CN111539561A - Electric energy random planning method considering condition risk value - Google Patents

Electric energy random planning method considering condition risk value Download PDF

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CN111539561A
CN111539561A CN202010273818.6A CN202010273818A CN111539561A CN 111539561 A CN111539561 A CN 111539561A CN 202010273818 A CN202010273818 A CN 202010273818A CN 111539561 A CN111539561 A CN 111539561A
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spot market
scene
scenes
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electricity price
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CN111539561B (en
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孙慧宇
王磊
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Southeast University
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses an electric energy random planning method considering condition risk value, which comprises the following steps: an original scene set is reduced through a backward reduction method, and a representative reduced scene set with a small scale is formed; a value of a confidence level alpha is designated, and a stochastic programming model based on a conditional risk value CVaR is constructed; solving an optimization model of the condition risk value CVaR to obtain a planning scheme and condition risk value CVaR and risk value VaR of the reduced scene set; and evaluating the scenes in the reduced scene set to obtain an effective scene set and an ineffective scene set, and further reducing the reduced scene set. According to the method, while the scheme and the CVaR value of the model are solved, invalid scenes in a scene set can be identified, and the optimal value of the objective function after the invalid scene set is removed is unchanged.

Description

Electric energy random planning method considering condition risk value
Technical Field
The invention relates to an electric energy planning technology of an electric power system, in particular to an electric energy random planning method considering condition risk value.
Background
The scene reduction method can approximately convert random variables in the random optimization problem into scenes with moderate quantity, so that the optimization problem is easier to solve. However, most scene reduction methods are designed aiming at the classical risk neutral random optimization problem; however, in the case of considering risk avoidance, a scene corresponding to high cost or high profit is more concerned. When optimizing a power system problem, optimization risks are generally considered, and a conditional risk value (CVaR) is introduced to evaluate the risks. The existing power system problem optimization has some invalid scenes, so that the optimization problem is complex, and the existing electric energy random planning method cannot effectively solve the optimal planning method.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides an electric energy random planning method considering condition risk values, which can identify invalid scenes in an original scene set while solving an optimal scheme, and the optimal value of an objective function after removing the invalid scene set is unchanged.
The technical scheme is as follows: in order to realize the purpose, the invention adopts the following technical scheme:
a random electric energy planning method considering condition risk values comprises the following steps:
(1) an original scene set is reduced through a backward reduction method, and a representative reduced scene set with a small scale is formed;
(2) a value of a confidence level alpha is designated, and a stochastic programming model based on a conditional risk value CVaR is constructed;
(3) solving an optimization model of the condition risk value CVaR to obtain an optimal decision and reduce the condition risk value CVaR and the risk value VaR of the scene set;
(4) and evaluating the scenes in the reduced scene set to obtain an effective scene set and an ineffective scene set, and further reducing the reduced scene set.
Further, the step (1) comprises the following steps:
(11) assume that there are initially N random planning scenarios for spot market price scenario variable ξ, represented in the form of a set { ξ }1,ξ2,...,ξNAnd setting the number of spot market electricity price target scenes obtained by backward subtraction as n, wherein n is<N；
(12) Pairing the initial N spot market electricity price scenes pairwise,taking the distance between each spot market electricity price scene pair as a vector 2 norm distance, and calculating the distance D between each pair of spot market electricity price scenesi,j，i＝1,…,N， j＝1,…,N，j≠i；Di,jThe calculation formula is as follows:
Di,j＝||ξi-ξj||2；
wherein, ξi，ξjRespectively an ith spot market electricity price scene and a jth spot market electricity price scene;
(13) power rate scenario ξ for the ith spot marketiCompare the ith spot market price scenario ξiThe distance between the current spot market price scene and other N-1 current spot market price scenes is found to be ξ closest to the ith current spot market price sceneiJth spot market electricity price scenario ξjThereby obtaining mini≠jDi,j；
(14) Solving for probability distance PDi：
PDi＝P(ξi)·mini≠jDi,j；
Wherein, P (ξ)i) For the ith spot market electricity price scenario ξiThe probability of occurrence;
for each pair of spot market electricity price scenes in the step (13), calculating the probability distance of the spot market electricity price scenes, and finding the spot market electricity price scene ξ corresponding to the minimum probability distancesThen PD iss＝min{PDi}；
(15) For spot market electricity rate scenario ξ determined in step (14)sAnd spot market price scenario ξ closest theretokDelete spot market price scenario ξ by certain principlessAnd scene ξkOne of them spot market price scene, the screening principle is:
(a) the spot market electricity price scene is also very close to other scenes, and the influence of deleting the spot market electricity price scene on the characteristics and information of the whole spot market electricity price scene is small;
(b) this spot market electricity price scenario presents itself with a relatively small probability of existence;
(16) after the corresponding spot market electricity price scene is eliminated in the step (15), the probability of the eliminated spot market electricity price scene needs to be superposed into the probability of another reserved spot market electricity price scene;
(17) and (5) repeating the steps (13) to (16) until the number of the reserved spot market power price scenes meets the requirement, and obtaining a reduction scene set with the target number of the spot market power price scenes being n and expressed as { ξ }1,ξ2,...,ξn}。
Further, the step (2) comprises the following steps:
(21) the yield of the spot market electricity price scene is a random variable, and is expressed by Z, a probability accumulation function F () is defined for the random variable Z, a confidence level is defined to be alpha epsilon [0,1], and then a risk value VaR of the random variable Z is:
VaRα[Z]:＝max{t|F(t)≥α}＝max{t|P(Z≤t)≥α}；
wherein t is a possible value of the random variable Z, and in the random planning, a scene set is used for representing the possible occurrence situation and the corresponding probability of the random variable Z;
(22) the conditional risk value CVaR for a random variable Z with a probability accumulation function F (.) and a confidence level α ∈ [0,1] is defined as:
Figure RE-GDA0002518134820000031
in the discrete case, CVaR is expressed as the optimal value of the following optimization problem:
Figure RE-GDA0002518134820000032
wherein η is the amount to be optimized, and ideally, η is the conditional risk value corresponding to the confidence level α when the optimization is completed, (a)+＝max(a,0)，FP[(η-Z)+]Is (η -Z)+The expectation regarding the probability distribution P;
(23) the CVaR is assumed to be optimized such that the risk is minimized, i.e. the yield of the worst-yielding set of back (1- α) scenes is also as large as possible; the optimization objective is therefore:
Figure RE-GDA0002518134820000033
wherein ξ is spot market price scenario variable, x is generator sales portfolio vector, G (x, ξ)i) Is the power price scene ξ of the combined vector x sold by the generator in the spot marketiThe following yields, restated as the optimization objective formula:
Figure RE-GDA0002518134820000034
adjusting the value of the confidence level a to balance the benefit and risk;
(24) for any given x, the optimum η - η (x) is defined by η -VaRα[G(x,ξ)]In addition, for any fixed x, when G (x, ξ) ≧ η, E [ (η -G (x, ξ))+Values of (c) are zero for all scenarios ξ that do not facilitate computation, particularly at the optimal solution (x)*,η*) Next, only G (x) is made*,ξ)<η(x*)＝ VaRα[G(x*,ξ)]The scenario of (2) helps to obtain the optimal objective function value.
Further, the step (3) comprises the following steps:
(31) and solving the optimization target to obtain an optimal solution (x, eta) of the optimization function:
Figure RE-GDA0002518134820000035
(32) obtaining the value of VaR as eta;
(33) to obtain
Figure RE-GDA0002518134820000036
Further, the step (4) comprises the following steps:
further evaluating the scenes in the reduced scene set obtained in step (1) by using x and η to obtain the effectiveness of the reduced scene setA scene set and an invalid scene set; thereby further reducing the scene; according to theory, those scenes with profit greater than VaR are invalid scenes, and the invalid scene set D*Comprises the following steps:
D*:＝{ξ:G(x*,ξ)>VaRα[G(x*,·)]}。
has the advantages that: compared with the prior art, the invention has the advantages that:
(1) the invention provides an objective function of
Figure RE-GDA0002518134820000041
The method defines the solution
Figure RE-GDA0002518134820000042
An effective set of scenarios for the problem.
(2) The invention provides an electric energy random planning method considering condition risk values, which can identify invalid scenes in a scene set while solving an optimization model and a CVaR value, and an objective function optimal value after the invalid scene set is removed is unchanged.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph illustrating α regulation at CVaR;
FIG. 3 is an original scene information;
FIG. 4 is a graph comparing the effects of the present invention and backward subtraction;
fig. 5 is a visual comparison diagram of a scene after reduction and a scene after reduction in backward subtraction according to the present invention.
Detailed Description
For further explanation of the technical solutions disclosed in the present application, the technical solutions of the present application will be described in detail below with reference to the accompanying drawings, and the present embodiment is only preferred and not intended to limit the scope of the claims of the present application.
As shown in fig. 1, a stochastic programming method for electric energy considering conditional risk values includes the following steps:
(1) an original scene set is reduced through a backward reduction method, and a representative reduced scene set with a small scale is formed;
(11) suppose initially we have N random planning scenarios for spot market price scenario variable ξ, represented in the form of a set { ξ }1,ξ2,...,ξNAnd setting the number of spot market electricity price target scenes obtained by backward subtraction as n, wherein n is<N；
(12) Pairing the initial N spot market electricity price scenes pairwise, taking the distance between each pair of spot market electricity price scenes as a vector 2-norm distance, and calculating the distance D between each pair of spot market electricity price scenesi,j，i＝1,…,N， j＝1,…,N，j≠i；Di,jThe calculation formula is as follows:
Di,j＝||ξi-ξj||2(1)；
wherein, ξi，ξjRespectively an ith spot market electricity price scene and a jth spot market electricity price scene;
(13) power rate scenario ξ for the ith spot marketiCompare the ith spot market price scenario ξiThe distance between the current spot market price scene and other N-1 current spot market price scenes is found to be ξ closest to the ith current spot market price sceneiJth spot market electricity price scenario ξjThereby obtaining mini≠jDi,j；
(14) Solving for probability distance PDi：
PDi＝P(ξi)·mini≠jDi,j(2)；
Wherein, P (ξ)i) For the ith spot market electricity price scenario ξiThe probability of occurrence;
for each pair of spot market electricity price scenes in the step (13), calculating the probability distance of the spot market electricity price scenes, and finding the spot market electricity price scene ξ corresponding to the minimum probability distancesThen PD iss＝min{PDi}；
(15) For spot market electricity rate scenario ξ determined in step (14)sAnd spot market price scenario ξ closest theretokDeleting the spot market electricity by a certain principlePrice scenario ξsAnd spot market price scenario ξkIn one scenario, the screening principle is as follows:
(a) the spot market electricity price scene is also very close to other spot market electricity price scenes, and the deletion of the spot market electricity price scene has little influence on the characteristics and information of the whole spot market electricity price scene;
(b) this spot market electricity price scenario presents itself with a relatively small probability of existence;
(16) after the corresponding spot market electricity price scene is eliminated in the step (15), the probability of the eliminated spot market electricity price scene needs to be superposed into the probability of another reserved spot market electricity price scene;
(17) and (5) repeating the steps (13) to (16) until the number of the reserved spot market power price scenes meets the requirement, and obtaining a reduction scene set with the target number of the spot market power price scenes being n and expressed as { ξ }1,ξ2,...,ξn}。
(2) A value of a confidence level alpha is designated, and a stochastic programming model based on a conditional risk value CVaR is constructed;
according to a reduced scene set with a smaller scale, the value of a confidence level alpha is adjusted, then an optimization model of a condition risk value CVaR is constructed, and the step (2) comprises the following steps:
(21) the scene profit is a random variable, which is expressed by Z, and for the random variable Z, a probability accumulation function F () is defined, a confidence level is defined as alpha ∈ [0,1], and then a risk value VaR of the random variable Z is:
VaRα[Z]:＝max{t|F(t)≥α}＝max{t|P(Z≤t)≥α} (3)；
where t is a possible value of the random variable Z. In stochastic programming, we characterize the possible occurrences of the stochastic variable Z and the corresponding probabilities with a set of scenarios.
(22) The conditional risk value CVaR for a random variable Z with a probability accumulation function F (.) and a confidence level α ∈ [0,1] is defined as:
Figure RE-GDA0002518134820000051
in the discrete case, CVaR is expressed as the optimal value of the following optimization problem:
Figure RE-GDA0002518134820000061
wherein η is the amount to be optimized, and ideally η is the conditional risk value for confidence level α when the optimization is complete (a)+＝max(a,0)，EP[(η-Z)+]Is (η -Z)+Regarding the expectation of the probability distribution P.
(23) The CVaR is assumed to be optimized such that the risk is minimized, i.e. the yield of the worst-yielding set of back (1- α) scenes is also as large as possible; the optimization objective is therefore:
Figure RE-GDA0002518134820000062
where ξ is the spot market price scenario variable x is the decision to be optimized, i.e. the generator sales portfolio vector, G (x, ξ)i) Is decision x in scene ξiThe following benefits, restated as equation (6):
Figure RE-GDA0002518134820000063
adjusting the value of the confidence level a to balance the benefit and risk;
(24) for any given x, the optimum η - η (x) is defined by η -VaRα[G(x,ξ)]In addition, for any fixed x, when G (x, ξ) ≧ η, E [ (η -G (x, ξ))+Values of (c) are zero for all scenarios ξ that do not facilitate computation, particularly at the optimal solution (x)*,η*) Next, only G (x) is made*,ξ)<η(x*)＝ VaRα[G(x*,ξ)]The scenario of (2) helps to obtain the optimal objective function value.
(3) Solving an optimization model of the condition risk value CVaR to obtain an optimal decision and reduce the condition risk value CVaR and the risk value VaR of the scene set;
the step (3) comprises the following steps:
(31) and solving the optimization target to obtain an optimal solution (x, eta) of the optimization function:
Figure RE-GDA0002518134820000064
(32) obtaining the value of VaR as eta;
(33) to obtain
Figure RE-GDA0002518134820000065
(4) Evaluating scenes in the reduced scene set to obtain an effective scene set and an ineffective scene set, and further reducing the reduced scene set;
further evaluating the scenes in the reduced scene set obtained in the step (1) by using x and η to obtain an effective scene set and an ineffective scene set in the reduced scene set, thereby further reducing the scenes, wherein the scenes with the profit larger than VaR are ineffective scenes according to the theory, and the ineffective scene set D is ineffective scenes*Comprises the following steps:
D*:＝{ξ:G(x*,ξ)>VaRα[G(x*,·)]} (9)；
the implementation case is as follows: taking a two-stage random planning as an example, the influence of the algorithm and the backward reduction method on the result is compared. Assuming that a generator is capable of generating 120MW of power, the generator needs to decide on a sales strategy in the futures market. Assuming that the futures market is 6 days in duration, divided into two 3 days, the bilateral contract data of alternative generators are shown in table 1.1:
1. at the beginning of the 6-day period, a power sale contract is made at a price of $ 25/MWh for electricity up to 50MW, with the contract time being the entire 6-day period.
2. The first 3 days of electricity purchase from the market before the day, and the second 3 days of electricity sale contract is signed to purchase electricity up to 40MW, and the purchase price of electricity is 26 dollars/MWh.
TABLE 1 bilateral electricity-selling contract data of electricity-generating trader
Figure RE-GDA0002518134820000071
In addition to double-sided electricity-selling contracts, power generators may sell electricity at constant power in spot markets during the first 3 days and the second 3 days.
In the electric power market, because the uncertainty of the spot market electricity price is large, electricity selling companies need to arrange long-term market and spot market electricity purchasing combination reasonably. It is assumed herein that the expected price of the spot market should be lower than the contract price of the bilateral electricity selling, and the electricity purchasing price of each spot market satisfies the normal distribution, the average value mu of the normal distribution1，μ2And standard deviation σ1，σ2The unit of electricity selling price is $/MWh.
TABLE 2 electric power purchase price parameter ($/MWh) of the spot-market
Figure RE-GDA0002518134820000072
Generating N1000 different spot market electricity price scenes by Latin hypercube sampling with ξ1,ξ2,...,ξ1000Scene information is as shown in fig. 2. For the invention
Figure RE-GDA0002518134820000073
And
Figure RE-GDA0002518134820000074
is represented in scene ξiNext first 3 days and second 3 days spot market electricity prices.
(1) According to the generated scenes, the scenes are cut down by using a backward cutting method, and the number of the scenes in the cut scene set obtained after cutting down is set to be n, which is 600.
(2) And establishing an optimization model. Is provided with
Figure RE-GDA0002518134820000075
For the decision to be optimized, the physical meaning is the generator sales portfolio vector, where xAIndicating the electricity selling amount of the generator according to the bilateral electricity selling contract A,
Figure RE-GDA0002518134820000076
shows that the bilateral electricity-selling contract A is in the scene ξiThe amount of electricity sold. Denotes xBThe generator sells the electricity according to the electricity selling amount of the bilateral electricity selling contract B,
Figure RE-GDA0002518134820000081
representing a bilateral electricity sale contract B in a scene ξiThe amount of electricity sold.
Figure RE-GDA0002518134820000082
And
Figure RE-GDA0002518134820000083
respectively representing the electricity selling quantity of the power generator in the first stage spot market and the second stage spot market, and using the electricity selling quantity
Figure RE-GDA0002518134820000084
And
Figure RE-GDA0002518134820000085
to represent a scene ξiWhen constructing the generator operating strategy model, α is confidence level, then scene ξiNext, the revenue function in this embodiment is:
Figure RE-GDA0002518134820000086
order to
Figure RE-GDA0002518134820000087
Wherein s (ξ)i) It is an auxiliary variable that facilitates the optimization of the present invention using cplex, η is the amount to be optimized referred to in the present invention, ideally the var corresponding to confidence level α, then the risk CVaR is:
Figure RE-GDA0002518134820000088
establishing an optimization model based on the condition risk value CVaR as follows:
Figure RE-GDA0002518134820000089
Figure RE-GDA00025181348200000810
Figure RE-GDA00025181348200000811
Figure RE-GDA00025181348200000812
Figure RE-GDA00025181348200000813
Figure RE-GDA00025181348200000814
Figure RE-GDA00025181348200000818
Figure RE-GDA00025181348200000815
Figure RE-GDA00025181348200000816
Figure RE-GDA00025181348200000817
the confidence level α is set to 0.8. As shown in fig. 2, the purpose of optimizing the conditional risk values is to avoid situations with lower revenues. The risk model aims to optimize the expected value of 1-alpha for which the profit is minimal. When alpha is reduced, corresponding to an aggressive strategy; when alpha is increased, a conservative strategy is used. As shown in fig. 3. When α is 0 means that only the overall yield is considered herein, but those low yield situations that may occur are disregarded.
(3) Solving the model to obtain the conditional risk value CVaR of 424952, η of the optimal η obtained after optimizing the model, namely the VaR value of 431570 and the electricity sales amount of the contract A
Figure RE-GDA0002518134820000091
I.e. full power supply.
(4) Let x be*Further evaluation of the scenes in the reduced scene set using x and η yields an effective scene set and an ineffective scene set in the reduced scene set, thereby further reducing the scenes*Comprises the following steps:
D*:＝{ξ:G(x*,ξ)>VaRα[G(x*,·)]} (13)；
after the verification, in the reduction of the scene set, the number of scenes with the profit smaller than the VaR is 145, the scenes are effective scenes, and the rest of the scenes can be further reduced. The number of scenes resulting from this method is thus 145. In contrast, we used backward pruning to directly reduce the number of original scenes to 145, and then solved the model. Fig. 4 shows the target value CVaR corresponding to the original scene, the scene obtained by the method and the scene obtained by the backward subtraction method. It can be seen that the target value of the scene obtained by the method is closer to the target value corresponding to the original scene than the backward subtraction method. Because our method can ensure that the further cut scenes are invalid scenes, the final CVaR value is not changed.
Further, these three scenarios are visualized herein. As shown in fig. 5(a) - (c), the horizontal and vertical axes represent the power prices on the first three-day and second three-day markets, and the color of the scatter represents the probability intensity of the corresponding scene. From fig. 5, it can be seen that the method herein differs significantly from backward subtraction, which is directed to preserve the similarity of the clipped scene and the original scene, while the method is directed to preserve the part of the scene that is effective for optimization.

Claims (5)

1. An electric energy random planning method considering condition risk value is characterized by comprising the following steps:
(1) an original scene set is reduced through a backward reduction method, and a representative reduced scene set with a small scale is formed;
(2) a value of a confidence level alpha is designated, and a stochastic programming model based on a conditional risk value CVaR is constructed;
(3) solving an optimization model of the condition risk value CVaR to obtain an optimal decision and reduce the condition risk value CVaR and the risk value VaR of the scene set;
(4) and evaluating the scenes in the reduced scene set to obtain an effective scene set and an ineffective scene set, and further reducing the reduced scene set.
2. The electric energy stochastic programming method considering the conditional risk value according to claim 1, wherein the step (1) comprises the following steps:
(11) assume that there are initially N random planning scenarios for spot market price scenario variable ξ, represented in the form of a set { ξ }1,ξ2,...,ξNAnd setting the number of spot market electricity price target scenes obtained by backward subtraction as n, wherein n is<N；
(12) Pairing the initial N spot market electricity price scenes pairwise, taking the distance between each pair of spot market electricity price scenes as a vector 2-norm distance, and calculating the distance D between each pair of spot market electricity price scenesi,j，i＝1,…,N，j＝1,…,N，j≠i；Di,jThe calculation formula is as follows:
Di,j＝||ξi-ξj||2；
wherein, ξi，ξjRespectively an ith spot market electricity price scene and a jth spot market electricity price scene;
(13) power rate scenario ξ for the ith spot marketiComparing the ith spot market electricity price fieldLandscape ξiThe distance between the current spot market price scene and other N-1 current spot market price scenes is found to be ξ closest to the ith current spot market price sceneiJth spot market electricity price scenario ξjThereby obtaining mini≠jDi,j；
(14) Solving for probability distance PDi：
PDi＝P(ξi)·mini≠jDi,j；
Wherein, P (ξ)i) For the ith spot market electricity price scenario ξiThe probability of occurrence;
for each pair of spot market electricity price scenes in the step (13), calculating the probability distance of the spot market electricity price scenes, and finding the spot market electricity price scene ξ corresponding to the minimum probability distancesThen PD iss＝min{PDi}；
(15) For spot market electricity rate scenario ξ determined in step (14)sAnd spot market price scenario ξ closest theretokDelete spot market price scenario ξ by certain principlessAnd scene ξkOne of them spot market price scene, the screening principle is:
(a) the spot market electricity price scene is also very close to other scenes, and the influence of deleting the spot market electricity price scene on the characteristics and information of the whole spot market electricity price scene is small;
(b) this spot market electricity price scenario presents itself with a relatively small probability of existence;
(16) after the corresponding spot market electricity price scene is eliminated in the step (15), the probability of the eliminated spot market electricity price scene needs to be superposed into the probability of another reserved spot market electricity price scene;
(17) and (5) repeating the steps (13) to (16) until the number of the reserved spot market power price scenes meets the requirement, and obtaining a reduction scene set with the target number of the spot market power price scenes being n and expressed as { ξ }1,ξ2,...,ξn}。
3. The method for stochastic planning of electric energy with consideration of conditional risk values as claimed in claim 1, wherein the step (2) comprises the following steps:
(21) the yield of the spot market electricity price scene is a random variable, and is expressed by Z, a probability accumulation function F () is defined for the random variable Z, a confidence level is defined to be alpha epsilon [0,1], and then a risk value VaR of the random variable Z is:
VaRα[Z]:＝max{t|F(t)≥α}＝max{t|P(Z≤t)≥α}；
wherein t is a possible value of the random variable Z, and in the random planning, a scene set is used for representing the possible occurrence situation and the corresponding probability of the random variable Z;
(22) the conditional risk value CVaR for a random variable Z with a probability accumulation function F (.) and a confidence level α ∈ [0,1] is defined as:
Figure FDA0002444076500000021
in the discrete case, CVaR is expressed as the optimal value of the following optimization problem:
Figure FDA0002444076500000022
wherein η is the amount to be optimized, and ideally, η is the conditional risk value corresponding to the confidence level α when the optimization is completed, (a)+＝max(a,0)，EP[(η-Z)+]Is (η -Z)+The expectation regarding the probability distribution P;
(23) the CVaR is assumed to be optimized such that the risk is minimized, i.e. the yield of the worst-yielding set of back (1- α) scenes is also as large as possible; the optimization objective is therefore:
Figure FDA0002444076500000023
wherein ξ is spot market price scenario variable, x is generator sales portfolio vector, G (x, ξ)i) Is the power price scene ξ of the combined vector x sold by the generator in the spot marketiThe return of restating the optimization objective formula as：
Figure FDA0002444076500000024
Adjusting the value of the confidence level a to balance the benefit and risk;
(24) for any given x, the optimum η - η (x) is defined by η -VaRα[G(x,ξ)]In addition, for any fixed x, when G (x, ξ) ≧ η, E [ (η -G (x, ξ))+Values of (c) are zero for all scenarios ξ that do not facilitate computation, particularly at the optimal solution (x)*,η*) Next, only G (x) is made*,ξ)<η(x*)＝VaRα[G(x*,ξ)]The scenario of (2) helps to obtain the optimal objective function value.
4. The electric energy stochastic programming method considering the conditional risk value according to claim 1, wherein the step (3) comprises the following steps:
(31) and solving the optimization target to obtain an optimal solution (x, eta) of the optimization function:
Figure FDA0002444076500000031
(32) obtaining the value of VaR as eta;
(33) to obtain
Figure FDA0002444076500000032
5. The electric energy stochastic programming method considering the conditional risk value according to claim 1, wherein the step (4) comprises the following steps:
further evaluating the scenes in the reduced scene set obtained in the step (1) by using x and η to obtain an effective scene set and an ineffective scene set in the reduced scene set, thereby further reducing the scenes, wherein the scenes with the profit larger than VaR are ineffective scenes according to the theory, and the ineffective scene set D is*Comprises the following steps:
D*:＝{ξ:G(x*,ξ)>VaRα[G(x*,·)]}。
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