An Effective Strategy for Achieving Economic Reliability by Optimal Coordination of Hybrid Thermal–Wind–EV System in a Deregulated System

Abstract

This paper describes an effective operating strategy for electric vehicles (EVs) in a hybrid facility that leverages renewable energy sources. The method is to enhance the profit of the wind–thermal–EV hybrid plant while maintaining the grid frequency (f_PG) and energy level of the EV battery storage system. In a renewable-associated power network, renewable energy producers must submit power supply proposals to the system operator at least one day before operations begin. The market managers then combine the power plans for the next several days based on bids from both power providers and distributors. However, due to the unpredictable nature of renewable resources, the electrical system cannot exactly adhere to the predefined power supply criteria. When true and estimated renewable power generation diverges, the electrical system may experience an excess or shortage of electricity. If there is a disparity between true and estimated wind power (TWP, EWP), the EV plant operates to minimize this variation. This lowers the costs associated with the discrepancy between actual and projected wind speeds (TWS, EWS). The proposed method effectively reduces the uncertainty associated with wind generation while being economically feasible, which is especially important in a deregulated power market. This study proposes four separate energy levels for an EV battery storage system (E_EV,max, E_EV,opt, E_EV,low, and E_EV,min) to increase system profit and revenue, which is unique to this work. The optimum operating of these EV battery energy levels is determined by the present electric grid frequency and the condition of TWP and EWP. The proposed approach is tested on a modified IEEE 30 bus system and compared to an existing strategy to demonstrate its effectiveness and superiority. The entire work was completed using the optimization technique called sequential quadratic programming (SQP).

1. Introduction

In recent years, the regulated power sector has been transformed to deregulated electrical compositions by replacing the old monopoly features. This electricity market has created a competitive environment among GENCOs (generation companies), TRANSCOs (transmission companies), DISCOs (distribution companies), and other market participants to provide financial benefits to consumers. The key solution to mitigate the severity of global warming is to decrease greenhouse gas emissions. To address this issue, various measures have been implemented worldwide to limit the release of greenhouse gases and minimize environmental damage. Many developing countries have introduced initiatives to stabilize carbon dioxide emissions at sustainable levels [1]. Recognizing that the electric power sector is a significant contributor to greenhouse gas emissions, renewable energy sources have played a crucial role in reducing these emissions in recent years [2]. Solar and wind energies are regarded as green sources of energy since they emit no hazardous elements into the environment [3]. However, renewable energy sources are unpredictable and variable, which poses security and stability concerns for the electrical system [4]. Therefore, it becomes essential to supplement these renewable energy sources with additional energy sources to ensure a consistent and balanced power supply [5]. EVs have gained significant popularity worldwide as an efficient, reliable, and environmentally friendly method of energy storage [6].

In a renewable-associated power network, the renewable power producers must submit their power supply proposals to the system operator at least one day before the start of operations. The market managers then unify the power plan for the upcoming days based on the bids received from both power producers and distributors. However, due to the random characteristics of renewable resources, the electrical grid cannot strictly adhere to the predetermined power supply conditions. This can result in an excess or shortage of power conditions within the electrical grid when there is a discrepancy between true and expected renewable power production [7]. In the power network, power production and requirements are continually varying with time. Consequently, the grid frequency also fluctuates with time. When renewable power plants are integrated with the existing thermal power system, the grid frequency becomes even more unstable and fluctuates more [8]. Therefore, maintaining grid frequency control becomes essential for the renewable power system [9]. In such a case, the optimum performance of the storage devices is crucial for preserving the grid frequency by compensating for the discrepancy between true and expected renewable output by providing additional power to the electrical network. Bazdar et al. [10] have carried out a comprehensive study on the utilization and features of CAES (compressed air energy storage) systems. In ref. [11], the coverage–percentage method is introduced to determine the prime sizing of CAES systems, aiming to attain the ideal working of the electrical grid in Ontario. Ref. [12] explores the robust scheduling of EV aggregators while considering price uncertainty. The study utilizes a robust optimization technique to effectively model the uncertainty in market prices by considering both the upper and lower bounds of upstream grid prices. The article [13] discusses the challenges that arise from the fluctuating nature of renewable energy sources in maintaining the security and stability of power systems, particularly in wind-integrated deregulated power networks.

The prime objective of ref. [14] is to enhance the efficiency of a V2G (vehicle-to-grid) integrated system, to reduce power construction costs, and to grow the overall system’s cost-effectiveness. The main consideration of ref. [15] is the involvement of EV aggregators in energy markets and the importance of managing uncertainty in capitalist energy markets to achieve economic objectives. The framework [16] presents a distributed deep reinforcement learning approach that ensures privacy while maximizing profits in multiple smart electric vehicle charging stations (EVCSs) that are equipped with photovoltaic and energy storage systems. The study [17] proposes a profit enhancement methodology for a D-EVSE (decentralized EV supply equipment) with a renewable energy system. This framework enables the D-EVSE to capitalize on the fluctuations in electricity prices by engaging in electricity transactions with EVs or the grid. Ref. [18] presents an optimization and control algorithm consisting of four stages. Its main objective is to minimize the operational expenses of an integrated smart charging station while enhancing customer attraction and operational performance. Ref. [19] provides an overview of the difficulties and strategies involved in identifying the most suitable sites for EVCSs. The improved whale optimization algorithm (IWOA) has been presented in ref. [20] to optimize the placement and size determination of EVCSs that possess non-convex and nonlinear characteristics. Ref. [21] presents a unique operating mechanism for EV charging stations that focuses on optimizing pricing, charging schedules, and admission control. The methodology presented in ref. [22] suggests PSO (particle swarm optimization) utilization to determine the most suitable locations and capacities for EVCSs in unbalanced radial distribution systems (URDS). The proposed strategy in ref. [23] aims to optimize the pricing of electricity for EVs by dividing regions and periods. This strategy is designed to encourage users to charge their EVs in districts with a higher number of charging stations.

Research [24] centers its attention on the economic factors surrounding EVCSs and presents a profit-oriented algorithm for scheduling the charging sessions. This algorithm aims to optimize the long-term turnover of the EVCS while minimizing the waiting time for EVs. Ref. [25] describes a unique method for controlling the charging of several EVs using workplace charging stations (WCSs) equipped with photovoltaic panels (PVs). The stochastic optimization framework presented in ref. [26] introduces a novel approach to developing a technical model for charging stations. This framework ensures long-term profitability by considering uncertainties in electricity prices and the number of vehicles. Article [27] presents a pragmatic method for modeling the uncertainty of solar irradiance and optimizing the day-ahead schedule of electricity markets. Study [27] assesses the financial and operational aspects of different battery energy storage systems (BESSs), non-BESS storage systems, and combustion turbines. Ref. [28] examines the implementation of EVCSs, considering variables like station capacity, charging time, and daily mileage, to minimize carbon and nitrogen oxide emissions. Reference [29] focuses on the necessity of profitable EV charging enterprises by suggesting a model to calculate the quantity of EV chargers and the capacity of supporting equipment, including power conditioning systems, battery energy storage systems, and on-site photovoltaic generation systems. Study [30] examines how EV chargers affect the dynamic behavior of power systems. It assesses the ability of standard static and dynamic load models to accurately depict the behavior of EV chargers. The primary target of [31] is to enhance the effectiveness of a commercial charging station (CCS) powered by a solar PV and equipped with a BESS. By considering the solar PV forecast and EV arrival, the paper aims to maximize profit. Ref. [32] introduces an integrated system that employs an appropriate scheduling method to achieve the most efficient functioning of a wind farm–CAES system to maximize profit and revenue while ensuring grid frequency stability. Ref. [33] introduces a strategy for managing a building’s energy system that considers uncertainties like electricity demands and temperature variations. Ref. [34] explores the effects of different types of ions on cyclodextrin supramolecular assemblies, focusing on structural changes and molecular interactions for the V2G system.

Following a thorough review of the literature, it was determined that various unanswered questions require addressing.

• It is crucial to explore the economic consequences of incorporating a WF (wind farm) into deregulated power systems.
• It is vital to examine the influence of renewable power production imbalances in the day-ahead power market.
• Furthermore, it is decisive to investigate the effects of the disparity between the TWS and EWS on system profit.
• Additionally, it is crucial to analyze the advantages of incorporating storage devices in the hybrid operation of renewable energy sources.
• Finally, it is decisive to explore the maintenance of the grid frequency by examining the functioning of the WF and storage hybrid systems.

During the last few years, research has been undertaken on the inclusion of storage devices in a renewable combined system [35]. However, no approach has been provided for sustaining grid frequency and increasing system profitability in the presence of discrepancy prices (DPs) by exploiting the energy levels of the battery bank of EVs. This research aims to fill that need. This work introduces an effective operating methodology for a thermal–wind–EV hybrid system that varies from the operating strategy proposed in the reference [32]. While reference [32] constructed a CAES system, this research applies a similar logic to the EV battery storage system and gets all important parameters based on the data supplied in [32]. Following that, the new operating strategy is applied and compared to the prior logic described in [32]. The work focuses primarily on the operating strategy of the energy levels of the EV’s battery system, stressing the procedure’s efficacy and emphasizing the differences from the technique described in reference [32]. The fundamental goal of this work is to elevate system profitability and assure grid frequency stability through efficient management and operation of the energy level in the EV battery storage system. Furthermore, the concept of DP is fully explained because it is very crucial in computing system profit. The entire study was carried out in deregulated electricity networks. This work introduces four different energy levels of the EV battery storage system (E_EV,max, E_EV,opt, E_EV,low, and E_EV,min) for the enhancement of the system’s profit and revenue. The optimum operation of these energy levels is decided based on the present electric grid frequency and the status of the TWP and EWP.

The proposed hybrid system is visually represented in Figure 1. The control station is the heart of this system, which plays a vital role in its overall functioning. The control station collects power from various sources such as the WF, thermal plant, and EV system. It then distributes this electricity to energy customers in an efficient manner by managing the grid frequency. The ability to control the grid frequency is critical for the system’s functionality. Consideration of the DP is crucial for the system’s profit in a renewable energy-based deregulated electrical system. It forms due to market contracts, which are usually prepared a day in advance of the operation. The DP can also have negative effects on the system. To counteract these effects, the use of a storage device is proposed.

• The proposed method presents the strategy to operate an EV system economically with the combination of both WF and thermal power systems. This hybrid approach effectively reduces the negative impact of DPs, while also ensuring a stable power supply and demand ratio. Additionally, it contributes to the long-term sustainability of the grid frequency.
• The distribution of the energy level of the EV battery storage system is one of the new characteristics of this study. This distribution, which consists of different levels, such as E_EV,max, E_EV,opt, E_EV,low, and E_EV,min, is carefully managed by considering the conditions of the TWP and EWP as well as the grid frequency. This management helps in maximizing the system profit while also ensuring the stability of the grid frequency.
• To accomplish the suggested method, a modified IEEE 30-bus system has been selected for testing purposes.
• In the wind-associated deregulated power network, the wind speed has been anticipated and the speed details have been submitted to the market operator at least one day in advance of the power operation.
• The power generation quantity at various wind speeds has been examined by analyzing the wind’s characteristic graph, as depicted in Figure 2 (where WS_ci, WS_r, and WS_co are represented as cut-in, rated, and cut-out wind speeds). For this study, the values of WS_ci, WS_r, and WS_co are assumed to be 3 m/s, 15 m/s, and 26 m/s.
• According to the EWP, the WF is expected to provide the estimated power output. But if the TWP varies from the forecast, the EV system needs to function in discharging mode and deliver the supplementary power to the grid for dipping the contrary impact of the DP.
• The EV system’s operation relies on four main factors: the expected wind power, true wind power, grid frequency, and the EV battery’s present energy level. By considering these factors, the strategy for EV operation aims to maximize the wind–thermal–EV hybrid plant’s net revenue and profit.

This paper is organized in the following manner: Section 2 is dedicated to presenting the necessary system models that are required for formulating the problem. Moving forward, Section 3 thoroughly defines the objective functions and constraints. Section 4 and Section 5 elaborate on the solution to the problem by visually depicting the proposed approach through a comprehensive flow-chart. This detailed illustration aids in understanding the step-by-step process of the proposed solution and the logic behind each decision made. Following this, Section 6 delves into showcasing the obtained results and engaging in a thorough discussion regarding the implications and significance of the findings. This section provides a detailed analysis of the results obtained through the proposed methodology, shedding light on the effectiveness and efficiency of the solution approach. Lastly, the conclusion of this paper is encapsulated in Section 7, where a comprehensive summary of the key findings, implications, and recommendations derived from the study are presented.

2. System Modeling

System design is an important step in the overall process of simulation, optimization, and analysis of results.

2.1. Proposed Hybrid System

The proposed hybrid plant is a combination of wind, thermal, and EV storage systems, which work together to fulfill the electricity demand. The power generation plant includes a WF where wind turbines are used to harness the power of the wind, and a thermal power plant which uses heat to generate electricity. The storage system is made up of an EV with different energy levels of batteries, which can be operated in different modes to maintain the electricity in the grid. This system ensures that there is a constant supply of electricity to meet energy demand, which refers to the amount of electricity consumed by customers. The control station of the power plant plays a crucial role in managing and controlling the operation of the entire system. In this work, four different energy levels of the EV battery storage system have been considered for optimization purposes. These energy levels, i.e., E_EV,max, E_EV,opt, E_EV,low, and E_EV,min, are important in maximizing the revenue and profit of the system. By optimizing the energy levels of the EV batteries, the power plant can generate and store electricity more efficiently, leading to increased profitability. The wind velocity data (TWS, EWS), as well as grid frequency, are used to control the operation of the storage system. If the TWS and EWS statistics differ, the market controllers may impose fines or provide incentives to the GENCOs. These fines or incentives are based on the extra or shortfall supply of power by the GENCOs to the electrical network. The goal of the model is to minimize the contrary impact of uncertainties in wind power by scheduling the thermal and wind power plants’ operation as well as the energy level of the EV battery storage system. When the EWS is higher than the TWS, the EV batteries operate in the discharging mode. This means that the stored electricity in the batteries is used to meet the power demand. On the other hand, when the TWS is higher, the EV battery storage system operates in the charging mode. This allows the system to store excess energy generated from the wind turbines for future use. The optimal operation of the EV battery storage system also plays a crucial role in maintaining grid frequency stability. By adjusting its operation mode, the system can stabilize the frequency of the electricity supplied to the grid.

2.2. LMP (Locational Marginal Pricing)

The LMP represents an approach that is employed to ascertain the cost of the energy delivered at a particular site within an electric system. The calculation of LMP encompasses several factors including energy prices, transmission congestion, as well as the marginal cost of generation and losses. Through the utilization of LMP, the market clearing price (MCP) is determined for different locations, commonly referred to as nodes, within the electric system. It is worth noting that LMP is sometimes denoted as ‘nodal pricing’ since it effectively computes the energy price at specific nodes within the system. The MCP holds immense importance in the calculation of LMP due to its role as a representation of the equilibrium between the supply and demand of electricity within the market. This essential factor is derived by considering the balance between the aforementioned supply and demand at various locations or nodes within an electrical system, which is commonly referred to as nodal pricing. By considering energy prices and transmission congestion, the MCP aids in determining the price of energy delivered at a specific location.

2.3. SQP (Sequential Quadratic Programming)

The SQP method is an optimization technique that generates a problem formulation and solution in a step-by-step manner by utilizing the quadratic sub-problems process. This method involves two essential processes: the line search process and the trust-region framework process. The line search process plays a crucial role in identifying the optimal step size that minimizes the objective function along the search direction. On the other hand, the trust-region framework process ensures that each step taken in every iteration remains within a trust region. This trust region represents a specific region where the quadratic approximation of the objective function accurately represents the real function. SQP has gained popularity due to its ability to handle both equality and inequality constraints efficiently, allowing it to converge to a local minimum effectively. This method shines particularly bright in solving nonlinear optimization problems that involve nonlinear objective functions and constraints.

Conceptually, SQP can be seen as a parallel process to Newton’s method. It strategically explores new steps away from the current point by minimizing a quadratic model of the problem. SQP is closely associated with two types of algorithms for solving nonlinear problems: the active set method and Newton’s method. These algorithms play a crucial role in the iterative process of SQP, which can be broken down into several steps.

• In Step 1, the variables are initialized, setting the stage for subsequent calculations.
• Step 2 involves defining the search direction of the variables for the objectives, ensuring that the subsequent steps are aligned with the desired goals.
• Step 3 is dedicated to defining and solving quadratic programming sub-problems, which are integral to the overall optimization process.
• In Step 4, the optimum result is checked. If the desired optimum result is achieved, the process proceeds to the next step. However, if the optimum result is not yet attained, the search size is adjusted, and the process loops back to Step 2, repeating the necessary calculations.
• Finally, in Step 5, the best solution is obtained, consolidating all the iterative steps into a robust and effective solution.

3. Objective Function

Let’s consider an electrical system that consists of a certain number of buses (NB_sys), as well as a specific number of loads (NL_sys) and a certain number of generators (NG_sys). The main goal of the proposed methodology is to increase the overall revenue generated by the hybrid system as well as to maximize the profit obtained from the hybrid plant. This approach takes various important factors such as the true and expected wind speed data, the frequency of the grid, and the energy level of the EV battery storage system, into account. By considering these factors, a comprehensive analysis is conducted to ensure that the profit of the system is accurately calculated. The calculation of the profit involves several key elements, including the revenue price of the hybrid system (RP_HS(s)), the shortfall price rate (SPR_HS(s)), the extra price rate (EPR_HS(s)), the discrepancy price (DP(s)), and the investment cost associated with wind power (Cost_W). The primary objective of this research is to optimize and maximize the profit generated (PHS(s)) by the hybrid power plant. To accomplish this, a detailed expression of the profit is provided, outlining the various factors and considerations that contribute to its calculation. The system profit can be increased by optimizing the operation of the EV battery storage energy level. PC_HS(s) represents the total generation/production cost of the hybrid power plant.

$$\mathrm{Max}. {\mathrm{P}}_{\mathrm{HS}}\left(\mathrm{s}\right)={\mathrm{RP}}_{\mathrm{HS}}\left(\mathrm{s}\right)+\mathrm{DP}\left(\mathrm{s}\right)-{\mathrm{PC}}_{\mathrm{HS}}\left(\mathrm{s}\right)$$

(1)

$${\mathrm{RP}}_{\mathrm{HS}}\left(\mathrm{s}\right)={\mathrm{RP}}_{\mathrm{Ther}}\left(\mathrm{s}\right)+{\mathrm{RP}}_{\mathrm{WF}-\mathrm{EV}}\left(\mathrm{s}\right)$$

(2)

$${\mathrm{RP}}_{\mathrm{Ther}}\left(\mathrm{s}\right)={{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{NG}}_{\mathrm{sys}}}{\mathrm{GP}}_{\mathrm{Ther}}\left(\mathrm{m},\mathrm{s}\right) .\mathsf{\omega }\left(\mathrm{m},\mathrm{s}\right)$$

(3)

$${\mathrm{RP}}_{\mathrm{WF}-\mathrm{EV}}\left(\mathrm{s}\right)=\left({\mathrm{RP}}_{\mathrm{WF}}\left(\mathrm{s}\right)+{ \mathrm{RP}}_{\mathrm{EV}}\left(\mathrm{s}\right)-{ \mathrm{RP}}_{\mathrm{TL}}\left(\mathrm{s}\right)\right)$$

(4)

${\mathrm{RP}}_{\mathrm{Ther}}\left(\mathrm{s}\right)$ and ${\mathrm{RP}}_{\mathrm{WF}-\mathrm{EV}}\left(\mathrm{s}\right)$ are the revenue of the thermal and WF–EV hybrid plant. ${\mathrm{GP}}_{\mathrm{Ther}}\left(\mathrm{m},\mathrm{s}\right)$ represents the power generation from the m^th thermal generator. $\mathsf{\omega }\left(\mathrm{m},\mathrm{s}\right)$ signifies the MCP at time ‘s’. ${\mathrm{RP}}_{\mathrm{WF}}\left(\mathrm{s}\right)$, ${\mathrm{RP}}_{\mathrm{EV}}\left(\mathrm{s}\right),$ and ${\mathrm{RP}}_{\mathrm{TL}}\left(\mathrm{s}\right)$ are the revenue of the WF, EV storage system, and transmission line loss components.

$${\mathrm{RP}}_{\mathrm{WF}}\left(\mathrm{s}\right)={\mathrm{P}}_{\mathrm{Del}-\mathrm{WF}-\mathrm{EG}}\left(\mathrm{s}\right) .\mathsf{\omega }\left(\mathrm{s}\right)$$

(5)

$${\mathrm{RP}}_{\mathrm{EV}}\left(\mathrm{s}\right)={\mathrm{RP}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right)-{\mathrm{RP}}_{\mathrm{EV}-\mathrm{cha}}\left(\mathrm{s}\right)$$

(6)

$${\mathrm{RP}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right)={\mathrm{P}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right). \mathsf{\omega }\left(\mathrm{m},\mathrm{s}\right)$$

(7)

$${\mathrm{RP}}_{\mathrm{EV}-\mathrm{cha}}\left(\mathrm{s}\right)={\mathrm{P}}_{\mathrm{Req}-\mathrm{cha}-\mathrm{WF}}\left(\mathrm{s}\right) .{ \mathrm{Cos}\mathrm{t}}_{\mathrm{W}}+{ \mathrm{P}}_{\mathrm{Req}-\mathrm{cha}-\mathrm{EG}}\left(\mathrm{s}\right) . \mathsf{\omega }\left(\mathrm{s}\right)$$

(8)

$${\mathrm{RP}}_{\mathrm{TL}}\left(\mathrm{s}\right)=\partial . \mathsf{\omega }\left(\mathrm{s}\right). \left[{\mathrm{P}}_{\mathrm{Sch}-\mathrm{HS}-\mathrm{EG}}\left(\mathrm{s}\right)-{\mathrm{P}}_{\mathrm{Del}-\mathrm{WF}-\mathrm{EG}}\left(\mathrm{s}\right)-{ \mathrm{RP}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right)\right]$$

(9)

The quantity of wind power transmitted to the electrical grid is denoted by ${\mathrm{P}}_{\mathrm{Del}-\mathrm{WF}-\mathrm{EG}}\left(\mathrm{s}\right)$. ${\mathrm{RP}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right)$ and ${\mathrm{RP}}_{\mathrm{EV}-\mathrm{cha}}\left(\mathrm{s}\right)$ are the EV system’s revenue in the discharging and charging modes of operation. ${\mathrm{P}}_{\mathrm{EV}-\mathrm{dis}}\left(\mathrm{s}\right)$ is the power generated by the EV battery storage system during the discharging operation. ${\mathrm{P}}_{\mathrm{Req}-\mathrm{cha}-\mathrm{WF}}\left(\mathrm{s}\right)$ is the electricity required from the wind farm, whereas ${\mathrm{P}}_{\mathrm{Req}-\mathrm{cha}-\mathrm{EG}}\left(\mathrm{s}\right)$ is the power required from the electric grid for the charging-mode functioning of the EV battery storage system. $\partial$ is the penalty factor for the scheme. The total scheduled electricity to be provided to the grid by the hybrid plant is denoted by ${\mathrm{P}}_{\mathrm{Sch}-\mathrm{HS}-\mathrm{EG}}\left(\mathrm{s}\right)$.

Depending on the expected wind speed, the calculation of the wind output power takes place. This indicates that the determination of the power generated by the wind plants is based on the forecasted wind speed. The derived value of this calculated output power is then committed within a day-ahead market scheme. In this scheme, the wind plants commit to supply a specific amount of power to the grid in advance of the actual day. The actual/true wind data often deviates from the predicted/expected data. This divergence between the TWP and EWP is utilized by the EV-integrated hybrid plant for its operational purposes. The EV battery storage system adjusts its operation to compensate for power variation. However, the difference between the true and expected wind speed can lead to the occurrence of the discrepancy price (DP). This implies that if there is a disparity between the TWP and EWP, there may be additional costs that need to be incurred. The expression of the discrepancy price (DP), shortfall price rate (SPR_HS(s)), and extra price rate (EPR_HS(s)) are provided in the following manner:

$$\mathrm{DP}\left(\mathrm{s}\right)={{\displaystyle \sum }}_{\mathrm{m}=1}^{{\mathrm{NG}}_{\mathrm{sys}}}\left({\mathrm{EPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)+{\mathrm{SPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)·{\left(\frac{\mathrm{EWP}\left(\mathrm{m},\mathrm{s}\right)}{\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)}\right)}^2\right)·\left(\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)-\mathrm{EWP}\left(\mathrm{m},\mathrm{s}\right)\right)$$

(10)

$${\mathrm{SPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)=\left(1+\mathsf{\vartheta }\right)·\mathsf{\omega }\left(\mathrm{m},\mathrm{s}\right),{ \mathrm{EPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)=0 \mathrm{if} \mathrm{EWP}\left(\mathrm{m},\mathrm{s}\right)>\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)$$

(11)

$${\mathrm{EPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)=\left(1-\mathsf{\vartheta }\right)· \mathsf{\omega }\left(\mathrm{m},\mathrm{s}\right),{ \mathrm{SPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)=0 \mathrm{if} \mathrm{EWP}\left(\mathrm{m},\mathrm{s}\right)<\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)$$

(12)

$${\mathrm{EPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)={ \mathrm{SPR}}_{\mathrm{HS}}\left(\mathrm{s}\right)=0 \mathrm{if} \mathrm{EWP}\left(\mathrm{m},\mathrm{s}\right)=\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)$$

(13)

$${\mathrm{PC}}_{\mathrm{HS}}\left(\mathrm{s}\right)={ \mathrm{PC}}_{\mathrm{Ther}}\left(\mathrm{s}\right)+{\mathrm{Cos}\mathrm{t}}_{\mathrm{W}}$$

(14)

$${\mathrm{PC}}_{\mathrm{Ther}}\left(\mathrm{s}\right)={{\displaystyle \sum }}_{\mathrm{m}=1}^{{\mathrm{NG}}_{\mathrm{sys}}}\left({\mathsf{\alpha }}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}}·\mathrm{TWP}\left(\mathrm{m},\mathrm{s}\right)+{ \mathsf{\gamma }}_{\mathrm{i}}·\mathrm{TWP}{\left(\mathrm{m},\mathrm{s}\right)}^2\right)$$

(15)

The extra price rate and shortfall price rates are used to calculate the discrepancy prices, which is the cost incurred due to the mismatch between the true and expected wind power output. $\vartheta$ is the discrepancy price coefficient, which is presumed to be 0.9 in this work. It is used to calculate the discrepancy price. $P{C}_{Ther}\left(s\right)$ represents the production cost of thermal power. ${\alpha }_i$, ${\beta }_i$, and ${\gamma }_i$ are production price coefficients, which are used to calculate the thermal power production cost.

3.1. Constraints for EV Battery System

$$P_{cha}\left(s\right)=P_{Req-cha-WF}\left(s\right)+P_{Req-cha-EG}\left(s\right)$$

(16)

$$P_{cha}^{min} \le P_{cha}\left(s\right) \le P_{cha}^{max}$$

(17)

$$P_{dis}^{min} \le P_{dis}\left(s\right) \le P_{dis}^{max}$$

(18)

$$E{L}_{EV-bat}\left(s+1\right)=E{L}_{EV-bat}\left(s\right)+\left[\left(P_{cha}\left(s\right). {\mathsf{\eta }}_{cha}\right)-\left(P_{dis}\left(s\right) / {\mathsf{\eta }}_{dis}\right)\right]$$

(19)

$$E{L}_{EV-bat}^{min} \le E{L}_{EV-bat}\left(s\right)\le E{L}_{EV-bat}^{max}$$

(20)

${\mathrm{P}}_{\mathrm{cha}}\left(\mathrm{s}\right)$ represents the total charging load of the EV battery storage system. ${\mathrm{P}}_{\mathrm{cha}}^{\max }$, ${\mathrm{P}}_{\mathrm{cha}}^{\min }$, ${\mathrm{P}}_{\mathrm{dis}}^{\max }$, and ${\mathrm{P}}_{\mathrm{dis}}^{\min }$ represent the highest and lowest charging and discharging limits of the EV battery storage system. ${\mathrm{EL}}_{\mathrm{EV}-\mathrm{bat}}\left(\mathrm{s}\right)$ represents the energy level of the EV battery system in MWhr. ${\mathsf{\eta }}_{\mathrm{cha}}$ and ${\mathsf{\eta }}_{\mathrm{dis}}$ represent the efficiency of the EV battery system when operating in charging and discharging modes. ${\mathrm{EL}}_{\mathrm{EV}-\mathrm{bat}}^{\min }$ and ${\mathrm{EL}}_{\mathrm{EV}-\mathrm{bat}}^{\max }$ denote the lowest and extreme EV battery system energy levels. The provided variables and parameters are used in the operating strategy for the EV battery system. These values are important for optimizing the operation of the hybrid plant and maximizing the profit and revenue of the wind–thermal–EV hybrid plant. The lowest and extreme limits for charging and discharging modes ensure that the EV battery system operates within its capacity. The energy level of the EV battery system is monitored and controlled to maintain a balance between energy supply and demand.

3.2. Constraints for Power Flow

$$V_{m,i}^{min}\le V_{m,i}\le V_{m,i}^{max} i=1,2,3\dots N{B}_{sys}$$

(21)

$$V_{a,i}^{min}\le V_{a,i}\le V_{a,i}^{max} i=1,2,3\dots N{B}_{sys}$$

(22)

$$L{L}_{T,l}\le L{L}_{T,i}^{max} l=1,2,3\dots N{L}_{sys}$$

(23)

$$P_{real,i}^{min}\le P_{real,i}\le P_{real,i}^{max} i=1,2,3\dots N{B}_{sys}$$

(24)

$$P_{react,i}^{min}\le P_{react,i}\le P_{react,i}^{max} i=1,2,3\dots N{B}_{sys}$$

(25)

The power flow equations are essential for understanding the behavior and performance of the power system. By solving these equations, anyone can determine the power generation, voltage levels, and losses in the system. The equations are also used in optimization algorithms to find the optimal operating conditions of the power system. The equations are based on fundamental principles of electrical engineering and are widely used in power system analysis and operation. ${\mathrm{V}}_{\mathrm{m},\mathrm{i}}$ and ${\mathrm{V}}_{\mathrm{a},\mathrm{i}}$ represent the magnitude and angle of the voltage, while ${\mathrm{V}}_{\mathrm{m},\mathrm{i}}^{\min }$, ${\mathrm{V}}_{\mathrm{m},\mathrm{i}}^{\max }$, ${\mathrm{V}}_{\mathrm{a},\mathrm{i}}^{\min }$, and ${\mathrm{V}}_{\mathrm{a},\mathrm{i}}^{\max }$ are the lowest and extreme limits. The thermal limit of the transmission line is denoted by ${\mathrm{LL}}_{\mathrm{T},\mathrm{l}}^{\max }$. The number of transmission lines in the electricity network is denoted by ${\mathrm{NL}}_{\mathrm{sys}}$. The active and reactive power generation is represented by ${\mathrm{P}}_{\mathrm{real},\mathrm{i}}$ and ${\mathrm{P}}_{\mathrm{react},\mathrm{i}}$, while the lowest and maximum limits are represented by ${\mathrm{P}}_{\mathrm{real},\mathrm{i}}^{\min }$, ${\mathrm{P}}_{\mathrm{real},\mathrm{i}}^{\max }$, ${\mathrm{P}}_{\mathrm{react},\mathrm{i}}^{\min }$, and ${\mathrm{P}}_{\mathrm{react},\mathrm{i}}^{\max }$.

4. Proposed Strategy

An idea has been presented here to improve the scheduling of the energy level in a hybrid wind, thermal, and EV system. The main goal of this strategy is to reduce the DP while maximizing the revenue and profit generated by the hybrid plant. To achieve this, the optimal power flow (OPF) problem is solved using the SQP method. To evaluate the effectiveness of the idea, both the TWS and EWS data along with grid frequency are assumed for 24 h. Using the true and expected wind speed data, the output power is calculated using a graph shown in Figure 1. The operation of the EV battery bank (charging, discharging, or idle) is determined based on the expected and true wind power, grid frequency, and the present energy level of the EV battery storage. These operating conditions are then used as constraints in an OPF simulation for the EV battery units, which aims to minimize power production costs. Since wind and EV battery generation have the lowest costs, maximizing their generation can lead to higher profits. The revenue and profit of the wind–thermal–EV hybrid plant are calculated based on the output power obtained from the OPF simulation. Ref. [32] provides a comprehensive description of an operating strategy that is specifically designed for a CAES-based power plant. This strategy depicts the distinctive pricing environment based on the grid frequency. The CAES plant’s operating schedule was determined by closely monitoring the frequency levels. However, a new approach is suggested in the current study to improve the plant’s operation. This new strategy introduces an additional constraint that focuses on the energy levels of the EV’s battery storage system (E_EV,max, E_EV,opt, E_EV,low, and E_EV,min). By considering these energy levels, the operation of the EV-integrated power plant becomes more optimized and efficient. The utilization of the presented strategy in operating the EV’s battery bank relies on several key parameters including TWP, EWP, f_PG, and the present energy level of the EV’s battery. Figure 3 illustrates a flow chart that outlines the various steps involved in operating the hybrid plant. In this flow chart, EV_char,min, and EV_char,max represent the minimum and maximum power limits when the EV battery is operated in the charging mode. Similarly, EV_dis,min, and EV_dis,max are defined as the minimum and maximum power limits when the EV battery operates in the discharging mode. Additionally, the variable P_WF-EG indicates the power supplied to the grid by the wind. E_char and E_dis represent the input power for charging and the generated power from the discharging mode of the EV battery system. The presented operating strategy encompasses a total of 11 distinct operating states. These states can be broadly categorized into 6 different scenarios, each with its own set of conditions. By carefully considering these operating states and their corresponding conditions, the overall operation of the hybrid plant can be finely tuned to ensure optimal performance and efficiency.

4.1. Scenario 1: TWP ≥ EWP and f_PG > 50 Hz

In this particular scenario, it is observed that the TWP is greater than the EWP. Additionally, the frequency of the electrical grid exceeds the standard frequency of 50 Hz. It is important to note that the WF is currently generating a larger amount of electricity than what it initially committed to supply. Consequently, this surplus of electricity that is being generated by the wind power plants is leading to an increase in the frequency of the grid. This increase in frequency is a direct result of the excess electricity being injected into the grid. As a result, the surplus of electricity available within the grid decreases the overall price of electricity because the supply of electricity surpasses the current demand. To capitalize on this advantageous situation of lower electricity prices and simultaneously reduce the surplus of electricity within the grid, the EV battery bank can effectively operate in the charging mode. Essentially, this means that the extra electricity is used to charge the battery and store the energy for later use.

4.2. Scenario 2: TWP ≥ EWP and 49.7 Hz ≤ f_PG ≤ 50 Hz

In this situation, it is observed that the effective output of wind power exceeds the initially anticipated value. However, the grid frequency falls within the range of 50 to 49.7 Hz. Here, the EV battery bank adopts the utilization of operating state 2 to fulfill its operational requirements. Furthermore, the committed power is efficiently supplied to the power grid. On the other hand, the additional power, also known as the surplus power, emerges as the discrepancy between the TWP and EWP. This excess power is ingeniously employed to facilitate the operation of the EV battery in charging mode.

4.3. Scenario 3: TWP ≥ EWP and f_PG < 49.7 Hz

This case presents a situation where the TWP is higher than the EWP. Despite this surplus of power, the frequency of the grid remains below 49.7 Hz. This specific frequency is indicative of a shortage of power within the grid. Here, it is important to consider the existence of three distinct operating states that are directly influenced by the energy levels present within the EV battery system. These three states of operations are determined by the range of usable energy levels that exist between the maximum and minimum storage levels of the EV battery system (E_EV,max and E_EV,min). Within this range, two further levels are designated as E_EV,opt, and E_EV,low. In situations where the EV battery energy level falls below the E_EV,low, the EV battery can only be operated in discharging mode under emergency conditions. This is scheduled to prevent any potential grid collapses that may arise as a result of a reduction in frequency. Alternatively, if the energy level of the EV battery drops below the E_EV,opt, it means there is a moderate amount of charge available in the battery storage. If the energy level exceeds the E_EV,opt, it indicates an excess of charge available in the battery bank. In such cases, discharging can be conducted at any time to maximize the profitability of the wind–thermal–EV hybrid system.

If it is found to be lower than the E_EV,low, the EV battery will remain inactive while the power generated from the wind is directed to the grid. This is conducted with the specific objective of improving the frequency, thus resulting in the system operating under the third operating state. If the energy level is between E_EV,opt and E_EV,low, it means the grid needs power. As a result, the power price will be much higher. To maximize revenue, the EV battery needs to operate in discharging mode, limited to half of its maximum discharging capacity. This is called the fourth state. In a different scenario, if the energy level exceeds the E_EV,opt, it indicates an abundance of storage in the EV battery system. In this situation, with a very high power price, the EV battery operates in discharging mode at its maximum capacity. This is known as the fifth operating state.

4.4. Scenario 4: TWP < EWP and f_PG > 50 Hz

In this case, it is observed that the EWP is higher than the TWP, and the frequency of the power exceeds the threshold of 50 Hz. Consequently, although the supply of power to the grid is falling short of the initially anticipated value, there exists an excess of power within the grid due to the frequency surpassing the 50 Hz mark. As a result, there is no immediate necessity to engage the EV battery to operate in discharging mode to meet the predicted power requirements, as this would further elevate the frequency. Instead, within the confines of this scenario, the EV battery is effectively operated in the charging mode with the primary objective of increasing the load applied to the system, thereby allowing for the preservation of the grid frequency at its standard and customary value of 50 Hz. In state 8, if the energy level of the EV battery bank is found to be less than the value of E_EV,opt, then the maximum charging limit is indicated and demonstrated. In essence, this signifies and implies that the EV battery is currently and actively operating at its ultimate and highest possible discharging capacity, ensuring the provision of the maximum output of power. On stage 9, if the energy level of the EV battery is greater than or at least equal to the value of E_EV,opt, then the charging operation will be carried out at precisely half the magnitude of the maximum charging limit. To put it succinctly, this essentially means that the EV battery system is now operating with a reduced and diminished capacity when it comes to charging power, thereby ensuring a more conservative and restrained utilization of resources. In both of these aforementioned operational scenarios, the power required for successful and efficient charging operation is primarily sourced and obtained from wind energy sources as opposed to relying on the procurement of power from the conventional grid system.

4.5. Scenario 5: TWP < EWP and 49.7 Hz ≤ f_PG ≤ 50 Hz

In this situation, the EV battery storage is designed to function in the discharging mode. In this mode, the primary purpose is to provide or supply the difference that exists between the committed power and the actual power that is being generated or produced. There are two suggested operating states for EV battery storage, which mainly consider the energy level of the plant. If the energy level of the EV battery storage is lower than a certain threshold value called E_EV,opt, then it will operate in the discharging mode. In this state, the EV system will effectively provide and supply the difference that exists between the TWP and EWP, as illustrated in operating state 10. Conversely, if the energy level of the EV battery storage surpasses or exceeds the threshold value E_EV,opt, then the EV battery storage will operate in the discharging mode. In this state, the EV battery storage can produce power at its highest capacity, which is the same as the maximum discharging capacity of the EV battery storage system. Moreover, the minimum power through the discharging of the EV batteries will be determined by the gap between the TWP and EWP, as shown in operating state 11.

4.6. Scenario 6: TWP < EWP and f_PG < 49.7 Hz

In the given scenario, it is observed that the EWP is higher than the TWP. This indicates a disparity between the forecasted and actual power outputs. Additionally, the frequency of the grid is found lower than the desired value of 49.7 Hz. This lower frequency signifies a considerably high power demand in the system. However, it is unfortunate that the hybrid plant is not capable of fulfilling this increased power demand. Consequently, the EV battery storage system came into action and operates in the discharging mode. This EV battery storage system comes into play when the energy level of the hybrid plant falls below a certain threshold value, denoted as E_EV,opt. In this situation, the EV battery storage system operates in discharging mode and provides at least the difference between the predicted and actual power outputs. This can be seen in operating state 6. However, if the energy level of the EV battery storage system is higher than the threshold value E_EV,opt, a different action is taken. In this case, the EV battery storage system sets the minimum power generation level as the difference between the actual and predicted power outputs. At the same time, the maximum power generation level is set to the maximum capacity of the EV battery storage system. This specific situation is shown in operating state 7.

5. Presented Hybrid System Operation

The presented strategy has been implemented by addressing and resolving the OPF problem by utilizing SQP methods. Through the solution of the OPF problem, the desired objectives are achieved while considering the various constraints that exist within the power system. This work includes 20 wind farms with a maximum capacity of 3.5 MW/unit. These turbines are located at bus number 5 in the system. So, the wind plant can produce a maximum power output of 70 MW when running at the rated speed. The implementation of the proposed logic is primarily focused on maximizing the overall profit and revenue of the system. To determine the investment cost associated with the wind power plant, reference [36] is consulted. Furthermore, it is considered that the EV battery storage system has a maximum energy storage capacity of 80 MWh. This particular EV battery storage system is connected to bus number 13 within the system. The operational functions of the EV battery storage system, whether it acts in the charging or discharging mode, are determined based on the proposed logic that is outlined in Figure 3. The choice is affected by different factors, such as the true and expected wind power, the grid’s frequency, and the energy level of the EV battery storage system. For this implementation, it is assumed that the EV battery storage system’s initial energy level is 41 MWh. Furthermore, specific values are assigned to E_EV,opt, E_EV,low, and E_EV,min, which are assumed to be 40, 20, and 10 MWh. The logic in Figure 3 provides a comprehensive breakdown of the power that is sold to the grid from the wind turbines as well as the charging and discharging limits of the EV battery storage systems. To find the lowest cost of generating power, the OPF problem is solved by considering the different constraints in the power system. It is important to note that the energy level constraints and the discharging/charging limits of the EV battery storage systems must be established before running the OPF. Given that wind and EV battery storage systems generation tend to have lower costs when compared to thermal plants, they are fully utilized within this competitive environment. The wind–thermal–EV hybrid system generates revenue by calculating the scheduled generating pattern. Ultimately, the results produced by the proposed logic are compared to those that are generated by the existing logic, as outlined in reference [32]. It is important to mention that the algorithm used in reference [32] is based on the artificial bee colony (ABC) approach. To facilitate a comprehensive comparison, the logic that is described in reference [32] is reprogrammed using the SQP algorithm.

6. Results and Analysis

To investigate the effectiveness of the proposed approach, a modified IEEE 30 bus system was utilized in this study. This system consists of 6 generator buses, 41 transmission lines, and 19 load buses [37]. Bus number 1 has been designated as the reference bus, and the reference MVA limit has been set at 100 MVA. All the necessary system data have been extracted from references [38,39]. For checking the efficacy of the presented scheme, the true and expected wind speed data from a specific location have been collected. The true and expected wind speed data, which serve as the input for validating and analyzing the proposed method, are exhibited in Figure 4. It is crucial to highlight that the wind speed is variable, and, therefore, different values are chosen for each hour. This variability stems from the unpredictable nature of wind speed in real-life scenarios.

It is worth mentioning that there is a possibility of disparity between the TWS and EWS, resulting in uncertainty regarding wind power generation. By conducting a thorough comparison between the true and expected wind speeds, one can effectively assess the extent to which the proposed approach succeeds in reducing the uncertainty associated with wind power. Moreover, the proposed approach has the potential to contribute towards minimizing the discrepancy between the true and expected wind power output. Furthermore, by incorporating the true wind speed data, the EV battery storage system can be operated in a manner that aims to reduce the discrepancy prices. In a completely deregulated power market, the combined operation of wind, thermal, and EV plants can play a significant role in economically diminishing the uncertainty surrounding wind power. The frequency of the grid, which refers to the frequency at which the electrical power system operates is typically kept at a constant value, such as 50 Hz, to ensure the stability and reliability of the system.

In the specific case of the EV battery storage system operation, the grid frequency is used for choosing their optimum operating conditions for enhancing the financial benefit of the hybrid system. The purpose of this random selection of grid frequency was to achieve the best possible results in terms of system security and to reduce the chances of grid failure. Figure 5 depicts the distribution of the grid frequency. Upon careful examination of this figure, it becomes evident that the grid frequency often falls below the desired 50 Hz mark for a significant portion of time. This is not desirable, as maintaining system security requires the grid frequency to remain within acceptable limits. To address this issue and maintain the grid frequency within acceptable limits, the proposed approach focuses on optimizing the scheduling of the EV battery storage system while considering the grid frequency. By carefully coordinating the operation of the EV battery storage system with the grid frequency, it is believed that the overall performance and reliability of the power system can be significantly improved. The proposed method seeks to address the challenge of maintaining an acceptable grid frequency in the power system. By considering the specific requirements of the EV battery storage system and optimizing their scheduling, it is hoped that the overall performance and reliability of the power system can be enhanced. The profit of an electrical system at a given time is reliant upon both the revenue generated by the system and the costs associated with power production.

The market clearing price is an important factor in determining the revenue of the power system. In cases where there is a discrepancy in price, the objective is still to maximize profit. This means that the focus is on finding ways to increase revenue and decrease costs or obtaining both to maximize the profit of the system. In the context of wind generator placement in the considered power network, they are initially placed at bus no. 5 of the chosen IEEE system. Once the wind generator is in place, the wind speed varies according to the data that is being used to examine the methodology. The discrepancy price, revenue, and profit of the wind-included thermal power station are then deliberate by solving the OPF and optimizing the generator re-scheduling to achieve the maximum economic benefit of the network.

Table 1. Discrepancy price and system economic benefit of wind combined thermal systems.

Time	Discrepancy Price ($/h)	Revenue ($/h)	Gen. Cost ($/h)	Profit ($/h)
1	−378.54	15,099.01	10,753.02	3967.45
2	−61.56	15,199.35	10,960.02	4177.77
3	−526.21	15,482.6	11,562.43	3393.96
4	9.23	15,383.35	11,349.69	4042.89
5	25.08	15,241.93	11,049.34	4217.67
6	2.79	15,539.39	11,684.9	3857.28
7	12.39	15,327.27	11,229.07	4110.59
8	9.05	15,213.08	10,989.73	4232.4
9	32.8	15,693.88	12,025.12	3701.56
10	−513.23	15,127.41	10,811.94	3802.24
11	−790.6	15,099.01	10,753.01	3555.4
12	−541.15	15,833.63	12,338.86	2953.62
13	−1485.08	15,184.86	10,930.32	2769.46
14	12.43	15,383.35	11,349.7	4046.08
15	−186.08	15,127.41	10,811.95	4129.38
16	12.64	15,539.39	11,684.9	3867.13
17	5.81	15,127.41	10,811.94	4321.28
18	−321.94	15,482.6	11,562.42	3598.24
19	88.15	15,594.8	11,808.01	3874.94
20	−1490.4	15,241.93	11,049.34	2702.19
21	134.67	15,944.6	12,592.93	3486.34
22	15.44	15,199.35	10,960.02	4254.77
23	9.33	15,524.98	11,654.21	3880.1
24	−1652.99	15,213.08	10,989.72	2570.37

delivers an inclusive view of the effect of the discrepancy price on the system’s economic benefit. It is important to note that a negative discrepancy price indicates a penalty imposed on GENCOS for a shortfall in the power supply, while a positive discrepancy price indicates a reward provided to GENCOS for an excess in the power supply. Based on the information presented in Table 1 and Figure 6, it can be concluded that profit is exploited when the discrepancy price negative effect on the system is curtailed, specifically when the difference between the TWS and EWS is at its lowest.

The proposed hybrid WF–thermal–EV system strategy aims to not only maximize profit but also minimize the effect of the discrepancy price and maintain the grid frequency. This is achieved by changing the operation mode of the EV battery storage system every hour according to the proposed approach, which is illustrated in Figure 3. By doing so, the system requirements can be met and the profit and revenue can be exploited. It is worth mentioning that generation scheduling plays a crucial role in the OPF problem.

Table 2. Revenue and economic profit proportional study for proposed strategy (In $/h).

Time	EV System Revenue (a)	Thermal Plant Revenue (b)	Overall Revenue of Hybrid System (c = a + b)	Thermal Power Production Cost (d)	Wind Power Production Cost (e)	Overall Production Cost (f = d + e)	Economic Profit (g = c − f)
1	2938.167	15,452.15	18,390.317	13,151.05	223.415	13,374.465	5015.8519
2	2510.544	15,985.05	18,495.594	13,523.76	208.115	13,731.875	4763.7191
3	3760.081	15,258.25	19,018.331	12,646.51	164.3525	12,810.863	6207.4687
4	3090.311	15,271.35	18,361.661	12,833.98	179.6525	13,013.633	5348.0287
5	1261.855	16,266.25	17,528.105	13,705.45	201.5525	13,907.003	3621.1028
6	3359.977	15,314.85	18,674.827	12,682.42	155.615	12,838.035	5836.7916
7	3683.298	15,102.85	18,786.148	12,551.18	188.4275	12,739.608	6046.5401
8	3091.583	15,173.95	18,265.533	12,891.86	205.9025	13,097.763	5167.7701
9	164.3232	16,729.75	16,894.073	14,043.53	131.54	14,175.07	2719.0032
10	2783.649	15,600.45	18,384.099	13,249.71	219.0275	13,468.738	4915.3614
11	4112.644	14,987.05	19,099.694	12,665.12	223.415	12,888.535	6211.1585
12	963.5857	16,742.35	17,705.936	14,053.19	109.6651	14,162.855	3543.0806
13	4236.41	15,072.45	19,308.86	12,714.07	210.29	12,924.36	6384.5003
14	2779.833	15,330.85	18,110.683	12,967.69	179.6525	13,147.343	4963.34
15	3027.925	15,303.15	18,331.075	13,047.76	219.0275	13,266.788	5064.2871
16	2457.998	15,486.65	17,944.648	13,069	155.615	13,224.615	4720.0329
17	1702.431	16,148.45	17,850.881	13,627.68	219.0275	13,846.708	4004.1734
18	3146.776	15,370.25	18,517.026	12,896.95	164.3525	13,061.303	5455.7231
19	2410.289	15,371.05	17,781.339	12,718.99	146.84	12,865.83	4915.5088
20	3618.917	15,241.65	18,860.567	12,996.39	201.5525	13,197.943	5662.6246
21	−1489.22	16,990.35	15,501.129	14,253.25	92.165	14,345.415	1155.7144
22	3895.248	14,974.45	18,869.698	12,476.86	208.115	12,684.975	6184.7226
23	2457.884	15,485.85	17,943.734	13,089.22	157.79	13,247.01	4696.7239
24	2342.767	16,236.45	18,579.217	13,685.76	205.9025	13,891.663	4687.5548

and

Table 3. EV battery storage energy level and MCP proportional study for proposed strategy.

Time	EV Battery Storage Energy Level (in MWh)	MCP (in $/MWh)	Time	EV Battery Storage Energy Level (in MWh)	MCP (in $/MWh)
1	42.26	53.8094	13	27.836	53.0422
2	50.66	54.5018	14	25.243	54.0099
3	39.549	53.68	15	26.713	53.5994
4	33.993	53.7689	16	24.12	54.5852
5	42.393	55.5041	17	32.52	55.084
6	31.282	53.8912	18	26.965	54.1341
7	20.171	53.1097	19	15.854	54.1007
8	18.227	53.4388	20	15.854	53.7007
9	26.627	57.2043	21	24.254	58.2019
10	30.547	54.1229	22	13.143	52.6438
11	24.991	52.7324	23	11.198	54.5858
12	33.391	57.2504	24	19.598	55.3988

provide a proportional study of various factors such as EV system revenue, hybrid network revenue, system financial profit, MCP, and new energy level of the EV battery storage system after applying the proposed method. From the table, it can be witnessed that the majority of the time, the energy levels of EV battery storage systems fluctuate between the minimum energy level and the optimal energy level.

This variation in energy levels contributes to the achievement of supreme profit and revenue for the power network. Additionally, wind power is utilized to a greater extent in the hybrid operation of the wind–thermal–EV hybrid plant. Figure 7 presents a pictorial representation that elucidates the maximum operating range of power for both the charging and discharging modes of the EV battery storage system after the implementation of the proposed strategy.

By examining the results in Figure 7, it is observed that the range of power reaches a value of zero at the 20th hour, thereby indicating that the EV plant is in an idle state during that specific time. This particular state of idleness suggests that no power generation or charging activity is occurring within the EV battery system during the 20th hour. In the context of a power system, it is important to remember that the generator offer price coefficients are firmly established and remain fixed for all generators. These coefficients play a crucial role in determining the cost associated with power generation for each generator. Consequently, the cost of generation is directly influenced by these coefficients, thereby impacting the overall cost of operation for each generator. By manipulating the generation schedule for a thermal power plant, the solution to the OPF problem aids in determining the most efficient power production cost. This optimization process involves adjusting the generation schedule to minimize the overall production cost for the thermal power plant.

Figure 8 provides an inclusive evaluation of the generation capacity exhibited by all generators over 24 h after the application of the proposed scheduling strategy within the hybrid plant. This scheduled strategy showcases the distribution of generation capacity among the various generators within the hybrid plant. By analyzing Figure 8, we can gain valuable insights into the generation capacity trends and patterns that occur throughout the 24 h. This information is essential in understanding the overall performance and efficiency of the hybrid plant. The revenue generated by an electrical system is heavily dependent on both the power generation and the MCP. These two factors collectively contribute to the overall revenue generated by the electrical system. The power generation aspect encompasses the amount of power being generated by the system, while the MCP reflects the price at which the generated power is cleared in the market. Therefore, the revenue generated by the electrical system will inherently fluctuate based on the prevailing power generation levels and the MCP. Figure 9 intricately depicts the variation of the MCP for all generator buses over 24 h after the implementation of a proposed strategy within a wind-integrated EV plant operating in a fully deregulated environment.

This proposed strategy effectively influences the generation re-scheduling process, thereby leading to variations in the MCP. Consequently, the MCP will fluctuate across different hours and for each generation bus as a direct result of the optimal generation re-scheduling. These variations in the MCP are significant as they directly impact the revenue generated by the thermal plant. During the 21st hour, it is noteworthy to mention that the MCP reaches its peak value for all generator buses. This peak value signifies the maximum revenue potential that can be achieved by the thermal plant during that specific hour. Therefore, it can be inferred that the 21st hour presents a prime opportunity for the thermal plant to maximize its revenue generation.

Result Assessment between Existing and Proposed Strategy

The comparison that is being made is between the proposed strategy and an already existing strategy, which can be found in reference [32], and this comparison is being made in the context of a common power system. In

Table 4. Revenue and economic profit proportional study for existing strategy [32] (In $/h).

Time	CAES System Revenue (a)	Thermal Plant Revenue (b)	Overall Revenue of Hybrid System (c = a + b)	Thermal Power Production Cost (d)	Wind Power Production Cost (e)	Overall Production Cost (f = d + e)	Economic Profit (g = c − f)
1	2938.167	15,452.15	18,390.317	13,151.05	223.415	13,374.465	5015.8519
2	2510.544	15,985.05	18,495.594	13,523.76	208.115	13,731.875	4763.7191
3	2716.585	15,482.15	18,198.735	13,150.01	164.3525	13,314.363	4884.3723
4	2750.632	15,343.95	18,094.582	12,997.04	179.6525	13,176.693	4917.8899
5	1261.855	16,266.25	17,528.105	13,705.45	201.5525	13,907.003	3621.1028
6	2368.306	15,526.25	17,894.556	13,158.11	155.615	13,313.725	4580.8312
7	2894.5	15,274.55	18,169.05	12,932.09	188.4275	13,120.518	5048.5326
8	3091.583	15,173.95	18,265.533	12,891.86	205.9025	13,097.763	5167.7701
9	164.3232	16,729.75	16,894.073	14,043.53	131.54	14,175.07	2719.0032
10	2783.649	15,600.45	18,384.099	13,249.71	219.0275	13,468.738	4915.3614
11	3607.122	15,098.85	18,705.972	12,911.54	223.415	13,134.955	5571.017
12	963.5857	16,742.35	17,705.936	14,053.19	109.6651	14,162.855	3543.0806
13	3728.845	15,184.55	18,913.395	12,961.96	210.29	13,172.25	5741.1445
14	2779.833	15,330.85	18,110.683	12,967.69	179.6525	13,147.343	4963.34
15	3027.925	15,303.15	18,331.075	13,047.76	219.0275	13,266.788	5064.2871
16	2457.998	15,486.65	17,944.648	13,069	155.615	13,224.615	4720.0329
17	1702.431	16,148.45	17,850.881	13,627.68	219.0275	13,846.708	4004.1734
18	2619.36	15,482.15	18,101.51	13,150.01	164.3525	13,314.363	4787.1474
19	2410.289	15,371.05	17,781.339	12,718.99	146.84	12,865.83	4915.5088
20	3618.917	15,241.65	18,860.567	12,996.39	201.5525	13,197.943	5662.6246
21	−1489.22	16,990.35	15,501.129	14,253.25	92.165	14,345.415	1155.7144
22	3176.352	15,133.95	18,310.302	12,825.44	208.115	13,033.555	5276.7469
23	2457.884	15,485.85	17,943.734	13,089.22	157.79	13,247.01	4696.7239
24	2342.767	16,236.45	18,579.217	13,685.76	205.9025	13,891.663	4687.5548

and

Table 5. EV battery storage energy level and MCP proportional study for existing strategy [32].

Time	CAES Storage Energy Level (in MWh)	MCP (in $/MWh)	Time	CAES Storage Energy Level (in MWh)	MCP (in $/MWh)	Time	CAES Storage Energy Level (in MWh)	MCP (in $/MWh)
1	42.26	53.8094	9	60.33	57.2043	17	77.335	55.084
2	50.66	54.5018	10	64.25	54.1229	18	77.335	54.5871
3	50.66	54.5871	11	64.25	53.1827	19	66.224	54.1007
4	48.716	54.0627	12	72.65	57.2504	20	66.224	53.7007
5	57.116	55.5041	13	72.65	53.4932	21	74.624	58.2019
6	56.467	54.744	14	70.057	54.0099	22	71.383	53.2817
7	53.875	53.8016	15	71.527	53.5994	23	69.439	54.5858
8	51.93	53.4388	16	68.935	54.5852	24	77.839	55.3988

, there is a presentation of a comprehensive study that has been conducted on various parameters including CAES system revenue, hybrid network revenue, system financial profit, MCP, and new energy level of the CAES storage system after applying the existing strategy [32]. It should be noted that the existing approach does not have any energy levels that are close to the minimum energy level. By carefully examining the information presented in the tables, it becomes clear that the new energy level tends to be much closer to the maximum energy level in the majority of hours. In contrast, the existing logic places a higher emphasis on the storage aspect of the CAES plant rather than focusing on the overall system profit.

Figure 10 and Figure 11 present an exhaustive comparison of the revenue generated by the storage system and the WF–thermal–storage hybrid system, respectively. Upon careful examination of Figure 10, it becomes evident that the proposed strategy leads to more favorable and economically viable outcomes in the majority of hours as compared to the existing strategy. Specifically, if the focus is given on the revenue generated by the storage system on that particular day, it amounts to a significant sum of 62,307.27 $/h for the proposed strategy, whereas the existing strategy only yields 56,884.23 $/h in revenue for the same time. Consequently, based on these findings, it can be confidently concluded that the proposed strategy surpasses and outperforms the existing strategy in terms of its effectiveness and efficiency. Additionally, it is worth noting that in the 21st hour, both logics experienced negative revenue. However, in this particular scenario, the thermal plant proactively assumes the responsibility of maintaining and enhancing the profitability of the hybrid system.

In this particular section, the comparison of the outcomes of the suggested strategy with an already established strategy [32] has been depicted, specifically regarding the generated revenue of the WF–thermal–storage hybrid plant. By delving into the details, we can see that when employing the existing strategy, the overall revenue for the hybrid plant reaches a total of 432,955 $/h. On the other hand, when implementing the proposed logic, the revenue climbs up to 434,372.032 $/h. Upon careful examination of Figure 11, it can easily be noticed that during the 21st hour, the revenue is at its minimum for both logics. This decrease in revenue is primarily attributed to the fact that the storage devices themselves generate the lowest amount of revenue during this particular time. Profit is achieved by subtracting the power production cost from the revenue, resulting in a financial gain. When the revenue surpasses the power generation cost, there is a positive profit. Conversely, if the revenue falls short of the generation cost, there is a negative profit, also known as a loss. In Figure 12, a detailed comparative analysis is presented, showcasing the distinction between the existing strategy and the proposed strategy for maximizing profit in a wind–thermal–EV hybrid plant. This visual representation effectively illustrates that by implementing the proposed strategy, the financial profit is significantly enhanced during periods of maximum time when compared to the existing strategy. The primary strategy outlined in this paper revolves around the optimization of the scheduling of the energy level within an EV battery storage system. To evaluate the efficacy of the proposed approach, a comprehensive study of the storage device’s energy level was undertaken, as depicted in Figure 13.

The exploration of the existing strategy revealed elevated energy levels each hour, while the proposed approach places greater emphasis on maintaining the grid frequency by modifying the mode of operation within the EV battery storage system. Furthermore, the proposed method strives to keep the energy level of the EV battery storage system near the optimal value of energy levels to maximize profit. The results obtained from the comparative study undeniably demonstrate the effectiveness of the proposed approach in not only maintaining the grid frequency but also optimizing the energy level of the EV battery storage system to achieve the highest possible profit.

The primary objective of this paper is to optimize the profit of a hybrid power plant. To attain this objective, a comparative analysis is conducted using

Table 6. Comparison of financial profit using different strategies.

Time	Financial Profit without Storage System	Financial Profit Using Existing Strategy [32]	Financial Profit Using Proposed Strategy
1	3967.45	5015.8519	5015.8519
2	4177.77	4763.7191	4763.7191
3	3393.96	4884.3723	6207.4687
4	4042.89	4917.8899	5348.0287
5	4217.67	3621.1028	3621.1028
6	3857.28	4580.8312	5836.7916
7	4110.59	5048.5326	6046.5401
8	4232.4	5167.7701	5167.7701
9	3701.56	2719.0032	2719.0032
10	3802.24	4915.3614	4915.3614
11	3555.4	5571.017	6211.1585
12	2953.62	3543.0806	3543.0806
13	2769.46	5741.1445	6384.5003
14	4046.08	4963.34	4963.34
15	4129.38	5064.2871	5064.2871
16	3867.13	4720.0329	4720.0329
17	4321.28	4004.1734	4004.1734
18	3598.24	4787.1474	5455.7231
19	3874.94	4915.5088	4915.5088
20	2702.19	5662.6246	5662.6246
21	3486.34	1155.7144	1155.7144
22	4254.77	5276.7469	6184.7226
23	3880.1	4696.7239	4696.7239
24	2570.37	4687.5548	4687.5548
Total	89,513.11	110,423.5	117,290.8

and Figure 14, which provide valuable insights into the profit generated by the hybrid power plant in three different scenarios: profit without storage, profit with the utilization of an existing logic as referenced in [32], and profit with the proposed logic. In the scenario where no energy storage system is employed, commonly referred to as “profit without storage”, the resulting profit is significantly lower. This highlights the importance of integrating an energy storage system, such as a CAES, EV battery storage system, to augment the profit generation capability of the hybrid plant. Table 6 and Figure 14 effectively illustrate the comparison of profits across these different scenarios, showcasing the superior performance of the proposed logic in maximizing the financial benefit of the hybrid system.

The results obtained from this research strongly indicate that the proposed strategy outperforms the existing strategy, leading to higher financial benefits for the hybrid power plant. The presence of energy storage plays a crucial role in mitigating the impact of discrepancy prices and ultimately maximizing economic profit. This finding further reinforces the significance of incorporating EV battery storage in the hybrid plant setup. Figure 14 provides in-depth insights into the relative learning of the profit generated by the hybrid power plant using both the proposed and existing strategies. The proposed logic consistently demonstrates its capability to yield maximum profit for every hour, effectively minimizing the adverse impact of discrepancy prices. However, it is noteworthy that in the 21st hour, there is a noticeable decrease in profit following the implementation of the storage system. This phenomenon can be attributed to the occurrence of “negative revenue” or “loss” from the storage system. The negative revenue signifies that the revenue generated by the EV battery storage falls below the generation cost, resulting in a loss for that particular hour. Nevertheless, when considering the overall performance, the proposed strategy proves to be highly effective in maximizing profit and minimizing discrepancy prices when compared to the existing strategy. It is evident that the inclusion of EV battery storage and the utilization of the proposed logic significantly contribute to the overall profitability of the hybrid system. Overall, this research contributes to the understanding of how the profit generation of a wind–thermal–EV hybrid plant can be optimized. The proposed strategy, coupled with the integration of energy storage proves to be a compelling solution for maximizing profit and minimizing discrepancy prices. This study lays the foundation for further advancements in the optimization of hybrid power plants, ultimately leading to a more sustainable and economically viable energy generation system.

7. Conclusions

The paper proposes a highly efficient operating strategy for a hybrid system that includes wind, thermal, and EV battery storage technology. This approach is designed specifically for use in a day-ahead power market, taking into account the frequency and energy level of the EV battery storage system. The fundamental purpose of the approach is to maximize the hybrid system’s total financial profit by utilizing the EV battery storage system’s capabilities to compensate for any uncertainties in wind power output while still meeting the contracted producing pattern. The presented study offered a new operating strategy for EV battery storage systems based on various wind velocity and grid frequency situations. The paper’s uniqueness is the scheduling method for the EV battery storage system, which is determined by the current state of the power system. This suggested strategy allows the hybrid system to surpass existing logic. This improvement is most visible in terms of revenue generation and reservoir capacity use. The proposed approach effectively reduces the uncertainties associated with wind energy, resulting in more consistent and reliable power generation. It also increases the hybrid system’s profit and income by making full use of the EV battery storage technology. Simulations are conducted hourly to assess the efficacy of the proposed technique, accounting for the variable loads on various buses. These simulations indicate that the recommended approach consistently outperforms the current strategy, providing more evidence of its superiority. Notably, the proposed approach demonstrates a more efficient use of a storage system’s energy level, which directly corresponds to increased income output for the hybrid system. The detailed operation of the EV system has not been considered in this work which will be performed in future work.