The Power Purchase Optimization Model in China considering the Renewable Energy Risks under Different Risk Preferences

To achieve the strategic target of energy conservation and emission reduction, China is vigorously developing its large-scale and distributed renewable energy power generation industry, dominated by wind power and photovoltaic power generation. In the new situation of renewable energy power interconnection, the grid company in China must fully consider the risks caused by renewable energy when making power purchase optimization decisions. This paper sets up a power purchasing model considering the risks of the renewable energy power interconnection and testifies to the effectiveness of the model through a case study. On this basis, this paper puts forward several reasonable suggestions to help the grid company make power purchase decisions under different risk preferences.


Introduction
In China's Twelfth Five-Year Plan, along with large-scale wind power and photovoltaic power generation interconnection, the situation of the power generation structure in China is experiencing significant changes.Large amounts of renewable energy power interconnection bring new risks to power purchasing of the grid company.Therefore, it is essential to consider fully the risks of the renewable energy power interconnection and set up a power purchase optimization model for the grid company against this background.
Many scholars have studied the optimization method of purchasing power.Reference [1] pointed out that, with the reforms of the power market, power industry will enter the retail competition phase from the monopoly phase.In the early stage, studies on the optimization of power purchasing did not fully consider the risks faced by the power purchasers [2].With the reforms of the power market, the grid company should face the risks of power purchase.Research on the optimization of power purchasing is always conducted on the basis that the electricity prices obey normal distribution [3][4][5]; actually, however, the electricity prices, the power purchasing costs, and the power quantity are all random variables, and the grid company should consider them fully.References [6,7] described the risks via the variances in the power purchasing costs.However, their premise is that the prices obey normal distribution.
The theory basis of power purchase optimization mainly includes risk measurements and the minimization of the power purchasing costs.Among them, the risk measurements theory mainly considers the risks of electricity price fluctuations and the uncertainty of the power quantity demand.The tools used to assess the power purchasing risks are mainly the value-at-risk indicators and the conditional valueat-risk indicators.As a risk measurement, VaR is currently widely used to assess the risks in the market.Reference [8] assessed the risks of power purchasing via the VaR indicators.Reference [9] considered both the probability and the extent of the expected risks in the future and confirmed the scale and the probability of the grid company's loss.The research revealed that the application of the VaR to portfolio optimization has some disadvantages.Reference [10] confirmed the power purchase allocation considering the adjustment of the ISO (independent system operator) market via mathematical analysis and simulated the power quantities of different power markets according to different demands.

Mathematical Problems in Engineering
The research results above provide feasible ways to solve the power purchase optimization problem under the condition of traditional risks.However, little of the existing research considers the risks of the renewable energy power interconnection, including wind power and photovoltaic power generation.Against this background, fully considering the risks that renewable energy power generation involves, we build up a linear programme model for electricity purchase optimization based on different risk preferences of the grid company.In accordance with the model and the results of the case study, we provide some practical methods and suggestions to the grid company for electricity purchasing.

The Operation Mode of the Power Market
According to the development of the power market, its operation modes can be categorized into four types: the vertical integration mode, the single-buyer mode, the wholesale competition mode, and the retail competition mode.China is currently in the second stage and will enter the third stage with the reforms of the power market.In the third stage, namely, the wholesale competition mode, the power market will include the contract market and the spot market.There will exist many power distributors and some large power users.The power distributors purchase the power from the independent power producers and sell the power to the common power users.The large power users purchase the power from the independent power producer directly.

The Analysis of the Renewable Energy Power Interconnection and Transaction Risks
With a large amount of renewable energy power interconnection, the power purchase risks of the grid company mainly consist of five aspects in the wholesale competition mode.

The Risks of Quantity Fluctuations in the Renewable
Energy Power Generation.The first kind of risks for the grid company's purchasing power is the risk of quantity fluctuations in the renewable energy power generation, represented as  1 .The output of wind power and photovoltaic power generation is volatile and difficult to predict accurately, and the fluctuations in the quantity of renewable energy power generation can affect the market profit of the grid company.
The specific value can be calculated with the probability theory method.

The Risk of Fluctuations in the Pool
Purchase Price.When one or several pool purchase prices of the power generation (including thermal power, wind power, hydropower, and photovoltaic power generation) change, the risk income and the fluctuation probability of the pool purchase price will affect the final profit of the grid company.Therefore, the second kind of risks is the risk of fluctuations in the pool purchase price, represented as  2 .The specific value needs to be calculated according to the probability distribution of the pool purchase price.

The Risk of Fluctuations in the Sales
Price and the Distribution Price.The sales price and the distribution price are important factors that affect the income of the grid company directly.When the sales price and the distribution price become volatile, the power selling income is bound to be affected.When the sales price of small users and large users fluctuates, the sales income of the grid company will change.Therefore, the third kind of risks is the risk of fluctuation in the sales price and the distribution price, represented as  3 .The specific value needs to be calculated according to the probability distribution of the sales price and the distribution price.

The Risk of Quantity Fluctuations in the Power
Sales.The accuracy of the load forecasting has a direct influence on the income of the grid company.The fourth kind of risks is the risk of fluctuations in the quantity of power sales, represented as  4 .The specific value can be determined according to the actual situation.

The Risk of the Direct-Purchase Quantity of Large Users.
The fifth kind of risks is the risk of the direct-purchase quantity of large users, represented as  5 .The proportion of the direct-purchase quantity of large users will affect the grid company's market share and profitability.The specific value can be calculated according to the proportion of purchasing power of big users.

The Power Purchase Optimization Model of the Grid Company
In the wholesale competition mode, in which the power transmission and distribution are not separated, without considering the costs and profit which have nothing to do with the power trade, we can define the profit of the grid company as follows: where Π() represents the profit achieved by providing power services for the users;  represents the total power demand;  1 represents the value-added tax rate;  2 represents the additional tax rate of the urban construction and education;  3 represents the income tax rate;  represents the directpurchase power proportion of the large users;  represents the sales price for the middle and small users;  0 represents the fixed costs;  represents the power purchase price;  represents the transmission and distribution price which is charged to large users by the grid company;  represents the income function of the grid company;  represents the cost function of the grid company.
represents the sales income of the grid company by providing power to the middle and small users; ][, ] represents the sales income by providing power to the large users.Under certain power purchasing conditions, the profit of the grid company is mainly related to the power purchase channels, the power purchase prices, the power sales structure, the sales prices, the proportion of the directpurchase power of the large users, and the transmission and distribution prices.However, the wholesale competition mode is different from the retail competition mode.In the wholesale competition mode, the government and the power supervision control the terminal sales price of residents and the small and medium industrial and commercial users who cannot carry out direct power purchases.The grid company cannot arbitrarily change the sales price.Therefore, trying to reduce the cost of purchasing power becomes the main strategy for the grid company to increase its profit.
Common optimization algorithms can obtain the optimal combination of the power purchase by solving the linear programming problem of maximizing the economic profit under the risk constraints or minimizing the risks under the constraints of maximizing the expected profit.
This paper mainly analyses the best power purchase portfolio strategy of the grid company in the wholesale competition mode.It also analyses some cases and verifies the applicability of the optimization methods.By comparing the profit of each strategy, we can seek the best combination of the power purchase.
Assume that   = [ 1 ,  2 , . . .,   ] ∈  is the power purchase portfolio ratio vector. is a feasible set of the power purchase combination.In addition,   represents the power purchase proportion in the market  of the distribution company, and it meets the following equation constraint: In formula (2),   represents the maximal amount of the power purchase of the grid company in market .
Assume that   is the power purchase price in market  and is the combination vector of the power purchase prices.Then, the cost of the power purchase combination is In a certain period, the sales price is a fixed price  confirmed by the government for medium and small users.For the direct purchase for large users, the grid company can only charge the net costs of the large users.Assume that the price of the net costs is  and the total power demand is .The proportion  (0 ≤  < 1) is the large users' net power quantity to .Then, the expected revenue function of the grid company is According to the risk theory, risks are usually defined as the product of the adverse events' probability and the possible disaster results.
The risks can be expressed by the following formula: where  is the scale of the risks;   represents the probability of risk event ;   is the loss of risk event ; and  is the number of risk events.The grid company's power purchase price in the contract market is the benchmark price now, which is set by the government.However, the grid company cannot precisely predict the power purchase price of the spot market in advance, so it must purchase part of the power in the contract market first based on the assessment of the risks and then purchase the rest of the power in the spot market.The grid company can only predict the power purchase price of the power market by relying on its own information.According to the predicted values, it can determine the proportions of the power purchase in the contract market and in the spot market.Meanwhile, in the contract market and in the spot market, the distribution company also needs to consider various factors and determine the optimal proportions of intraprovincial and extraprovincial power purchase and the proportions of the power purchase from different intraprovincial power supplies, as shown in Figure 1.
As shown in the figure, the distribution company needs to determine the proportions of the power purchase under the risk situation of power purchase price fluctuations.According to the regulation, the distribution company must follow the full acquisition of wind power and photovoltaic generation.The power purchase prices  1 ,  2 ,  3 ,  4 , and  5 are determined by long-term contracts in the long-term contract market.They can be considered as fixed values.Meanwhile, the power purchase prices  6 ,  7 ,  8 ,  9 , and  10 are variable in the spot market.Assume that the power purchase prices obey the triangular probability distribution and the power purchase optimization problem becomes how to optimize the power purchase proportions under the condition in which the price probability distribution is uncertain.
If the probability density of the random variables  is   obeys the triangular distribution.The lower limit and the upper limit of  are, respectively,  and .The mode of  is .
The probability distribution of the power purchase prices  6 ,  7 ,  8 ,  9 , and  10 in the spot market can be expressed as follows: where   represents the power price;   min is the minimum value of the power purchase prices;   is the most probable value of the power purchase price; and   max is the maximum value of the power purchase prices.
Based on the assumptions above, the risks of profit fluctuations brought about by the pool purchase price fluctuations are In order to protect the interests of the grid company, the government implements a minimum price policy in the short term for the power purchase market: In formula ( 8),  = 6, 7, 8, 9, 10.   is the power purchase price of the short-term market. 0 is the minimum value of the power purchase price, which is set by the government.
To protect the interests of the renewable energy power generation companies and to promote the development of In formula (9),  wind  is the capacity of wind power. solar  is the capacity of photovoltaic power generation.
In addition, the extraprovincial power purchase must satisfy the physical constraints of the power transmission channel capacity.Assuming that the maximal allowable transmission power capacity is  out max , it needs to satisfy the following constraint: Based on the assumptions above and under the condition of the risk constraints, the distribution company's power purchase model for the profit optimization problem can be expressed as follows: In formula (11),  max represents the control value of the profit fluctuation risks.It is determined by the grid company according to its risk tolerance.In the case study, we carry out the analysis according to the tolerance capacity of three different kinds of risks.

The Case Study
5.1.The Basic Data.The basic data of the power purchase prices assumed in the model are shown in Table 1.
According to the price of the short-term contract subject to the triangular distribution hypothesis and the definition of the risks in the model, we can calculate the scale of the profit fluctuation risks generated by the fluctuations in the power purchase prices: The basic data of the distribution company's sales price and distribution price assumed in the model are shown in Table 2.
The sales price of the medium and small users is determined by the long-term contract, so it is not variable.However, the transmission and distribution price that is paid to the grid company by the large users may change.If the price is approved by the government, it is not variable.Assuming that it obeys triangular distribution, we can calculate the scale of the profit fluctuation risks to the grid company.The risk influence of the grid company on the power sales side is mainly caused by the fluctuations in the transmission and distribution prices: The basic data of the power purchase constraints assumed in the model are shown in Table 3.
According to the condition of the extraprovincial power transmission, we assume that the maximal capacity of the extraprovincial trade is 2 billion kWh and the fixed costs of the grid company are 15 billion yuan per year in this region.
Generally speaking, the load forecasting obeys normal distribution.We assume that the random variables of the total power demand obey normal distribution, the mean value is 115 billion kWh, and the standard deviation is 0.05 billion kWh.
Assume that in the super short term the power purchase price of the grid company, due to the lack of purchasing power, is 0.8 RMB per kWh.The power price is 0 because the power supply is too large to sell out.We can calculate the scale of the profit fluctuation risks brought about by the fluctuations in the power demand: In the case analysis, we do not regard the proportion of large users in the power purchase as a risk source but as a hypothesis while analysing.For example, there is no direct power purchase for large users when  = 0.The power market model changes from the wholesale competition mode to the single-buyer mode.We take  = 0,  = 5%, and  = 10% separately and three modes are analysed in the cases.
Under the condition of the given value , the directpurchase power for the large users no longer appears as a risk source.Then,  5 = 0.
Assume that, in accordance with the provisions, the lowest price constraints of the grid company in the short-term contract market are shown in Table 4.
The weather conditions have great influence on wind power and photovoltaic power generation.Furthermore, wind power and photovoltaic power generation are volatile.Therefore, the capacity of the wind power and photovoltaic power generation can be assumed to be a random variable.This paper assumes that the capacity of wind power and photovoltaic power generation obeys uniform distribution.
We assume that the capacity of wind power obeys the uniform distribution of 138 to 142 and the capacity of the photovoltaic power generation obeys the uniform distribution of 14 to 16.According to the probability theory, the random variable mean of wind power is 14 billion kWh and the standard deviation is 0.1155 billion kWh.The mean value of the photovoltaic power generation random variable is 1.5 billion kWh and the standard deviation is 0.0577 billion kWh.
According to the renewable energy power generation forecast, the power status of wind power or photovoltaic power generation can change.Assume that in the super short term the power purchase price due to the lack of power is 0.8 yuan/kWh.The power price is 0 because the power supply is too large to sell out.We can calculate the scale of the profit fluctuation risks that are produced by the change in the status of the wind power and photovoltaic power generation capacity: According to the data above, the grid company's profit fluctuation risks of the total power purchase satisfy the following equation: (18) 5.2.The Optimization Analysis.For the three different kinds of situations, we assume different proportion scenarios of the direct power purchase for large users in the calculation.5.2.1. = 0.This situation means that the proportion of the direct power purchase for large users is 0. There is no direct power purchase for large users.That is to say, the power market changes from the wholesale competition mode to the single-buyer mode.The distribution company's requirement and restrictions in relation to the power purchase risks are shown in Table 5.
The risks and profit in the model can be quantitative: When  max = 0.2505 billion yuan, we calculate that the maximal profit is 2.8744 billion RMB.The optimal proportions of the power purchase are shown in Table 6.
When  max = 0.25 billion yuan, we calculate that the maximal profit is 2.8632 billion yuan.The optimal proportion of the power purchase is shown in Table 7.
When  max = 0.2495 billion yuan, we calculate that the maximal profit is 2.8033 billion yuan.The optimal proportion of the power purchase is shown in Table 8.
When  max = 0.249 billion yuan, there is no feasible solution.In this case, the distribution company could not reduce the profit fluctuations of the power purchase to less than 0.249 billion yuan.

𝑘 = 5%
. This situation means that the proportion of the direct power purchase for the large users is 0.05.We assume that the distribution company's requirement and restrictions to the power purchase risks are shown in Table 9.
Table 10: The optimal power purchase proportion of the grid company when  = 5% and  max = 0.2515 billion yuan.
Table 14: The optimal power purchase proportion of the grid company when  = 10% and  max = 0.2525 billion yuan.

Types of contract
The purchased quantity from the extraprovincial market (100 GWh) The purchased quantity from the intraprovincial market (  the direct power purchase for large users will have an adverse impact on the grid company.

Conclusions
This paper considers in depth the background of China's large-scale renewable energy power interconnection.Fully considering the risks that renewable energy power generation brings, we build up a linear programme model for power purchase optimization based on different risk preferences on the power purchase side.The feasibility of the model is verified by the case study.Through the research, we reach the following conclusions: (1) Since wind power and photovoltaic power generation and their output are not controllable, the amount of power generation cannot be predicted accurately.This brings new risks to the grid company's power purchase.Therefore, we need to conduct research constantly to improve the precision of the forecasting method of wind power and photovoltaic power generation to reduce the risks.(2) Along with the increase in large users' direct-purchase power ratio, the distribution company's risks will increase and the risk profit will decrease.Thus, direct purchasing has adverse impacts on the grid company.With the background of the power market reform and large users' direct-purchase power increasing, the grid company must take action early and improve the service quality for large users to reduce the power system reforms' influence on the grid company.(3) The risk profit of the grid company increases along with the increase in risk tolerance.This complies with the principle of "the greater the risks are, the greater the profit is." Therefore, in the process of purchasing power, the grid company should fully consider its risk tolerance and control the risks within a reasonable scope to seek the maximal profit.(4) After using the linear programming optimization model recommended in this paper, the grid company's economic income level will experience a certain improvement.It means that the model reflects the power purchase risks well and solves the power purchase optimization problem of the grid company under these conditions.

Figure 1 :
Figure 1: The power purchase optimization problem of the provincial grid company.

Figure 2 :
Figure 2: The risk profile of the grid company under different ratios of direct power purchase for large users.

Table 2 :
The probability distribution of electricity selling price and transmission prices.

Table 3 :
The power quantity constraints of the grid company (unit: 100 GWh).

Table 4 :
The constraints of the minimal price in short-term contracts (unit: yuan/kWh).

Table 15 :
The optimal power purchase proportion of the grid company when  = 10% and  max = 0.252 billion yuan.

Table 16 :
The optimal power purchase proportion of the grid company when  = 10% and  max = 0.2515 billion yuan.