CVaR‐based method for optimizing the contract bidding strategy of PV power stations

With the rapid development of the new power system, the proportion of renewable energy participating in the electricity market is constantly increasing, and the uncertainty of renewable energy power output and market clearing price brings risks to its participation in long‐term contract bidding. Therefore, a method of contract bidding involving bidding amount and bidding price of PV power station is proposed. Firstly, the multi‐order weighted Markov chain model is used to forecast the distribution of weather states in the trading cycle, and the fuzzy C‐means (FCM) method is used to cluster the joint samples of power output indicators and market clearing price indicators, and then Latin hypercube sampling is used to generate power output scenarios and market clearing price scenarios. Then, an optimization method for long‐term contract bidding strategy of PV power station considering conditional value at risk (CVaR) and transaction probability is established, and the model is divided into two stages and solved in an alternate iterative way. Finally, an example is used to verify that the constructed model enables PV power stations to effectively avoid risks and obtain more stable revenue.


INTRODUCTION
The proposal of carbon peaking and carbon neutrality goals provides guidance for China's low-carbon transformation of industrial and energy structures. 1 With the increasing installed capacity of renewable energy and the continuous improvement of effective utilization level, it has become a general trend for renewable energy generation to promote the development of green energy and fully stimulate the potential of both supply and demand by participating in electricity market trading.Various green electricity trading schemes have been introduced.In August 2021, the National Development and Reform Commission and the National Energy Administration approved the "Pilot Work Plan of Green Electricity Trading", which opened a new journey for the pilot construction of green electricity trading in China.In February 2022, the "Southern Regional Green Electricity Trading Rules (Trial)" jointly compiled and issued by various power exchange centers in the southern region is the first regional green electricity trading rule in China.In May 2022, Beijing Power Exchange Center issued the "Beijing Power Exchange Center Green Electricity Trading Implementation Rules", which clarified the definition, rules, and mechanisms of green electricity trading in the State Grid region.With the rapid development of renewable energy and the improvement of green electricity trading system and mechanism, the participation of renewable energy as a market subject in market transactions will become the new normal of future market development.
Long-term trading in China is still mainly based on the quantity of electricity.Dispatching agencies need to formulate corresponding power generation plans according to the contracted electricity quantity of each power station to ensure that each power station generates the electricity quantity agreed upon in the contract. 2At present, the decomposition of contracted electricity quantities.decomposition is mainly based on the principle of "energy balance and typical day power check," and adopts methods such as average distribution, load ratio, or power station capacity ratio.However, considering the inherent power output fluctuations of renewable energy power stations, the subdivision of contracted quantity by dispatching agencies will bring greater deviation.Therefore, how to participate in long-term contract bidding has become a key problem for renewable energy.In 2021, the National Development and Reform Commission put forward the requirement of "six signatures" for the signing of long-term contracts and proposed to encourage market entities participating in the trading to sign long-term electricity contracts by negotiating electricity quantity and price in different sub-periods.When renewable power stations participate in long-term contract bidding, compared with traditional quantity contracts, allowing renewable power stations to decide bidding amount and bidding price puts forward higher requirements for the optimization method for revenue.Therefore, how power stations participate in the contract bidding and make reasonable decisions through risk management measures is an urgent problem to be solved.
Due to the randomness of renewable energy power output and market clearing price, the decision-making problem of renewable energy power stations participating in long-term contract bidding is often described as an optimization problem under high uncertainty.Common methods for dealing with uncertainties include stochastic optimization and robust optimization.In, 3 the risk measurement methods commonly used in stochastic programming models are summarized in detail, including profit variance method, value at risk (VaR) method, conditional value at risk (CVaR), etc.Among them, CVaR is a consistent risk measurement model proposed by Rockafeller and Uryase, which is defined as the conditional expectation of losses given that the loss exceeds a threshold value (VaR value).CVaR can reflect all potential losses of decision results, and it does not depend on the symmetric distribution of the decision-making revenue, especially in the case of heavy-tailed distribution, which has great advantages.As an effective risk measurement method, it has been widely used in power system risk management.Reference [4] proposes a multi-stage risk-constrained stochastic complementarity model to derive the optimal offering strategy of a wind-power producer that participates in both the day-ahead and the balancing markets.Reference [5] presents a model for optimal trading of wind power in day-ahead electricity markets under uncertainty in wind power and prices, and utility theory and CVAR are used to represent the risk preferences of wind power producers.In Reference [6], a two-stage dispatching model with optimized bidding and operating strategy in the day-ahead and real-time market for the virtual power plant is proposed, and CVaR is adopted to address the risk encountered by the uncertainty of the electricity spot market price.In Reference [7], a stochastic optimization model is established to co-optimize the profits of solar power offering and virtual bidding, where seasonal autoregressive integrated moving average (SARIMA) model is used for scenario generation and CVaR is used as a risk measure.In Reference [8], CVaR is chosen as a time-consistent and dynamic risk measure to describe a dynamic multistage stochastic programming framework for sequential decision-making under uncertainty that allows wind power producers to maximize their profit for a given risk level on profit variability.However, CVaR is mainly used for risk measurement in the participation of renewable energy and microgrid in the day-ahead and real-time markets, and there is a lack of research on applying it to the long-term contract bidding strategy model of renewable energy power stations to quantify the effect of risk avoidance.
Therefore, this paper constructs an optimization method for long-term contract bidding strategy for PV power stations based on CVaR.Considering that the power output of PV power stations and market clearing price are affected by weather states, the multi-order weighted Markov chain model is used to forecast the distribution of weather states in the trading cycle.Then, the power output data of the PV power station and the market clearing price data are processed to obtain the evaluation indicators of power output and market clearing price.After FCM clustering according to the joint samples of the indicators, Latin hypercube sampling is carried out to obtain the power output scenarios and market clearing price scenarios.The optimization method of PV power station for contract bidding strategy based on CVaR is established, and maximizing expected revenue is taken as the goal under the condition of mitigating extreme loss risks.Finally, the feasibility of the model is verified by the data of PV power station power output and market clearing price.The results show that the power station revenue considering risk measurement is more stable, which can effectively avoid the risk of loss in extreme cases.

Trading process
With the implementation of the dual-carbon target strategy, vigorously developing renewable energy has become the general trend.However, due to the technical characteristics such as the unstable power output of renewable energy, it is necessary to make innovations in institutional mechanisms and market construction in order to achieve multiple goals such as low-carbon transformation, safety and reliability, and economic affordability.Under the long-term trading framework, green electricity trading is prioritized in organization, execution, and settlement, which is not only conducive to obtaining long-term stable prices and stable investment returns but also can be used as an important basis for green energy planning and is of great significance to the development of renewable energy.
Long-term trading is mainly divided into bilateral negotiation, centralized bidding, and platform listing.According to the trading cycle, it can be divided into annual, multi-month, monthly, and intra-month trading.In order to stimulate the development potential of both sides of the renewable energy supply and demand, according to the power output characteristics and trading methods of renewable energy, this paper takes PV power station as an example and proposes a long-term contract bidding method based on the decision-making of bidding amount and bidding price.The generation side considers the risk brought by the uncertainty of renewable energy power output and transaction probability and makes decisions on the bidding amount and bidding price to maximize expected revenue.The specific process involves the power generation side determining the bidding amount and bidding price, and then publishing the offer including the power output curve and the time-of-use price.The consumption side chooses whether or not to accept the offer.The trading process is shown in Figure 1.

Deviation settlement of green electricity trading
It is assumed that the contract electricity and deviation electricity of renewable energy power stations participating in long-term trading are settled separately, and the settlement is carried out following the principle of "paying without negotiation, settling for deviations."The deviation electricity is the actual power output of the renewable energy power station minus the bidding amount in each period.Positive deviation electricity refers to the excess electricity generated, which earns revenue from selling electricity; negative deviation electricity refers to the shortfall in electricity generated, which incurs electricity purchase costs.Therefore, the uncertainty of the power output characteristics of PV power stations and the market clearing price will affect the decision-making and expected revenue of power stations.An optimization model for contract bidding strategy considering the uncertainty of power output and market clearing price is established to maximize the expected revenue of PV power stations considering the revenue risks.The specific model framework is shown in Figure 2. Specific steps are as follows.
1. Considering that the PV power station power output and market clearing price are affected by weather states, the multi-order weighted Markov chain model is adopted, and its stationary property is used to forecast the distribution of weather states in the trading cycle.
F I G U R E 1 Long-term trading process diagram.

F I G U R E 2
CVaR-based model framework.
2. In order to generate the scenarios of PV power station power output and market clearing price in the trading cycle, the indicators of power output and market clearing price are constructed.The FCM method is used to cluster the joint samples composed of output and price indicators under different weather states, and then the Latin hypercube sampling is used to generate scenarios.3.In order to obtain the optimal bidding amount and bidding price, an optimization model for long-term contract bidding strategy is established, CVaR and transaction probability are introduced to quantify the revenue risk, and the risk preference level is represented by adjusting the risk preference factor.The model quantifies the risks caused by uncertain factors when the power station participates in the contract bidding and provides the optimal decision scheme of bidding amount and bidding price.

Weather forecast based on the multi-order weighted Markov chain
The power output of PV power station has obvious meteorological characteristics, which is mainly manifested in that the power output of PV power station changes with changes in meteorological conditions.Therefore, when formulating the power output curve of PV power station, it is necessary to judge the weather distribution in the trading cycle.
In this paper, Markov chain is used to forecast the distribution of weather states.Markov chain is a discrete-time stochastic process model with Markov properties, which has the characteristics of discreteness, randomness, and no aftereffect, that is, the past (the historical state before the current state) is irrelevant to forecasting the future (the future state after the current state).In addition, since the change of weather states is related to the meteorological conditions of several days in history, or a certain climatic phenomenon lasts for a long time, it is necessary to consider the influence of continuous multi-step historical states on forecast accuracy.Therefore, the multi-order weighted Markov chain model is used to forecast weather states to make full use of historical weather information.
The transition between weather states during different days can be represented by state transition probability matrix P s W . Different weather states are denoted as different state numbers.This paper divides the weather states into three categories: sunny, cloudy, rainy, and numbered 1, 2, and 3 respectively.After obtaining the weather states of each day according to historical data, the transition frequency between each state is counted to get s order state transition probability matrix P s W . 9 where x i+s and x i+s represent the weather state of the i day and i + s day, respectively, n s ab and p s ab represent the frequency and probability of the transition from state a to state b, a, b ∈ {1, 2, 3}.A schematic diagram of Markov chain for weather forecasting is shown in Figure 3.
After obtaining the state probability matrix of different orders, the corresponding weight is confirmed according to its contribution to the accuracy of the forecast results, and the weighted transition probability matrix P W is calculated.If the consistency between the historical weather state and the current weather state is stronger, the influence of the historical weather state on the current weather state is greater, which means that the forecast accuracy of the Markov chain model of this order is higher, and the weight coefficient should be larger.Therefore, the autocorrelation coefficient of each order r s , that is, the correlation between the weather states on days 1∼T − s and days 1 + s∼T is used to judge the degree of correlation between historical and current weather states and determine the weight.Firstly, r s is calculated to judge the strength of the relationship between the history and the current weather states, and it is normalized and used as the weight of each order transition probability matrix.Finally, the weighted sum is obtained as P W .The whole model is shown below.In order to obtain the future weather distribution for a long time, Markov chain stationary distribution characteristic can be used to calculate the recurrence period of each weather state.For the finite state aperiodic irreducible Markov chain, the limit distribution of the chain can be obtained according to the ergodic theorem, that is, the stationary distribution.Therefore, this feature is used to calculate the average recurrence period and stability probability of each weather state in the trading cycle.The formulas are as follows. 3 where p ab is the probability of the weighted transition probability matrix from state a to state b,  a is the stable probability of the weather state numbered as a.

Generation of power output and market clearing price scenarios based on FCM clustering
When the PV power station in the region accounts for a relatively large proportion, the market clearing price will be affected by the PV power output and change.In order to generate power output and market clearing price scenarios, typical features of historical PV power output and market clearing price of each day in historical data under different weather states are extracted, and evaluation indicators are designed and calculated to represent their typical features.FCM clustering is made on the joint samples composed of power output and market clearing price indicators.Then Latin hypercube sampling is conducted according to the clustering results.
For the power output data of PV power station, its characteristics are measured from three dimensions: individual point, overall system, and fluctuation.
The individual point evaluation indicators of power output are selected as the maximum daily power output P max and the corresponding time t max .
where P t is the power output of the PV power station at time t, t ∈ {1, 2, • • • , T}, T is the total number of time periods.The overall system evaluation indicators are selected as the expected value of power output P av and the probability of reaching half of the rated power output p 0.5∼1 .
where T 0.5∼1 is the number of points when the power output of the PV power station reaches 50% of its rated power output.Since the power output data of PV power station is affected by meteorological conditions such as solar irradiance, temperature, and other factors, it has obvious randomness, and fluctuation indicator is needed to measure the random fluctuation of power output.Therefore, the maximum fluctuation ratio ΔP max is selected as the representative indicator of fluctuation.
where P N is the rated power output of the PV power station.
For market clearing price data, its characteristics are measured from three dimensions: single point, overall system, and price difference.
Due to the bimodal characteristic of market clearing price, one of the peaks is reached in the morning, and market clearing price tends to decrease during the solar peak hours in the afternoon.Therefore, the single point evaluation indicators of market clearing price data are selected as the maximum daytime market clearing price p max and the minimum market clearing price at noon p min,noon .
p min,noon = min where p t represents market clearing price at time t.
The overall system evaluation indicator is selected as the expected value of daytime market clearing price p av .
Since the daytime market clearing price has obvious peak-valley characteristic, the peak-valley price difference Δp noon is taken as the price difference evaluation indicator.
After calculating all the indicators according to the power output and market clearing price, the joint samples composed of output and price indicators are clustered by the FCM method.FCM clustering is an iterative optimization algorithm aiming at minimizing the sum of the distance between each joint sample and each clustering center with the corresponding fuzzy membership degree.Fuzzy membership degree is used to describe the degree to which each group of joint samples belongs to a certain clustering center.It is determined according to the distance between the sample point and the clustering center.The larger the membership degree is, the closer the sample point is to the clustering center. 10,11he FCM clustering algorithm flowchart is shown in Figure 4.
Finally, according to the distribution of weather states in the trading cycle forecast by the above Markov chain model, Latin hypercube sampling is used to simulate the power output and market clearing price scenarios.Latin Hypercube sampling is a stratified random sampling method, where the method is stratified according to the clustering results.According to the number and corresponding proportion of joint samples under each type in the clustering results, Latin Hypercube sampling is carried out proportionally. 12

CVAR-BASED OPTIMIZATION METHOD FOR CONTRACT BIDDING STRATEGY
In order to solve the bidding amount, bidding price, and revenue of power stations participating in long-term contract bidding, an optimization method for contract bidding strategy based on CVaR is established and is divided into two stages.By incorporating the scenarios generated by Latin hypercube sampling into the model, the risk of loss in extreme cases can be avoided while maximizing the power station's revenue.Therefore, the obtained decision results enable the power station to obtain more stable revenue.

CVaR-based risk measurement method
When a PV power station participates in long-term contract bidding, the uncertainty of power output and market clearing price will bring risks to the revenue of the power station, so CVaR is adopted in this paper for risk measurement.The diagram of VaR and CVaR is shown in Figure 5. Risk measurement refers to the estimation and measurement of the probability of a specific risk or the extent and degree of loss.Calculation methods of risk measurement include historical simulation method and stochastic simulation method. 13This paper uses historical simulation method, that is, generating scenarios based on historical data to calculate risks.VaR reflects the maximum potential loss of a portfolio at a given confidence level  ∈ (0, 1). 14,15Let f (x, y) be the loss function, x be the decision variable, and y be the random variable.Assuming that the joint probability density of random variables y is p(y), the probability that the loss function f (x, y) does not exceed a certain loss level is: where (x, ) is the cumulative distribution function of losses of the decision variable x.Then for a given confidence level , the calculation formulas of VaR and CVAR are: where V VaR, (x) and V CVaR, (x) are VAR and CVAR at the confidence level .Since V VaR, (x) contained in V CVaR, (x) is difficult to be solved directly, transformation function CVaR  is used to replace V CVaR, (x) 16 : where  is the value of VaR.The integral term is discretized to obtain the expected value, which is simplified as shown in formula (20):

Optimization model based on CVaR
When the PV power station participates in the contract bidding, the uncertainty of its power output puts the power station at risk of deviation settlement, and the uncertainty of market clearing price makes the bidding price of the power station face the risk of successful transaction.Therefore, the objective function of the power station participating in the long-term contract bidding comprehensively considers both revenue and risk, and adopts CVaR as the risk measurement method.
The model aims at maximizing revenue and minimizing risk.The objective function can be expressed as: where E(R) is the expected revenue of the power station under different scenarios. is the risk preference factor, indicating the degree of risk aversion of decision-makers.The larger  indicates that the decision-makers are more conservative, and the smaller  indicates that the decision-makers are more inclined to high risk.(i) is the probability of power output scenario i. N is the number of power output scenarios.R i is the revenue under scenario i. p R is the transaction probability when the decision offer is  t .
R i is the difference between the revenue of bidding amount and deviation settlement under scenario i. P t and  t are the bidding amount and bidding price of the power station at time t.P t,i is the actual power output at time t.When the actual power output is larger than the bidding amount, the difference between the two is the excess electricity P + t,i .The power station obtains the revenue from selling electricity, and the unit revenue is  + .When the bidding amount is larger than the actual power output, the difference between the two is the shortfall in electricity generated P − t,i .The power station pays the electricity purchase cost, and the unit electricity purchase cost is  − .The transaction probability p R is related to the market clearing price and revenue distribution.The market clearing price in the trading cycle will affect the transaction intention of the consumption side.The transaction probability is different under different market clearing prices, which brings uncertainty to the PV power station. 16In this paper, the non-parametric kernel density method, which can effectively fit any distribution, is used to fit the revenue probability density function. 17,18The formulas are as follows: where R j is market revenue, N j is the number of samples, f (R) is the kernel density estimate of revenue, K(⋅) is the kernel density function, h is the bandwidth.In this paper, Gaussian kernel function is selected as the kernel density function, and the expression of the Gaussian kernel function is: The relationship between transaction probability and market revenue is: where F(R) is the distribution function of market revenue.For formulas ( 24) and ( 25), combined with the objective function, they can be transformed into linear constraints: In addition, the constraints also include power station bidding amount, ramp rate, and bidding price constraints.
where P max,t is the maximum power output limit of the power station.ΔP u max and ΔP d max are the limits of the maximum power increase and decrease per unit time. min,t and  max,t are the minimum and maximum limits of bidding price.
The meaning of optimal CVaR is to minimize the CVaR loss value at the confidence level .According to formula (20), the loss function f (x, y) is defined as −E(R), that is: The process of determining bidding amount and bidding price is as follows: 1.According to the distribution of weather states forecast by the weighted Markov chain, Latin hypercube sampling is performed to generate scenarios.2. Bidding amount P t in the first-stage problem is obtained, that is, the optimal bidding amount decision model based on CVaR. 3.According to the decision result P t in the first-stage problem, the revenue probability distribution function is calculated, and bidding price  t in the second-stage problem is obtained.4. Solve P t and  t iteratively until the convergence condition is met, that is, The flowchart of the two-stage solution method is shown in Figure 7.

Scenario generation
In this paper, the market clearing price data is selected from day-ahead spot price for Austria in the European data set AT_price. 21The power output data is selected from the local 50 MW PV power station, and the data interval is 1 h.Since the PV power station only outputs during the day when there is solar radiation, the power output is zero at night.Therefore, the sunrise to sunset period of the power station power output and market clearing price data is extracted, that is, the data within 7-16 h.Taking the PV power station participating in long-term contract bidding as an example, the bidding amount and bidding price of the power station in January this year are determined, and Gurobi is used to solve the problem through MATLAB R2021.
Since the power output of PV power station is closely related to the weather state, it is first necessary to forecast the distribution of weather states in January based on historical data.In order to test the reliability of the forecast results of the proposed multi-order weighted Markov model, the data in January of the previous year is taken as an example to verify, and the weather states of winter in December to February are counted.The comparison between the forecast results of various-order Markov chains and the actual situation is shown in Figure 8.The legends "s = 1, s = 3, s = 5 and actual conditions" respectively correspond to the forecast results when the order is equal to 1, 3, 5 and actual weather states.The forecast result is the best when the order is 5, so the five-order Markov chain model is used for the weather forecast in January this year.The weather states of the previous two winters are counted and the autocorrelation coefficients of each order are calculated, as shown in Table 1.The autocorrelation coefficients of weather states for the first two orders are the largest, indicating that the weather in the previous 2 days has the greatest impact on the weather of the current day.
The weighted transition probability matrix P W is calculated according to the first five-order transition probability matrices and autocorrelation coefficients.
0.5385 0.2308 0.2308 0.4286 0.2857 0.2857 0.3750 0.2500 0.3750 After getting P W , stable probability  1 = 0.4544,  2 = 0.3602,  3 = 0.1839 can be obtained according to the ergodic theorem of Markov chain, that is, the stable distribution of three weather states: sunny, cloudy, and rainy in winter.The weather states in January this year are roughly distributed as 14 days of sunny days, 11 days of cloudy days, and 6 days of rainy days.
According to historical data, the power output and market clearing price data indicators under three weather types are calculated and clustered by the FCM method.The proportion of clustering results of power output and market clearing price is shown in Table 2.
Figure 9 is the clustering results of the joint samples under sunny weather.Based on the overall level and fluctuation of power output and the overall level and peak-valley difference of market clearing price, the historical data under sunny weather are divided into three categories.Among them, the average power output of the first category is the largest and has little fluctuation, and the market clearing price is maintained at a low level.The second category of average power output is the second, but the fluctuation is the strongest, so the fluctuation of market clearing price is also the largest.The average power output of the third category is the smallest, and the market clearing price is maintained at a high level.
Figure 10 shows the clustering results of the joint samples under cloudy weather, which are divided into four categories from the dimensions of average power output, peak time, and fluctuations.Among them, the average power output of the Output/MW Time/h first category is the largest and the market clearing price is the lowest.The power output of the second category is larger in the morning, drops sharply at noon, and decreases in the afternoon.The power output of the third category is small in the morning, and increases in the noon and afternoon periods.The fourth category of all-day power output fluctuation is obvious.
Figure 11 is the clustering results of the joint samples under rainy weather, which are divided into three categories from the dimensions of average power output and peak time.As can be seen from the figure, the average power output of the first category is the largest and reaches the peak at noon.The second category of power output peaks in the morning or afternoon and there is a sudden rise or fall.The average power output of the third category is the lowest.
In order to simulate the power output and market clearing price under various weather states in January this year, according to the distribution of weather states within 31 days forecast by the Markov chain model and the FCM clustering results of power output and electricity price, Latin hypercube sampling is used to generate scenarios under each weather state according to the proportion.

Analysis of bidding amount and bidding price
Unit electricity sales revenue  + is set as the minimum value of market clearing price ×0.8 in the generated market clearing price scenario.Unit electricity purchase cost  − is set as the maximum value of market clearing price ×1.2 in the generated market clearing price scenario, and the confidence level  is 0.95.According to the generated power output scenarios and market clearing price scenarios, the initial bidding amount is calculated according to the upper model, as shown in Figure 12.The legends " = 0,  = 0.5, and  = 1" correspond to the initial bidding amount when the risk preference factor is equal to 0, 0.5, and 1.
After the initial bidding amount is obtained, it is substituted into the lower model to calculate the optimal bidding price.After the optimal bidding price is obtained, it is resubstituted into the upper model to obtain the optimal bidding amount until the convergence condition is met to end the iteration.The changes in revenue during the iteration process are shown in Table 3.
The optimal bidding amount and bidding price of PV power station under different risk preference factors obtained through iterative calculation are shown in Figures 13 and 14.The legends " = 0,  = 0.5, and  = 1," respectively, correspond to the optimal bidding amount and bidding price when the risk preference factor is equal to 0, 0.5, and 1.It can be seen from the figure that the decision-making bidding amount and bidding price basically conform to the peak-valley characteristics of power output and electricity price.The bidding amount presents a parabolic trend of first rising and then falling, and the bidding price presents a trend of first falling and then rising.When  = 0, that is, ignoring the risk, the objective function only focuses on the maximum expected revenue, without considering the risk of loss caused by uncertainty, so the bidding amount is larger.As the risk preference factor increases, the risk attitude tends to be conservative, and the bidding amount becomes smaller, gradually realizing risk control.

Analysis of revenue under different scenarios
The comparison of expected revenue and CVaR values of PV power station under different risk preference factors is shown in Figure 15.The legends "Expected revenue, and CVaR" respectively correspond to the expected revenue and   CVaR values under different risk preference factors.The change trends of the expected revenue and CVaR values are opposite, indicating the decision maker's choice between revenue and risks.When the risk preference factor is small, the decision-maker mainly considers the revenue.With the increase of the risk preference factor, the expected revenue of the power station decreases, and the CVaR value increases, which indicates that the degree of risk aversion increases and the decision-making tends to be conservative.When the risk preference factor is larger than 0.7, the expected revenue and CVaR value change little.Under three weather states, when the risk preference factor changes, the comparison of revenue under different risk preference factors is shown in Figures 16-18.The legends " = 0,  = 0.5, and  = 1," respectively correspond to the revenue of different scenarios under the corresponding weather when the risk preference factor is equal to 0, 0.5, and 1.It can be seen from the figure that the smaller the risk preference factor on sunny days, the greater the revenue of the power station.The smaller the risk preference factor in cloudy and rainy days, the more drastic the fluctuation of revenue, and even losses.On sunny days, due to the generally large and stable power output, ideal scenarios account for  a large proportion.When the risk preference factor is not considered, the objective function only focuses on maximizing the expected revenue, so its overall revenue is greater than that after considering the risk preference factor.However, due to the small power output and strong randomness on cloudy and rainy days, the probability of the power station facing risks increases.Therefore, when the risk preference factor is not considered, the revenue decreases and fluctuates sharply under different scenarios, and even losses may occur in extremely unfavorable circumstances.The larger the risk preference factor is, the greater the weight of the risk measurement part is, and the more conservative the decision-making risk attitude is.Therefore, the trend of revenue changes in different scenarios is gentler, and the revenue is more stable.When the risk preference factor is large, the revenue is more stable.Although it cannot make the power station obtain higher revenue under ideal scenarios, it avoids the risk of extremely low revenue or even loss in extreme cases, which is conducive to the power station to obtain sustainable revenue and control risks.

TA B L E 3
Therefore, when participating in long-term contract bidding and making practical decisions, PV power stations should consider the uncertainties in the trading cycle, weigh revenue and risks according to their own risk preferences, set reasonable risk preference factor to obtain ideal revenue and avoid losses in extreme cases, and make rational decisions.Therefore, under the risk avoidance strategy, decision-makers hold a pessimistic attitude and expect to ensure a certain minimum revenue, so the risk preference factor should be large.However, under the speculative arbitrage strategy, the decision makers are optimistic and expect to get higher revenues, so the risk preference factor should be small.

CONCLUSION
This paper studies the optimization method for PV power stations participating in long-term contract bidding.According to the multi-order weighted Markov model, the weather states during the trading cycle are forecast.The power output and market clearing price data under different weather states are processed to obtain the evaluation indicators of power output and market clearing price, and then joint samples of the indicators are clustered by the FCM method.A decision method for bidding amount and bidding price considering CVAR is proposed, and the bidding amount and bidding price results of different risk preference factors are compared.The conclusions are as follows: 1. Based on the forecast weather states during the trading cycle, historical data is processed to calculate the evaluation indicators of power output and electricity price, and then joint samples of the indicators are clustered by the FCM method.The Latin hypercube sampling method is used to generate power output and market clearing price scenarios, making the decision-making results more scientific and reasonable.2. When the risk preference factor is not considered, the power station's expected revenue is greater, but ignoring the risk will lead to the weak ability of the power station to avoid low revenue or even losses when facing extreme situations.3.With the increase of risk preference factor, the revenue fluctuations in different scenarios are smaller and the revenue is more stable, which is conducive to the realization of risk control and sustainable revenue for the power stations participating in the contract bidding.4. Decision-makers should comprehensively consider revenue and risks, and determine reasonable risk preference factors according to their own risk preference and risk tolerance, so as to achieve a balance between revenue and risks.

) 3
Schematic diagram of Markov chain for weather forecasting.

F I G U R E 5
y)≥V VaR, (x) f (x, y)p(y)dy (18) Diagram of VaR and CVaR.

F I G U R E 8
Comparison between the forecast results of various-order Markov chains and the actual situation.TA B L E 1 ACF for each order of weather states.

9
FCM clustering results of power output and market clearing price under sunny weather.(A) Type I; (B) Type II; (C) Type III.

F
U R E 10 FCM clustering results of power output and market clearing price under cloudy weather.(A) Type I; (B) Type II; (C) Type III; (D) Type IV.I G U R E 11 FCM clustering results of power output and market clearing price under rainy weather.(A) Type I; (B) Type II; (C) Type III.

F I G U R E 12
Initial bidding amount curve at different risk preference factors.

F I G U R E 13
Optimal bidding amount curve at different risk preference factors.F I G U R E 14Optimal bidding price curve at different risk preference factors.

F I G U R E 15
Expected revenue and CVaR value at different risk preference factors.

F I G U R E 16
Revenue comparison of each sunny scenario under different risk preference factors.

F
I G U R E 17 Revenue comparison of each cloudy scenario under different risk preference factors.F I G U R E 18Revenue comparison of each rainy scenario under different risk preference factors.
The proportion of clustering results of power output and market clearing price.
TA B L E 2 Revenue changes during iteration.