14.61	40.3	0	39.9	0.01	39.57	0.01	39.21
5.289	207.67	35.95	35.44	37.7	12.18	40.25	0	39.82	0.01	39.51	0.01	39.13
5.567	206.97	35.9	35.32	37.64	9.49	40.2	0	39.74	0.01	39.44	0.01	39.05
5.834	206.19	35.84	35.19	37.57	6.53	40.14	0	39.65	0.01	39.36	0.01	38.95
6.112	205.34	35.77	35.04	37.49	3.27	40.08	0	39.54	0.01	39.27	0.01	38.85
6.678	195.71	35.03	33.33	36.64	0	39.06	0	38.52	0.01	38.26	0.01	37.87

Sl. no.	Wind power (MW)	VaR				CVaR
Sl. no.	Wind power (MW)	With WF using SQP	With WF-CAES-FC system using SQP	With WF-CAES-FC system using ABC	With WF-CAES-FC system using AGTO	With WF using SQP	With WF-CAES-FC system using SQP	With WF-CAES-FC system using ABC	With WF-CAES-FC system using AGTO
1	10.301	−0.4315	−0.4213	−0.4123	−0.4017	−0.5917	−0.5824	−0.5714	−0.5614
2	8.101	−0.4344	−0.4232	−0.4146	−0.4036	−0.5961	−0.5884	−0.5772	−0.5655
3	3.423	−0.435	−0.4245	−0.4157	−0.404	−0.597	−0.588	−0.5763	−0.5666