A Mechanism Framework for Clearing Prices in Electricity Market Based on Trusted Capacity of Power Generation Resources

Abstract

A reasonable capacity market mechanism is conducive to exploring the capacity value of different power generation resources and ensuring the adequacy of power supply capacity in power systems. In response to the challenges faced by the existing capacity market mechanism under the background of energy transformation, such as the unreasonable quantification of the support effect of different power generation resources on the power capacity of power system and the imperfect pricing mechanism of power capacity, a capacity market mechanism for power systems with high proportion renewable energy has been designed. To quickly clarify the capacity support effect of different power generation resources, a capacity credibility factor is introduced to quantify the actual contribution of different power generation resources in capacity supply and to deeply explore the capacity value of power generation resources. Based on the uniform marginal clearing price in the capacity market, the marginal clearing price of different power generation resources is corrected by using the cost ratio factor, which includes the difference in the cost structure of power generation resources. By comparing and analyzing examples, the proposed cost ratio factor can effectively optimize the capacity price; the maximum price difference is 18.2 yuan/MW, the overall capacity cost of the system is reduced by 53.70%, and the effective connection between fixed cost and variable cost of power generation resources is realized.

1. Introduction

The dual carbon strategy goal has accelerated the pace of energy transformation in China, making the power industry a major emitter of carbon [1,2,3]. By increasing the proportion of installed capacity of renewable energy to optimize the power structure, it will be beneficial to accelerate the decarbonization process. However, the randomness and volatility of the high proportion of renewable energy output increase the uncertainty of capacity supply, resulting in a severe challenge to the capacity adequacy of the power system [4]. In addition, with the gradual operation and improvement of the power spot market, renewable energy with a low variable cost is participating in market trading at a price far lower than that of traditional units, which squeezes the profit margin of traditional units while obtaining more generation opportunities, significantly dampens the investment willingness of traditional units, and further aggravates the risk of insufficient system capacity [5]. Traditional power-generating units with high reliability have difficulty achieving cost recovery over the expected lifespan through the pure electric energy market in the context of a high proportion of renewable energy power systems. It is urgent to explore the capacity value of different power generation resources, quantify the support effect of power capacity, recover fixed costs through differentiated compensation methods, and ensure the stable supply and sufficient demand of power capacity in the power system.

As an important component of the electric market system and an effective supplement to the electric energy market, the capacity market dynamically characterizes the capacity value of different power generation resources using centralized optimization and marginal clearing trading methods, effectively guiding economic investment and rational allocation of diversified power generation resources, and achieving optimal allocation of power generation resources. Currently, research on the capacity market focuses more on domestic and foreign construction experiences and inspirations [6,7,8,9,10], as well as the refinement of compensation mechanisms [11,12,13]. There is less exploration of capacity market mechanisms for power systems with a high proportion of renewable energy [14], and there is a lack of consideration for the capacity equivalence of different power generation resources and the structural differentiation of power costs. Therefore, quantifying the capacity support effect of different power generation resources and optimizing the pricing mechanism of the capacity market has become a key link in the mechanism design of the capacity market, which is conducive to exploring the capacity value of power generation resources and guiding power investment.

The actual capacity supply required for different power generation resources to achieve the same capacity support effect in the power system varies. As different power generation resources enter the capacity market on a scale, the capacity market mechanism should reasonably quantify the trusted capacity differences caused by the operation characteristics of different power generation resources. The accurate calculation of trusted capacity can avoid the risk of sufficient system capacity caused by the uncertainty of power generation resource capacity supply and is conducive to further exploring the capacity value of different power generation resources. To effectively evaluate the credible capacity of power generation resources, references [15,16,17] fully consider the output uncertainties of generating units with new energy and measure the credible capacity of new energy in the capacity market by mining the correlation between power source and load. References [18,19] focus on the evaluation of credible capacity under the interaction of diverse power generation resources, improving the credible capacity of hybrid power generation resources through output complementarity and optimization coordination. Reference [20] explains that the PJM capacity markets in the UK and the US use reliability indicators to characterize the credible capacity of different power generation resources, analyze and compare the applicability of different calculation methods for credible capacity, and provide insights for the Chinese capacity market. In order to improve the convenience of the trusted capacity calculation of power generation resources, Reference [21] is based on component modeling, taking into account the operational characteristics of different power generation resources and using the sequential Monte Carlo method and virtual unit idea to solve the credible capacity of different power generation resources. The above research discusses the substitution effect of different power generation resources in the capacity support of the system and puts forward an effective calculation method of the trusted capacity of power generation resources from the perspectives of equivalent reliability of the system and the correlation of output curves. However, a single perspective makes it difficult to effectively and comprehensively characterize the differences in the effectiveness of power capacity support for different power generation resources. At the same time, conducting reliability quantification for massive power generation resources separately is too cumbersome, and it is necessary to explore the similarity of the credible capacity of similar power generation resources to simplify the difficulty and workload of evaluating credible capacity.

There are significant differences in the cost structure of different power generation resources. Capacity market mechanisms for power systems with a high proportion of renewable energy should effectively map the different cost recovery demands caused by the differences in the cost structure of power sources. By optimizing the pricing mechanism of the capacity market, investment signals for the capacity market can be formed to assist power generation resources in solving fixed cost recovery and avoiding capacity overcompensation, undercompensation, and other problems [22,23]. For example, in reference [24], entry barriers are set for new energy stations to improve the reasonable benefits of traditional power generation units with high reliability in order to avoid new energy stations with higher generation opportunities in the electricity market using low quotations to seize power generation capacity. Based on the difference in power cost structure, literature [25] divides new energy and traditional power generation units into two types, establishes two types of market platforms, conducts capacity market transactions, and implements differentiated capacity compensation mechanisms formed by different fixed cost ratios of different power generation resources. The above research addresses the correlation between fixed and variable costs of power sources from the perspectives of parameter settings and platform partitioning in order to achieve reasonable compensation for different power generation resources.

In order to cope with the risk of system capacity adequacy brought by large-scale grid connection of renewable energy, explore the capacity value of different power generation resource system capacity supply, and meet the demand of differentiated fixed cost recovery, this paper designs a capacity market mechanism for high-proportion renewable energy power system. The main contributions of this paper are as follows:

(1)

The capacity trust factor is introduced to describe the actual degree of contribution of different power generation resources in response to the capacity support demand of the system. The trusted capacity evaluation method of power generation re-sources is proposed considering the reliability of the system and the correlation of source and charge. The equivalent capacity support capacity and capacity value of different power generation resources are deeply explored from multiple perspectives, and the fairness of capacity compensation of different power generation resources is improved;

(2)

This paper proposes a cost proportion factor to map the cost structure differences of different types of power generation resources in response to the differential compensation problem of different power generation resources. By quantifying the cost recovery demands caused by cost structure differences of different power generation resources, the pricing mechanism of marginal clearing in the existing capacity market is optimized, forming multiple capacity price signals, establishing differential compensation mechanisms for different power generation resources, and guiding rational investment and optimization allocation of power generation resources.

Section 1 of the manuscript is a description of the eye background and contribution points. Section 2 constructs the market mechanism of the capacity market and related clearance process. Section 3 is about the capacity market value model building. Section 4 carries out a case analysis.

2. The Overall Framework and Clearance Process of Capacity Market Mechanism

2.1. The Overall Framework of Capacity Market Mechanism

To ensure the capacity adequacy of power systems with a high proportion of renewable energy in the context of energy transformation (the proportion of renewable energy is more than 30%), a capacity market mechanism is proposed that takes into account the actual contribution of different power generation resources to the capacity support of power system, the structural differences in power supply costs, and the coordinated evolution trend of energy structure. The overall framework design for the capacity market with a high proportion of renewable energy is shown in Figure 1. The specific content of the framework can be described as follows:

(1)

Based on multiple information such as system load forecast, reliability demand, and actual operation, the power dispatching agency shall formulate flexible system capacity demand curves, release them to the capacity market players, and organize the power generation resource declaration volume and price curves. At the same time, combined with the evaluation of the system capacity support effect, taking the lowest capacity cost of the target year as the objective function, the system balance constraint and other constraint sets of different power generation resource clearance models are constructed so as to form the bid capacity and clearance price of different power generation resources in the target year;

(2)

The main entities of power generation resources formulate a capacity declaration plan and investment plan for new power sources in the target year using the capacity demand curve released by the power dispatching agency, and together with maintenance plans, forced outage rates, and other parameters, submits them to the power dispatching agency. Based on the winning bid results, capacity delivery is completed in the target year.

2.2. Capacity Market Mechanism Clearing Process Taking into Account Trusted Capacity and Power Cost Structure

The price-clearing process of the electric capacity market for power systems with a high proportion of renewable energy is shown in Figure 2. The clearing of the electric capacity market is divided into four stages: pre-market opening, bidding by market entities, centralized clearing of capacity, and capacity delivery.

In order to effectively address the challenges faced by the power system in the context of China’s energy transformation, this paper is based on the centralized optimization and marginal clearing of the PJM power capacity market in the United States [26], as well as the transaction process. Starting from the two core objectives of the capacity market to ensure the overall capacity adequacy of the power system and the fixed cost recovery of auxiliary power generation resources, a capacity market mechanism for power system with a high proportion of renewable energy is designed, achieving differentiated compensation for different power generation resources. This mechanism introduces parameters such as capacity credibility factor, cost proportion factor, and energy structure constraints to effectively quantify the power capacity support effect and cost structure differences of different power generation resources, promoting the consistency between the clearing results of the capacity market and the energy transformation route, and guiding the rational investment and allocation of power generation resource entities to ensure the adequacy of power supply capacity in power system.

3. Capacity Market Mechanism for Power Systems with a High Proportion of Renewable Energy

3.1. Development of Capacity Demand Curve

The capacity demand curve is a key link in the capacity market mechanism and a prerequisite for subsequent trading activities. It is formulated by the power dispatching agency based on factors such as the actual operating status of the power system, target annual load forecasting, and investment cost of new generation resources, and directly affects the clearing results of the capacity market. The formulation of the capacity demand curve depends on the reliability requirements of the power system. The capacity demand of the power system in the target year is calculated suing pre-set reliability requirements (approved by the power dispatching agency, such as the PJM capacity market in the United States and the New England capacity market setting reliability requirements at 0.1d/a [27,28]) and the existing power supply structure, while considering the marginal investment cost of new generating units, forming a capacity demand curve that includes capacity and price.

In addition, to enhance the fairness of power generation resources participating in the capacity market, the current capacity market mechanism introduces key nodes in the process of forming the capacity demand curve, optimizes capacity prices through subsidies, and forms an elastic capacity demand curve for power system, in order to avoid the irrational investment of power generation resources leading to the accumulation of wind power capacity resources and the proliferation of market power applications. When the capacity is insufficient to support the reliability requirements of the power system, the capacity price approaches the upper limit value, and with the continuous increase of power generation resources, the capacity price significantly decreases, and vice versa. It can be found that the capacity demand curve of an elastic power system can effectively map the dynamic relationship between the capacity demand of the power system and the supply of power generation capacity, making the marginal clearance capacity price signal more reasonable. The capacity demand curve of the elastic power system used in this paper is shown in Figure 3.

In Figure 3, points A, B, and C determine the basic trend and price upper limit of the capacity demand curve of the power system, respectively mapping the degree of demand for supporting the capacity of the power system under different reliability requirements, making the capacity demand curve elastic. A. The specific horizontal and vertical coordinates of points B and C can be expressed as follows:

$$\left\{\begin{array}{c}{p}^{\mathrm{A}}={\displaystyle \frac{\max \left\{C_{\mathrm{new}},1.5C_{\mathrm{net}}\right\}}{1-R_{\mathrm{EFORD}}}}\\ R^{\mathrm{A}}=R^{\mathrm{re}}{\displaystyle \frac{1+M-{\lambda }^A}{1+M}}\end{array}\right.$$

(1)

$$\left\{\begin{array}{c}{p}^{\mathrm{B}}={\displaystyle \frac{0.75C_{\mathrm{net}}}{1-R_{\mathrm{EFORD}}}}\\ R^{\mathrm{B}}=R^{\mathrm{re}}{\displaystyle \frac{1+M+{\lambda }^B}{1+M}}\end{array}\right.$$

(2)

$$\left\{\begin{array}{c}{p}^{\mathrm{C}}=0\\ R^{\mathrm{C}}=R^{\mathrm{re}}{\displaystyle \frac{1+M+{\lambda }^C}{1+M}}\end{array}\right.$$

(3)

where $p^{\mathrm{A}}$, $p^{\mathrm{B}}$, and $p^{\mathrm{C}}$ is the capacity prices corresponding to points A, B, and C respectively; $R^{\mathrm{A}}$, $R^{\mathrm{B}}$ and $R^{\mathrm{C}}$ is the demand capacity of the power system corresponding to points A, B, and C, respectively; $C_{\mathrm{new}}$ is the total cost of the planed generating units for peak shaving, which is the total cost of marginal generating units that meet the capacity requirements of power system in the target year; $C_{\mathrm{net}}$ is the net cost of the planed generating units for peak shaving, which is the total cost minus the expected revenue of the units in electricity market; $R_{\mathrm{EFORD}}$ is the average unit equivalent forced outage rate of power system; $R^{\mathrm{re}}$ is capacity requirements of to meet the reliability of power system; $M$ is the reserve margin of installed capacity; ${\lambda }^A$, ${\lambda }^B$, and ${\lambda }^C$ is the relaxation coefficients corresponding to points A, B, and C., respectively.

3.2. Credible Capacity Factor

3.2.1. Credible Capacity Factor

In the context of the current situation of “money shortage” faced by the pure electric energy market and the lack of trading varieties that make it difficult to characterize the existing capacity value of power generation resources, the capacity market as a supporting component of the electric energy market has been proposed and widely applied. Through centralized optimization and marginal clearing mechanisms, the capacity market mechanism enhances the fairness and autonomy of different power generation resource entities in providing capacity support to power systems and guides the investment intentions of power generation resource entities through market-oriented methods. However, in power systems with a high proportion of renewable energy, compared to new energy generating units, traditional generating units have more stable and reliable capacity support capabilities, which can achieve the same capacity support effect with less capacity, effectively reducing the capacity cost of power system and ensuring the power supply capacity adequacy of the power system. Although existing capacity market rules [26,28] have begun to explore the capacity substitution effects of different power generation resources while maintaining the reliability requirements of power system unchanged, and differentiated payments are made based on the capacity support effects of different power generation resources, the measurement of the credible capacity of power generation resources is not only closely related to the reliability of power system but also greatly influenced by the correlation between power sources and loads. Especially for renewable energy, correlation analysis in the refined evaluation of specific new energy stations will significantly change the evaluation results, which reduces the willingness of new energy entities to participate in the capacity market. Therefore, evaluating the credible capacity of power generation resources solely based on reliability not only fails to fully characterize the capacity support effect but also hinders the fairness of the capacity market.

This paper uses the capacity credible factor to characterize the actual contribution of different power generation resources in response to the capacity support demand of power systems. It deeply explores the equivalent capacity support capacity and capacity value of different power generation resources from multiple perspectives, optimizes the evaluation process of existing capacity market mechanisms in terms of credible capacity, and improves the fairness of capacity compensation for different power generation resources. The capacity credible factor is defined as the ratio of the credible capacity of any power generation resource that meets the reliability requirements of the power system in the target year to its own installed capacity. The capacity credible factor maybe expressed using the following mathematical formula:

$${\xi }^k={\displaystyle \frac{R_{tc}^k}{R_{ic}^k}}$$

(4)

where ${\xi }^k$ is the capacity credible factor of the $k\mathrm{th}$ power generation resource; $R_{tc}^k$ is the credible capacity of the $k\mathrm{th}$ power generation resource; $R_{ic}^k$ is the installed capacity of the $k\mathrm{th}$ power generation resource.

The result of correcting the capacity credible factor for the available capacity declared by the $k\mathrm{th}$ power generation resource entity is formulated:

$$R_s^k\to R_{ic}^k\times {\xi }^k=R_{tc}^k$$

(5)

where $R_s^k$ represents the available capacity declared by the $k\mathrm{th}$ generation resource for the capacity market in target year, and $\to$ represents the replacement symbol.

3.2.2. The Credible Capacity of Power Generation Capacity Resources

The credible capacity is the basis for calculating the capacity credible factor of power generation resources, which maps the actual capacity support capacity of different power generation resources. The equivalent fixed capacity (EFC) method is used to evaluate the credible capacity of different power generation resources from two perspectives: power supply reliability and the correlation between power supply and load. The method of evaluating the credible capacity of different types of power generation resources by using different generation resources and ideal generation resources (with the same credible capacity and installed capacity) that meet the same effect of capacity support in the power system while considering the impact of the correlation between power source and load on the assessment of credible capacity and refining the credible capacity of independent power generation resources.

The formula for evaluating the credible capacity of the $k\mathrm{th}$ power generation resource using the equivalent reliable capacity EFC is given:

$$D\left(R_{\sum },L\right)=D\left(R_{\sum }-R_{ic}^k+R_{tc}^k,L\right)$$

(6)

where $R_{\sum }$ represents the total existing capacity of power system; $L$ is the load power; $D\left(R_{\sum },L\right)$ is the expression for the reliability index of power system with a capacity of $R_{\sum }$ and a system load of $L$.

In addition, considering the abundant power generation resources in the power system, conducting a separate credible capacity assessment for each unit to obtain the capacity credible factor will significantly increase the computational workload and result in redundancy. The operational characteristics and capacity support effects of different power generation resources vary, while the performance of the same type of power generation resources is generally similar. Therefore, a unified model can be constructed for the same type of power generation resources with similar operating characteristics, and their credible capacity can be evaluated from the perspective of power generation resource types. The subtle differences in installed capacity, forced outage rate, power source, and load correlation of the same type of power generation resources can be used to evaluate the credible capacity of different power generation resources finely. The evaluation of credible capacity for different power generation resources mainly includes four steps: modeling of different types of power generation resources, selection and calculation of reliability indicators, evaluation of trusted capacity for different types of power generation resources, and evaluation of credible capacity for independent power generation resources. The specific process is shown in Figure 4.

(1)

Modeling of different types of power generation resources

Traditional generating units such as coal-fired power and nuclear power operate relatively stably, and the output power is relatively close to the rated power after deducting factors such as planned maintenance and forced shutdown. The output power of new energy-generating units, such as wind power and photovoltaic power generation, has significant uncertainties. In the modeling process, it is necessary to consider factors such as planned maintenance and forced shutdowns and combine the output power prediction results [29]. Hydropower is also influenced by natural environmental hydrology and has obvious characteristics of high and low water flow. In the modeling process, it is necessary to consider the output plans formed by different scheduling methods [29].

(2)

Selection and calculation of reliability indicators for power systems

The reliability index of the power system is the basis for measuring the capacity demand of the power system, and it is also a prerequisite for calculating the reliable capacity of power generation resources. The evaluation indicators for the reliability of power systems often adopt the probability of power shortage, expected value of power shortage date, expected value of power shortage during small periods, and expected value of power shortage. To effectively measure the severity of power outages caused by power generation resource shortages, this article selects Expected Energy Not Supplied (EENS) as the system reliability index, and the calculation formula is as follows:

$$R_{\mathrm{EENS}}={\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^{24}\max \left\{\left(L_{a,d,t}-R_{a,d,t}\right),0\right\}p\left(L_{a,d,t}>R_{a,d,t}\right)}}$$

(7)

where $L_{a,d,t}$ is the load power at the $t\mathrm{th}$ time period on the $d\mathrm{th}$ day of the target year; $R_{a,d,t}$ is the total capacity of power generation resources at the $t\mathrm{th}$ time period on the $d\mathrm{th}$ day of the target year; $p\left(L_{a,d,t}>R_{a,d,t}\right)$ is the probability that the load power at the $t\mathrm{th}$ time period on the $d\mathrm{th}$ day of the target year is greater than the total capacity of the power generation resources.

Considering the output synergy of different power generation resources at the time scale, the Monte Carlo simulation method may be used to calculate the expected reliability index value of insufficient electricity in the power system.

(3)

Assessment of credible capacity for different types of power generation resources.

Based on the calculation results of the initial value of the expected reliability index for insufficient electricity in the power system, the installed capacity of the same type of power generation resource, which is represented by the letter K, is counted as the upper limit value for the credible capacity evaluation of that type of power generation resource. The lower limit is set to 0 (i.e., the contribution of the capacity support of this type of power generation resource is 0). Introducing ideal power generation resources to replace the capacity of the $K\mathrm{th}$ type of generation resource category (with the same upper and lower limits), using the binary search method to repeatedly iterate and update the upper and lower limits of the ideal power generation resources until the actual value of the expected reliability index formed by the ideal power generation resources is insufficient and the initial value meets the iteration termination condition, thus obtaining the credible capacity $R_{tc}^K$ and capacity credible factor ${\xi }^K$ of the $K\mathrm{th}$ type of generation resource category.

(4)

Evaluation of the credible capacity of independent power generation resources.

The difference in the credible capacity of the same type of power generation resources is relatively small. The credible factor of the same type of power generation resources can be calculated based on the above steps. At the same time, the credible capacity of the power generation resources can be determined by using their installed capacity, the auxiliary power consumption rate, maintenance time ratio, equivalent forced outage rate, and the correlation coefficient between the power source and load. The calculation formula is given:

$$R_{tc}^k=R_{ic}^k{\xi }^K{\psi }^{K,k}$$

(8)

$${\psi }^{K,k}={\delta }^{K,k}(1-{\rho }^{K,k})(1-{\epsilon }^{K,k})(1-{\gamma }^{K,k})$$

(9)

where ${\psi }^{K,k}$ is the correction coefficient for the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category; ${\delta }^{K,k}$, ${\rho }^{K,k}$, ${\epsilon }^{K,k}$ and ${\gamma }^{K,k}$ represent the correlation coefficient between the power source and load of the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category, as well as the auxiliary power consumption rate, maintenance time ratio, and equivalent forced outage rate.

In the process of finely calculating the credible capacity of independent power generation resources, the correlation coefficient between the power source and load of the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category can be selected and calculated from three aspects: the correlation coefficient between the output of the $k\mathrm{th}$ power generation resource and the load power curve, the correlation coefficient between the output of the $k\mathrm{th}$ power generation resource and the comprehensive output of the $K\mathrm{th}$ type of generation resource category, and the correlation coefficient between the output of different power generation resources in the $K\mathrm{th}$ type of generation resource category.

(a)

Calculation of the correlation coefficient between the output of the kth power generation resource and the load power curve

When the output power curve of a certain power generation resource is closer to the load power curve in each time period, it indicates that the ability of the power generation resource to track load demand is stronger, and the corresponding correlation coefficient value between the power source and load should be larger.

The grey correlation analysis method is used to calculate the correlation coefficient value between the output of the $k\mathrm{th}$ power generation resource and the load power curve, which can be mathematically expressed as follows:

$${\mathrm{\Delta }}_t^k=\left|P_t^{K,k}-L_t\right|$$

(10)

$${\varphi }_t^{K,k}={\displaystyle \frac{\underset{1\le k\le N_k}{\min }\underset{1\le t\le 24}{\min }{\mathrm{\Delta }}_t^k+\underset{1\le k\le N}{\rho \max }\underset{1\le t\le 24}{\max }{\mathrm{\Delta }}_t^k}{{\mathrm{\Delta }}_t^k+\underset{1\le k\le N}{\rho \max }\underset{1\le t\le 24}{\max }{\mathrm{\Delta }}_t^k}}$$

(11)

$${\delta }_1^{K,k}={\displaystyle \frac{{\displaystyle \sum _{t=1}^{24}{\varphi }_t^{K,k}}}{\frac{1}{N_k}{\displaystyle \sum _{k=1}^{N_k}{\displaystyle \sum _{t=1}^{24}{\varphi }_t^{K,k}}}}}$$

(12)

where $P_t^{K,k}$ is the predicted output of the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category at $t$ time period; $L_t$ is the load power prediction of the system at $t$ time period; ${\mathrm{\Delta }}_t^k$ is the difference between the predicted output of the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category and the system load power at the time; ${\varphi }_t^{K,k}$ is the correlation coefficient between the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category and the load power at $t$ time period; $\rho$ is the resolution coefficient, usually taken as 0.5.

(b)

Calculation of the correlation coefficient between the output of the kth generation resource and the comprehensive output of the Kth type of generation resource category

The greater the output of a single power generation resource, the greater the impact on the evaluation results of the credible capacity of the same type of power generation resource, which is beneficial for improving the upper limit value of the evaluation results. Therefore, the greater the output of power generation resources among the same type of power generation resources, the higher the correlation coefficient between the power source and load should be obtained. The correlation coefficient between the output of the $k\mathrm{th}$ power generation resource and the comprehensive output of the $K\mathrm{th}$ type of generation resource category is calculated using the following formula:

$${\delta }_2^{K,k}={\displaystyle \frac{\frac{1}{{\displaystyle \sum _{t=1}^{24}{P}_t^{K,k}}}}{\frac{1}{N_k}{\displaystyle \sum _{k=1}^{N_k}\frac{1}{{\displaystyle \sum _{t=1}^{24}{P}_t^{K,k}}}}}}$$

(13)

(c)

Calculation of the correlation coefficient between the output of different power generation resources in the Kth type of generation resource category

The correlation between the output of different power generation resources in the same type of power generation resources will affect the frequency of power interdependence of power generation resources, thereby affecting the magnitude of the correlation coefficient between power sources and loads. Especially for renewable energy, the power complementarity between the generators with different renewable energy sources is clearly very obvious, while traditional generating units such as coal-fired power are less affected by uncertainties. The greater the correlation coefficient between a single power generation resource, the closer its output power is to the remaining power generation resources of the same type, and the lower the power complementarity effect. The corresponding correlation coefficient between the power source and load should be smaller.

The Pearson correlation coefficient method can be used to calculate the correlation between different power generation resources of the same type. The calculation formula for the correlation coefficient between the output of the $k\mathrm{th}$ generation resource and the comprehensive output of the $K\mathrm{th}$ type of generation resource category is given as follows:

$${\gamma }^{K,k,g}={\displaystyle \frac{{\displaystyle \sum _{t=1}^{24}\left(P_t^{K,k}-{\tilde{P}}_t^{K,k}\right)\left({\tilde{P}}_t^{K,k}-{\tilde{P}}_t^{K,g}\right)}}{\sqrt{{\displaystyle \sum _{t=1}^{24}{\left(P_t^{K,k}-{\tilde{P}}_t^{K,k}\right)}^2}{\displaystyle \sum _{t=1}^{24}{\left(P_t^{K,g}-{\tilde{P}}_t^{K,g}\right)}^2}}}}$$

(14)

$${\gamma }^{K,k}={\displaystyle \frac{{\displaystyle \sum _{k=1,k\ne g}^{N_k-1}{\gamma }^{K,k,g}}}{N_k-1}}$$

(15)

$${\delta }_3^{K,k}={\displaystyle \frac{\frac{1}{{\gamma }^{K,k}}}{\frac{1}{N_k}{\displaystyle \sum _{k=1}^{N_k}\frac{1}{{\gamma }^{K,k}}}}}$$

(16)

where ${\gamma }^{K,k,g}$ is the correlation between the $k\mathrm{th}$ generation resource and the $g\mathrm{th}$ generation resource in the $K\mathrm{th}$ type of generation resource category; ${\tilde{P}}_t^{K,k}$ is the average predicted output of the $k\mathrm{th}$ generation resource in the $K\mathrm{th}$ type of generation resource category at time; ${\gamma }^{K,k}$ is the correlation degree between the $k\mathrm{th}$ generation resource in the $K\mathrm{th}$ type of generation resource category and other generation resources of the same type.

The entropy weight method is used to weight the sub-coefficients of the correlation coefficient between the power source and load, and the correlation coefficient between the power source and load of the $k\mathrm{th}$ power generation resource in the $K\mathrm{th}$ type of generation resource category is obtained:

$${\delta }^{K,k}={\theta }_1{\delta }_1^{K,k}+{\theta }_2{\delta }_2^{K,k}+{\theta }_3{\delta }_3^{K,k}$$

(17)

where ${\theta }_1$, ${\theta }_2$, and ${\theta }_3$ are the proportion coefficients calculated by the entropy weighting method for the subdivision coefficients ${\delta }_1^{K,k}$, ${\delta }_2^{K,k}$, and ${\delta }_3^{K,k}$, respectively.

3.3. Cost Proportion Factor

To ensure the capacity adequacy of the power system, diversified power generation resources are introduced into the capacity market, and investment is guided by capacity price signals formed with the marginal clearing method. However, due to renewable energy gaining more power generation opportunities in the pure electric energy market, the majority of fixed costs have been recovered (with basically no variable costs). Renewable energy entities can develop effective pricing strategies in the pure electric energy market, such as using low pricing methods to seize the share of power generation resources in the capacity market. This behavior distorts the capacity price signal and often leads to frequent hitchhikes in renewable energy. The existing capacity market mechanism makes it difficult to effectively avoid the phenomenon of renewable energy “hitchhiking”, resulting in the possibility of overcompensation for some renewable energy generators, which in turn makes it difficult to recover the fixed costs of traditional generators and leads to a sharp decline in investment willingness. The fairness of the market is significantly reduced, which goes against the original intention of establishing a capacity market. In addition, although the capacity credible factor can indirectly achieve differentiated compensation for different power generation resources, the capacity credible factor is more of a reflection of the capacity value of power generation resources. The core of building a capacity market is not only to ensure the adequacy of the power system’s capacity but also to assist in the fixed cost recovery of power generation resources. Without considering the cost structure differences of different power generation resources, the capacity price signal makes it difficult to map the cost recovery demands of power generation resource differentiation effectively.

This paper proposes a cost proportion factor to map the cost structure differences of different types of power generation resources in response to the differential compensation problem of different power generation resources. By quantifying the cost recovery demands caused by cost structure differences of different power generation resources, the pricing mechanism of marginal clearance in the existing capacity market is optimized, forming multiple capacity price signals, establishing differential compensation mechanisms for different power generation resources, and guiding rational investment and optimization allocation of power generation resources. The cost proportion factor is defined as the ratio of the net cost of any power generation resource to the fixed cost, which can be expressed using the following mathematical formula:

$${\chi }^k={\displaystyle \frac{C_{\mathrm{net}}^k}{C_{\mathrm{s}}^{\mathsf{\omega }}}}$$

(18)

$$C_{\mathrm{net}}^k=C_{\mathrm{s}}^k+C_{\mathrm{v}}^k-I_{\mathrm{p}}^k$$

(19)

where ${\chi }^k$ is the cost proportion factor for the $k\mathrm{th}$ power generation resource; $C_{\mathrm{s}}^k$ is the fixed cost of the $k\mathrm{th}$ power generation resource; $C_{\mathrm{net}}^k$ is the net cost of the $k\mathrm{th}$ power generation resource, with a value of 0 when the net cost is negative; $C_{\mathrm{v}}^k$ is the variable cost of the $k\mathrm{th}$ power generation resource; $I_{\mathrm{p}}^k$ represents the expected return of the $k\mathrm{th}$ power generation resource for the target year in electricity market; $C_{\mathrm{s}}^{\omega }$ is the fixed cost of marginal generating units planned and constructed in capacity market.

The cost proportion factor can effectively reveal the impact of cost structure differences of different power generation resources on capacity prices, and ${\chi }^k=1$ is the key boundary point for differentiated compensation of power generation resources due to cost structure. ${\chi }^k>1$ indicates that the winning power generation resource failed to recover fixed costs in the electricity market, and the larger the cost proportion factor, the more net costs need to be recovered; ${\chi }^k<1$ indicates that the winning power generation resource has recovered some fixed costs in the electricity market, and the smaller the cost proportion factor, the more fixed costs have been recovered. To avoid overcompensation and undercompensation problems caused by significant differences in the cost structure of power generation resources, it is necessary to map the cost proportion factor to a certain interval. The following Tanh function is used with ${\chi }^k=1$ as the center point, and the function trend is equivalent to the [0, 2] interval.

$${\chi }^k=\left\{\begin{array}{cc}1-\mathrm{Tan}\mathrm{h}\left|{\chi }^k\right|& {\chi }^k<1\\ {\chi }^k& {\chi }^k\ge 1\end{array}\right.$$

(20)

where $\mathrm{Tan}\mathrm{h}$ is the activation function (hyperbolic tangent function), which can be expressed as:

$$\mathrm{Tan}\mathrm{h}\left|{\chi }^k\right|={\displaystyle \frac{e^{\left|{\chi }^k\right|}-e^{-\left|{\chi }^k\right|}}{e^{\left|{\chi }^k\right|}+e^{-\left|{\chi }^k\right|}}}$$

(21)

The cost proportion factor ${\chi }^k$ optimizes the clearing price of power generation resources in the capacity market, and the result can be expressed using the following formula:

$$p_a^k={\chi }^k\times {\widehat{p}}_a$$

(22)

where ${\widehat{p}}_a$ is the marginal clearing capacity price of the winning power generation resources for the target annual in capacity market, and $p_a^k$ is the capacity price of the $k\mathrm{th}$ power generation resource optimized by cost proportion factor in the target year.

3.4. Settlement Mechanism

The cost settlement of the capacity market is closely related to factors such as the actual capacity delivery of power generation resources in the target year, the credible capacity factor, and the power cost structure. It is necessary to calculate based on the actual capacity delivery of power generation resources in the target year, and the power dispatching agency needs to evaluate the effectiveness of the capacity delivery results of power generation resources. Therefore, capacity fees are generally settled afterward. In this article, the capacity cost of power generation resources is settled using the following formula:

$$I_C^k=R_{ic}^{k,r}{\xi }^k{\chi }^k{\widehat{p}}_a$$

(23)

where $I_C^k$ represents the capacity market revenue of the $k\mathrm{th}$ winning power generation resource in the target year and $R_{ic}^{k,r}$ is the actual installed capacity delivered by the $k\mathrm{th}$ winning power generation resource in the target year.

4. The Studying Cases

4.1. Data Sources and Settings

This paper takes the next three years as the target year for the opening of the capacity market without considering the incremental auction market. Based on the transaction organization process of the PJM power capacity market, it simulates the declaration and clearance process of multiple types of power generation resources in a certain region. Using the capacity price signal formed by the marginal clearance price, the capacity credible factor, cost proportion factor, and energy structure constraints are introduced to optimize the capacity market mechanism and conduct simulation calculations and analysis. Using the multi-scenario analysis method, the effectiveness of the capacity market mechanism established in this paper is verified in a power system with a high proportion of renewable energy.

(1)

Capacity demand curve

Given that the majority of provinces or regions in China still rely mainly on coal-fired generating units in their power supply structure, this article sets coal-fired generating units as marginal peak-shaving units in the process of formulating the capacity demand curve. The upper limit of the capacity price of the capacity demand curve is determined based on the current average annual investment cost of different coal-fired generators and the expected annual returns of the electricity market. As the proportion of renewable energy continues to increase, marginal units will be updated to renewable energy generating units. The parameter for the capacity demand curves A, B, and C for the target year in the power system is shown in

Table 1. The key parameters of the capacity demand curve of the power system.

Key Point Parameters	Capacity Price/(Yuan/MW)	Capacity Demand/MW	Relaxation Coefficient/%	Capacity Demand of Power $\mathbf{System}{\mathit{R}}^{\mathit{r}\mathit{e}}$/MW	Capacity Reserve Margin $\mathit{M}$/MW	$\mathbf{Equivalent}\mathbf{Forced}\mathbf{Outage}\mathbf{Rate}{\mathit{R}}_{\mathit{E}\mathit{F}\mathit{O}\mathit{R}\mathit{D}}$/%	The Total Cost of Planning and Constructing Marginal Units/(Yuan /MW)	The Net Cost of Planning and Constructing Marginal Units/(Yuan /MW)
A	18.07	3857.5	1.2%	3900	10%	4.52%	325	230
B	9.04	3967.4	1.9%
C	0	4176.5	7.8%

.

(2)

Declaration information for the capacity market of power generation resources

Three coal-fired generators (CFG), two nuclear-driven generators (NDG), two hydro-power-driven generators (HDG), three wind-driven generators(WDG), and two photovoltaic generation systems (PV) are set with a total of 12 power generation resources (five types of power generation resources) participating in the target year’s capacity market declaration. The available capacity and capacity price table for different power generation resources participating in the target year’s mid-capacity market declaration are shown in

Table 2. Declaration information of different power generation resources in the capacity market.

Power Generation Resource	Available Capacity/MW	Capacity Price/(Yuan/MW)	Power Generation Resources	Available Capacity/MW	Capacity Price/(Yuan/MW)
CFG1	1300	18	HDG7	360	7.5
CFG2	1100	16.5	WDG8	330	5
CFG3	700	15	WDG9	240	5
NDG4	760	13	WDG10	270	5
NDG5	665	9	PV11	210	5
HDG6	510	6	PV12	240	5

.

(3)

Parameter settings for power generation resources

The parameters of different power generation resources participating in capacity market bidding are shown in

Table 3. The parameters of different power generation resources participating in capacity market bidding.

Power Generation Resource	Installed Capacity/MW	Fixed Cost /(Yuan/MW)	Variable Costs /(Yuan/MW)	Payback Period /Year	Auxiliary Power Consumption Rate/%	Equivalent Forced Outage Rate/%	Maintenance Time Ratio/%
CFG1	1500	350	270	20	5.81	6.23	2.39
CFG2	1200	320	260	20	5.38	6.35	2.16
CFG3	800	300	240	20	5.53	6.57	2.18
NDG4	800	1200	80	30	6.72	1.78	2.78
NDG5	700	1300	95	30	6.57	1.83	2.56
HDG6	850	800	60	30	0.51	8.27	5.79
HDG7	600	1000	55	30	0.36	7.98	6.21
WDG8	550	650	0	20	3.42	3.47	4.67
WDG9	400	700	0	20	3.55	3.29	4.38
WDG10	450	680	0	20	3.18	3.13	4.56
PV11	350	500	0	20	2.43	2.60	3.28
PV12	400	570	0	20	2.58	2.43	3.43

.

4.2. Analysis of the Impact of Credible Capacity Factor on Clearance Results

Using the evaluation process of credible capacity for different power generation resources, 12 power generation resources are evaluated for their credible capacity, and the corresponding capacity credible factor is calculated using the installed capacity of different power generation resources. In the process of evaluating the reliable capacity of power generation resources, the general selection method of typical daily operating curves [29] is used to calculate the reliability index EENS of the power system, the correlation coefficient between power source and load, and obtain the capacity credible factor of different types of power generation resources and each power generation resource. The typical daily operating curve of system load is shown in Figure 5, Operation curves of different power generation resources on a typical day are shown in Figure 6, and the correlation coefficients between power sources and loads for different power generation resources are shown in

Table 4. Correlation coefficient and subdivision coefficient between power sources and loads of different power generation resources.

Power Generation Resource	$\mathbf{Correlation}\mathbf{Coefficient}\mathbf{Between}\mathbf{Power}\mathbf{Sources}\mathbf{and}\mathbf{Loads}{\mathit{\delta }}^{\mathit{K},\mathit{k}}$	${\mathit{\delta }}_1^{\mathit{K},\mathit{k}}$	${\mathit{\delta }}_2^{\mathit{K},\mathit{k}}$	${\mathit{\delta }}_3^{\mathit{K},\mathit{k}}$	${\mathit{\theta }}_1$	${\mathit{\theta }}_2$	${\mathit{\theta }}_3$
CFG1	0.9494	0.8334	1.0305	0.9843	1/3	1/3	1/3
CFG2	1.0012	0.9837	0.9986	1.0214	1/3	1/3	1/3
CFG3	1.0494	1.1829	0.9709	0.9943	1/3	1/3	1/3
NDG4	1.0056	1.0137	1.0217	0.9814	1/3	1/3	1/3
NDG5	0.9944	0.9863	0.9783	1.0186	1/3	1/3	1/3
HDG6	1.0460	1.0782	1.0653	0.9945	1/3	1/3	1/3
HDG7	0.9540	0.9218	0.9347	1.0055	1/3	1/3	1/3
WDG8	1.1080	1.0892	1.1021	1.1326	1/3	1/3	1/3
WDG9	0.9782	0.9769	0.9733	0.9843	1/3	1/3	1/3
WDG10	0.9139	0.9339	0.9246	0.8831	1/3	1/3	1/3
PV11	1.0462	1.0618	0.9899	1.0870	1/3	1/3	1/3
PV12	0.9538	0.9382	1.0101	0.913	1/3	1/3	1/3

.

To verify the effectiveness of the proposed capacity credible factor in characterizing the capacity support effect of different power generation resources for power systems, three cases are set up for comparative analysis. Case 1: Correction of available capacity without considering the impact of capacity credible factor on power generation resources [14]. Case 2: Correction of available capacity when considering the impact of capacity credible factor on power generation resources, and the correlation coefficient between the power source and load of power generation resources is not considered in the calculation of capacity credible factor [20]. Case 3: Correction of available capacity when considering the impact of capacity credible factor on power generation resources and considering the correlation coefficient between the power source and load of power generation resources in the calculation of capacity credible factor. The evaluation results of the credible capacity of power generation resources in different cases are shown in Figure 7.

From Figure 7, it can be observed that there are significant differences in the evaluation results of the credible capacity of power generation resources in different cases. The evaluation results of the credible capacity in Case 2 and Case 3 are relatively close, with small fluctuations. Compared to Case 2 and Case 3, Case 1 has larger data on the evaluation results of the credible capacity of most power generation resources. This is because Case 1 uses the self-declared available capacity of power generation resources as the evaluation result of the trusted capacity. Due to the lack of experience in self-evaluation of power generation resources, the evaluation results of credible capacity in Case 1 are much higher than those in other cases. The problem of virtual high in credible capacity evaluation will bring the risk of insufficient capacity adequacy of the power system to the subsequent clearance of the capacity market. In Cases 2 and 3, based on the reliability evaluation method, the accuracy of the evaluation results has been significantly improved. Due to the lack of consideration of the impact of the correlation between power supply and load on the evaluation results in Case 2, especially the uncertainties of output power of generators with new energy, new energy sources with a high correlation between power supply and load often have higher credible capacity, resulting in a decrease in the evaluation effect of renewable energy in Case 2. According to

Table 5. The capacity credible factor of different power generation resources.

Power Generation Resource	Capacity Credible Factor
	Case 1 [14]	Case 2 [20]	Case 3
CFG1	/	0.7643	0.7256
CFG2	/	0.8424	0.8434
CFG3	/	0.7998	0.8393
NDG4	/	0.8786	0.8835
NDG5	/	0.8842	0.8792
NDG6	/	0.7219	0.7551
HDG7	/	0.7376	0.7037
HDG8	/	0.3642	0.4035
HDG9	/	0.3778	0.3696
HDG10	/	0.4013	0.3667
PV11	/	0.2753	0.2880
PV12	/	0.2618	0.2497

Note: Case 1 did not use a credible capacity factor, therefore all results were missing.

, there is a significant difference in the reliability factor of capacity for different power generation resources, with traditional units generally having higher reliability factors. Nuclear-driven generating units, as base load power sources, undertake important supply guarantee tasks with generally high annual utilization decimals. On the other hand, due to poor regulation ability and huge start-up and shutdown costs of nuclear power, nuclear-driven generating units often operate close to their rated power when responding to grid capacity requirements. Therefore, the capacity credible factor of nuclear power units is relatively high and is close to 0.9. Coal-fired generators are similar to nuclear-driven generators, but due to their strong regulation ability, they are often used for peak shaving, frequency regulation, and other needs, and their output is limited to a certain extent. Hydro-driven generators have obvious characteristics of high and low water flow, and their operation is limited by scheduling methods. Compared with coal-fired generators, their capacity credible factor is significantly reduced. Due to the uncertainty of output, the ability of new energy generation units to respond to the capacity demand of the power grid is relatively weak. The reverse peak shaving characteristics of wind-driven generators and the nighttime no output characteristics of photovoltaic power generation systems determine that their capacity reliability factor is maintained at around 0.3. As the penetration rate of new energy increases, their capacity credible factor also increases. Simulation calculation data and analysis show that the capacity credible factor of different power generation resources is closely related to the operational characteristics of the power generation resources themselves, effectively mapping their actual contribution to the capacity support of the power system, which is conducive to mining the capacity value of power generation resources and achieving payment based on the difference in the capacity support effect of the power system.

Due to the lack of a credible capacity evaluation process, the displayed results are the available capacity declared by power generation resources in the capacity market. The evaluation results of capacity credible factors for different cases are shown in Table 5.

The winning capacities of power generation resources in the capacity market under different cases are shown in Figure 8. From Figure 8, it can be seen that compared to Case 1, the bidding capacity of wind and photovoltaic resources in Case 2 and Case 3 has significantly decreased, with a maximum decrease of 58.38%. The bidding capacity of hydropower, nuclear power, and thermal power have all been improved to a certain extent. In addition, the output randomness and volatility of new energy-generating units reduce the credible capacity, and the capacity credible factor is higher than that of new energy. Traditional coal-fired generators and nuclear-driven generators bear more capacity in the power system, becoming the basis for ensuring sufficient capacity. Analysis shows that the capacity credible factor can effectively characterize the capacity support effect of power systems with different generation resources, which is conducive to reasonable compensation based on the actual capacity value of generation resources in the capacity support of power systems and improves the fairness of the capacity market.

The change in the bidding capacity of power generation resources will inevitably cause fluctuations in the clearing price of the capacity market and the capacity cost of the power system. The clearing price of the capacity market in different cases is shown in Figure 9.

Figure 9 shows that there is a certain degree of difference in the clearing prices of the capacity market in different cases, with case 1 having lower capacity prices than Cases 2 and 3. This is because Case 1 uses the available capacity declared by power generation resources in the capacity market as the credible capacity to participate in market clearing. The lack of evaluation ability results in the vast majority of power generation resources having a generally high credible capacity in Case 1, and the marginal units of clearing results fall into coal-fired generators with relatively lower priced, resulting in lower capacity prices than Case 2 and Case 3. However, high credible capacity can lead to potential capacity demand gaps in power systems due to frequent uncertainty in renewable energy output, and the emergence of a capacity adequacy crisis deviates from the original intention of establishing a capacity market. The capacity prices in Case 2 and Case 3 are consistent because the evaluation values of the credible capacity in Case 2 and Case 3 are similar. Compared to Case 2, Case 3 takes into account the impact of the correlation between power supply and load on the credible capacity of various power generation resources. It mainly uses the correlation coefficient between power supply and load to conduct a more refined evaluation of the credible capacity of power generation resources. Through an in-depth exploration of the capacity value of different power generation resources from multiple perspectives, the evaluated credible capacity is more fair and effective. Simulation calculations and analysis show that the credible capacity of power generation resources optimized by the capacity credible factor characterizes their actual contribution to the capacity support of the power system, allowing different power generation resources to obtain more reasonable profits based on their own capacity support effects. Although the introduction of capacity credible factors has increased the capacity clearing price, the increase in power generation capacity it brings is conducive to ensuring the sufficient capacity demand of the power system in the target year, enhancing the system’s safe and stable operation ability, and maintaining supply–demand balance.

Capacity market returns of each power generation resource under different cases are shown in

Table 6. Capacity market returns of each power generation resource in different cases.

Power Generation Resource	Capacity Benefits/10,000 Yuan
	Case 1	Case 2	Case 3
CFG1	0	0	0
CFG2	0	2460	1762
CFG3	4725	10,557	11,079
NDG4	11,400	11,598	11,662
NDG5	9975	10,213	10,155
HDG6	7650	10,125	10,590
HDG7	5400	7302	6967
WDG8	4950	3305	3662
WDG9	3600	2493	2439
WDG10	4050	2980	2723
PV11	3150	1590	1663
PV12	3600	1728	1648

. From Table 6, it can be observed that there are significant differences in capacity benefits obtained by various power generation resource entities in different cases. From the perspective of traditional power generation resources, the capacity benefits in Case 2 and Case 3 are significantly higher than those in Case 1, especially the significant increase in benefits for coal-fired generators and hydro-driven generators, while the degree of improvement for nuclear-driven generators is limited. The capacity benefits of traditional generating units in Case 2 and Case 3 are in line with the original intention of establishing a capacity market. Due to the reduction of revenue space for traditional generating units in the pure electric energy market, it is necessary to recover fixed costs through the capacity market. In addition, traditional generating units themselves have high reliability and are close to installed capacity in credible capacity assessment. They play a pivotal role in supporting the capacity of the power system and should receive higher capacity returns. From the perspective of new energy generation resources, compared to Case 1, Case 2 and Case 3 have reduced their capacity benefits, while the capacity benefits of photovoltaic resources have decreased by nearly 50%, which is more in line with the fact that the output uncertainty of new energy generation generating units can easily lead to poor capacity support effects in power system. Simulation calculations and analysis show that the use of capacity credible factors can characterize the actual capacity support effects of different power generation resources, indirectly achieving differentiated compensation, which is conducive to improving the fairness of different power generation resources participating in the capacity market from the perspective of capacity value.

4.3. Impact Analysis of Power Cost Proportion Factor on Clearance Results

Based on the corrected capacity credible factor of each bidding power generation resource, the cost proportion factor of each power generation resource can be calculated, and its corresponding clearing price can be optimized using fixed cost and other parameters. The calculation results of cost proportion factors for different power generation resources are shown in

Table 7. Cost proportion factors for different power generation resources.

Power Generation Resource	Cost Proportion Factors	Power Generation Resource	Cost Proportion Factors
CFG1	1.1567	HDG7	0.4215
CFG2	0.9743	WDG8	0.2317
CFG3	0.8927	WDG9	0.1578
NDG4	0.3652	WDG10	0.0518
NDG5	0.3701	PV11	0.2896
HDG6	0.4634	PV12	0.2870

.

To verify the effectiveness of the proposed cost proportion factor in optimizing the pricing mechanism of the capacity market, two cases are set up for comparative analysis. Case 1: Using capacity credible factor to adjust the available capacity of power generation resources and optimizing the capacity prices of each power generation resource using the marginal clearing method [30]. Case 2: Using a credible capacity factor to adjust the available capacity of power generation resources and a cost proportion factor to optimize the capacity prices of each power generation resource with marginal clearance. The clearing prices of various power generation resources in the capacity market under different cases are shown in Figure 10.

From Figure 10, it can be observed that considering the influence of cost proportion factors, compared to Case 1, Case 2 has more drastic fluctuations in capacity prices and a more distinct capacity price signal, with a maximum price difference of 18.2 ¥/MW, indicating significant differences in capacity prices for different power generation resources. The optimized capacity price of coal-fired generators fluctuates around the clearing price formed in Case 1, which means that compared to other power generation resources, the net cost recovery difference of coal-fired generators is the largest. The construction of a capacity market is conducive to assisting them in recovering fixed costs, effectively alleviating the money shortage problem they face in the pure electric energy market, and encouraging thermal power resource entities to invest and optimize their allocation reasonably in order to ensure the reliability and capacity adequacy of power system operation. Among them, coal-fired generator 1 has the highest capacity price, which is 2.6 ¥/MW higher than that in Case 1. Compared to Case 1, the clearance prices formed by the capacity prices of nuclear power resources, hydropower, and new energy resources have significantly decreased, with a general decrease of about 40% and volatility. This indicates that these power generation resources have achieved partial recovery of fixed costs in the pure electric energy market, with relatively low net costs. The introduction of cost proportion factor optimized capacity prices effectively solves the hitchhiking phenomenon of this part of power generation resources while avoiding overcompensation of nuclear power, hydropower, and new energy resources and achieving differentiated compensation for different power generation resources. Simulation calculations and data analysis show that the cost proportion factor can effectively map the different fixed cost recovery demands of different power generation resources due to cost structure differences, clarify the coupling relationship between fixed cost and variable cost in electric energy markets for different power generation resources, optimize the capacity prices of different power generation resources to achieve effective connection and differential compensation between fixed cost and variable cost of power generation resources, and form more reasonable capacity price signals, effectively guide different power generation resources to participate in the capacity market, enrich the types of entities in the capacity market and ensure the adequacy of power supply capacity in power systems.

To further verify the effectiveness of the cost proportion factor in differential compensation of different power generation resources in the capacity market, the profit results of different power generation resources in the capacity market are calculated for different cases, as shown in

Table 8. Capacity market returns of different power generation resources in different cases.

Power Generation Resource	Capacity Benefits/10,000 Yuan
	Case 1 [30]	Case 2
CFG1	0	0
CFG2	1762	1717
CFG3	11,079	9890
NDG4	11,662	4259
NDG5	10,155	3758
HDG6	10,590	4908
HDG7	6967	2936
WDG8	3662	848
WDG9	2439	385
WDG10	2723	141
PV11	1663	482
PV12	1648	473
Total	64,350	29,797

. From Table 8, it can be observed that there are significant differences in the market returns of each power generation resource under different cases. Taking into account the impact of cost proportion factors, compared to Case 1, Case 2 reduced the cost expenditure of the capacity market by 34.553 million yuan, a decrease of up to 53.70%. From the perspective of power generation resource types, the decrease in market returns and cost proportion factors for different power generation resources is consistent, while the decrease in thermal power resources is relatively low, which is not much different from Case 1: The decline in hydropower and nuclear power resources is moderate; the decrease in wind and photovoltaic resources is significant, especially the profit decrease of wind power resource 10 in capacity market is as high as 94.82%, indicating that this power generation resource has basically achieved fixed cost recovery in the pure electric energy market. There is a possibility of overcompensation in the capacity compensation formed in Case 1. Simulation calculations and data analysis show that introducing cost proportion factors is beneficial for reducing the capacity cost of power systems and achieving differentiated compensation for different generation resources.

It is worth noting that although the capacity market revenue of some power generation resources (nuclear power, hydropower, and new energy) has significantly decreased, their guaranteed consumption in the electric energy market, environmental attribute subsidies, and extremely low variable costs have promoted their fixed cost recovery, and power generation resources still have considerable profits. Therefore, the reduction of capacity market returns will not significantly affect the investment willingness of this portion of power generation resources. The capacity market price optimized by the cost proportion factor provides more reasonable capacity compensation for flexible power generation resources such as thermal power, effectively incentivizing their investment willingness to ensure flexibility demand and safe and stable operation in power systems with a high proportion of renewable energy.

5. Conclusions

To cope with the capacity adequacy risk of power systems brought about by the large-scale grid-connection of high proportion renewable energy, this paper designs a capacity market mechanism for power systems with high proportion renewable energy from two perspectives: ensuring the capacity adequacy of power systems and recovering fixed costs of auxiliary power generation resources. The capacity support effect of different power generation resources is depicted, and the cost recovery demand caused by the difference in power cost structure is taken into account. The capacity value of different power generation resources is deeply explored, and a differentiated compensation mechanism for capacity benefits is established. The following conclusion is drawn:

(1)

The effectiveness of different power generation resources in responding to the capacity support demand of power systems varies. The introduction of a capacity credible factor is used to characterize the actual contribution of different power generation resources in responding to the capacity support demand of power systems. A method for evaluating the credible capacity of power generation resources, considering the reliability of the power system and the correlation between power source and load, is proposed. From multiple perspectives, the equivalent capacity support capacity and capacity value of different power generation resources are deeply explored, improving the fairness of capacity compensation for different power generation resources;

(2)

A method is proposed to optimize capacity prices by using cost proportion factors that map the cost structure differences of different power generation resources to address the issue of differentiated compensation for different power generation resources. The maximum price difference can reach 18.2 yuan/MW, reducing the overall capacity cost of the power system by 53.70%. This effectively connects the fixed cost and variable cost of power generation resources and provides differentiated compensation, which is conducive to forming a more reasonable and distinct capacity price signal to guide the rational investment and optimization allocation of power generation resources;

(3)

Thermal power and nuclear power can be reasonably quoted in the capacity market according to the cost recovery situation, and the income of the capacity market can subsidize the income loss of the electricity market and realize the cost recovery.

In the current market environment, this paper only considers the benefits of power generation resources in the energy market in the cost structure of power generation resources and does not involve the benefits of power generation resources used for regulating services such as peak shaving and frequency regulation, as well as environmental product benefits. In subsequent research, the revenue channels of power generation resources can be refined and included in consideration of clearing prices in the capacity market, forming a more reasonable and fair differentiated compensation. In addition, flexible resources such as energy storage are also an important force in the capacity market, and highly flexible regulation capabilities can be utilized to respond to the abundant demand for peak shaving capacity in the power grid. With the increasing proportion of renewable energy, the capacity adequacy of power systems is facing more severe challenges. It is urgent to accept high-reliability power generation resources such as energy storage to participate in the capacity market while enriching the types of power generation resources in the capacity market and ensuring capacity adequacy.