CN114139821A - Power generation group double-layer game bidding method and system in power spot market environment - Google Patents

Power generation group double-layer game bidding method and system in power spot market environment Download PDF

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CN114139821A
CN114139821A CN202111487014.7A CN202111487014A CN114139821A CN 114139821 A CN114139821 A CN 114139821A CN 202111487014 A CN202111487014 A CN 202111487014A CN 114139821 A CN114139821 A CN 114139821A
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周子青
刘晓林
王旭
蒋传文
华文
邓晖
房乐
章枫
王钰山
龚开
江婷
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Abstract

The invention discloses a double-layer game bidding method and system for a power generation group in a power spot market environment. The method of the invention comprises the following steps: firstly, constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein electric energy and standby service quotation of the power generation group are linear 'electricity price-electricity quantity' curves, secondly, converting the double-layer bidding model into a single-layer model through a KKT condition and a binary expansion method, converting a bidding strategy of the power generation group into a discrete strategy set, and eliminating a nonlinear item existing in the single-layer model, so that the single-layer model is solved through a common commercial solver and a global optimal solution is obtained; and finally, solving a game equilibrium quotation result of the power generation group based on a quotation adjustment mechanism. According to the invention, a double-layer bidding model of the power generation group is constructed, so that modeling behaviors are simplified; and the double-layer bidding model is converted into a single-layer model by applying a KKT condition and a binary extension method, so that the calculation difficulty is reduced.

Description

Power generation group double-layer game bidding method and system in power spot market environment
Technical Field
The invention relates to the field of power spot markets, in particular to a power generation group double-layer game bidding method and system in a power spot market environment.
Background
The electric power spot market is an important component of an electric power reform business, and not only can strengthen market subject competition, but also can promote new energy consumption. Since 2019, the spot market simulation test operation and settlement test operation work are carried out in a plurality of test-point provinces and regions in China, including Zhejiang and Guangdong, the spot markets in a plurality of provinces adopt a centralized market mode to carry out combined optimization clearing of electric energy and auxiliary services, and the decisive action of the market on power resource allocation is fully exerted. However, the spot market has a plurality of trades and the trading behavior is complex and changeable; in the initial development stage of the spot market, inherent defects are not completely eliminated, competition among main bodies is insufficient, obvious group shortages exist on the power generation side, and the potential market force is large. The game bidding method of the power generation group is researched, the bidding behavior of the power generation group is simulated and deduced, and the competitive game equilibrium state of the main market body of the power generation side can be grasped in advance.
At present, a bidding method of a power generation group based on a spot market environment is lacked, particularly a bidding method of the power generation group simultaneously participating in electric energy and an auxiliary service market is lacked, and the mutual restriction relationship between bidding of the power generation group and clearing of the spot market cannot be effectively reflected; in addition, a linear 'electricity price-electricity quantity' curve is often declared when a power generation group quotes, so that on one hand, a power generation group bidding strategy has infinite possibilities, on the other hand, a nonlinear term is introduced, and a double-layer model solving method capable of effectively solving the problems does not exist.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a power generation group double-layer game bidding method and a power generation group double-layer game bidding system in a power spot market environment, wherein a power generation group double-layer bidding model is constructed to simplify modeling behaviors; and converting the double-layer bidding model into a single-layer model by applying a KKT condition and a binary extension method so as to reduce the calculation difficulty.
Therefore, the invention adopts the following technical scheme: a power generation group double-layer game bidding method in a power spot market environment comprises the following steps: firstly, constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein electric energy and standby service quotation of the power generation group are linear 'electricity price-electricity quantity' curves, secondly, converting the double-layer bidding model into a single-layer model through a KKT condition and a binary expansion method, converting a bidding strategy of the power generation group into a discrete strategy set, and eliminating a nonlinear term existing in the single-layer model, so that the single-layer model is solved through a general commercial solver and a global optimal solution is obtained; and finally, solving a game equilibrium quotation result of the power generation group based on a quotation adjustment mechanism.
The other technical scheme adopted by the invention is as follows: a power generation group double-layer game bidding method in a power spot market environment comprises the following steps:
1) acquiring basic clearing rules and day-ahead clearing boundary conditions of the power system;
2) constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein an upper layer model reflects the bidding behavior of the power generation group, a lower layer model reflects the clearing process of a spot market, and random optimization is applied to the uncertainty of the output and the load of new energy of a real-time market;
3) based on a KKT condition and a binary extension method, the double-layer bidding model is converted into a single-layer model, nonlinear terms in the single-layer model are eliminated, and meanwhile, a power generation group bidding strategy is converted into a discrete strategy set.
Further, the double-layer bidding model of the power generation group is as follows:
1) an upper layer model: bidding model of power generation group
The objective function of the upper model is expressed as:
Figure BDA0003397854770000021
in the formula, ke,i,kr,iExpressing the quotation coefficient as a decision variable; t represents the time-sharing period number of the market in the day ahead; piωThe omega scene occurrence probability; n is a radical ofjRepresenting the total number of the thermal generator sets in the power generation group j;
Figure BDA0003397854770000022
respectively representing the normal bid price and the medium bid electric quantity of the unit i at the moment t of the day-ahead electric energy market;
Figure BDA0003397854770000023
respectively representing the bid price and the bid electric energy adjustment quantity of the unit i at the real-time market t moment under an omega scene;
Figure BDA0003397854770000024
the standby bid price and the intermediate scalar quantity of the unit i at the moment t of the day-ahead standby service market are obtained by a lower-layer model; ciThe total cost of the standard-out power in the unit i is represented and simplified into a quadratic form:
Figure BDA0003397854770000025
in the formula, am,i、bm,i、cm,iRespectively a quadratic term cost coefficient, a primary term cost coefficient and a constant term cost coefficient;
Figure BDA0003397854770000026
the total bid amount of the unit i in the spot market under the omega scene is represented as:
Figure BDA0003397854770000027
decision variables of the upper layer model are quotation strategies of each unit in the generator set in the day-ahead electric energy market and the day-ahead standby service market; the linear quotation curve of the unit in the electric energy market is based on marginal cost, and the standard quotation curve of experience history is referred to in the future standby service market and is expressed as follows:
λe,m,i(P)＝ke,m,i(am,iP+bm,i)，
λr,m,i(r)＝kr,m,i(αm,ir+βm,i)，
wherein λ ise,m,i,λr,m,iRespectively showing the quotation curves of the unit i in the day-ahead electric energy market and the day-ahead standby service market, P, r respectively showing the reported electric quantity of the day-ahead electric energy market and the reported capacity a of the day-ahead standby service marketm,i,bm,i,αm,i,βm,iIs a constant related to cost, ke,m,i,kr,m,iAll represent the quotation coefficient, are decision variables, and satisfy the following constraints:
Figure BDA0003397854770000031
Figure BDA0003397854770000032
in the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000033
are each ke,m,i,kr,m,iAn upper limit value of (d);
2) the lower layer model: spot market clearing model
The objective function of the underlying model is to minimize the spot market electricity purchase cost, expressed as:
Figure BDA0003397854770000034
wherein, the electricity purchasing cost comprises three items of the current electricity purchasing cost, the standby service calling cost and the real-time electricity purchasing cost, M represents the total number of the spot market electricity generation group,
Figure BDA0003397854770000035
deciding a variable set for a lower layer;
further, the day-ahead spot market constraints include:
1) node power balance constraints
Figure BDA0003397854770000036
In the formula ib,jbRepresents a network node;
Figure BDA0003397854770000037
respectively indicate the time t is connected to the point ibTotal bid power quantity of thermal power generating units in node market day ahead, output power of new energy source unit and load predicted value, KLRepresents a collection of lines in a network topology,
Figure BDA0003397854770000038
representing the line trend of the market at the day-ahead,
Figure BDA0003397854770000039
is a lagrange multiplier;
2) line flow equality constraints
Figure BDA00033978547700000310
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000311
for node i at time tbAnd jbThe phase angle of (a) is,
Figure BDA00033978547700000312
is a node ibAnd jbThe impedance of the line between the two lines,
Figure BDA00033978547700000313
is a lagrange multiplier;
3) line capacity constraint
Figure BDA00033978547700000314
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000315
is a node ibAnd jbThe maximum transmission capacity of the inter-line,
Figure BDA00033978547700000316
is a lagrange multiplier;
4) unit output constraint
Figure BDA00033978547700000317
Figure BDA00033978547700000318
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000319
respectively the maximum and minimum output values of the generator sets i under the generating group m,
Figure BDA00033978547700000320
Figure BDA0003397854770000041
is a lagrange multiplier;
5) spare capacity constraint
Figure BDA0003397854770000042
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000043
minimum spare capacity for time period t; mu.sr,tIs the Lagrange coefficient;
6) power justification rate constraints
Figure BDA0003397854770000044
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000045
the maximum up-regulation and down-regulation output force of the unit i in unit time,
Figure BDA0003397854770000046
is a lagrange multiplier;
7) phase angle constraint
Figure BDA0003397854770000047
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000048
is a lagrange multiplier;
further, real-time market constraints include:
1) node power balance constraints
Figure BDA0003397854770000049
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000410
is a node ibProcessing the difference value between the output value corresponding to the time interval t of the thermal power generating unit under the scene omega and the scalar in the market before the day;
Figure BDA00033978547700000411
is a node ibThe difference value between the output value corresponding to the time interval t of the new energy unit under the scene omega and the scalar in the market before the day;
Figure BDA00033978547700000412
is a node ibDifference values of load values corresponding to the time period t under the scene omega and the market predicted values in the day before;
Figure BDA00033978547700000413
is a node ibThe difference value between the line power flow corresponding to the time period t under the scene omega and the line power flow of the market at the day before;
Figure BDA00033978547700000414
is the Lagrange coefficient;
2) line flow equality constraints
Figure BDA00033978547700000415
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000416
are respectively node ib,jbThe difference value between the phase angle corresponding to the time period t in the scene omega and the day-ahead market phase angle;
Figure BDA00033978547700000417
is a lagrange multiplier;
3) line capacity constraint
Figure BDA00033978547700000418
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000419
is a node ib,jbMaximum capacity of inter-line transmission;
Figure BDA00033978547700000420
is the Lagrange coefficient;
4) unit output constraint
Figure BDA0003397854770000051
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000052
is a lagrange multiplier;
5) phase angle constraint
Figure BDA0003397854770000053
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000054
is a lagrange multiplier;
further, the specific process of solving the double-layer bidding model is as follows:
firstly, expressing a lower layer model problem by using an equivalent KKT condition, linearizing a complementary relaxation condition based on a large M rule, explicitly unifying upper and lower layer variables, changing a double-layer bidding model into a single-layer model, wherein a binary variable product term still exists in the model, linearizing the binary product term by using a binary expansion method, and simultaneously converting a power generation group bidding strategy into a discrete strategy set, so that the subsequent game equilibrium solution is conveniently solved.
Further, when the underlying model is analyzed alone, the variable ke,m,i,kr,m,iA decision variable of an upper layer model is regarded as a constant; therefore, the lower model problem is a quadratic convex optimization problem containing linear constraint, and the decision variables are continuous variables, so that the application requirements of the KKT condition are met.
Further, the lower model equivalent KKT condition is expressed as:
Figure BDA0003397854770000055
Figure BDA0003397854770000056
Figure BDA0003397854770000057
Figure BDA0003397854770000058
Figure BDA0003397854770000059
Figure BDA00033978547700000510
Figure BDA00033978547700000511
wherein, the complementary relaxation conditions are expressed in a form that x ^ y is more than or equal to 0 and less than or equal to 0, and a large enough constant M and a 0-1 variable u are introduced for linearization treatment;
at the moment, the double-layer bidding model is converted into a single-layer model, but the binary variable product term still exists in the single-layer model
Figure BDA00033978547700000512
Figure BDA00033978547700000513
And kr,m,irm,i,tConsidering k, considere,m,i,kr,m,iThe binary extension method is applied to solve the two problems.
Further, the games among the power generation groups will eventually reach a nash equilibrium state, and in this state, no market subject can obtain greater profit by relying on self decision, that is, the games among the power generation groups can finally reach a nash equilibrium state, that is, no market subject can obtain greater profit by relying on self decision
Figure BDA0003397854770000061
Wherein i represents the subject of interest, riAny bidding strategy on behalf of the subject is,
Figure BDA0003397854770000062
on behalf of the subject's bid balancing strategy,
Figure BDA0003397854770000063
representing a competitive bidding balancing strategy, wherein the formation of a Nash balancing solution depends on a quotation adjusting mechanism in the market;
BAE based round-by-round offers in a spot market environment comprises the following steps:
the first step, before the market is cleared in the day, the power generation group reports an initial quotation curve and unit technical parameters to a dispatching and trading center; the dispatching and trading center discloses quotation information of all the power generation groups, user-side report information and other related network and unit parameters, and starts a first bidding round;
secondly, each power generation group obtains a new round of quotation and reports the quotation to a dispatching and trading center within a certain time limit according to an initial quotation curve of a competitor and a double-layer bidding model;
thirdly, the dispatching transaction center obtains a new round of quotation result, if the quotation of each power generation group is the same as that of the previous round, the game is ended, and the quotation result of the round is a Nash balance result; if the power generation group adjustment strategy still exists, the dispatching transaction center continuously discloses the quotation condition of the round to the whole society, and carries out bidding of the next round until all the power generation groups do not change the quotation strategy.
The invention adopts another technical scheme that: a power generation group double-layer game bidding system in a power spot market environment comprises an information acquisition module, a bidding analysis module, a model conversion and solving module, a quoted price adjusting module and a data output module;
the information acquisition module acquires the boundary condition information of market clearing;
the bidding analysis module forms a power generation group bidding model according to the boundary conditions;
the model conversion and solution module simplifies and solves the double-layer model;
the quotation adjusting module supports the power generation group to quotation round by round until a balanced solution is achieved;
and the data output module formats and outputs the bidding strategy and the market balance point information of the power generation group.
The invention has the following beneficial effects:
1. the invention models the bidding behaviors of the power generation group participating in the main energy and standby market on the basis of a double-layer bidding model. The double-layer bidding model clearly shows the bidding behaviors of the power generation group and the clearing process of the spot market, and can simplify the modeling process of the market behaviors of the power generation group.
2. The invention converts the double-layer bidding model into a single-layer model by a KKT condition and a binary expansion method and linearizes the nonlinear term. Compared with a double-layer model and a nonlinear problem, the single-layer model and the linear problem avoid the problem of infinite quotation strategies, are convenient to solve by using a commercial solver, and greatly reduce the calculation difficulty.
3. The invention can realize the automation of the processes of quotation information acquisition, bid analysis, model solution and data output by using the technology of an integrated modular system, thereby saving a large amount of labor cost.
4. The method has automation and generalizability, can be used for migrating and applying to the current market simulation analysis of the power grid company, and can greatly improve the analysis and utilization efficiency of data.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a block diagram of the system of the present invention;
FIG. 3 is a graph of baseline load and non-optimizable unit output over a typical day of the invention;
FIG. 4 is a diagram of the game balanced electric energy market quotation coefficients of the generating group according to the present invention;
fig. 5 is a diagram of the game equilibrium reserve market quotation coefficients of the power generation group of the present invention.
Detailed Description
The invention is further described with reference to the drawings and the detailed description.
Example 1
The embodiment provides a power generation group double-layer game bidding method in a power spot market environment, as shown in fig. 1, the steps are as follows:
firstly, obtaining basic information such as basic clearing rules and day-ahead clearing boundary conditions of a power system, and constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein electric energy and standby service quotations of the power generation group are linear power price-electric quantity curves; secondly, converting a double-layer bidding model into a single-layer model through a KKT condition and a binary extension method, converting a power generation group bidding strategy into a discrete strategy set, and eliminating a nonlinear term existing in the single-layer model, so that the single-layer model is solved through a general commercial solver to obtain a global optimal solution; and finally, solving and outputting a game balanced quotation result of the power generation group based on a quotation adjusting mechanism.
The double-layer bidding model of the power generation group comprises the following steps:
1) an upper layer model: bidding model of power generation group
The objective function of the upper model is expressed as:
Figure BDA0003397854770000071
in the formula, ke,i,kr,iExpressing the quotation coefficient as a decision variable; t represents the time-sharing period number of the market in the day ahead; piωThe omega scene occurrence probability; n is a radical ofjRepresenting the total number of the thermal generator sets in the power generation group j;
Figure BDA0003397854770000072
respectively representing the normal bid price and the medium bid electric quantity of the unit i at the moment t of the day-ahead electric energy market;
Figure BDA0003397854770000073
respectively representing the bid price and the bid electric energy adjustment quantity of the unit i at the real-time market t moment under an omega scene;
Figure BDA0003397854770000081
the standby bid price and the intermediate scalar quantity of the unit i at the moment t of the day-ahead standby service market are obtained by a lower-layer model; ciThe total cost of the standard-out power in the unit i is represented and simplified into a quadratic form:
Figure BDA0003397854770000082
in the formula, am,i、bm,i、cm,iRespectively a quadratic term cost coefficient, a primary term cost coefficient and a constant term cost coefficient;
Figure BDA0003397854770000083
the total bid amount of the unit i in the spot market under the omega scene is represented as:
Figure BDA0003397854770000084
decision variables of the upper layer model are quotation strategies of each unit in the generator set in the day-ahead electric energy market and the day-ahead standby service market; the linear quotation curve of the unit in the day-ahead electric energy market is based on marginal cost, and the standard quotation curve of experience history is referred to in the day-ahead standby service market and is expressed as follows:
λe,m,i(P)＝ke,m,i(am,iP+bm,i)，
λr,m,i(r)＝kr,m,i(αm,ir+βm,i)，
wherein λ ise,m,i,λr,m,iRespectively showing the quotation curves of the unit i in the day-ahead electric energy market and the standby service market, wherein P, r respectively represents the reported electric quantity of the day-ahead electric energy market and the reported capacity a of the standby service marketm,i,bm,i,αm,i,βm,iIs a constant related to cost, ke,m,i,kr,m,iAll represent the quotation coefficient, are decision variables, and satisfy the following constraints:
Figure BDA0003397854770000085
Figure BDA0003397854770000086
in the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000087
are each ke,m,i,kr,m,iAn upper limit value of (d);
2) the lower layer model: spot market clearing model
The objective function of the underlying model is to minimize the spot market electricity purchase cost, expressed as:
Figure BDA0003397854770000088
wherein, the electricity purchasing cost comprises three items of the current electricity purchasing cost, the standby service calling cost and the real-time electricity purchasing cost, M represents the total number of the spot market electricity generation group,
Figure BDA0003397854770000089
the set of variables is decided for the lower layer.
Further, the day-ahead spot market constraints include:
1) node power balance constraints
Figure BDA00033978547700000810
In the formula ib,jbRepresents a network node;
Figure BDA00033978547700000811
respectively indicate the time t is connected to the point ibTotal bid power quantity of thermal power generating units in node market day ahead, output power of new energy source unit and load predicted value, KLRepresents a collection of lines in a network topology,
Figure BDA0003397854770000091
representing the line trend of the market at the day-ahead,
Figure BDA0003397854770000092
is a lagrange multiplier;
2) line flow equality constraints
Figure BDA0003397854770000093
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000094
for node i at time tbAnd jbThe phase angle of (a) is,
Figure BDA0003397854770000095
is a node ibAnd jbThe impedance of the line between the two lines,
Figure BDA0003397854770000096
is a lagrange multiplier;
3) line capacity constraint
Figure BDA0003397854770000097
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000098
is a node ibAnd jbThe maximum transmission capacity of the inter-line,
Figure BDA0003397854770000099
is a lagrange multiplier;
4) unit output constraint
Figure BDA00033978547700000910
Figure BDA00033978547700000911
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000912
respectively the maximum and minimum output values of the generator sets i under the generating group m,
Figure BDA00033978547700000913
Figure BDA00033978547700000914
is lagrange multiplicationA seed;
5) spare capacity constraint
Figure BDA00033978547700000915
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000916
minimum spare capacity for time period t; mu.sr,tIs the Lagrange coefficient;
6) power justification rate constraints
Figure BDA00033978547700000917
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000918
the maximum up-regulation and down-regulation output force of the unit i in unit time,
Figure BDA00033978547700000919
is a lagrange multiplier;
7) phase angle constraint
Figure BDA00033978547700000920
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700000921
is a lagrange multiplier.
Further, real-time market constraints include:
1) node power balance constraints
Figure BDA0003397854770000101
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000102
is a node ibProcessing the difference value between the output value corresponding to the time interval t of the thermal power generating unit under the scene omega and the scalar in the market before the day;
Figure BDA0003397854770000103
is a node ibThe difference value between the output value corresponding to the time interval t of the new energy unit under the scene omega and the scalar in the market before the day;
Figure BDA0003397854770000104
is a node ibDifference values of load values corresponding to the time period t under the scene omega and the market predicted values in the day before;
Figure BDA0003397854770000105
is a node ibThe difference value between the line power flow corresponding to the time period t under the scene omega and the line power flow of the market at the day before;
Figure BDA0003397854770000106
is the Lagrange coefficient;
2) line flow equality constraints
Figure BDA0003397854770000107
In the formula (I), the compound is shown in the specification,
Figure BDA0003397854770000108
are respectively node ib,jbThe difference value between the phase angle corresponding to the time period t in the scene omega and the day-ahead market phase angle;
Figure BDA0003397854770000109
is a lagrange multiplier;
3) line capacity constraint
Figure BDA00033978547700001010
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700001011
is a node ib,jbMaximum capacity of inter-line transmission;
Figure BDA00033978547700001012
is the Lagrange coefficient;
4) unit output constraint
Figure BDA00033978547700001013
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700001014
is a lagrange multiplier;
5) phase angle constraint
Figure BDA00033978547700001015
In the formula (I), the compound is shown in the specification,
Figure BDA00033978547700001016
is a lagrange multiplier.
Further, the specific process of solving the double-layer bidding model is as follows:
firstly, expressing a lower layer model problem by using an equivalent KKT condition, linearizing a complementary relaxation condition based on a large M rule, explicitly unifying upper and lower layer variables, changing a double-layer bidding model into a single-layer model, wherein a binary variable product term still exists in the model, linearizing the binary product term by using a binary expansion method, and simultaneously converting a power generation group bidding strategy into a discrete strategy set, so that the subsequent game equilibrium solution is conveniently solved.
Further, when the underlying model is analyzed alone, the variable ke,m,i,kr,m,iA decision variable of an upper layer model is regarded as a constant; therefore, the lower model problem is a quadratic convex optimization problem containing linear constraint, and the decision variables are continuous variables which meet the requirement of the KKT conditionAnd (5) using the product.
Further, the lower model equivalent KKT condition is expressed as:
Figure BDA0003397854770000111
Figure BDA0003397854770000112
Figure BDA0003397854770000113
Figure BDA0003397854770000114
Figure BDA0003397854770000115
Figure BDA0003397854770000116
Figure BDA0003397854770000117
wherein, the complementary relaxation conditions are expressed in a form that x ^ y is more than or equal to 0 and less than or equal to 0, and a large enough constant M and a 0-1 variable u are introduced for linearization treatment;
at the moment, the double-layer model is converted into a single-layer model, but a binary variable product term still exists in the single-layer model
Figure BDA0003397854770000118
Figure BDA0003397854770000119
And kr,m,irm,i,tConsider thatTo ke,m,i,kr,m,iThe binary extension method is applied to solve the two problems.
The core idea of binary extension method is to use discrete value set to replace the value range of original continuous variable approximately
Figure BDA00033978547700001110
For example, first, a continuous variable k is sete,m,iIs equally divided into
Figure BDA00033978547700001111
Segment, then ke,m,iIs approximated as one comprising
Figure BDA00033978547700001112
A set of discrete points.
Figure BDA00033978547700001113
Wherein k is1And
Figure BDA00033978547700001114
respectively represents ke,m,iThe infimum and supremum of the original value domain. Each discrete point in the value range is associated with an nkBit binary number corresponding to the discrete point represented by the binary number1Is a distance of
Figure BDA00033978547700001115
xji,kThe j-th bit of the binary number is represented,
Figure BDA00033978547700001116
representing a decimal number corresponding to a binary number. Δ k represents the equally spaced intervals of successive value ranges.
Then
Figure BDA00033978547700001117
The term can be approximatedIs shown as
Figure BDA00033978547700001118
Figure BDA0003397854770000121
0≤yji,k≤Gkxji,k
At this time, the upper layer objective function still has binary variable product terms
Figure BDA0003397854770000122
And
Figure BDA0003397854770000123
the lower layer clearing model can know the price of the power at the day-ahead market clearing node
Figure BDA0003397854770000124
Wherein ib＝{(m,i)∈ΦgThe node where the ith unit in the power generation group m is located is represented by the same method; real-time market clearing node electricity price
Figure BDA0003397854770000125
Spare service calling electricity price
Figure BDA0003397854770000126
Consistent for all nodes in the network.
In view of
Figure BDA0003397854770000127
And ri,tAnd the infimum and infimum are existed, so that the nonlinear terms existed in the upper layer objective function are linearized by adopting a binary extension method. To be provided with
Figure BDA0003397854770000128
By way of example, by
Figure BDA0003397854770000129
The discretization process of (a) may result in relaxed constraint expressions.
Figure BDA00033978547700001210
Figure BDA00033978547700001211
0≤yji,t,p≤Gpxji,t,p
Wherein p is1·Is composed of
Figure BDA00033978547700001212
Infimum,. DELTA.p is the dividing interval, GpIs a sufficiently large constant. Of the above only objective function
Figure BDA00033978547700001213
Is processed to restrict
Figure BDA00033978547700001214
Still a continuous variable. Therefore, the two results which should be the same inevitably have a difference in decision making, and in order to minimize the difference between the two results and ensure the accuracy of the linearization process, constraints are required to be added so that the error of the decision making result of the power consumption in the continuous type and the discrete type is kept at an extremely low level. The error of the two can be limited within half of the equal division interval, and n is properly increased on the premise of considering the solving speedpThe error can be further reduced to an acceptable range by the value of (2).
Figure BDA00033978547700001215
And after the double-layer bidding model is converted into the single-layer model, all nonlinear terms are subjected to linearization treatment, and the single-layer mixed integer linear programming model can be directly solved through a common commercial solver.
When bidding decision is made by the power generation groups, the bidding of competitors needs to be referred to, and competitive game relations exist among the power generation groups. Although a small alliance consisting of a plurality of units is formed inside the power generation group, each unit belongs to a beneficial agent, the problem of benefit distribution does not need to be considered, and the structure of the small alliance is determined and cannot be changed. Thus, in essence, gaming between power generation groups will eventually reach nash equilibrium. In this state, no market entity can rely solely on its own decision to gain greater revenue. Namely, it is
Figure BDA0003397854770000131
Wherein i represents the subject of interest, riOn behalf of the subject arbitrary bidding strategy, ri *On behalf of the subject's bid balancing strategy,
Figure BDA0003397854770000132
representing a competitive bid balancing strategy. The formation of nash equilibrium solutions relies on the mechanisms of price adjustment in the market. BAE based round-by-round offers in a spot market environment comprises the following steps:
firstly, before the market is cleared in the day, the power generation group reports an initial quotation curve, unit technical parameters and the like to a dispatching and trading center. And the dispatching and trading center discloses the quotation information of all the power generation groups, the report information of the user side and other related network and unit parameters, and starts the first bidding.
And secondly, each power generation group obtains a new round of quotation and reports the quotation to a dispatching and trading center within a certain time limit according to an initial quotation curve of a competitor and a double-layer bidding model.
And thirdly, the dispatching and trading center obtains a new round of quotation result, and if the quotation of each power generation group is the same as that of the previous round. The game is over and the quoted result in the round is the Nash equilibrium result. If the power generation group adjustment strategy still exists, the dispatching transaction center continuously discloses the quotation condition of the round to the whole society, and carries out bidding of the next round until all the power generation groups do not change the quotation strategy.
Example 2
The embodiment provides a power generation group double-layer game bidding system in a power spot market environment, which comprises an information acquisition module, a bidding analysis module, a model conversion and solving module, a quotation adjustment module and a data output module, as shown in fig. 2.
The information acquisition module acquires the boundary condition information of market clearing; the bidding analysis module forms a power generation group bidding model according to the boundary conditions; the model conversion and solution module simplifies and solves the double-layer bidding model; the quotation adjusting module supports the power generation group to quotation round by round until a balanced solution is achieved; and the data output module formats and outputs the bidding strategy and the market balance point information of the power generation group.
For the part not described in detail in example 2, reference is made to example 1.
Application example
The invention discloses an application of a power generation group double-layer game bidding method in a spot market environment, which comprises the following steps:
1) an IEEE118 node standard system is adopted as a detection system, a reference load and an unoptimizable unit output curve in a typical day is shown in figure 3, and parameters of various types of units on the power generation side are shown in tables 1 and 2.
TABLE 1 optimizable train parameters
Figure BDA0003397854770000133
Figure BDA0003397854770000141
TABLE 2 non-optimizable train parameters
Figure BDA0003397854770000142
2) And constructing a double-layer bidding model of the power generation group participating in the main energy market and the standby service market, simplifying the double-layer model based on a KKT condition and a binary extension method, and finally solving the model through a general commercial solver.
3) And solving a game equilibrium quotation result of the power generation group based on a quotation adjusting mechanism. The results are shown in FIGS. 4-5 and Table 3.
TABLE 3 Game Balanced Bidding result of Power Generation group
Figure BDA0003397854770000143
Figure BDA0003397854770000151
Compared with the prior art, the method has the advantages that a double-layer game bidding strategy model of the power generation group in the spot market environment is constructed, the bidding behaviors of the power generation group participating in the main energy market and the standby service market at the same time are analyzed, the mutual restriction relationship between the power generation low-price bidding behavior and the spot market discharge is considered, and a double-layer model simplification and solving method is provided; and designing a quotation adjusting mechanism to obtain the game balanced quotation of the power generation group. The invention makes up the defects of the prior patent on the research of the field of bidding behaviors of members in the spot market, creatively constructs a power generation group bidding model and provides a double-layer bidding model solving method containing a large number of nonlinear terms.

Claims (10)

1. A power generation group double-layer game bidding method in a power spot market environment is characterized in that,
firstly, constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein the electric energy and the standby service quotation of the power generation group are linear 'electricity price-electricity quantity' curves; secondly, converting a double-layer bidding model into a single-layer model through a KKT condition and a binary extension method, converting a power generation group bidding strategy into a discrete strategy set, and eliminating a nonlinear term existing in the single-layer model, so that the single-layer model is solved through a general commercial solver to obtain a global optimal solution; and finally, solving a game equilibrium quotation result of the power generation group based on a quotation adjustment mechanism.
2. A power generation group double-layer game bidding method in a power spot market environment is characterized by comprising the following steps:
1) acquiring basic clearing rules and day-ahead clearing boundary conditions of the power system;
2) constructing a double-layer bidding model of a power generation group participating in a day-ahead main energy market and a day-ahead standby service market, wherein an upper layer model reflects the bidding behavior of the power generation group, a lower layer model reflects the clearing process of a spot market, and random optimization is applied to the uncertainty of the output and the load of new energy of a real-time market;
3) based on a KKT condition and a binary extension method, the double-layer bidding model is converted into a single-layer model, nonlinear terms in the single-layer model are eliminated, and meanwhile, a power generation group bidding strategy is converted into a discrete strategy set.
3. The power generation group double-layer game bidding method in the power spot market environment according to claim 1 or 2, wherein the power generation group double-layer game bidding model is as follows:
1) an upper layer model: bidding model of power generation group
The objective function of the upper model is expressed as:
Figure FDA0003397854760000011
in the formula, ke,i,kr,iExpressing the quotation coefficient as a decision variable; t represents the time-sharing period number of the market in the day ahead; piωThe omega scene occurrence probability; n is a radical ofjRepresenting the total number of the thermal generator sets in the power generation group j;
Figure FDA0003397854760000012
respectively representing the normal bid price and the medium bid electric quantity of the unit i at the moment t of the day-ahead electric energy market;
Figure FDA0003397854760000013
respectively representing the bid price and the bid electric energy adjustment quantity of the unit i at the real-time market t moment under an omega scene;
Figure FDA0003397854760000014
the standby bid price and the intermediate scalar quantity of the unit i at the moment t of the day-ahead standby service market are obtained by a lower-layer model; ciThe total cost of the standard-out power in the unit i is represented and simplified into a quadratic form:
Figure FDA0003397854760000015
in the formula, am,i、bm,i、cm,iRespectively a quadratic term cost coefficient, a primary term cost coefficient and a constant term cost coefficient;
Figure FDA0003397854760000016
the total bid amount of the unit i in the spot market under the omega scene is represented as:
Figure FDA0003397854760000017
decision variables of the upper layer model are quotation strategies of each unit in the generator set in the day-ahead electric energy market and the day-ahead standby service market; the linear quotation curve of the unit in the day-ahead electric energy market is based on marginal cost, and the standard quotation curve of experience history is referred to in the day-ahead standby service market and is expressed as follows:
λe,m,i(P)＝ke,m,i(am,iP+bm,i)，
λr,m,i(r)＝kr,m,i(αm,ir+βm,i)，
wherein λ ise,m,i,λr,m,iRespectively showing the quotation curves of the unit i in the day-ahead electric energy market and the day-ahead standby service market, P, r respectively representing the day-ahead electric energyReported electric quantity of volume market and reported capacity of day-ahead standby service market, am,i,bm,i,αm,i,βm,iIs a constant related to cost; k is a radical ofe,m,i,kr,m,iAll represent the quotation coefficient, are decision variables, and satisfy the following constraints:
Figure FDA0003397854760000021
Figure FDA0003397854760000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000023
are each ke,m,i,kr,m,iAn upper limit value of (d);
2) the lower layer model: spot market clearing model
The objective function of the underlying model is to minimize the spot market electricity purchase cost, expressed as:
Figure FDA0003397854760000024
wherein, the electricity purchasing cost comprises three items of the current electricity purchasing cost, the standby service calling cost and the real-time electricity purchasing cost, M represents the total number of the spot market electricity generation group,
Figure FDA0003397854760000025
the set of variables is decided for the lower layer.
4. The power generation group double-deck game bidding method in the power spot market environment according to claim 3, wherein the day-ahead spot market constraints comprise:
1) node power balance constraints
Figure FDA0003397854760000026
In the formula ib,jbRepresents a network node;
Figure FDA0003397854760000027
respectively indicate the time t is connected to the point ibTotal bid power quantity of thermal power generating units in node market day ahead, output power of new energy source unit and load predicted value, KLRepresents a collection of lines in a network topology,
Figure FDA0003397854760000028
representing the line trend of the market at the day-ahead,
Figure FDA0003397854760000029
is a lagrange multiplier;
2) line flow equality constraints
Figure FDA00033978547600000210
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000211
for node i at time tbAnd jbThe phase angle of (a) is,
Figure FDA00033978547600000212
is a node ibAnd jbThe impedance of the line between the two lines,
Figure FDA0003397854760000031
is a lagrange multiplier;
3) line capacity constraint
Figure FDA0003397854760000032
In the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000033
is a node ibAnd jbThe maximum transmission capacity of the inter-line,
Figure FDA0003397854760000034
is a lagrange multiplier;
4) unit output constraint
Figure FDA0003397854760000035
Figure FDA0003397854760000036
In the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000037
respectively the maximum and minimum output values of the generator sets i under the generating group m,
Figure FDA0003397854760000038
Figure FDA0003397854760000039
is a lagrange multiplier;
5) spare capacity constraint
Figure FDA00033978547600000310
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000311
minimum spare capacity for time period t; mu.sr,tIs the Lagrange coefficient;
6) power justification rate constraints
Figure FDA00033978547600000312
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000313
the maximum up-regulation and down-regulation output force of the unit i in unit time,
Figure FDA00033978547600000314
is a lagrange multiplier;
7) phase angle constraint
Figure FDA00033978547600000315
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000316
is a lagrange multiplier.
5. The power generation group double-deck game bidding method in the power spot market environment according to claim 3, wherein the real-time market constraints comprise:
1) node power balance constraints
Figure FDA00033978547600000317
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000318
is a node ibProcessing the difference value between the output value corresponding to the time interval t of the thermal power generating unit under the scene omega and the scalar in the market before the day;
Figure FDA00033978547600000319
is a node ibThe difference value between the output value corresponding to the time interval t of the new energy unit under the scene omega and the scalar in the market before the day;
Figure FDA00033978547600000320
is a node ibDifference values of load values corresponding to the time period t under the scene omega and the market predicted values in the day before;
Figure FDA00033978547600000321
is a node ibThe difference value between the line power flow corresponding to the time period t under the scene omega and the line power flow of the market at the day before;
Figure FDA0003397854760000041
is the Lagrange coefficient;
2) line flow equality constraints
Figure FDA0003397854760000042
In the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000043
are respectively node ib,jbThe difference value between the phase angle corresponding to the time period t in the scene omega and the day-ahead market phase angle;
Figure FDA0003397854760000044
is a lagrange multiplier;
3) line capacity constraint
Figure FDA0003397854760000045
In the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000046
is a node ib,jbMaximum capacity of inter-line transmission;
Figure FDA0003397854760000047
is the Lagrange coefficient;
4) unit output constraint
Figure FDA0003397854760000048
In the formula (I), the compound is shown in the specification,
Figure FDA0003397854760000049
is a lagrange multiplier;
5) phase angle constraint
Figure FDA00033978547600000410
In the formula (I), the compound is shown in the specification,
Figure FDA00033978547600000411
is a lagrange multiplier.
6. The power generation group double-layer game bidding method in the power spot market environment according to claim 1 or 2, wherein the double-layer bidding model is solved by the following specific process:
firstly, expressing a lower layer model problem by using an equivalent KKT condition, linearizing a complementary relaxation condition based on a large M rule, explicitly unifying upper and lower layer variables, changing a double-layer model into a single-layer model, still having a binary variable product term in the model, linearizing the binary product term by a binary expansion method, and simultaneously converting a power generation group bidding strategy into a discrete strategy set, thereby facilitating the subsequent game equilibrium solution.
7. The power generation group double-layer game bidding method in the power spot market environment according to claim 6, wherein the variable k is obtained by analyzing the lower layer model alonee,m,i,kr,m,iIs an upper layer moldA decision-making variable, treated as a constant; therefore, the lower model problem is a quadratic convex optimization problem containing linear constraint, and the decision variables are continuous variables, so that the application requirements of the KKT condition are met.
8. The power generation group double-layer game bidding method in the power spot market environment according to claim 6, wherein the lower layer model equivalent KKT condition is expressed as:
Figure FDA0003397854760000051
Figure FDA0003397854760000052
Figure FDA0003397854760000053
Figure FDA0003397854760000054
Figure FDA0003397854760000055
Figure FDA0003397854760000056
Figure FDA0003397854760000057
wherein, the complementary relaxation conditions are expressed in a form that x ^ y is more than or equal to 0 and less than or equal to 0, and a large enough constant M and a 0-1 variable u are introduced for linearization treatment;
at the moment, the double-layer bidding model is converted into a single-layer model, but the binary variable product term still exists in the single-layer model
Figure FDA0003397854760000058
Figure FDA0003397854760000059
And kr,m,irm,i,tConsidering k, considere,m,i,kr,m,iThe binary extension method is applied to solve the two problems.
9. The power generation group double-layer game bidding method in the power spot market environment according to claim 1 or 2, wherein the game among the power generation groups eventually reaches a Nash equilibrium state, and no market subject can obtain greater profit by relying on self decision-making alone in the state that no market subject can obtain greater profit
Figure FDA00033978547600000510
Wherein i represents the subject of interest, riOn behalf of the subject arbitrary bidding strategy, ri *On behalf of the subject's bid balancing strategy,
Figure FDA00033978547600000511
representing a competitive bidding balancing strategy, wherein the formation of a Nash balancing solution depends on a quotation adjusting mechanism in the market;
BAE based round-by-round offers in a spot market environment comprises the following steps:
the first step, before the market is cleared in the day, the power generation group reports an initial quotation curve and unit technical parameters to a dispatching and trading center; the dispatching and trading center discloses quotation information of all the power generation groups, user-side report information and other related network and unit parameters, and starts a first bidding round;
secondly, each power generation group obtains a new round of quotation and reports the quotation to a dispatching and trading center within a certain time limit according to an initial quotation curve of a competitor and a double-layer bidding model;
thirdly, the dispatching transaction center obtains a new round of quotation result, if the quotation of each power generation group is the same as that of the previous round, the game is ended, and the quotation result of the round is a Nash balance result; if the power generation group adjustment strategy still exists, the dispatching transaction center continuously discloses the quotation condition of the round to the whole society, and carries out bidding of the next round until all the power generation groups do not change the quotation strategy.
10. A power generation group double-layer game bidding system in a power spot market environment is characterized by comprising an information acquisition module, a bidding analysis module, a model conversion and solving module, a quotation adjusting module and a data output module;
the information acquisition module acquires the boundary condition information of market clearing;
the bidding analysis module forms a power generation group bidding model according to the boundary conditions;
the model conversion and solution module simplifies and solves the double-layer model;
the quotation adjusting module supports the power generation group to quotation round by round until a balanced solution is achieved;
and the data output module formats and outputs the bidding strategy and the market balance point information of the power generation group.
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CN115423508A (en) * 2022-08-29 2022-12-02 大连川禾绿能科技有限公司 Strategic bidding method of cascade hydropower in uncertain carbon-electricity coupling market
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CN114692994A (en) * 2022-04-19 2022-07-01 国网福建省电力有限公司 Balanced optimization device based on electric power green certificate market combined clearing model
CN115423508A (en) * 2022-08-29 2022-12-02 大连川禾绿能科技有限公司 Strategic bidding method of cascade hydropower in uncertain carbon-electricity coupling market
CN115423508B (en) * 2022-08-29 2023-07-18 大连川禾绿能科技有限公司 Strategy bidding method for cascade hydropower in uncertain carbon-electricity coupling market
CN115630750A (en) * 2022-11-10 2023-01-20 国家电网有限公司华东分部 Method and device for optimizing spot market clearing and checking coupling and electronic equipment
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