CN113437757B - Electric quantity decomposition method of wind-storage combined system based on prospect theory - Google Patents
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Abstract
The invention relates to a foreground theory-based wind-storage combined system electric quantity decomposition method, which is used for predicting wind power output and day-ahead market electricity price and establishing a random simulation scene; representing scenes with similar probability distances by using typical scenes to form a typical scene set with a certain probability value; establishing a total income model of the wind-storage combined system in the middle-long term and day-ahead markets; establishing an optimization model of the electric quantity decomposition of the wind-storage combined system by taking the comprehensive foreground utility of the electric quantity decomposition scheme as a target; and solving the optimization model to obtain a medium-and long-term electric quantity decomposition scheme with the maximum comprehensive prospect utility. The method establishes an optimization model of the wind-storage combined system with the maximum comprehensive prospect utility value as a target, solves to obtain an optimal medium-and-long-term electric quantity decomposition scheme, improves the supply and demand balance relation of medium-and-long-term market electric quantity and day-ahead market electric quantity, and promotes resource optimization configuration.
Description
Technical Field
The invention belongs to the field of new energy optimization control, and particularly relates to a method for decomposing electric quantity of a wind-storage combined system based on a prospect theory.
Background
In order to realize medium-long-term stable supply of electric quantity, a power grid company and a wind-storage combined system operation company sign medium-long-term contracts. The real-time natural wind power output has obvious intermittence and uncertainty, the day-ahead market is influenced by the power supply and demand relationship, and the electricity price also has great uncertainty, so that when the wind-storage combined system is in the long-term market and the power distribution of the day-ahead market, the decision can be made only through uncertain information such as the predicted wind power output and day-ahead and real-time electricity prices. In the future, when the actual conditions of uncertain variables are all determined, a better medium-and-long-term electricity decomposition scheme is likely to be available, for example, when the actual day-ahead electricity price is known, the wind-storage combined system tends to distribute more electricity to the day-ahead market in a high electricity price period to obtain more benefits so as to control risks, and if the deviation of real-time wind power output is too large, the wind-storage combined system tends to distribute electricity to the medium-and-long-term market in a distribution process so as to avoid a greater punishment risk.
Disclosure of Invention
The invention has the technical problems that the real-time natural output of wind power has obvious intermittence and uncertainty, the power demand also has uncertainty, when the wind-storage combined system operator distributes the power in the long-term market and the day-ahead market, the risk of loss caused by low power price when the power supply of the market is over-demand and the risk of punishment that the power of the medium-long term contract cannot be completed are faced, and how to select a proper medium-long term power decomposition scheme is adopted to reduce the loss risk and improve the power supply and demand balance relation.
The invention aims to solve the problems, provides a wind-storage combined system electric quantity decomposition method based on a prospect theory, predicts wind power output and day-ahead market electricity price, forms a typical scene set, determines a utility function of net income and loss of a power generator and a corresponding weight function under each medium-and-long-term electric quantity decomposition scheme, establishes an optimization model of wind-storage combined system electric quantity decomposition by taking the comprehensive prospect utility value as a target, solves the medium-and-long-term electric quantity decomposition scheme with the maximum comprehensive prospect utility value, improves the supply-demand balance relation of medium-and-long-term market and day-ahead market electric quantity, and reduces the loss risk of the power generator.
The technical scheme of the invention is a wind-storage combined system electric quantity decomposition method based on a foreground theory, which comprises the following steps:
step 1: predicting wind power output and day-ahead market electricity price, and establishing a random simulation scene;
step 2: using Kantorovich probability distance scene reduction to represent scenes with similar probability distances by using typical scenes to form a typical scene set with a certain probability value;
and step 3: establishing a total income model of the wind-storage combined system in the middle-long term and day-ahead markets;
and 4, step 4: establishing an optimization model of the electric quantity decomposition of the wind-storage combined system by taking the comprehensive foreground utility value of the electric quantity decomposition scheme as a target;
step 4.1: determining a probability distribution function of the total profit obtained under the medium-and-long-term electricity decomposition scheme;
step 4.2: selecting a profit reference point of the medium-and-long-term electricity decomposition scheme;
step 4.3: determining a utility function of net income and loss of the medium and long-term electric quantity decomposition scheme and a corresponding weight function;
step 4.4: obtaining a comprehensive prospect utility function of the medium-and-long-term electric quantity decomposition scheme;
step 4.5: establishing an objective function and constraint conditions of an optimization model for electric quantity decomposition of the wind-storage combined system;
and 5: and solving the optimization model to obtain a medium-and long-term electric quantity decomposition scheme with the maximum comprehensive prospect utility.
In step 1, predicting medium and long term wind power output q according to historical data t ＝{q c,1 +q s,1 ,q c,2 +q s,2 ,…,q c,T +q s,T And day-ahead market price sequence P r,t ＝{P r,1 ,P r,2 ,…,P r,T Wherein q is c,i I is 1,2 … T represents the predicted output of the wind farm on day i during the time period T; q. q.s s,i The i is 1, and 2 … T represents the predicted output of the pumped-storage power station on the ith day in the time period T; p r,i I is 1,2 … T represents the predicted electricity price of the market on the ith day before the day in the time period T, and T represents the time period of the medium and long term; and calculating the output of the wind power plant and the prediction error of the day-ahead market electricity price according to the historical data and the predicted value, assuming that the uncertain variables obey normal distribution, and establishing a random simulation scene by using a Monte Carlo method.
The medium-long term benefits of the wind-storage combined system comprise the benefits of medium-long term contract electric quantity, the benefits of participating in the market electric quantity in the day, the benefits of excess electric quantity according to the medium-long term contract and the penalty cost of electric quantity shortage in the medium-long term contract, and the calculation formula of the total benefits R (x) of the wind-storage combined system is as follows:
R(x)＝R c +R r +R s -R m (1)
profit R of medium and long term contract electric quantity c Is calculated as follows:
in the formula, P c Representing medium and long term contract electricity prices; x is the number of t The distribution coefficient represents the distribution of the electric quantity to the medium-and long-term markets at the moment t; q. q.s t The electric quantity at the moment t; x is the number of t q t Representing the amount of electricity allocated to the medium and long-term markets at time t; t denotes the time period of the medium and long term.
Revenue R of participating in day-ahead market electricity r Is calculated as follows:
in the formula, P r,t The electricity price of the market at the day before the t period; (1-x) t )q t Indicating the amount of power allocated to the market at time t.
Settlement profit R corresponding to medium and long term contract electric quantity excess part s Is calculated as follows:
in the formula P s The settlement price, P, corresponding to the medium and long term contract electricity excess part s ＝(1-τ)P c (ii) a Tau represents a penalty coefficient according to the medium-long term contract electric quantity unbalance;
indicating actual settlement of wind-storage combined systemSupply of electricity to the medium and long term markets; q. q.s c The method is the medium and long term contract electric quantity of the wind-storage combined system.
Penalty cost R corresponding to electric quantity shortage part of medium-long term contract m Is calculated as follows:
in the formula, P m Penalty price, P, corresponding to medium-and long-term contract electric quantity shortage m ＝τP c 。
The yield deviation Delta R of the wind-storage combined system is the actual yield and the yield reference point R 0 For representing the net gain and loss of the decision maker, with the expression Δ R ═ R (x) -R 0 。
The utility function V (Δ R) of the net gain of the combined wind-storage system when Δ R is greater than or equal to 0 + The following were used:
when Δ R < 0, the utility function V (Δ R) of the loss of the combined wind-storage system - The following were used:
in the formula, f [ R (x)]A probability density function of the total yield R (x); r max And R min Respectively the upper limit and the lower limit of the total profit, and taking R according to the characteristics of normal distribution max ＝μ R +3σ R And R min ＝μ R -3σ R ，μ R And σ R Respectively the mean value and the variance of the actual profit R (x) of the wind-storage combined system; α is a risk preference coefficient; beta is a risk avoidance coefficient; λ is the coefficient of sensitivity to loss and revenue, the larger λ the more sensitive the generator is to loss.
Probability p of a generator realizing a net profit E Comprises the following steps:
p E ＝F(R max )-F(R 0 ) (8)
in the formula, F () represents a probability accumulation function of the total profit of the power generator.
Probability p of loss of generator L Comprises the following steps:
p L ＝F(R 0 )-F(R min ) (9)
when net income and loss of a generator are caused, the probability weight of occurrence of an event is respectively as follows:
in the formula, omega (p) + And ω (p) - Probability weight functions of net income and loss of the power generator are respectively; theta is a risk attitude coefficient of the net income of the power generator; δ is the risk attitude coefficient for loss of the generator.
And calculating the comprehensive prospect utility value of each electric quantity decomposition scheme, wherein the calculation formula of the comprehensive prospect utility value of the wind-storage combined system is as follows:
U i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (12)
in the formula of U i The comprehensive prospect utility value of the power generator under the ith electric quantity decomposition scheme is obtained; v (Δ R) i ) + 、V(ΔR i ) - Respectively is a utility function of net income and loss of the power generator in the ith electric quantity scheme; omega (p) i ) + 、ω(p i ) - And the probability weight functions of net income and loss of the power generator under the ith electric quantity decomposition scheme are respectively.
Establishing an optimization model of wind-storage combined system electric quantity decomposition by taking the maximum comprehensive foreground utility value as a target, wherein the target function is as follows:
maxU i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (13)
the constraints are as follows:
1) wind power station output q c Constraining
0≤q c ≤q cmax (14)
In the formula, q c max Representing the maximum output of the wind power plant.
2) Output q of pumped storage power station s Constraining
q smin ≤q s ≤q smax (15)
q pmin,t ≤q p,t ≤q pmax,t (17)
In the formula q p max 、q s max Respectively representing the maximum installed capacity of a water turbine and a water pump; q. q.s pmax,t 、q pmin,t Respectively representing the maximum and minimum running power of the water pump in the t period; q. q.s smin,t And q is smax,t Respectively representing the maximum and minimum operating power of the water turbine in the time period t; e max And E min Respectively representing maximum and minimum energy storage, E, of pumped storage power station reservoir t Representing the stored energy of a reservoir t time period of the pumped storage power station; eta p 、η h Respectively representing the pumping efficiency and the power generation efficiency of a pumped storage power station; Δ t represents a time step.
3) Reservoir energy storage restraint
In the formula, E t+1 Storing energy for a pumped storage power station reservoir at a time period t + 1; q. q.s p,t The running power of the water pump in the time period t is obtained; q. q.s s,t The running power of the water turbine in the time period t is obtained.
4) Combined force constraint
q min,t ≤q t ≤q max,t (20)
In the formula, q max,t And q is min,t The maximum and minimum electric quantities of the wind-storage combined system in the t period are respectively.
Compared with the prior art, the invention has the beneficial effects that:
1) the method establishes an optimization model of the wind-storage combined system with the maximum comprehensive prospect utility value as a target, solves and obtains an optimal medium-and-long-term electric quantity decomposition scheme, improves the supply and demand balance relation of medium-and-long-term market and day-ahead market electric quantity, and realizes resource optimization configuration;
2) according to the method, the uncertainty of the wind power output and the current price of the day ahead market is considered, the wind power output and the current price of the day ahead market are described as random variables based on predicted values, a multi-price scene is constructed by adopting a Monte Carlo sampling method, and then the scene is reduced by utilizing a k-means clustering algorithm, so that the calculated amount related to the electricity price scene is reduced, and the efficiency is improved;
3) the method adopts the chaotic particle swarm algorithm to solve and obtain the medium-and-long-term electricity decomposition scheme with the maximum comprehensive prospect utility, overcomes the defect that the particle swarm optimization method and the like are easy to get early and fall into the local optimal solution, and improves the optimization performance.
Drawings
The invention is further illustrated by the following figures and examples.
Fig. 1 is a schematic flow chart of a method for decomposing electric quantity of a wind-storage combined system according to an embodiment of the present invention.
Fig. 2 is a schematic diagram illustrating a process of generating and reducing a random simulation scenario according to an embodiment of the present invention.
Fig. 3 is a schematic flow chart of an optimization model solution for power decomposition of the wind-storage combined system according to the embodiment of the present invention.
Fig. 4 is a schematic diagram of distribution coefficients of an optimal electric quantity decomposition scheme of the wind-storage combined system according to the embodiment of the present invention.
Fig. 5a is a schematic diagram of an optimal power decomposition scheme of different profit reference points according to the method of the present invention.
Fig. 5b is a schematic diagram of an optimal power decomposition scheme for different revenue reference points of expected utility usage.
Detailed Description
As shown in fig. 1, the method for decomposing the electric quantity of the wind-storage combined system based on the foreground theory includes the following steps:
step 1: forecasting medium and long term wind power output q according to historical data t ＝{q c,1 +q s,1 ,q c,2 +q s,2 ,…,q c,T +q s,T And day-ahead market price sequence P r,t ＝{P r,1 ,P r,2 ,…,P r,T Wherein q is c,i I is 1,2 … T represents the predicted output of the wind farm per day for a time period T; q. q.s s,i The i is 1, and 2 … T represents the predicted output of the pumped-storage power station every day in the time period T; p r,i I is 1,2 … T represents the predicted electricity price of the market on each day before the day for a time period T, T represents a time period of medium and long term, in the embodiment T is one week; and calculating the output of the wind power plant and the prediction error of the day-ahead market electricity price according to the historical data and the predicted value, assuming that the uncertain variables obey normal distribution, and establishing a random simulation scene by using a Monte Carlo method.
And 2, step: and respectively generating scenes for the wind power output and the day-ahead market electricity price by using a Monte Carlo sampling method, and ensuring that the probability distribution of the scene set obtained by sampling on each time period surface obeys the distribution of scene prediction errors. And then, an improved k-means clustering algorithm is used for reducing scenes, and on the premise of keeping important characteristics of wind power output and day-ahead market electricity price scenes, the number of the scenes is reduced as much as possible, and the solving efficiency of the model is improved.
As shown in FIG. 2, the specific process of using the improved k-means clustering algorithm to cut down scenes is as follows:
1) initializing sample scene samples N, and reducing the number of samples N d ；
2) Setting prediction data and probability distribution according to the calculation result of the step 1;
3) obtaining N scene samples by adopting Monte Carlo sampling;
4) judgment of N d Whether or not less than N, if N d If the value is less than N, executing the step 5), otherwise, ending;
5) for each scene ω i Calculating the residual scene omega j And finding the minimum probability distance KD value min { KD (omega) } by the probability distance KD between the two i ,ω j )}；
6) Each scene omega i The corresponding minimum probability distance KD value is multiplied by the scene probability ρ (ω) i ) Searching the minimum value in N scenes;
7) the scene corresponding to the minimum value is recorded as scene omega m And scene omega n Satisfies rho (omega) m )≤ρ(ω n )；
8) Let scene omega m 、ω n The two-in-one is cut down, and the scene probability rho (omega) is updated n )＝ρ(ω n )+ρ(ω m )；
9) Updating the value N, wherein N is N-1;
10) output N d And finishing the number of scenes and the probability of the scenes.
The monte carlo sampling method of the examples refers to the monte carlo method disclosed in the article "evaluation of reliability of photovoltaic power plant based on markov chain monte carlo method" published in journal 3, 2017, of juxiong et al. The improved k-means clustering algorithm of the embodiment refers to an improved k-means clustering algorithm disclosed in a journal paper "wind/light/load typical scene reduction method and application in power grid planning" of university of fat industry, university of 2017.
And step 3: establishing a total income model of the wind-storage combined system in the middle-long term and day-ahead markets;
the medium-long term benefits of the wind-storage combined system comprise the benefits of medium-long term contract electric quantity, the benefits of participating in the market electric quantity in the day, the benefits of excess electric quantity according to the medium-long term contract and the penalty cost of electric quantity shortage in the medium-long term contract, and the calculation formula of the total benefits R (x) of the wind-storage combined system is as follows:
R(x)＝R c +R r +R s -R m (1)
profit R of medium and long term contract electric quantity c Is calculated as follows:
in the formula, P c Representing medium and long term contract electricity prices; x is the number of t The distribution coefficient represents the distribution of the electric quantity at the time t to the medium-long-term market; q. q.s t The electric quantity at the moment t; x is the number of t q t Representing the amount of electricity allocated to the medium and long-term markets at time t; t denotes the time period of the medium and long term.
Profit R of participating in day-ahead market electricity r Is calculated as follows:
in the formula, P r,t The electricity price of the market at the day before the t period; (1-x) t )q t Indicating the amount of power allocated to the market at time t.
Settlement profit R corresponding to electric quantity excess part according to medium and long term contract s Is calculated as follows:
in the formula, P s The settlement price, P, corresponding to the medium and long term contract electricity excess part s ＝(1-τ)P c (ii) a Tau represents a penalty coefficient according to the medium-long term contract electric quantity unbalance;
the electric quantity of the medium and long-term market in the supply which represents the actual settlement of the wind-storage combined system; q. q.s c The method is the medium and long term contract electric quantity of the wind-storage combined system.
Penalty cost R corresponding to electric quantity shortage part of medium-long term contract m Is calculated as follows:
in the formula, P m Penalty price, P, corresponding to medium-and long-term contract electric quantity shortage m ＝τP c 。
And 4, step 4: establishing an optimization model of the electric quantity decomposition of the wind-storage combined system by taking the comprehensive foreground utility value of the electric quantity decomposition scheme as a target; the yield deviation Delta R of the wind-storage combined system is the actual yield and the yield reference point R 0 Is used to represent the net gain and loss of the decision maker, expressed as ar ═ R (x) -R 0 。
Utility function V (Δ R) of net benefit of combined wind-storage system when Δ R is greater than or equal to 0 + The following were used:
the utility function V (Δ R) of the losses of the combined wind-storage system when Δ R < 0 - The following were used:
in the formula, f [ R (x)]A probability density function of the total yield R (x); r is max And R min Respectively the upper limit and the lower limit of the total profit, and taking R according to the characteristics of normal distribution max ＝μ R +3σ R And R min ＝μ R -3σ R ，μ R And σ R Respectively the mean value and the variance of the actual profit R (x) of the wind-storage combined system; α is a risk preference coefficient; beta is a risk avoidance coefficient; λ is the coefficient of sensitivity to loss and revenue, the larger λ the more sensitive the generator is to loss.
When net income or loss occurs to the generator, the probability p of realizing the net income by the generator is combined with the definition of the distribution function E Comprises the following steps:
p E ＝F(R max )-F(R 0 ) (8)
in the formula, F () represents a probability accumulation function of the total profit of the power generator.
Probability p of loss of generator L Comprises the following steps:
p L ＝F(R 0 )-F(R min ) (9)
when net income and loss of a generator are caused, the probability weight of occurrence of an event is respectively as follows:
in the formula, omega (p) + And ω (p) - Probability weight functions of net income and loss of the power generator are respectively; theta is a risk attitude coefficient of the net income of the power generator; δ is the risk attitude coefficient for loss of the generator.
Calculating the comprehensive foreground utility value of each electric quantity decomposition scheme, wherein the calculation formula of the comprehensive foreground utility value of the wind-storage combined system is as follows:
U i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (12)
in the formula of U i The comprehensive prospect utility value of the power generator under the ith electric quantity decomposition scheme is obtained; v (Δ R) i ) + 、V(ΔR i ) - Respectively is a utility function of net income and loss of the power generator in the ith electric quantity scheme; omega (p) i ) + 、ω(p i ) - And the probability weight functions of net income and loss of the power generator under the ith electric quantity decomposition scheme are respectively.
Establishing an optimization model of wind-storage combined system electric quantity decomposition by taking the maximum comprehensive foreground utility value as a target, wherein the target function is as follows:
maxU i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (13)
the constraints are as follows:
1) wind power station output q c Constraining
0≤q c ≤q cmax (14)
In the formula, q c max Representing the maximum output of the wind power plant;
2) output q of pumped storage power station s Constraining
q smin ≤q s ≤q smax (15)
q pmin,t ≤q p,t ≤q pmax,t (17)
In the formula q p max And q is s max Respectively representing the maximum installed capacities of a water turbine and a water pump; q. q.s pmax,t And q is pmin,t Respectively representing the maximum and minimum running power of the water pump in the t period; q. q.s smin,t And q is smax,t Respectively representing the maximum and minimum operating power of the water turbine in the time period t; e max And E min Respectively representing maximum and minimum energy storage, E, of pumped storage power station reservoir t Representing the stored energy of a reservoir t time period of the pumped storage power station; eta p And η h Respectively representing the pumping efficiency and the power generation efficiency of a pumped storage power station; Δ t represents a time step;
3) reservoir energy storage restraint
In the formula, E t+1 Storing energy for a pumped storage power station reservoir at a time period t + 1; q. q.s p,t The running power of the water pump in the time period t is obtained; q. q.s s,t The operating power of the water turbine in the time period t is obtained;
4) combined force constraint
q min,t ≤q t ≤q max,t (20)
In the formula q max,t And q is min,t The maximum and minimum electric quantities of the wind-storage combined system in the t period are respectively.
And 5: as shown in fig. 3, the electric quantity decomposition model of the wind-storage combined system is solved by using a chaotic particle swarm algorithm, so as to obtain a medium-and-long-term electric quantity decomposition scheme with the maximum comprehensive prospect utility. The chaotic particle swarm optimization is disclosed by referring to a chaotic particle swarm optimization disclosed by a paper of Liu Yong et al published in the automation of a power system in 2005, No. 7, based on a chaotic particle swarm optimization method.
In the embodiment, an expert scoring method is adopted to obtain a profit reference point R according to historical profit data of the wind-storage combined system 0 Is $ 195000. By using the electric quantity decomposition method, the optimal distribution coefficient of the wind-storage combined system is obtained, as shown in fig. 4. As can be seen from fig. 4, the power distribution strategy of the wind-storage combined system can reflect the power price change situation of the market at the present day. The day-ahead market electricity price on Monday and weekend is lower, and the distribution coefficient x of the optimal electricity decomposition scheme is increased, so that more electricity is distributed to the medium-and-long-term market, stable income can be guaranteed, and risks are reduced. And the electricity price of the market on Tuesday and Friday day before is higher, the distribution coefficient x of the optimal electricity decomposition scheme is reduced, and more electricity is distributed to the market on day before to obtain higher income. Therefore, the distribution coefficient x of the optimal electricity decomposition scheme reflects the electricity price change situation, the wind-storage combined system distributes electricity to the medium-term and long-term markets to keep basic income when the electricity price of the day-ahead market is low, and distributes electricity to the day-ahead market to obtain more income when the electricity price is high.
Table 1 shows the comparison of the calculation results of the wind-storage combined system in the medium and long term market and the day-ahead market electric quantity distribution between the method of the present invention and the expected effect method.
TABLE 1 comparison of benefits of the method of the present invention with expected utility
As can be seen from Table 1, the method of the present invention and the expected utility method use the same revenue function and constraint condition, and set the same revenue reference point R 0 $ 185000. Compared with the expected effectiveness method, the method provided by the invention has the advantages that the expected yield of the day-ahead market is improved by 18.2%, the shortage punishment of medium-long term contracts is increased by 22%, and the proportion of electric quantity input into the day-ahead market by the method is increased, so that the method provided by the invention is more favorable for the day-ahead market with high yield. Compared with the expected utility method, the total profit is improved by 3%, the target realization probability is reduced by 0.05, and the method improves the weight of a high-profit small-probability scene through a weight function, so that the prospect utility value of a high-profit small-probability strategy is improved. Therefore, the method selects the electric quantity decomposition scheme with the most satisfactory profit and risk.
In order to analyze the optimal allocation decision of the wind-storage combined system to different income reference points, the expected income value is floated up and down by taking the reference point of $ 195000 as a reference, and 5 different income reference points are obtained. The calculation results of the optimal distribution coefficients of the method and the expected utility method under the condition of 5 different profit reference points are respectively shown in fig. 5a and 5 b.
The amount of power put into the medium and long term market in the method of the present invention is relatively high when the revenue reference point is low at $ 175000, because when R is 0 When smaller, the actual revenue is higher than the revenue reference point. At the moment, the wind-storage combined system operator has a strong loss avoidance tendency, and can select a conservative strategy to avoid loss. As the revenue reference point increases from 185000 to $ 215000, the amount of power put into the day-ahead market by the method of the present invention is relatively high due to R 0 When the actual income is larger than the income reference point, the operator of the wind-storage combined system tends to pursue a small probability decision with high income, and the method increases the weight of the small probability decision with high income through a probability weight function, so that more electric quantity is distributed to the market at present. When the revenue reference point increases to $ 235000, the invention nowThe electric quantity of the method for the medium-long term market is increased, and extra benefits cannot be brought due to the overhigh risk, so that more electric quantity is distributed to the medium-long term contract market to guarantee the available income, and the high risk of the day-ahead market electricity price fluctuation is avoided.
Table 2 and table 3 show the comparison between the method of the present invention and the calculation result of the optimal decision gain of the expected utility method disclosed in the paper published in "power system automation" 2006, 9 th year, "power generation company multi-trading market power generation amount distribution strategy considering the expected profit objective".
TABLE 2 revenue sheet of the method of the present invention at different revenue reference points
TABLE 3 revenue Table for expected usage at different revenue reference points
As shown in table 2, when the profit reference point is $ 175000, the profit of the electricity decomposition scheme obtained by the method of the present invention is reduced by 0.2% compared with the expected utility method, but the generated medium-long term contract shortage penalty amount is reduced by 4% compared with the expected utility method, and the risk of the wind-storage combined system is effectively reduced. As the revenue reference point increased from 185000 to $ 215000, the revenue obtained by the method of the present invention increased gradually compared to the expected usage, suggesting that the operator tended to "beat" in a small probability scenario facing high revenue when the risk was not high. When the expected profit increases to $ 235000, the risk is also increasing, and the profit obtained by the method of the invention is reduced by 11% compared with the expected utility method, but the amount of the resulting medium-long term contract default penalty is reduced by 70% compared with the expected utility method, reflecting that the operator is inclined to the "guarantee bottom" strategy when the high profit is also high risk.
The above-mentioned embodiments further describe the object and technical solution of the present invention in detail. The above description is only exemplary of the present invention, and is not intended to limit the scope of the present invention. It is expressly intended that all such equivalent changes, substitutions and improvements which may be made in accordance with the claims be embraced by the present invention.
Claims (3)
1. The method for decomposing the electric quantity of the wind-storage combined system based on the prospect theory is characterized by comprising the following steps of:
step 1: forecasting wind power output and day-ahead market electricity price, and establishing a random simulation scene;
step 2: using Kantorovich probability distance scene reduction to represent scenes with similar probability distances by using typical scenes to form a typical scene set with probability values;
and 3, step 3: establishing a total income model of the wind-storage combined system in the middle-long term and day-ahead markets;
and 4, step 4: establishing an optimization model of the electric quantity decomposition of the wind-storage combined system by taking the comprehensive foreground utility value of the electric quantity decomposition scheme as a target;
step 4.1: determining a probability distribution function of the total profit obtained under the medium-and-long-term electricity decomposition scheme;
step 4.2: selecting a profit reference point of the medium-and-long-term electricity decomposition scheme;
step 4.3: determining a utility function of net income and loss of the medium and long-term electric quantity decomposition scheme and a corresponding weight function;
step 4.4: obtaining a comprehensive prospect utility function of the medium-and-long-term electric quantity decomposition scheme;
step 4.5: establishing an objective function and constraint conditions of an optimization model for electric quantity decomposition of the wind-storage combined system;
and 5: solving the optimization model to obtain a medium-and long-term electric quantity decomposition scheme with the maximum comprehensive prospect utility;
in step 1, predicting medium and long term wind power output q according to historical data t ＝{q c,1 +q s,1 ,q c,2 +q s,2 ,…,q c,T +q s,T And day-ahead market price sequence P r,t ＝{P r,1 ,P r,2 ,…,P r,T Wherein q is c,i The i is 1, and 2 … T represents the predicted output of the wind farm on the ith day in the time period T; q. q.s s,i The i is 1, and 2 … T represents the predicted output of the pumped-storage power station on the ith day in the time period T; p r,i I is 1,2 … T represents the predicted electricity price of the market on the ith day before the day in the time period T, and T represents the time period of the medium and long term; calculating the output of the wind power plant and the prediction error of the day-ahead market electricity price according to the historical data and the predicted value, adopting a normal distribution function for uncertain variables, and establishing a random simulation scene by using a Monte Carlo method;
in step 3, the medium-and-long term benefits of the wind-storage combined system comprise benefits of medium-and-long term contract electric quantity, benefits of participating in the market electric quantity in the day ahead, benefits of excess electric quantity according to the medium-and-long term contract and penalty cost of electric quantity shortage in the medium-and-long term contract, and the total benefits R (x) of the wind-storage combined system are calculated as follows:
R(x)＝R c +R r +R s -R m (1)
profit R of medium and long term contract electric quantity c Is calculated as follows:
in the formula P c Representing medium and long term contract electricity prices; x is the number of t The distribution coefficient represents the distribution of the electric quantity at the time t to the medium-long-term market; q. q.s t The electric quantity at the moment t; x is the number of t q t The electric quantity allocated to the medium-term and long-term markets at the moment t is represented; t represents a medium-long term time period;
revenue R of participating in day-ahead market electricity r Is calculated as follows:
in the formula, P r,t The electricity price of the market at the day before the t period; (1-x) t )q t Representing the amount of power allocated to the market at time t;
settlement profit R corresponding to medium and long term contract electric quantity excess part s Is calculated as follows:
in the formula, P s The settlement price, P, corresponding to the medium and long term contract electricity excess part s ＝(1-τ)P c (ii) a Tau represents a penalty coefficient according to the medium-long term contract electric quantity unbalance;
the electric quantity of the medium and long-term market in the supply which represents the actual settlement of the wind-storage combined system; q. q.s c The medium-long term contract electric quantity of the wind-storage combined system is obtained;
penalty cost R corresponding to electric quantity shortage part of medium-long term contract m Is calculated as follows:
in the formula, P m Penalty price, P, corresponding to medium-and long-term contract electric quantity shortage m ＝τP c 。
2. The method for decomposing the electric quantity of the wind-storage combined system based on the prospect theory as claimed in claim 1, wherein in the step 4, the income deviation Delta R of the wind-storage combined system is the actual income and income reference point R 0 Is used to represent the net gain and loss of the decision maker, expressed as ar ═ R (x) -R 0 ；
The utility function V (Δ R) of the net gain of the combined wind-storage system when Δ R is greater than or equal to 0 + The following were used:
the utility function V (Δ R) of the losses of the combined wind-storage system when Δ R < 0 - The following were used:
in the formula f [ R (x)]A probability density function of the total yield R (x); r max 、R min Respectively representing the upper limit and the lower limit of the total profit, and taking R according to the characteristics of normal distribution max ＝μ R +3σ R And R min ＝μ R -3σ R ，μ R 、σ R Respectively the mean value and the variance of the actual profit R (x) of the wind-storage combined system; α is a risk preference coefficient; beta is a risk avoidance coefficient; λ is a sensitive coefficient for loss and profit, and the larger λ is, the more sensitive the generator is to loss;
probability p of a generator realizing a net profit E Comprises the following steps:
p E ＝F(R max )-F(R 0 ) (8)
wherein F () represents a probability accumulation function of the total profit of the generator;
probability p of loss of generator L Comprises the following steps:
p L ＝F(R 0 )-F(R min ) (9)
when net income and loss of a generator are caused, the probability weight of occurrence of an event is respectively as follows:
in the formula omega (p) + 、ω(p) - Probability weight functions of net income and loss of the power generator are respectively; theta is a risk attitude coefficient of the net income of the power generator; deltaRisk attitude coefficients for generator losses;
calculating the comprehensive foreground utility value of each electric quantity decomposition scheme, wherein the calculation formula of the comprehensive foreground utility value of the wind-storage combined system is as follows:
U i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (12)
in the formula of U i The comprehensive prospect utility value of the power generator under the ith electric quantity decomposition scheme is obtained; v (Δ R) i ) + 、V(ΔR i ) - Respectively is a utility function of net income and loss of the power generator in the ith electric quantity scheme; omega (p) i ) + 、ω(p i ) - And the probability weight functions of net income and loss of the power generator under the ith electric quantity decomposition scheme are respectively.
3. The method for decomposing the electric quantity of the wind-storage combined system based on the foreground theory as claimed in claim 2, wherein in the step 4, an optimization model for decomposing the electric quantity of the wind-storage combined system is established with the maximum comprehensive foreground utility value as a target, and an objective function is as follows:
maxU i ＝V(ΔR i ) + ω(p i ) + +V(ΔR i ) - ω(p i ) - (13)
the constraints are as follows:
1) wind power station output q c Constraining
0≤q c ≤q cmax (14)
In the formula, q cmax Representing the maximum output of the wind power plant;
2) output q of pumped storage power station s Constraining
q smin ≤q s ≤q smax (15)
q pmin,t ≤q p,t ≤q pmax,t (17)
In the formula, q pmax And q is smax Respectively representing the maximum installed capacity of a water turbine and a water pump; q. q.s pmax,t And q is pmin,t Respectively representing the maximum and minimum running power of the water pump in the t period; q. q.s smin,t And q is smax,t Respectively representing the maximum and minimum operating power of the water turbine in the time period t; e max And E min Respectively representing the maximum energy storage and the minimum energy storage of a reservoir of the pumped storage power station; e t Representing the stored energy of a reservoir t time period of the pumped storage power station; eta p 、η h Respectively representing the pumping efficiency and the power generation efficiency of a pumped storage power station; Δ t represents a time step;
3) reservoir energy storage restraint
In the formula, E t+1 Storing energy for a pumped storage power station reservoir at a time period t + 1; q. q of p,t The running power of the water pump in the time period t is obtained; q. q.s s,t The operating power of the water turbine in the time period t is obtained;
4) combined force constraint
q min,t ≤q t ≤q max,t (20)
In the formula, q max,t 、q min,t Respectively representing the maximum and minimum electric quantity of the combined wind-storage system in the period t.
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