CN110930070A - Improved blocking cost distribution method based on Shapley value - Google Patents

Improved blocking cost distribution method based on Shapley value Download PDF

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CN110930070A
CN110930070A CN201911263040.4A CN201911263040A CN110930070A CN 110930070 A CN110930070 A CN 110930070A CN 201911263040 A CN201911263040 A CN 201911263040A CN 110930070 A CN110930070 A CN 110930070A
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郭莉
吴晨
苗曦云
丛小涵
王蓓蓓
谈健
牛文娟
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Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a blocking cost distribution method based on Shapley value improvement, which comprises the following steps: (1) calculating the running state of the power system considering network constraint and not considering network constraint to obtain the blocking cost at each moment; (2) forming alliances by taking the load as a participant according to a user revocation mode, taking the negative blocking cost as a characteristic function, obtaining the characteristic function of each alliance and forming a cooperative game model; (3) solving a Shapley value of the cooperative game model; (4) establishing a cooperative game solving model improved based on a Shapley value, namely an equity minimum core solving model; (5) and carrying out blocking cost distribution according to the distribution strategy obtained by solving. The invention has higher stability.

Description

Improved blocking cost distribution method based on Shapley value
Technical Field
The invention relates to the power technology, in particular to a blocking cost distribution method based on Shapley value improvement.
Background
With the massive synchronization of renewable energy sources, the scale of long-distance trans-regional transmission is continuously increased, so that the safe operation pressure of a power grid is increased, and particularly, an important transmission section blocking phenomenon caused by influencing peak shaving requirements occurs. The reasonable and stable fair allocation of the blocking cost has more and more important practical significance. The fairest allocation mode is a Shapley value method using cooperative game theory, but the allocation mode only has fairness and has no stability.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides an improved blocking cost distribution method based on a Shapley value, and the stability is higher.
The technical scheme is as follows: the invention discloses a congestion cost distribution method based on Shapley value improvement, which comprises the following steps:
(1) calculating the running state of the power system considering network constraint and not considering network constraint to obtain the blocking cost at each moment;
(2) forming alliances by taking the load as a participant according to a user revocation mode, taking the negative blocking cost as a characteristic function, obtaining the characteristic function of each alliance and forming a cooperative game model;
(3) solving a Shapley value of the cooperative game model;
(4) establishing a cooperative game solving model improved based on a Shapley value, namely an equity minimum core solving model;
(5) and carrying out blocking cost distribution according to the distribution strategy obtained by solving.
Further, the method further comprises:
(6) and verifying the performance of the minimum core solution model from the aspects of effectiveness, individuality, fairness and stability.
Further, the Shapley value calculation formula in step (3) is as follows:
Figure BDA0002312093310000011
in the formula:
Figure BDA0002312093310000012
sharley value for participant i; v (S) is a characteristic function of federation S; v (S/i) is a characteristic function of a new alliance formed after the participant i in the alliance S is removed; | S | represents the number of participants in federation S; n is the number of participants; n is 2 that all participants can formn-a set of 1 subsets.
Further, the step (4) specifically comprises:
(4-1) calculating minimum core z of cooperative game model*The physical meaning is to minimize the maximum dissatisfaction, and the model is as follows:
Figure BDA0002312093310000021
in the formula: z is an objective function, the minimum core of the cooperative game model, z*Is the z-best solution; x (S) is the sum of the contributions of participants in federation S; x (N) is the apportioned sum of participants in big alliance N; v (N) is a characteristic function of the big federation N; e (x, S) represents the dissatisfaction degree of union S under a certain allocation mode;
(4-2) minimum core z obtained according to step (4-1)*And (4) establishing a cooperative game solving model improved based on the Shapley value, namely a least fair core solving model, wherein the model is as follows:
Figure BDA0002312093310000022
in the formula: taking the minimum canonical distance of the share and Shapley values of the participants as an objective function; x is the apportionment vector for all participants, x ═ x1,x2,…xi,…,xn]；
Figure BDA0002312093310000023
Is the sharley value split of all participants,
Figure BDA0002312093310000024
v ({ i }) is a characteristic function when there is only participant i in the federation.
Further, the step (6) specifically comprises:
(6-1) measurement of effectiveness: the additional cost of all participants to form a large federation is fully amortized, i.e.
Figure BDA0002312093310000025
(6-2) measurement of individuality: when the cost shared by the participant i is less than the cost borne by the participant alone, the participant has the willingness of joining the alliance, namely, only when v ({ i }) is more than or equal to xiThen the participants would like to join the federation;
(6-3) measure fairness: using Jain index
Figure BDA0002312093310000026
In measurement, the closer the Jain index is to 1, the more fair the apportionment result is;
(6-4) measurement of stability: calculating an index
Figure BDA0002312093310000031
The larger the index value is, the more stable the result of the allocation is.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention establishes a cooperation solving model improved based on a Shapley value, namely an impartial minimum core solving model, wherein the impartial minimum core solution has impartiality of the Shapley value and stability of a minimum core.
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FIG. 1 is a schematic flow diagram of an improved congestion cost allocation method based on a Shapley value provided by the present invention;
FIG. 2 is a simplified grid diagram of a grid of a province;
FIG. 3 is the system predicted load at system time t;
FIG. 4 is a histogram comparing the result of blocking cost apportionment under the Shapley value method and the least fair core solution method;
fig. 5 shows fairness index and stability index results under the sharey value method and the fairness minimum kernel solution method.
Detailed Description
The embodiment provides an improved congestion cost allocation method based on a sharley value, as shown in fig. 1, including the following steps:
(1) and calculating the running conditions of the power system in consideration of the network constraint and in consideration of the network constraint to obtain the blocking cost at each moment.
In the embodiment, the established fairest minimum core solution model is adopted to distribute the blocking cost aiming at the blocking cost generated by the blocking of the cross-river section in the power system. An IEEE-14 node is used for replacing a developed province power grid in the east of China, as shown in figure 2. By taking the power supply and load distribution structure of a certain power grid in east China as a reference, the south-north power allocation conditions are shown in table 1, and the operation of a unit in south of the Yangtze river is slightly lower than that of a unit in north of the Yangtze river.
TABLE 1 power load apportionment ratio between south and north of the river
Figure BDA0002312093310000032
The predicted system load at time t is shown in fig. 3. And according to the coefficient prediction conformity and allocation conditions, establishing a blocking scheduling model, and calculating the blocking cost at the time t obtained by considering the network constraint and the system operation condition without considering the network constraint, wherein the blocking cost is 3283941.68 yuan.
(2) And forming alliances by taking the load as participants according to a user revocation mode, taking the negative blocking cost as a characteristic function, obtaining the characteristic function of each alliance and forming a cooperative game model.
In the embodiment, 14 loads are taken as participants, alliances are formed according to a user revocation mode, negative blocking cost is taken as a characteristic function, and the characteristic function of each alliance is obtained. The characteristic functions of the partial leagues (single-person league and large league) are given below and are shown in table 2.
TABLE 2 characteristic functions of partial federation (single-person federation and large federation)
Federation Characteristic function v (S)
S＝{1} -165844.03
S＝{2} -165844.03
S＝{3} -165844.03
S＝{4} -119194.16
S＝{5} -119194.16
S＝{6} -65394.96
S＝{7} -168776.68
S＝{8} -168776.68
S＝{9} -65394.96
S＝{10} -65394.96
S＝{11} -243562.01
S＝{12} -65394.96
S＝{13} -65394.96
S＝{14} -65394.96
N＝{1,2,…,14} -3283942.68
(3) And solving a Shapley value of the cooperative game model.
Wherein, the Shapley value calculation formula is as follows:
Figure BDA0002312093310000041
in the formula:
Figure BDA0002312093310000042
sharley value for participant i; v (S) is a characteristic function of federation S; v (S/i) is a characteristic function of a new alliance formed after the participant i in the alliance S is removed; | S | represents the number of participants in federation S; n is the number of participants; n is 2 that all participants can formn-a set of 1 subsets. The sharley values calculated in this example are shown in table 3.
Table 32 comparison of the results of the cooperative game
Figure BDA0002312093310000051
(4) And establishing a cooperative game solving model improved based on a Shapley value, namely an impartial minimum core solving model.
The method specifically comprises the following steps:
(4-1) calculating minimum core z of cooperative game model*The physical meaning is to minimize the maximum dissatisfaction, and the model is as follows:
Figure BDA0002312093310000052
in the formula: z is an objective function, the minimum core of the cooperative game model, z*Is the z-best solution; x (S) is the sum of the contributions of participants in federation S; x (N) is the apportioned sum of participants in big alliance N; v (N) is a characteristic function of the big federation N; e (x, S) represents the dissatisfaction degree of union S under a certain allocation mode;
(4-2) minimum core z obtained according to step (4-1)*And (4) establishing a cooperative game solving model improved based on the Shapley value, namely a least fair core solving model, wherein the model is as follows:
Figure BDA0002312093310000061
in the formula: taking the minimum canonical distance of the share and Shapley values of the participants as an objective function; x is the apportionment vector for all participants, x ═ x1,x2,…xi,…,xn]；
Figure BDA0002312093310000062
Is the sharley value split of all participants,
Figure BDA0002312093310000063
v ({ i }) is a characteristic function when there is only participant i in the federation.
In this example z*＝3.995×105. The results of the two methods are compared to a histogram in fig. 4 (plotting the negative contribution results facilitates finding which participants need to pay the blocking cost).
(5) And carrying out blocking cost distribution according to the distribution strategy obtained by solving.
(6) And verifying the performance of the minimum core solution model from the aspects of effectiveness, individuality, fairness and stability. The method specifically comprises the following steps:
(6-1) measurement of effectiveness: the additional cost of all participants to form a large federation is fully amortized.
(6-2) measurement of individuality: when the cost shared by the participant i is less than the cost borne by the participant alone, the participant has the willingness of joining the alliance, namely, only when v ({ i }) is more than or equal to xiThe participants would like to join the federation.
(6-3) measure fairness: the sharley value method is apportioned according to the marginal contribution of each participant, and the higher the marginal contribution, the more apportioned, and therefore, the sharley value method is considered to be the most fair solution of the cooperative game. And measuring the fairness of the cooperative game solution by adopting the Jain index:
Figure BDA0002312093310000064
the closer the Jain index is to 1, the more fair the apportionment result.
(6-4) measurement of stability: when the apportioned result satisfies
Figure BDA0002312093310000065
At this time, all participants have no intention to break away from the alliance, and the apportionment result is most stable at this time. The stability of the apportioned results was measured using the following criteria:
Figure BDA0002312093310000066
the larger the index value is, the more stable the result of the allocation is.
Comparing the method of the embodiment with the sharley value method, the final measurement result is as follows:
① effectiveness, all participants fully apportion the cost of congestion to meet effectiveness;
② individual rationality that the solving methods of the two cooperative games both satisfy the individual rationality, namely both satisfy v ({ i }) ≧ xi；
③ fairness the congestion cost is split based on the average of the cumulative marginal contributions of the load to congestion, reflecting the liability to cause congestion, the higher the split congestion cost with higher marginal contributions, the fairness of the fairest minimum core solution is slightly lower than that of the sharey value method, but the fairness of the fairest minimum core solution reaches above 0.97, also has higher fairness.
④ stability the satisfy index under both solving methods is shown in figure 5. the satisfaction of the fairest minimum kernel is much higher than that of the sharley value.
Through the analysis, compared with a Shapley value method, the fairest minimum core solution has higher stability and higher fairness. The user is more satisfied with the result of the allocation of the blocking cost, and the user can adjust the power utilization mode according to the allocated blocking cost, so that the blocking of the output resistor is relieved in a certain sense.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (5)

1. A method for improved congestion cost allocation based on sharley values, the method comprising:
(1) calculating the running state of the power system considering network constraint and not considering network constraint to obtain the blocking cost at each moment;
(2) forming alliances by taking the load as a participant according to a user revocation mode, taking the negative blocking cost as a characteristic function, obtaining the characteristic function of each alliance and forming a cooperative game model;
(3) solving a Shapley value of the cooperative game model;
(4) establishing a cooperative game solving model improved based on a Shapley value, namely an equity minimum core solving model;
(5) and carrying out blocking cost distribution according to the distribution strategy obtained by solving.
2. The method for improved congestion cost allocation based on sharley values of claim 1, wherein: the method further comprises the following steps:
(6) and verifying the performance of the minimum core solution model from the aspects of effectiveness, individuality, fairness and stability.
3. The method for improved congestion cost allocation based on sharley values of claim 1, wherein: the Shapley value calculation formula in the step (3) is as follows:
Figure FDA0002312093300000011
in the formula:
Figure FDA0002312093300000012
sharley value for participant i; v (S) is a characteristic function of federation S; v (S/i) is a characteristic function of a new alliance formed after the participant i in the alliance S is removed; | S | represents the number of participants in federation S; n is the number of participants; n is 2 that all participants can formn-a set of 1 subsets.
4. The method for improved congestion cost allocation based on sharley values of claim 1, wherein: the step (4) specifically comprises the following steps:
(4-1) calculating minimum core z of cooperative game model*The physical meaning is to minimize the maximum dissatisfaction, and the model is as follows:
min z
Figure FDA0002312093300000013
x(N)＝v(N)
in the formula: z is an objective function, the minimum core of the cooperative game model, z*Is the z-best solution; x (S) isThe sum of the contributions of participants in the alliance S; x (N) is the apportioned sum of participants in big alliance N; v (N) is a characteristic function of the big federation N; e (x, S) represents the dissatisfaction degree of union S under a certain allocation mode;
(4-2) minimum core z obtained according to step (4-1)*And (4) establishing a cooperative game solving model improved based on the Shapley value, namely a least fair core solving model, wherein the model is as follows:
Figure FDA0002312093300000021
Figure FDA0002312093300000022
x(N)＝v(N)
xi≤v({i}),i＝1,2,…,n
in the formula: taking the minimum canonical distance of the share and Shapley values of the participants as an objective function; x is the apportionment vector for all participants, x ═ x1,x2,…xi,…,xn]；
Figure FDA0002312093300000023
Is the sharley value split of all participants,
Figure FDA0002312093300000024
v ({ i }) is a characteristic function when there is only participant i in the federation.
5. The Shapley-value-based improved blocking cost assignment method of claim 2, wherein: the step (6) specifically comprises the following steps:
(6-1) measurement of effectiveness: the additional cost of all participants to form a large federation is fully amortized, i.e.
Figure FDA0002312093300000025
(6-2) measurement of individuality: when the participantThe cost of i sharing is less than that of the participant which is born by one person, the participant has the willingness of joining the alliance, namely, only when v ({ i }) is more than or equal to xiThen the participants would like to join the federation;
(6-3) measure fairness: using Jain index
Figure FDA0002312093300000026
In measurement, the closer the Jain index is to 1, the more fair the apportionment result is;
(6-4) measurement of stability: calculating an index
Figure FDA0002312093300000027
The larger the index value is, the more stable the result of the allocation is.
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Cited By (4)

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CN111952967A (en) * 2020-08-11 2020-11-17 广东电网有限责任公司广州供电局 Power failure fault recovery method, system and equipment for multi-microgrid system
CN112381360A (en) * 2020-10-28 2021-02-19 广西大学 Power system parallel recovery partitioning method based on label propagation algorithm and game theory
CN113240066A (en) * 2021-05-14 2021-08-10 中国民航大学 Improved ant colony algorithm based on Shapley value
JP7221370B1 (en) 2021-12-06 2023-02-13 株式会社日立パワーソリューションズ power management device

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CN105160490A (en) * 2015-09-30 2015-12-16 南京邮电大学 Cooperative game and DEA (Data Envelopment Analysis) based method for sharing fixed cost of power transmission system
CN109840808A (en) * 2019-01-31 2019-06-04 国网河南省电力公司经济技术研究院 A kind of methodology based on the load aggregation quotient's profit for improving Shapley value

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CN105160490A (en) * 2015-09-30 2015-12-16 南京邮电大学 Cooperative game and DEA (Data Envelopment Analysis) based method for sharing fixed cost of power transmission system
CN109840808A (en) * 2019-01-31 2019-06-04 国网河南省电力公司经济技术研究院 A kind of methodology based on the load aggregation quotient's profit for improving Shapley value

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111952967A (en) * 2020-08-11 2020-11-17 广东电网有限责任公司广州供电局 Power failure fault recovery method, system and equipment for multi-microgrid system
CN111952967B (en) * 2020-08-11 2022-07-08 广东电网有限责任公司广州供电局 Power failure fault recovery method, system and equipment for multi-microgrid system
CN112381360A (en) * 2020-10-28 2021-02-19 广西大学 Power system parallel recovery partitioning method based on label propagation algorithm and game theory
CN113240066A (en) * 2021-05-14 2021-08-10 中国民航大学 Improved ant colony algorithm based on Shapley value
JP7221370B1 (en) 2021-12-06 2023-02-13 株式会社日立パワーソリューションズ power management device
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