research article the power purchase optimization model in...

Research ArticleThe Power Purchase Optimization Model in China consideringthe Renewable Energy Risks under Different Risk Preferences

Yongxiu He,1 Dacheng Li,1 Tian Xia,1,2 Dong Song,1 and Bo Zhou1

1School of Economics and Management, North China Electric Power University, Beijing 102206, China2Gansu Electric Power Corporation, Lanzhou 730050, China

Correspondence should be addressed to Yongxiu He; [email protected]

Received 8 January 2015; Revised 7 April 2015; Accepted 22 April 2015

Academic Editor: Zoran Gajic

Copyright © 2015 Yongxiu He et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To achieve the strategic target of energy conservation and emission reduction, China is vigorously developing its large-scale anddistributed renewable energy power generation industry, dominated by wind power and photovoltaic power generation. In the newsituation of renewable energy power interconnection, the grid company in China must fully consider the risks caused by renewableenergy when making power purchase optimization decisions. This paper sets up a power purchasing model considering the risksof 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 differentrisk preferences.

1. Introduction

InChina’s Twelfth Five-Year Plan, alongwith large-scale windpower and photovoltaic power generation interconnection,the situation of the power generation structure in China isexperiencing significant changes. Large amounts of renew-able energy power interconnection bring new risks to powerpurchasing of the grid company. Therefore, it is essentialto consider fully the risks of the renewable energy powerinterconnection and set up a power purchase optimizationmodel for the grid company against this background.

Many scholars have studied the optimization method ofpurchasing power. Reference [1] pointed out that, with thereforms of the power market, power industry will enter theretail competition phase from the monopoly phase. In theearly stage, studies on the optimization of power purchasingdid not fully consider the risks faced by the power purchasers[2]. With the reforms of the power market, the grid companyshould face the risks of power purchase. Research on theoptimization of power purchasing is always conducted onthe basis that the electricity prices obey normal distribution[3–5]; actually, however, the electricity prices, the powerpurchasing 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 thepower purchasing costs. However, their premise is that theprices obey normal distribution.

The theory basis of power purchase optimization mainlyincludes risk measurements and the minimization of thepower purchasing costs. Among them, the riskmeasurementstheory mainly considers the risks of electricity price fluctu-ations and the uncertainty of the power quantity demand.The tools used to assess the power purchasing risks aremainly the value-at-risk indicators and the conditional value-at-risk indicators. As a risk measurement, VaR is currentlywidely used to assess the risks in the market. Reference[8] assessed the risks of power purchasing via the VaRindicators. Reference [9] considered both the probability andthe extent of the expected risks in the future and confirmedthe scale and the probability of the grid company’s loss.The research revealed that the application of the VaR toportfolio optimization has some disadvantages. Reference[10] confirmed the power purchase allocation considering theadjustment of the ISO (independent system operator) marketviamathematical analysis and simulated the power quantitiesof different power markets according to different demands.

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 493845, 11 pageshttp://dx.doi.org/10.1155/2015/493845

2 Mathematical Problems in Engineering

The research results above provide feasible ways tosolve the power purchase optimization problem under thecondition of traditional risks. However, little of the existingresearch considers the risks of the renewable energy powerinterconnection, including wind power and photovoltaicpower generation. Against this background, fully consideringthe risks that renewable energy power generation involves, webuild up a linear programme model for electricity purchaseoptimization based on different risk preferences of the gridcompany. In accordance with the model and the resultsof the case study, we provide some practical methods andsuggestions to the grid company for electricity purchasing.

2. The Operation Mode of the Power Market

According to the development of the power market, itsoperation modes can be categorized into four types: the ver-tical integration mode, the single-buyer mode, the wholesalecompetition mode, and the retail competition mode. Chinais currently in the second stage and will enter the thirdstage with the reforms of the power market. In the thirdstage, namely, the wholesale competition mode, the powermarket will include the contract market and the spot market.There will exist many power distributors and some largepower users.The power distributors purchase the power fromthe independent power producers and sell the power to thecommon power users. The large power users purchase thepower from the independent power producer directly.

3. The Analysis of the RenewableEnergy Power Interconnection andTransaction Risks

With a large amount of renewable energy power interconnec-tion, the power purchase risks of the grid company mainlyconsist of five aspects in the wholesale competition mode.

3.1. The Risks of Quantity Fluctuations in the RenewableEnergy Power Generation. The first kind of risks for the gridcompany’s purchasing power is the risk of quantity fluctua-tions in the renewable energy power generation, representedas 𝛾1. The output of wind power and photovoltaic powergeneration is volatile and difficult to predict accurately, andthe fluctuations in the quantity of renewable energy powergeneration can affect the market profit of the grid company.The specific value can be calculated with the probabilitytheory method.

3.2.The Risk of Fluctuations in the Pool Purchase Price. Whenone or several pool purchase prices of the power generation(including thermal power, wind power, hydropower, andphotovoltaic power generation) change, the risk income andthe fluctuation probability of the pool purchase price willaffect the final profit of the grid company. Therefore, thesecond kind of risks is the risk of fluctuations in the poolpurchase price, represented as 𝛾2. The specific value needs tobe calculated according to the probability distribution of thepool purchase price.

3.3. The Risk of Fluctuations in the Sales Price and theDistribution Price. The sales price and the distribution priceare important factors that affect the income of the gridcompany directly. When the sales price and the distributionprice become volatile, the power selling income is bound tobe affected.When the sales price of small users and large usersfluctuates, the sales income of the grid company will change.Therefore, the third kind of risks is the risk of fluctuationin the sales price and the distribution price, represented as𝛾3. The specific value needs to be calculated according to theprobability distribution of the sales price and the distributionprice.

3.4. The Risk of Quantity Fluctuations in the Power Sales. Theaccuracy of the load forecasting has a direct influence on theincome of the grid company. The fourth kind of risks is therisk of fluctuations in the quantity of power sales, representedas 𝛾4. The specific value can be determined according to theactual situation.

3.5. The Risk of the Direct-Purchase Quantity of Large Users.The fifth kind of risks is the risk of the direct-purchasequantity of large users, represented as 𝛾5. The proportion ofthe direct-purchase quantity of large users will affect the gridcompany’s market share and profitability. The specific valuecan be calculated according to the proportion of purchasingpower of big users.

4. The Power Purchase Optimization Model ofthe Grid Company

In the wholesale competition mode, in which the powertransmission and distribution are not separated, withoutconsidering the costs and profit which have nothing to dowith the power trade, we can define the profit of the gridcompany as follows:

Π (𝑄) = (1 − 𝑡3) {[1 −

𝑡1

1 + 𝑡1

× (1 + 𝑡2)]

⋅ {𝑈 [𝐹, (1 − 𝑘)𝑄] +𝑈 (𝑓, 𝑘𝑄)} − [1 −𝑡1

1 + 𝑡1

]

⋅ 𝐶 (𝑝, 𝑄) −𝐶0} ,

(1)

where Π(𝑄) represents the profit achieved by providingpower services for the users; 𝑄 represents the total powerdemand; 𝑡1 represents the value-added tax rate; 𝑡2 representsthe additional tax rate of the urban construction and educa-tion; 𝑡3 represents the income tax rate; 𝑘 represents the direct-purchase power proportion of the large users; 𝐹 representsthe sales price for the middle and small users; 𝐶0 representsthe fixed costs; 𝑝 represents the power purchase price; 𝑓represents the transmission and distribution price which ischarged to large users by the grid company; 𝑈 representsthe income function of the grid company; 𝐶 represents thecost function of the grid company. [1 − 𝑡1/(1 + 𝑡1) × (1 +

𝑡2)]𝑈[𝐹, (1 − 𝑘)𝑄] represents the sales income of the grid

Mathematical Problems in Engineering 3

company by providing power to the middle and small users;(1 − 𝑡1/(1 + 𝑡1))𝐶[𝑝, 𝑄] represents the power purchase costs;[1−𝑡1/(1+𝑡1)× (1+𝑡2)]𝑈[𝑓, 𝑘𝑄] represents the sales incomeby providing power to the large users.

Under certain power purchasing conditions, the profitof the grid company is mainly related to the power pur-chase channels, the power purchase prices, the power salesstructure, the sales prices, the proportion of the direct-purchase power of the large users, and the transmissionand distribution prices. However, the wholesale competitionmode is different from the retail competition mode. In thewholesale competition mode, the government and the powersupervision control the terminal sales price of residentsand the small and medium industrial and commercial userswho cannot carry out direct power purchases. The gridcompany cannot arbitrarily change the sales price.Therefore,trying to reduce the cost of purchasing power becomesthe main strategy for the grid company to increase itsprofit.

Commonoptimization algorithms can obtain the optimalcombination of the power purchase by solving the linearprogramming problem of maximizing the economic profitunder the risk constraints or minimizing the risks under theconstraints of maximizing the expected profit.

This paper mainly analyses the best power purchaseportfolio strategy of the grid company in the wholesalecompetitionmode. It also analyses some cases and verifies theapplicability of the optimization methods. By comparing theprofit of each strategy, we can seek the best combination ofthe power purchase.

Assume that 𝑥𝑇 = [𝑥1, 𝑥2, . . . , 𝑥𝑛] ∈ 𝑋 is the powerpurchase portfolio ratio vector. 𝑋 is a feasible set of thepower purchase combination. In addition, 𝑥

𝑖represents the

power purchase proportion in themarket 𝑖 of the distributioncompany, and it meets the following equation constraint:

𝑥𝑖≥ 0,

𝑛

∑

𝑖=1𝑥𝑖= 1,

𝑥𝑖𝑄 ≤ 𝑄

𝑖.

(2)

In formula (2), 𝑄𝑖represents the maximal amount of the

power purchase of the grid company in market 𝑖.Assume that 𝑦

𝑖is the power purchase price in market 𝑖

and 𝑦𝑇= [𝑦1, 𝑦2, . . . , 𝑦𝑛] 𝑦𝑖 ≥ 0.

𝑦𝑇 is the combination vector of the power purchase

prices. Then, the cost of the power purchase combination is∑𝑛

𝑖=1 𝑥𝑖𝑦𝑖.In a certain period, the sales price is a fixed price 𝐹

confirmed by the government for medium and small users.For the direct purchase for large users, the grid company canonly charge the net costs of the large users. Assume that theprice of the net costs is 𝑓 and the total power demand is 𝑄.The proportion 𝑘 (0 ≤ 𝑘 < 1) is the large users’ net power

quantity to𝑄.Then, the expected revenue function of the gridcompany is

max (1 − 𝑡3)

⋅ [1 − 𝑡1𝑡2

1 + 𝑡1

𝐹 (1 − 𝑘) +1 − 𝑡1𝑡2

1 + 𝑡1

𝑓𝑘−1

1 + 𝑡1

𝑥𝑇𝑦]𝑄

− (1 − 𝑡3) 𝐶0.

(3)

According to the risk theory, risks are usually defined asthe product of the adverse events’ probability and the possibledisaster results.

The risks can be expressed by the following formula:

𝛾 =

𝑛

∑

𝑖=1𝑃𝑖× 𝐼𝑖, (4)

where 𝛾 is the scale of the risks; 𝑃𝑖represents the probability

of risk event 𝑖; 𝐼𝑖is the loss of risk event 𝑖; and 𝑛 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 thegovernment. However, the grid company cannot preciselypredict the power purchase price of the spot market inadvance, so it must purchase part of the power in the contractmarket first based on the assessment of the risks and thenpurchase the rest of the power in the spot market. The gridcompany can only predict the power purchase price of thepower market by relying on its own information. Accordingto the predicted values, it can determine the proportionsof the power purchase in the contract market and in thespot market. Meanwhile, in the contract market and inthe spot market, the distribution company also needs toconsider various factors and determine the optimal propor-tions of intraprovincial and extraprovincial power purchaseand the proportions of the power purchase from differentintraprovincial power supplies, as shown in Figure 1.

As shown in the figure, the distribution company needs todetermine the proportions of the power purchase under therisk situation of power purchase price fluctuations. Accordingto the regulation, the distribution company must follow thefull acquisition of wind power and photovoltaic generation.The power purchase prices 𝑦1, 𝑦2, 𝑦3, 𝑦4, and 𝑦5 are deter-mined by long-term contracts in the long-term contractmarket. They can be considered as fixed values. Meanwhile,the power purchase prices 𝑦6, 𝑦7, 𝑦8, 𝑦9, and 𝑦10 are variablein the spot market. Assume that the power purchase pricesobey the triangular probability distribution and the powerpurchase optimization problem becomes how to optimize thepower purchase proportions under the condition in whichthe price probability distribution is uncertain.

If the probability density of the random variables𝑋 is

𝑓 (𝑥 | 𝑎, 𝑏, 𝑐) =

{{{

{{{

{

2 (𝑥 − 𝑎)

(𝑏 − 𝑎) (𝑐 − 𝑎)𝑎 ≤ 𝑥 ≤ 𝑐

2 (𝑏 − 𝑥)

(𝑏 − 𝑎) (𝑏 − 𝑐)𝑐 < 𝑥 ≤ 𝑏,

(5)


Determination of optimumproportion in purchasing power

Contract market (long-term market) Spot market (short-term market)

Outside province In province Outside province In province

Bundlingpower

Hyd

ropo

wer

Hyd

ropo

wer

Ther

mal

pow

er

Ther

mal

pow

er

Phot

ovol

taic

gene

ratio

n

Phot

ovol

taic

gene

ratio

n

Bundlingpower

Win

d po

wer

Win

d po

wer

Price ofpurchasing

power

Proportion ofpurchasing

power

y1

x1

y2

x2

y3

x3

y4

x4

y5

x5

y6

x6

y7

x7

y8

x8

y9

x9

y10

x10

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

𝑋 obeys the triangular distribution. The lower limit and theupper limit of 𝑋 are, respectively, 𝑎 and 𝑏. The mode of 𝑋 is𝑐.

The probability distribution of the power purchase prices𝑦6, 𝑦7, 𝑦8, 𝑦9, and 𝑦10 in the spot market can be expressed asfollows:

𝑓 (𝑦𝑖| 𝑦𝑖min, 𝑦𝑖, 𝑦𝑖max)

=

{{{{{

{{{{{

{

2 (𝑦𝑖− 𝑦𝑖min)

(𝑦𝑖− 𝑦𝑖min) (𝑦𝑖max − 𝑦

𝑖min)𝑦𝑖min ≤ 𝑦

𝑖≤ 𝑦𝑖

2 (𝑦𝑖max − 𝑦

𝑖)

(𝑦𝑖max − 𝑦

𝑖) (𝑦𝑖max − 𝑦

𝑖min)𝑦𝑖≤ 𝑦𝑖≤ 𝑦𝑖max,

(6)

where 𝑦𝑖represents the power price; 𝑦

𝑖min is the minimumvalue of the power purchase prices; 𝑦

𝑖is the most probable

value of the power purchase price; and 𝑦𝑖max is the maximum

value of the power purchase prices.

Based on the assumptions above, the risks of profit fluctu-ations brought about by the pool purchase price fluctuationsare

𝛾 = 𝑥𝑖𝑄×∫

𝑦𝑖max

𝑦𝑖

(𝑦𝑖−𝑦𝑖) 𝑓 (𝑦

𝑖) 𝑑𝑦𝑖

= 𝑥𝑖𝑄×

(𝑦𝑖max − 𝑦

𝑖)2

3 (𝑦𝑖max − 𝑦

𝑖min).

(7)

In order to protect the interests of the grid company, thegovernment implements aminimumprice policy in the shortterm for the power purchase market:

𝑦𝑖≥ 𝑦𝑖0. (8)

In formula (8), 𝑖 = 6, 7, 8, 9, 10. 𝑦𝑖is the power purchase

price of the short-term market. 𝑦𝑖0 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


Table 1: The probability distribution of the power purchase prices.

Type Value The extraprovincialmarket

The intraprovincial market

Hydropower Thermalpower

Windpower

Photovoltaicgeneration

Long-termcontract

The most probable value 0.3047 0.22 0.32 0.31 0.31The minimal value 0.3047 0.22 0.32 0.31 0.31The maximal value 0.3047 0.22 0.32 0.31 0.31

Short-termcontract


renewable energy power, we carry out full acquisition ofrenewable energy power:

𝑥4 +𝑥9 = 𝑥wind,

𝑥5 +𝑥10 = 𝑥solar.(9)

In formula (9), 𝑥wind𝑄 is the capacity of wind power.𝑥solar𝑄 is the capacity of photovoltaic power generation.

In addition, the extraprovincial power purchase mustsatisfy the physical constraints of the power transmissionchannel capacity. Assuming that the maximal allowabletransmission power capacity is𝑄outmax, it needs to satisfy thefollowing constraint:

(𝑥1 +𝑥6) 𝑄 ≤ 𝑄outmax. (10)

Based on the assumptions above and under the conditionof the risk constraints, the distribution company’s powerpurchase model for the profit optimization problem can beexpressed as follows:

max (1 − 𝑡3) [

1 − 𝑡1𝑡2

1 + 𝑡1

𝐹 (1 − 𝑘) +1 − 𝑡1𝑡2

1 + 𝑡1

𝑓𝑘−1

1 + 𝑡1

𝑥𝑇𝑦]𝑄

− (1 − 𝑡3) 𝐶0

s.t.10∑

𝑖=1𝑥𝑖= 1

𝑥𝑖𝑄 ≤ 𝑄

𝑖

𝑦𝑗≥ 𝑦𝑗0

𝑥4 +𝑥9 = 𝑥wind

𝑥5 +𝑥10 = 𝑥solar

(𝑥1 +𝑥6) 𝑄 ≤ 𝑄outmax

𝛾 ≤ 𝛾max

𝑥𝑖≥ 0

𝑦𝑖≥ 0

𝑖 = 1, 2, . . . , 10.

(11)

In formula (11), 𝛾max represents the control value of theprofit fluctuation risks. It is determined by the grid companyaccording to its risk tolerance. In the case study, we carryout the analysis according to the tolerance capacity of threedifferent kinds of risks.

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

Types of the powerusers

The sales prices ofsmall- and

medium-sizedcustomers

Large users’electricity prices oftransmission and

distributionThe most possiblevalues of theelectricity prices(yuan/kWh)

0.505 0.132

The minimal valueof the electricityprice (yuan/kWh)

0.505 0.127

The maximal valueof the electricityprice (yuan/kWh)

0.505 0.137

5. The Case Study

5.1. The Basic Data. The basic data of the power purchaseprices assumed in the model are shown in Table 1.

According to the price of the short-term contract subjectto the triangular distribution hypothesis and the definition ofthe risks in the model, we can calculate the scale of the profitfluctuation risks generated by the fluctuations in the powerpurchase prices:

𝛾2 = 0.00006 (𝑥6 +𝑥9 +𝑥10) 𝑄

+ 0.00083 (𝑥7 +𝑥8) 𝑄.(12)

The basic data of the distribution company’s sales priceand distribution price assumed in the model are shown inTable 2.

The sales price of the medium and small users is deter-mined by the long-term contract, so it is not variable.However, the transmission and distribution price that is paidto the grid company by the large usersmay change. If the priceis approved by the government, it is not variable. Assumingthat it obeys triangular distribution, we can calculate the scaleof the profit fluctuation risks to the grid company. The riskinfluence of the grid company on the power sales side ismainly caused by the fluctuations in the transmission anddistribution prices:

𝛾3 = 0.00083𝑘𝑄. (13)


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

Type Value Power purchased fromthe extraprovincial market

Power purchased from the intraprovincial market

Hydropower Thermalpower

Windpower

Photovoltaicgeneration

Long-termcontract


Short-termcontract


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

Types of contract Short-term contract

Sources Power purchased from theextraprovincial market

Power purchased from the intraprovincial marketHydropower Thermal power Wind power Photovoltaic generation

Lowest price 0.43 0.23 0.32 0.3 0.3

The basic data of the power purchase constraints assumedin the model are shown in Table 3.

According to the condition of the extraprovincial powertransmission, we assume that the maximal capacity of theextraprovincial trade is 2 billion kWh and the fixed costs ofthe grid company are 15 billion yuan per year in this region.

Generally speaking, the load forecasting obeys normaldistribution.We assume that the randomvariables of the totalpower demand obey normal distribution, the mean value is115 billion kWh, and the standard deviation is 0.05 billionkWh.

Assume that in the super short term the power purchaseprice of the grid company, due to the lack of purchasingpower, is 0.8 RMB per kWh. The power price is 0 becausethe power supply is too large to sell out. We can calculatethe scale of the profit fluctuation risks brought about by thefluctuations in the power demand:

𝛾4 = (0.6− 0) × 0.5+ (0.8− 0.4) × 0.5 = 0.5. (14)

In the case analysis, we do not regard the proportion oflarge users in the power purchase as a risk source but as ahypothesis while analysing. For example, there is no directpower purchase for large users when 𝑘 = 0.The powermarketmodel changes from the wholesale competition mode to thesingle-buyer mode. We take 𝑘 = 0, 𝑘 = 5%, and 𝑘 = 10%separately and three modes are analysed in the cases.

Under the condition of the given value 𝑘, the direct-purchase power for the large users no longer appears as a risksource. Then, 𝛾5 = 0.

Assume that, in accordance with the provisions, thelowest price constraints of the grid company in the short-termcontract market are shown in Table 4.

The weather conditions have great influence on windpower and photovoltaic power generation. Furthermore,wind power and photovoltaic power generation are volatile.Therefore, the capacity of the wind power and photovoltaicpower generation can be assumed to be a random variable.

This paper assumes that the capacity of wind power andphotovoltaic power generation obeys uniform distribution.

We assume that the capacity of wind power obeys theuniform distribution of 138 to 142 and the capacity of thephotovoltaic power generation obeys the uniform distribu-tion of 14 to 16. According to the probability theory, therandom variable mean of wind power is 14 billion kWh andthe standard deviation is 0.1155 billion kWh. The mean valueof the photovoltaic power generation random variable is 1.5billion kWh and the standard deviation is 0.0577 billion kWh.

According to the renewable energy power generationforecast, the power status of wind power or photovoltaicpower generation can change. Assume that in the super shortterm the power purchase price due to the lack of power is0.8 yuan/kWh.The power price is 0 because the power supplyis too large to sell out. We can calculate the scale of theprofit fluctuation risks that are produced by the change in thestatus of the wind power and photovoltaic power generationcapacity:

𝛾1 = (0.6− 0) × 1.732+ (0.8− 0.4) × 1.732 = 1.732. (15)

According to the data above, the grid company’s profitfluctuation risks of the total power purchase satisfy thefollowing equation:

𝛾 = 𝛾1 + 𝛾2 + 𝛾3 + 𝛾4 + 𝛾5,

𝛾 = 0.00006 (𝑥6 +𝑥9 +𝑥10) 𝑄

+ 0.00083 (𝑥7 +𝑥8 + 𝑘)𝑄+ 2.232.

(16)

After adding the actual values to the equations above, thetotal profit of the distribution company is

𝑅 = [0.84× 0.5 (1− 𝑘) + 0.84× 0.2𝑘 − 0.8610∑

𝑖=1𝑥𝑖𝑦𝑖]

× 0.75𝑄− 112.5.

(17)


The model can be expressed asmax 𝑅

= [0.84× 0.5 (1− 𝑘) + 0.84× 0.2𝑘 − 0.8610∑


× 0.75𝑄− 112.5

s.t.10∑

𝑖=1𝑥𝑖= 1

𝑦1 = 0.3047

𝑦2 = 0.22

𝑦3 = 0.32

𝑦4 = 0.31

𝑦5 = 0.31

𝑦6 = 0.45

𝑦7 = 0.2443

𝑦8 = 0.3329

𝑦9 = 0.3249

𝑦10 = 0.3249

𝑦6 ≥ 0.43

𝑦7 ≥ 0.23

𝑦8 ≥ 0.32

𝑦9 ≥ 0.3

𝑦10 ≥ 0.3

𝑥4 =6115

𝑥5 =1115

𝑥9 =5115

𝑥10 =5

1150

0 ≤ 𝑥1 ≤101150

0 ≤ 𝑥2 ≤2401150

0 ≤ 𝑥3 ≤3001150

0 ≤ 𝑥6 ≤5

1150

0 ≤ 𝑥7 ≤2001150

0 ≤ 𝑥8 ≤8001150

𝑥1 +𝑥6 ≤201150

𝛾 ≤ 𝛾max

𝑖 = 1, 2, . . . , 10.(18)

5.2. The Optimization Analysis. For the three different kindsof situations, we assume different proportion scenarios of thedirect power purchase for large users in the calculation.

5.2.1. 𝑘 = 0. This situation means that the proportion ofthe direct power purchase for large users is 0. There is nodirect power purchase for large users.That is to say, the powermarket changes from the wholesale competition mode to thesingle-buyer mode. The distribution company’s requirementand restrictions in relation to the power purchase risks areshown in Table 5.

The risks and profit in the model can be quantitative:

𝛾 = 0.00006 (𝑥6 +𝑥9 +𝑥10) 𝑄

+ 0.00083 (𝑥7 +𝑥8 + 𝑘)𝑄+ 2.232

= 0.0069 (𝑥6 +𝑥9 +𝑥10) + 0.9545 (𝑥7 +𝑥8)

+ 2.232,

𝑅 = [0.84× 0.5 (1− 𝑘) + 0.84× 0.2𝑘 − 0.8610∑


× 0.75𝑄− 112.5

= (0.42− 0.8610∑

𝑖=1𝑥𝑖𝑦𝑖)× 862.5− 112.5.

(19)

When 𝛾max = 0.2505 billion yuan, we calculate thatthe maximal profit is 2.8744 billion RMB. The optimalproportions of the power purchase are shown in Table 6.

When 𝛾max = 0.25 billion yuan, we calculate that themaximal profit is 2.8632 billion yuan.The optimal proportionof the power purchase is shown in Table 7.


When 𝛾max = 0.249 billion yuan, there is no feasiblesolution. In this case, the distribution company could notreduce the profit fluctuations of the power purchase to lessthan 0.249 billion yuan.

5.2.2. 𝑘 = 5%. This situationmeans that the proportion of thedirect power purchase for the large users is 0.05. We assumethat the distribution company’s requirement and restrictionsto the power purchase risks are shown in Table 9.


Table 5: The risk tolerance of the grid company when 𝑘 = 0 (unit: 100 million yuan).

The endurance threshold ofincome fluctuation High endurance Medium endurance Low endurance Extremely low endurance

𝛾max 2.505 2.5 2.495 2.49

Table 6: The optimal power purchase proportion of the grid company when 𝑘 = 0 and 𝛾max = 0.2505 billion yuan.

Types of contractThe purchased quantity

from the extraprovincialmarket (100GWh)

The purchased quantity from the intraprovincial market(100GWh) The maximal profit

(billion RMB)Hydropower Thermalpower Wind power Photovoltaic

generationLong-term contract 10 240 300 60 10 2.8744Short-term contract 0 200 275 50 5






generationLong-term contract 10 240 300 60 10 2.8632Short-term contract 3.06 200 271.94 50 5







Table 9: The risk tolerance of the grid company when 𝑘 = 5% (unit: 100 million yuan).


𝛾max 2.515 2.51 2.505 2.5


𝛾 = 0.00006 (𝑥6 +𝑥9 +𝑥10) 𝑄

+ 0.00083 (𝑥7 +𝑥8 + 𝑘)𝑄+ 2.232

= 0.0069 (𝑥6 +𝑥9 +𝑥10) + 0.9545 (𝑥7 +𝑥8)

+ 2.32745,

𝑅 = [0.84× 0.5 (1− 𝑘) + 0.84× 0.2𝑘 − 0.8610∑


× 0.75𝑄− 112.5

= (0.3998− 0.8610∑

𝑖=1𝑥𝑖𝑦𝑖)× 862.5− 112.5.

(20)




When 𝛾max = 0.25 billion yuan, there is no feasiblesolution. In this case, the distribution company could notreduce the profit fluctuations of the power purchase to lessthan 250 million yuan.

5.2.3. 𝑘 = 10%. This situation means that the proportion ofthe direct power purchase for the large users is 0.1.We assume


Table 10: The optimal power purchase proportion of the grid company when 𝑘 = 5% and 𝛾max = 0.2515 billion yuan.


















Table 13: The risk tolerance of the grid company when 𝑘 = 10% (unit: 100 million yuan).


𝛾max 2.525 2.52 2.515 2.51

that the distribution company’s requirement and restrictionsto the power purchase risks are shown in Table 13.


𝛾 = 0.00006 (𝑥6 +𝑥9 +𝑥10) 𝑄

+ 0.00083 (𝑥7 +𝑥8 + 𝑘)𝑄+ 2.232

= 0.0069 (𝑥6 +𝑥9 +𝑥10) + 0.9545 (𝑥7 +𝑥8)

+ 2.4229,

𝑅 = [0.84× 0.5 (1− 𝑘) + 0.84× 0.2𝑘 − 0.8610∑


× 0.75𝑄− 112.5

= (0.3948− 0.8610∑

𝑖=1𝑥𝑖𝑦𝑖)× 862.5− 112.5.

(21)

When 𝛾max = 0.2525 billion yuan, we calculate that themaximal profit is 485.2 million yuan.The optimal proportionof the power purchase is shown in Table 14.



When 𝛾max = 0.251 billion yuan, there is no feasiblesolution. In this case, the distribution company could notreduce the profit fluctuations of the power purchase to lessthan 251 million yuan.

5.3. The Analysis of the Results. Based on the analysis resultsabove, Figure 2 shows the relationship of the profit’s volatilityrisk threshold and the expected profit under different ratiosof direct power purchase for large users after considering therisks of renewable energy power interconnection.

From Figure 2, we can see that the maximum risk profitof the distribution company increases with an increase in theallowable profit’s fluctuation risk threshold. It complies withthe principle of “the greater the risks are, the greater the profitis.” Besides, alongwith the increase in the ratio of direct powerpurchase for large users, the distribution company’s risks willincrease and the risk profit will decrease.Thus, the increase in
















from the extraprovincialmarket (100 GWh)

The purchased quantity from the intraprovincial market(100 GWh) The maximal profit



4

2

0Risk

pro

fit(b

illio

n RM

B)

0.249 0.2495 0.25 0.2505 0.251 0.2515 0.252 0.2525 0.253

Endurance of profit fluctuation (billion RMB)

k = 0k = 5%

k = 10%

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

the direct power purchase for large users will have an adverseimpact on the grid company.

6. Conclusions

This paper considers in depth the background of China’slarge-scale renewable energy power interconnection. Fullyconsidering the risks that renewable energy power generationbrings, we build up a linear programme model for powerpurchase optimization based on different risk preferenceson the power purchase side. The feasibility of the model isverified by the case study.Through the research, we reach thefollowing conclusions:

(1) Since wind power and photovoltaic power generationand their output are not controllable, the amount

of power generation cannot be predicted accurately.This brings new risks to the grid company’s powerpurchase. Therefore, we need to conduct researchconstantly to improve the precision of the forecastingmethod of wind power and photovoltaic power gen-eration to reduce the risks.

(2) Alongwith the increase in large users’ direct-purchasepower ratio, the distribution company’s risks willincrease and the risk profit will decrease. Thus, directpurchasing has adverse impacts on the grid company.With the background of the power market reformand large users’ direct-purchase power increasing, thegrid company must take action early and improve theservice quality for large users to reduce the powersystem reforms’ influence on the grid company.

(3) The risk profit of the grid company increases alongwith the increase in risk tolerance.This complies withthe principle of “the greater the risks are, the greaterthe profit is.” Therefore, in the process of purchasingpower, the grid company should fully consider its risktolerance and control the risks within a reasonablescope to seek the maximal profit.

(4) After using the linear programming optimizationmodel recommended in this paper, the grid com-pany’s economic income level will experience a cer-tain improvement. It means that the model reflectsthe power purchase risks well and solves the powerpurchase optimization problem of the grid companyunder these conditions.


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

The work described in this paper was supported by theNational Natural Science Foundation of China (Grant no.71273089) and the National Social Science Foundation ofChina (Grant no. 14BJY063).

References

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[3] F. A. Longstaff and A. W. Wang, “Electricity forward prices: ahigh-frequency empirical analysis,”The Journal of Finance, vol.59, no. 4, pp. 1877–1900, 2004.

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[5] E. Eberlen and G. Stahl, “Both sides of the fence: a statisticaland regulatory view of electricity risk,” Energy Power RiskManagement, vol. 8, no. 6, pp. 34–38, 2003.

[6] Y. Liu and X. H. Guan, “Purchase allocation and demandbidding in electric power markets,” IEEE Transactions on PowerSystems, vol. 18, no. 1, pp. 106–112, 2003.

[7] R. T. Rockafellar and S. Uryasev, “Optimization of conditionalvalue-at-risk,” Journal of Risk, vol. 2, no. 3, pp. 21–41, 2000.

[8] C.-K. Woo, R. I. Karimov, and I. Horowitz, “Managing electric-ity procurement cost and risk by a local distribution company,”Energy Policy, vol. 32, no. 5, pp. 635–645, 2004.

[9] H. Mausser and D. Rosen, “Beyond VaR: parametric andsimulation-based risk management tools,” in Proceedings ofthe IEEE/IAE Conference on Computational Intelligence forFinancial Engineering (CIFEr ’99), pp. 159–162, March 1999.

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