CN108921595B - Method for calculating influence of virtual bidding on price difference of nodes in day-ahead power market - Google Patents

Method for calculating influence of virtual bidding on price difference of nodes in day-ahead power market Download PDF

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CN108921595B
CN108921595B CN201810588506.7A CN201810588506A CN108921595B CN 108921595 B CN108921595 B CN 108921595B CN 201810588506 A CN201810588506 A CN 201810588506A CN 108921595 B CN108921595 B CN 108921595B
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day
power market
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CN108921595A (en
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张广伦
钟海旺
马子明
陈连福
夏清
康重庆
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Tsinghua University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G06Q30/02—Marketing; Price estimation or determination; Fundraising
    • G06Q30/0201—Market modelling; Market analysis; Collecting market data
    • G06Q30/0206—Price or cost determination based on market factors
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S50/00—Market activities related to the operation of systems integrating technologies related to power network operation or related to communication or information technologies
    • Y04S50/14—Marketing, i.e. market research and analysis, surveying, promotions, advertising, buyer profiling, customer management or rewards

Abstract

The invention provides a method for calculating the influence of virtual bidding on the price difference of nodes in the power market in the day, and belongs to the technical field of power market trading. The method comprises the steps of firstly, obtaining calculated power grid system transaction basic data corresponding to a day-ahead power market, and constructing a day-ahead power market power transaction unified clearing model according to the basic data; establishing a security constraint economic dispatching model of the power market in the day ahead by using the solving result of the model and solving to obtain a feasible bid amount interval and a node price difference corresponding to the set virtual bid amount; after repeated iteration, a step-shaped curve of the influence of virtual bids taking the virtual bid amount as an independent variable and the node price difference as a dependent variable on the node price difference of the power market in the day before is finally obtained. The method solves the problem of accurately describing the nonlinear relation between the virtual projection quantity and the node price difference of the day-ahead power market, can provide a calculation tool for screening the projection space of market members in advance, and guarantees the high efficiency and the orderliness of the power market.

Description

Method for calculating influence of virtual bidding on price difference of nodes in day-ahead power market
Technical Field
The invention belongs to the technical field of electric power market trading, and particularly provides a method for calculating the influence of virtual bidding on the price difference of nodes in a current electric power market.
Background
The electric power financial market is used as an important component of an electric power market trading system, can provide effective financial tools for market members to avoid the risk of the spot market, can absorb a large amount of capital to enter the electric power market, improves the liquidity of the trading in the electric power market, and promotes the efficient and stable operation of the electric power market. The virtual bid is taken as an electric power financial derivative, and can affect the electric power spot market while trading in the electric power financial market, such as blocking a specific day-ahead electric power market line; by utilizing the influence, market members can make speculation to artificially change the electricity price of the day-ahead power market node in a virtual bidding mode, so that huge profits can be obtained in other financial derivative markets which refer to the electricity price of the day-ahead power market node, such as financial transmission right markets. Therefore, the relationship between the possible virtual bids on the nodes and the resulting day-ahead power market node electricity price difference in the day-ahead power market is discovered on the rainy day and on the earth, and is the key for the supervision of such illegal arbitrage behaviors by the supervision organization.
Documents and patents related to the price difference of the nodes of the power market at the day before caused by virtual bidding are not elaborated at present; a traditional and visual method is to enumerate a virtual projection scalar quantity by a certain step length, repeatedly solve a day-ahead power market clearing model containing the virtual projection scalar quantity, obtain the day-ahead power market node electricity price and further obtain the day-ahead power market node price difference. The method mainly comprises the following steps:
1) acquiring trading basic data of a power grid system corresponding to a power market in the day ahead;
the basic data of the power grid system transaction corresponding to the day-ahead power market comprises: the power market corresponds to power grid system topology data, load demand of each node in the power grid system and basic data of each generator set in the day ahead.
Wherein, the power grid system topology data corresponding to the day-ahead power market comprises: the day-ahead electric power market corresponds to the interconnection relationship between the nodes and the lines of the power grid system and the active power flow limit of each power transmission line;
the basic data of each generator set comprises: the maximum and minimum power generation capacity of the unit, the maximum climbing rate of the unit, the minimum continuous on-off time of the unit, the single-time starting cost of the unit and the running cost data of the unit;
the active power flow limit of each power transmission line is the maximum allowable value of active power flow transmitted in any direction on each power transmission line in the system, and the unit is MW;
the maximum and minimum generating capacity of the unit is the maximum and minimum allowable values of the supplied electric quantity in any time period when each unit in the system is in a starting state, and the unit is MW;
the maximum climbing rate of the unit is the maximum allowable value of the variable quantity of the supplied electric quantity in any two adjacent time periods when each unit in the system is in a starting state, and the unit is MW/h;
the minimum continuous on-off time of the unit is a minimum allowed time value which is required to pass from the next on-off state switching after each unit in the system is switched between the on-off states, and the unit is h;
the unit single starting cost is the cost required to be borne by each unit in the system when the unit is switched from a shutdown state to a startup state, and the unit is element;
the unit operation cost data is an operation cost value corresponding to each supply electric quantity of each unit in the system in a starting state, and is generally given in a quadratic function mode, and the unit is an element;
2) selecting the line where the virtual bidding node of the power market in the day before is located as j0(j0∈{1,2,...,nB}) of which two end nodes are k respectively0,k1(k0,k1E {1, 2.., n }), the calculated time period is t0(t0∈{1,2,...,T})。nBN and T are the total number of lines, the total number of nodes and the total number of time periods in the system respectively. When at t0Time of day, kth for the day-ahead power market0The node performs a projection quantity of
Figure GDA0003061510990000021
When the virtual time scale (when the time scale is positive, it represents the virtual load, and when the time scale is negative, it represents the virtual machine group), line j0Node price difference is generated at two ends;
selecting bid amount
Figure GDA0003061510990000022
Is enumerated step size Δ PvbFor iteration, the smaller the step size is, the more accurate the result isHowever, the solution time consumption is greatly increased, and is generally 0.01; setting initial value of projection quantity
Figure GDA0003061510990000023
3) Constructing a unified clearing model of the day-ahead power market power trading with a virtual projection scalar as a parameter, which is composed of a target function and constraint conditions, according to the day-ahead power market corresponding power grid system trading basic data obtained in the step 1); the method comprises the following specific steps
3-1) constructing a target function of a power trading unified clearing model of a power market in the day before, wherein the expression is as follows:
Figure GDA0003061510990000024
the objective function represents that the comprehensive cost of all units in the whole time period of the power market is minimum in the day, and the comprehensive cost of a single unit in a single time period consists of three parts, namely the running cost, the starting cost and the shutdown cost of the single unit in the time period; wherein i is the number of the unit, nGThe total number of the units in the system; t is the number of the time period, and T is the total number of the time periods;
Figure GDA0003061510990000025
is a model variable and represents the power generation output of the ith unit in the t period,
Figure GDA0003061510990000026
the power generation output of the ith unit in the t period is
Figure GDA0003061510990000027
Running cost, unit: an element given in the form of a quadratic function;
Figure GDA0003061510990000028
the unit of the starting cost of the ith unit in the t time period is as follows: element;
Figure GDA0003061510990000029
for closing the ith unit in the t-th time periodThe machine cost can be ignored in the invention, and the unit is: and (5) Yuan.
Cost of starting up
Figure GDA00030615109900000210
Wherein
Figure GDA00030615109900000211
The single starting cost of the ith unit is given as a constant;
Figure GDA00030615109900000212
the model is also variable and represents the on-off state of the ith unit in the t-th time period, the values are limited to 0,1,
Figure GDA00030615109900000213
the unit is shown to be in a starting state,
Figure GDA00030615109900000214
indicating the unit is in a shutdown state, preset
Figure GDA00030615109900000215
At this time, when the unit is powered off in the current time period and powered on in the later time period, the unit will generate the size of
Figure GDA00030615109900000216
The cost of (a).
Running cost function
Figure GDA0003061510990000031
Given by a quadratic function form, in order to make the model meet the linear requirement of a linear programming solver on the model, the model needs to be solved before
Figure GDA0003061510990000032
And carrying out piecewise linearization. Piecewise linearization is the following process: the definition domain of the function is equally divided into N sections, and the function curve in each section of the interval is approximately replaced by the line sections connected with the corresponding points of the function values at the end points of the interval. The number of the segments N can be arbitrarily selected; the smaller the value of N is, the more the approximate effect isPreferably, the slower the solution speed is, the invention takes N as 10;
3-2) determining constraint conditions of the unified clearing model of the electric power trade of the electric power market in the day before, wherein the constraint conditions are as follows:
3-2-1) energy balance constraints:
Figure GDA0003061510990000033
the expression (2) indicates that the sum of the output of all units of the system should be balanced with the sum of the load demands of all nodes in the system in any time period, namely, the energy balance. Wherein k is the serial number of the node, and n is the total number of the nodes in the system;
Figure GDA0003061510990000034
load demand of the kth node in the t period is MW;
Figure GDA0003061510990000035
is at the t0Time period pair k0Virtual projection quantities of the nodes;
3-2-2) rotational standby constraint:
Figure GDA0003061510990000036
the sum of the capacities (i.e. the sum of the maximum allowable outputs of the units) of all units in the system in the on state is the maximum possible output of the system in the time period. The formula (3) requires that the maximum possible output of the system in any time period can meet a certain rotating standby load on the premise of meeting the total load demand of the system so as to deal with possible accidents in the system. Wherein the content of the first and second substances,
Figure GDA0003061510990000037
the capacity of the ith unit, namely the maximum allowable output, is expressed in MW; the rotational load reserve is often expressed as a proportion of the total load demand of the system, rreserveCalled the required load reserve of the system；
3-2-3) restraining the upper limit and the lower limit of the output of the unit:
Figure GDA0003061510990000038
equation (4) requires that the unit output of any unit in the on state must be kept between the maximum and minimum allowed outputs of the unit in any time interval. Wherein the content of the first and second substances,
Figure GDA0003061510990000039
the minimum allowable output in MW is the minimum allowable output of the ith unit in the starting state;
3-2-4) maximum climbing rate constraint of the unit:
Figure GDA00030615109900000310
Figure GDA00030615109900000311
formulas (5) and (6) require that for any unit, if the unit is in a starting state in two adjacent time periods, the difference of the output forces of the units in the two time periods does not exceed the maximum allowable climbing rate of the unit; the condition that the output is increased in the later period of time compared with the previous period of time is called climbing, and the condition that the output is reduced in the later period of time compared with the previous period of time is called climbing; if the on-off states of two adjacent time periods are different, the difference of the output force of the unit is determined by the maximum and minimum allowable output force of the unit. Wherein the content of the first and second substances,
Figure GDA0003061510990000041
the maximum allowable climbing speed for climbing under the ith unit,
Figure GDA0003061510990000042
the maximum allowable climbing speed of climbing on the ith unit is MW/h;
3-2-5) minimum continuous on-off time constraint of the unit:
Figure GDA0003061510990000043
Figure GDA0003061510990000044
equations (7) and (8) require that for any unit, the previous on/off state is maintained for a certain time period when the on/off state is to be changed in the next period; for example, when the power-on state is changed into the power-off state in the next time interval, the power-on state is required to be kept to exceed the minimum allowable continuous power-on time until the time interval; similarly, the power-off state is changed into the power-on state. Wherein the content of the first and second substances,
Figure GDA0003061510990000045
for the minimum allowed continuous boot time of the ith unit,
Figure GDA0003061510990000046
the minimum allowable continuous shutdown time of the ith unit is h; it is preset that when t is less than or equal to 0,
Figure GDA0003061510990000047
before the 1 st time period, all the units are in a shutdown state for a long time;
3-2-6) maximum active power flow constraint of the power transmission line:
Figure GDA0003061510990000048
Figure GDA0003061510990000049
equations (9), (10) require that for any transmission line, the active power flow transmitted on it in any time period does not exceed the maximum allowable active power of the line in any directionTidal current; according to the direct current power flow model of the power system, the active power flow on the line is composed of two parts, namely the influence of the output of all the generator sets and the influence of the load demand of all the nodes. Where j is the number of the line, nBThe total number of lines in the system;
Figure GDA00030615109900000410
the maximum allowable active power flow of the jth power transmission line is in unit MW; pj,kIn a direct current power flow model of a power transmission system, a jth row and a kth column of elements of a Power Transmission Distribution Factor (PTDF) matrix are the influence of unit load change of a kth node on the delivery of active power flow of a jth line;
4) solving the day-ahead power market power transaction unified clearing model established in the step 2) by adopting a linear programming solver, and obtaining a day-ahead power market power transaction unified clearing result when the solving is successful
Figure GDA00030615109900000411
And
Figure GDA00030615109900000412
if no optimal solution exists, jumping to the step 9);
5) the variables obtained by the solution in the step 4)
Figure GDA00030615109900000413
And (3) substituting the current power market power trading unified clearing model in the step 3) to obtain a current power market Safety Constraint Economic Dispatch (SCED) model, which is specifically as follows:
5-1) objective function of SCED model of day-ahead electric power market, the expression is as follows:
Figure GDA0003061510990000051
the formula (11) requires the minimum sum of the running costs of all the units in the whole time period; the on-off state of each unit is solved in the step 3), so that the on-off cost is determined and does not need to be included in an objective function;
5-2) determining the constraint conditions of the SCED model of the power market at the day before, wherein the constraint conditions are as follows:
5-2-1) energy balance constraints:
Figure GDA0003061510990000052
the formula (12) is the same as the formula (2), and the formula (11) requires any time interval, and the sum of the output of all the units of the system is balanced with the sum of the load requirements of all the nodes of the system;
5-2-2) restraining the upper limit and the lower limit of the output of the machine set:
Figure GDA0003061510990000053
Figure GDA0003061510990000054
equations (13) and (14) require that the output force be maintained between its maximum and minimum allowable output forces when the unit is in the on state; when the unit is in a shutdown state, the output of the unit is necessarily 0;
5-2-3) maximum climbing rate constraint of the unit:
Figure GDA0003061510990000055
the requirement of the formula (15) is that for any unit, when the two adjacent time periods are in the starting state, the difference of the output power does not exceed the maximum climbing speed of the upper climbing when climbing the slope, and does not exceed the maximum climbing speed of the lower climbing when climbing the slope; when the power on/off state changes in two adjacent time periods, the output in the time period of the power off state is necessarily 0 due to the limitation of the formulas (12) and (13), so that the difference between the output in the time period of the power on state and the output in the time period of the adjacent power on state is not limited by the maximum climbing rate but limited by the upper and lower limits of the output of the unit;
5-2-4) maximum active power flow constraint of the power transmission line:
Figure GDA0003061510990000056
Figure GDA0003061510990000057
equations (16), (17) are the same as equations (9), (10), and require any time period of the transmission active power flow of any line, and the maximum allowable active power flow of the line is not exceeded in any direction;
6) solving the SCED model of the formulas (11) - (17) by adopting a linear programming solver to obtain the clearing result of the SCED model of the day-ahead power market
Figure GDA0003061510990000061
7) According to node electricity price formula
Figure GDA0003061510990000062
Solving the node electricity price of all the nodes of the system in each time period, wherein lambdatIs a dual variable of the constraint (11),
Figure GDA0003061510990000063
an upper-bound dual variable and a lower-bound dual variable of the constraint condition (15) respectively; at this time, the node price difference
Figure GDA0003061510990000064
Wherein k is1Is a node k in question0Connected nodes;
8) iteration: amount of virtual bid
Figure GDA0003061510990000065
Returning to the step 2);
9) the iterative process is complete and all feasible bid amounts have been enumerated. Recording the bid amount during each enumeration
Figure GDA0003061510990000066
To corresponding nodeThe price difference delta p is used as an independent variable and a dependent variable respectively to obtain a stair-shaped curve of the influence of the virtual bid on the price difference of the node.
As can be seen from the above solving steps, each time the virtual projection amount is enumerated, the virtual projection amount is calculated
Figure GDA0003061510990000067
The unified clearing model of the electric power trade of the day-ahead electric power market and the SCED model of the day-ahead electric power market are required to be solved once respectively, so that the solving efficiency is extremely low, and the model can hardly be used when the system is complex; meanwhile, the accuracy of the solution result is greatly limited by the enumeration step Δ PvbTo the degree of accuracy of the process.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for calculating the influence of virtual bidding on the price difference of nodes in the current electric power market. The method solves the problem of accurately describing the nonlinear relation between the virtual projection quantity and the node price difference of the day-ahead power market, can provide a calculation tool for screening the projection space of market members in advance, and guarantees the high efficiency and the orderliness of the power market.
The invention provides a method for calculating the influence of virtual bidding on the price difference of nodes in the power market in the day, which is characterized by comprising the following steps of:
1) acquiring the trading basic data of the power grid system corresponding to the power market in the day ahead, wherein the trading basic data comprises the following steps: the method comprises the following steps that the power market corresponds to power grid system topology data, load demand of each node in the power grid system and basic data of each generator set in the day ahead;
wherein, the power grid system topology data corresponding to the day-ahead power market comprises: the day-ahead electric power market corresponds to the interconnection relationship between the nodes and the lines of the power grid system and the active power flow limit of each power transmission line;
the basic data of each generator set comprises: the maximum and minimum power generation capacity of the unit, the maximum climbing rate of the unit, the minimum continuous on-off time of the unit, the single-time starting cost of the unit and the running cost data of the unit;
2) selecting the line where the virtual bidding node of the power market in the day before is located as j0Wherein j is0∈{1,2,...,nB}；j0The nodes at both ends are respectively k0,k1Wherein k is0,k1E {1, 2.., n }; selecting the time interval as t0Wherein t is0∈{1,2,...,T}；nBN and T are the total number of lines, the total number of nodes and the total number of time periods in the system respectively;
3) let the initial value r of iteration number r be 0, let the initial bid amount
Figure GDA0003061510990000068
4) Constructing a power market power trading unified clearing model in the day ahead; the method comprises the following specific steps:
4-1) constructing a target function of a power trading unified clearing model of a power market in the day before, wherein the expression is as follows:
Figure GDA0003061510990000071
wherein i is the number of the unit, nGThe total number of the units in the system; t is a time interval number;
Figure GDA0003061510990000072
representing the power generation output of the ith unit in the t time period during the r iteration,
Figure GDA0003061510990000073
the power generation output of the ith unit in the t period is
Figure GDA0003061510990000074
The cost of operation;
Figure GDA0003061510990000075
the starting cost of the ith unit in the t time period;
Figure GDA0003061510990000076
the shutdown cost of the ith unit in the t time period;
cost of starting up
Figure GDA0003061510990000077
Wherein
Figure GDA0003061510990000078
The single starting cost of the ith unit;
Figure GDA0003061510990000079
the state of the startup and shutdown of the ith unit in the t time interval during the r iteration is represented as a variable of 0 and 1,
Figure GDA00030615109900000710
the unit is shown to be in a starting state,
Figure GDA00030615109900000711
indicating the unit is in a shutdown state
Figure GDA00030615109900000712
4-2) determining constraint conditions of the unified clearing model of the electric power trade of the electric power market in the day before, wherein the constraint conditions are as follows:
4-2-1) energy balance constraints:
Figure GDA00030615109900000713
wherein k is the number of the node;
Figure GDA00030615109900000714
the load demand of the kth node in the t period;
Figure GDA00030615109900000715
at the t-th in the day-ahead power market for the r-th iteration0Time period pair k0A bid amount of a virtual bid made by a node;
4-2-2) rotational standby constraint:
Figure GDA00030615109900000716
wherein the content of the first and second substances,
Figure GDA00030615109900000717
the maximum allowable output of the ith unit; r isreserveThe load reserve rate of the system;
4-2-3) restraining the upper limit and the lower limit of the output of the machine set:
Figure GDA00030615109900000718
wherein the content of the first and second substances,
Figure GDA00030615109900000719
the minimum allowable output of the ith unit;
4-2-4) maximum climbing rate constraint of the unit:
Figure GDA00030615109900000720
Figure GDA00030615109900000721
wherein the content of the first and second substances,
Figure GDA00030615109900000722
the maximum allowable climbing speed for climbing under the ith unit,
Figure GDA00030615109900000723
the maximum allowable climbing speed of the climbing on the ith unit is obtained;
4-2-5) minimum continuous on-off time constraint of the unit:
Figure GDA0003061510990000081
Figure GDA0003061510990000082
wherein the content of the first and second substances,
Figure GDA0003061510990000083
for the minimum allowed continuous boot time of the ith unit,
Figure GDA0003061510990000084
the minimum allowable continuous shutdown time of the ith unit is obtained; when t is less than or equal to 0,
Figure GDA0003061510990000085
4-2-6) maximum active power flow constraint of the power transmission line:
Figure GDA0003061510990000086
Figure GDA0003061510990000087
wherein j is the serial number of the line;
Figure GDA0003061510990000088
the maximum allowable active power flow of the jth power transmission line; pj,kThe method comprises the steps that the jth row and kth column elements of a power transmission distribution factor matrix in a direct current power flow model of a power transmission system are defined;
5) solving the power trading unified clearing model of the power market in the day before established in the step 4) and judging: if the optimal solution exists, obtaining the unified clearing result of the power trading of the power market in the day before the r iteration
Figure GDA0003061510990000089
And
Figure GDA00030615109900000810
entering step 6); if no optimal solution exists, jumping to the step 16);
6) obtained by solving in the step 4)
Figure GDA00030615109900000811
Substituting the current power market power trading unified clearing model in the step 4) to obtain a current power market safety constraint economic dispatching SCED model; the method comprises the following specific steps:
6-1) constructing an objective function of the SCED model of the day-ahead power market, wherein the expression is as follows:
Figure GDA00030615109900000812
6-2) determining the constraint conditions of the SCED model of the power market at the day before, wherein the constraint conditions are as follows:
6-2-1) energy balance constraints:
Figure GDA00030615109900000813
6-2-2) restraining the upper and lower limits of the unit output:
Figure GDA00030615109900000814
Figure GDA00030615109900000815
6-2-3) maximum climbing rate constraint of the unit:
Figure GDA0003061510990000091
6-2-4) maximum active power flow constraint of the power transmission line:
Figure GDA0003061510990000092
Figure GDA0003061510990000093
7) converting the SCED model of the day-ahead power market established in the step 6) into a linear programming model in a standard form, wherein the expression is as follows:
Figure GDA0003061510990000094
wherein A is a constraint condition coefficient matrix, and each row in the constraint condition coefficient matrix A corresponds to each constraint condition in the formulas (11) to (17); b(r)Is a constraint right-end constant vector at the time of the r-th iteration, cTIs a target function value coefficient vector, lb is a variable lower limit vector, ub is a variable upper limit vector; x is the number of(r)The model variable vector at the r iteration is;
8) and (3) judging the value of r: if r is 0, go to step 9); if r ≠ 0, then proceed to step 10);
9) when r is 0, make the bid amount
Figure GDA0003061510990000095
And (12) and (17) are updated, the expressions (11), (13), (14), (15) and (16) are kept unchanged, and the future electric power market SCED model at the moment is derived in a standard form, wherein the expressions are as follows:
Figure GDA0003061510990000096
wherein, b*As bid amount
Figure GDA0003061510990000097
Constraint conditions of time right-hand constant vectors;
10) solving the standard form of the SCED model of the day-ahead electric power market shown in the formula (18) by a simplex method and judging: if no feasible solution exists, the step 5) is returned again, and the current projection quantity is solved again
Figure GDA0003061510990000098
Time each machine setOn/off state of
Figure GDA0003061510990000099
If a feasible solution exists, obtaining a clear result x of the r-th iteration of the SCED model of the power market in the day before(r)Wherein x is(r)The partial variable with the value of 0 is the non-base variable, the partial variable with the value of 0 is the base variable, x is(r)The line number sets of the middle base variable and the non-base variable are respectively marked as
Figure GDA0003061510990000101
11) According to node electricity price formula
Figure GDA0003061510990000102
Solving node electricity prices of all time periods of all nodes of system in the nth iteration
Figure GDA0003061510990000103
Wherein λt,(r)Is a dual variable of the constraint (12),
Figure GDA0003061510990000104
the upper bound dual variable and the lower bound dual variable of the constraint conditions (16) and (17) respectively; at this time, j is the amount of no bid in the r-th iteration0Cost difference of line node
Figure GDA0003061510990000105
12) In the constraint condition coefficient matrix A, a base variable row number set is selected
Figure GDA0003061510990000106
The corresponding columns form a submatrix B(r)(ii) a Calculating the influence coefficient vector delta b of the virtual bid on the right constant vector b of the constraint condition(r)＝(B(r))-1(b*-b(0))；
13) Solving inequality
Figure GDA0003061510990000107
Obtaining bid amount
Figure GDA0003061510990000108
Feasible projection scalar interval
Figure GDA0003061510990000109
Respectively throwing scalar quantities under the condition of keeping node price difference unchanged during the r-th iteration
Figure GDA00030615109900001010
The lower limit and the upper limit of allowable variation of (2);
14) updating a projection quantity
Figure GDA00030615109900001011
Epsilon is less than 0.01 so that the bid amount
Figure GDA00030615109900001012
Is greater than
Figure GDA00030615109900001013
15) Let r be r +1, model variables in equations (11) to (17)
Figure GDA00030615109900001014
Returning to the step 7) again;
16) completing iteration, recording all feasible projection quantity intervals in each iteration process
Figure GDA00030615109900001015
With corresponding node price difference Δ p(r)(ii) a In bid amount
Figure GDA00030615109900001016
And obtaining a step-shaped curve of the influence of the virtual bid on the node price difference of the electric power market in the day before by taking the node price difference as a dependent variable, and ending the method.
The invention has the technical characteristics and beneficial effects that:
the invention provides a method for solving the planning problem by adopting a simple form table based on a parameter planning idea, which can quickly calculate the node price difference among nodes in the current electric power market caused by virtual bidding; compared with the traditional enumeration method, the method has extremely high accuracy and greatly improved efficiency. The method can accurately describe the nonlinear relation between the virtual bid amount and the price difference of the nodes of the power market in the day before, and is helpful for a power market related supervision mechanism to provide an effective supervision tool for behaviors of market members who speculate and use virtual bids to cause line blockage so as to be arbitraged in other derivative markets such as financial power transmission rights and the like, thereby improving the efficiency and the safety of power market transaction.
Detailed Description
The invention provides a method for calculating the influence of virtual bidding on the price difference of nodes in the power market in the future, which is further described in detail by combining a specific embodiment; it should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a method for calculating the influence of virtual bidding on the price difference of nodes in the power market in the day, which comprises the following steps:
1) acquiring trading basic data of a power grid system corresponding to a power market in the day ahead;
the basic data of the power grid system transaction corresponding to the day-ahead power market comprises: the power market corresponds to power grid system topology data, load demand of each node in the power grid system and basic data of each generator set in the day ahead.
Wherein, the power grid system topology data corresponding to the day-ahead power market comprises: the day-ahead electric power market corresponds to the interconnection relationship between the nodes and the lines of the power grid system and the active power flow limit of each power transmission line;
the basic data of each generator set comprises: the maximum and minimum power generation capacity of the unit, the maximum climbing rate of the unit, the minimum continuous on-off time of the unit, the single-time starting cost of the unit and the running cost data of the unit;
the active power flow limit of each power transmission line is the maximum allowable value of active power flow transmitted in any direction on each power transmission line in the system, and the unit is MW;
the maximum and minimum generating capacity of the unit is the maximum and minimum allowable values of the supplied electric quantity in any time period when each unit in the system is in a starting state, and the unit is MW;
the maximum climbing rate of the unit is the maximum allowable value of the variable quantity of the supplied electric quantity in any two adjacent time periods when each unit in the system is in a starting state, and the unit is MW/h;
the minimum continuous on-off time of the unit is a minimum allowed time value which is required to pass from the next on-off state switching after each unit in the system is switched between the on-off states, and the unit is h;
the unit single starting cost is the cost required to be borne by each unit in the system when the unit is switched from a shutdown state to a startup state, and the unit is element;
the unit operation cost data is an operation cost value corresponding to each supply electric quantity of each unit in the system in a starting state, and is generally given in a quadratic function mode, and the unit is an element; 2) selecting the line where the virtual bidding node of the power market in the day before is located as j0(j0∈{1,2,...,nB})，j0The nodes at both ends are respectively k0,k1(k0,k1E to {1,2,. eta., n }), selecting the time period as t0(t0∈{1,2,...,T})。nBN and T are the total number of lines, the total number of nodes and the total number of time periods in the system respectively. When at t0Time of day, kth for the day-ahead power market0The node performs a projection quantity of
Figure GDA0003061510990000111
When the virtual time scale (when the time scale is positive, it represents the virtual load, and when the time scale is negative, it represents the virtual machine group), line j0Both ends will produce a node price difference.
3) Making the initial value r of the iteration number r equal to 0; the initial bid amount is made to be the initial bid amount because the virtual bid is not considered in the first solution model
Figure GDA0003061510990000112
4) The day-ahead electric power city obtained according to step 1)Trading basic data of field-corresponding power grid system and virtual bid amount after the r-th iteration
Figure GDA0003061510990000113
Constructing a day-ahead electric power market electric power trading unified clearing model which is composed of a target function and constraint conditions and contains virtual scalar quantity parameters; the variable superscript r in the model uniformly represents the iteration number. The method comprises the following specific steps:
4-1) constructing a target function of a power trading unified clearing model of a power market in the day before, wherein the expression is as follows:
Figure GDA0003061510990000114
the objective function represents that the comprehensive cost of all units in the whole time period of the power market is minimum in the day, wherein the comprehensive cost of a single unit in a single time period consists of three parts, namely the running cost, the starting cost and the shutdown cost of the single unit in the time period; wherein i is the number of the unit, nGThe total number of the units in the system; t is the time interval number, and T is the total time interval number;
Figure GDA0003061510990000121
is a model variable and represents the power generation output of the ith unit in the t time period during the r iteration,
Figure GDA0003061510990000122
the power generation output of the ith unit in the t period is
Figure GDA0003061510990000123
Running cost, unit: an element given in the form of a quadratic function;
Figure GDA0003061510990000124
the unit of the starting cost of the ith unit in the t time period is as follows: element;
Figure GDA0003061510990000125
the shutdown cost of the ith unit in the t time period can be ignored in the invention: and (5) Yuan.
Cost of starting up
Figure GDA0003061510990000126
Wherein
Figure GDA0003061510990000127
The single starting cost of the ith unit is given as a constant;
Figure GDA0003061510990000128
the model variable represents the on-off state of the ith unit in the t time interval during the r iteration and is a 0,1 variable,
Figure GDA0003061510990000129
the unit is shown to be in a starting state,
Figure GDA00030615109900001210
indicating the unit is in a shutdown state, preset
Figure GDA00030615109900001211
At this time, when the unit is powered off in the current time period and powered on in the later time period, the unit will generate the size of
Figure GDA00030615109900001212
The cost of (a).
Running cost function
Figure GDA00030615109900001213
Given by a quadratic function form, in order to make the model meet the linear requirement of a linear programming solver on the model, the model needs to be solved before
Figure GDA00030615109900001214
And carrying out piecewise linearization. Piecewise linearization is the following process: the definition domain of the function is equally divided into N sections, and the function curve in each section of the interval is approximately replaced by the line sections connected with the corresponding points of the function values at the end points of the interval. The number of the segments N can be arbitrarily selected; the smaller the value of N is, the better the approximation effect is, but the slower the solution speed is, the cost isIn the invention, N is 10.
4-2) determining constraint conditions of the unified clearing model of the electric power trade of the electric power market in the day before, wherein the constraint conditions are as follows:
4-2-1) energy balance constraints:
Figure GDA00030615109900001215
and (2) expressing that the sum of the output of all the units of the system is equal to the sum of the load demands of all the nodes in the system in any time period, namely energy balance. Wherein k is the serial number of the node, and n is the total number of the nodes in the system;
Figure GDA00030615109900001216
load demand of the kth node in the t period is MW;
Figure GDA00030615109900001217
at the t-th in the day-ahead power market for the r-th iteration0Time period pair k0The bid amount of the virtual bid made by the node. Since virtual bids are equally well established in the day-ahead power market as physical bids, they are also counted as part of the "load" in energy balance.
4-2-2) rotational standby constraint:
Figure GDA00030615109900001218
the sum of the capacities (i.e. the sum of the maximum allowable outputs of the units) of all units in the system in the on state is the maximum possible output of the system in the period. The formula (3) requires that the maximum possible output of the system in any time period can meet a certain rotating standby load on the premise of meeting the total load demand of the system so as to deal with possible accidents in the system. Wherein the content of the first and second substances,
Figure GDA00030615109900001219
for the capacity of the i-th unit, i.e. the maximum allowable output, onlyThe bit is MW; the rotational load reserve is often expressed as a proportion of the total load demand of the system, rreserveCalled the required load reserve of the system;
4-2-3) restraining the upper limit and the lower limit of the output of the machine set:
Figure GDA0003061510990000131
the formula (4) requires that the unit output of any unit in the starting state is kept between the maximum and minimum allowed output of the unit in any time period. Wherein the content of the first and second substances,
Figure GDA0003061510990000132
the minimum allowable output of the ith unit is MW;
4-2-4) maximum climbing rate constraint of the unit:
Figure GDA0003061510990000133
Figure GDA0003061510990000134
formulas (5) and (6) require that for any unit, if the unit is in a starting state in two adjacent time periods, the difference of the output forces of the units in the two time periods does not exceed the maximum allowable climbing rate of the unit; the condition that the output is increased in the later period of time compared with the previous period of time is called climbing, and the condition that the output is reduced in the later period of time compared with the previous period of time is called climbing; if the on-off states of two adjacent time periods are different, the difference of the output force of the unit is determined by the maximum and minimum allowable output force of the unit. Wherein the content of the first and second substances,
Figure GDA0003061510990000135
the maximum allowable climbing speed for climbing under the ith unit,
Figure GDA0003061510990000136
the maximum allowable climbing speed of climbing on the ith unit is MW/h;
4-2-5) minimum continuous on-off time constraint of the unit:
Figure GDA0003061510990000137
Figure GDA0003061510990000138
equations (7) and (8) require that for any unit, the previous on/off state is maintained for a certain time period when the on/off state is to be changed in the next period; for example, when the power-on state is changed into the power-off state in the next time interval, the power-on state is required to be kept to exceed the minimum allowable continuous power-on time until the time interval; similarly, the power-off state is changed into the power-on state. Wherein the content of the first and second substances,
Figure GDA0003061510990000139
for the minimum allowed continuous boot time of the ith unit,
Figure GDA00030615109900001310
the minimum allowable continuous shutdown time of the ith unit is hour; it is preset that when t is less than or equal to 0,
Figure GDA00030615109900001311
i.e. before period 1, all units are in and remain in a shutdown state long enough.
4-2-6) maximum active power flow constraint of the power transmission line:
Figure GDA00030615109900001312
Figure GDA0003061510990000141
formulas (9) and (10)) Requiring that the maximum allowable active power flow of the line in any direction for the active power flow transmitted on any transmission line during any period of time; according to the direct current power flow model of the power system, the active power flow on the line is composed of two parts, namely the influence of the output of all the generator sets and the influence of the load demand of all the nodes. Where j is the number of the line, nBThe total number of lines in the system;
Figure GDA0003061510990000142
the maximum allowable active power flow of the jth power transmission line is in unit MW; pj,kThe method comprises the steps that the element of the jth row and the kth column of a Power Transmission Distribution Factor (PTDF) matrix in a direct current power flow model of a power transmission system is the influence of unit load change of a kth node on the transmission of active power flow of a jth line;
5) solving the unified clearing model of the electric power trade of the day-ahead electric power market established in the step 4) by adopting a linear programming solver, and judging: if the optimal solution exists, obtaining the unified clearing result of the power trading of the power market in the day before the r iteration
Figure GDA0003061510990000143
And
Figure GDA0003061510990000144
entering step 6); if no optimal solution exists, jumping to the step 16);
6) the variables obtained by the solution in the step 4) are processed
Figure GDA0003061510990000145
And (3) substituting the current power market power trading unified clearing model in the step 4) to obtain a current power market Safety Constraint Economic Dispatch (SCED) model, which is specifically as follows:
6-1) constructing an objective function of the SCED model of the day-ahead power market, wherein the expression is as follows:
Figure GDA0003061510990000146
formula (11) requires that the whole time is organicThe sum of the operating costs of the groups is minimal; due to the on-off state ui of each unitGT, (r) has been solved in step 5), so the boot cost has been determined and need not be included in the objective function;
6-2) determining the constraint conditions of the SCED model of the power market at the day before, wherein the constraint conditions are as follows:
6-2-1) energy balance constraints:
Figure GDA0003061510990000147
the formula (12) is the same as the formula (2), and the formula (12) requires any time interval, and the sum of the output of all the units of the system is balanced with the sum of the load requirements of all the nodes of the system.
6-2-2) restraining the upper and lower limits of the unit output:
Figure GDA0003061510990000148
Figure GDA0003061510990000149
equations (13) and (14) require that the output force be maintained between its maximum and minimum allowable output forces when the unit is in the on state; when the unit is in a shutdown state, the output power is 0;
6-2-3) maximum climbing rate constraint of the unit:
Figure GDA0003061510990000151
the requirement of the formula (15) is that for any unit, when the unit is in a starting state in two adjacent time periods, the difference of the output force does not exceed the maximum climbing speed of an upper climbing slope when the unit is in the ascending state, and does not exceed the maximum climbing speed of a lower climbing slope when the unit is in the descending state; when the on-off state changes in two adjacent time periods, the output in the time period of the off state is 0 due to the limitation of the formulas (13) and (14), so that the difference between the output in the time period of the off state and the output in the time period of the adjacent on state is not limited by the maximum climbing rate but limited by the upper and lower limits of the output of the unit.
6-2-4) maximum active power flow constraint of the power transmission line:
Figure GDA0003061510990000152
Figure GDA0003061510990000153
equations (16) and (17) require that the delivered active power flow for any period of any one line does not exceed the maximum allowable active power flow for that line in any direction.
7) Converting the SCED model of the day-ahead power market established in the step 6) into a linear programming model in a standard form;
exporting the SCED model of the day-ahead power market obtained in the step 6) into a form shown in a formula (16) in a standard form of a linear programming model; the linear programming model expression in the standard form is obtained as follows:
Figure GDA0003061510990000154
wherein A is a constraint condition coefficient matrix, and each row in the constraint condition coefficient matrix A corresponds to each constraint condition in the formulas (11) to (17); b(r)Is a constraint right-end constant vector at the time of the r-th iteration, cTIs a target function value coefficient vector, lb is a variable lower limit vector, ub is a variable upper limit vector; x is the number of(r)Model variable vectors at the r-th iteration, and a part of the model variable vectors correspond to model variables in SCED model expressions (11) - (17) of the power market in the day-ahead
Figure GDA0003061510990000155
The other part corresponds to auxiliary relaxation variables added when the other part is in a standard form;
8) and (3) judging the value of r: if r is 0, go to step 9); if r ≠ 0, then proceed to step 10);
9) when in useWhen r is 0, this step is performed to obtain the influence of the projection amount on the standard formal model represented by equation (18). Amount of bid
Figure GDA0003061510990000156
Updating (12) and (17), keeping the formulas (11), (13), (14), (15) and (16) unchanged, and exporting the SCED model of the current electric power market in a standard form; projection quantity
Figure GDA0003061510990000157
Only the right-end constant vector of the constraint is affected by the change of (2), so the derived standard form is shown as the following formula:
Figure GDA0003061510990000161
wherein A is a constraint condition coefficient matrix and b*As bid amount
Figure GDA0003061510990000162
Constraint of time right-hand constant vector, cTThe vector of the objective function value coefficient, lb is a variable lower limit vector and ub is a variable upper limit vector;
10) solving a standard form of the SCED model of the day-ahead power market shown in the formula (18) by a simplex method by adopting a linear programming solver, and judging: if no feasible solution exists, the step 5) is returned again, and the current projection quantity is solved again
Figure GDA0003061510990000163
On-off state of each unit
Figure GDA0003061510990000164
If a feasible solution exists, obtaining a clear result x of the r-th iteration of the SCED model of the power market in the day before(r)Wherein x is(r)And the partial variable with the value of 0 is the non-base variable, and the partial variable with the value of not 0 is the base variable. X is to be(r)The line number sets of the middle base variable and the non-base variable are respectively marked as
Figure GDA0003061510990000165
11) According to node electricity price formula
Figure GDA0003061510990000166
Solving node electricity prices of all time periods of all nodes of system in the nth iteration
Figure GDA0003061510990000167
Wherein λt,(r)Is a dual variable of the constraint (12),
Figure GDA0003061510990000168
the upper bound dual variable and the lower bound dual variable of the constraint conditions (16) and (17) respectively; at this time, j is the amount of no bid in the r-th iteration0Cost difference of line node
Figure GDA0003061510990000169
12) In the constraint condition coefficient matrix A, a base variable row number set is selected
Figure GDA00030615109900001610
The corresponding columns form a submatrix B(r)(ii) a Calculating the influence coefficient vector of the virtual bid on the right constant vector b of the constraint condition
Figure GDA00030615109900001611
Wherein, the vector b(0),b*Directly from steps 7) and 8);
13) solving inequality
Figure GDA00030615109900001612
Obtaining bid amount
Figure GDA00030615109900001613
Feasible projection scalar interval
Figure GDA00030615109900001614
Holding nodes for the r-th iteration respectivelyThrowing scalar quantity under the condition of constant price difference
Figure GDA00030615109900001615
The lower limit and the upper limit of allowable variation of (2); when bid amount
Figure GDA00030615109900001616
When the SCED model is changed in the range, the line number set of the basic variable and the non-basic variable when the SCED model obtains the optimal solution in the day ahead
Figure GDA00030615109900001617
Does not change, and has a node price difference delta p(r)Also remains unchanged;
14) for solving bid amount greater than
Figure GDA00030615109900001618
The price difference of the time node and the updated projection quantity
Figure GDA00030615109900001619
Wherein epsilon is a minimum value, which is less than 0.01, and is 0.001; projection quantity
Figure GDA00030615109900001620
Greater than the node valence difference Δ p(r)Maximum allowable bid amount when held constant
Figure GDA00030615109900001621
15) Iteration: let r be r +1, model variables in equations (11) to (17)
Figure GDA00030615109900001622
Returning to the step 7) again;
16) the iteration process is completed, and all feasible projection quantities are solved. Recording all feasible projection quantity intervals in each iteration process
Figure GDA00030615109900001623
With corresponding node price difference Δ p(r). In bid amount
Figure GDA00030615109900001624
The node price difference is a dependent variable, and a stair-shaped curve can be drawn. According to the step-shaped curve, the influence condition of the virtual bidding on the price difference of the nodes of the electric power market in the day before can be directly obtained.
The relation curve obtained in the step 16) with the virtual bid amount as an independent variable and the node price difference as a dependent variable enables a user to visually observe the node price difference of the power market in the day before caused by virtual bidding, and provides technical support for a supervising agency to supervise arbitrage behavior in which the virtual bidding participates.
Thus, the method provided by the invention is implemented.
It is worth mentioning that the objective function in the implementation steps provided by the invention can be flexibly selected and customized according to needs, constraint conditions can be added and deleted according to actual needs, and the expandability is strong; therefore, the above implementation steps are only used for illustrating and not limiting the technical solution of the present invention; any modification or partial replacement without departing from the spirit and scope of the present invention should be covered in the claims of the present invention.

Claims (1)

1. A method for calculating the influence of virtual bidding on the price difference of nodes in the power market in the day before is characterized by comprising the following steps:
1) acquiring the trading basic data of the power grid system corresponding to the power market in the day ahead, wherein the trading basic data comprises the following steps: the method comprises the following steps that the power market corresponds to power grid system topology data, load demand of each node in the power grid system and basic data of each generator set in the day ahead;
wherein, the power grid system topology data corresponding to the day-ahead power market comprises: the day-ahead electric power market corresponds to the interconnection relationship between the nodes and the lines of the power grid system and the active power flow limit of each power transmission line;
the basic data of each generator set comprises: the maximum and minimum power generation capacity of the unit, the maximum climbing rate of the unit, the minimum continuous on-off time of the unit, the single-time starting cost of the unit and the running cost data of the unit;
2) selecting day aheadThe line of the virtual bidding node in the power market is marked as j0Wherein j is0∈{1,2,...,nB}；j0The nodes at both ends are respectively k0,k1Wherein k is0,k1E {1, 2.., n }; selecting the time interval as t0Wherein t is0∈{1,2,...,T}；nBN and T are the total number of lines, the total number of nodes and the total number of time periods in the system respectively;
3) let the initial value r of iteration number r be 0, let the initial bid amount
Figure FDA0003061510980000011
4) Constructing a power market power trading unified clearing model in the day ahead; the method comprises the following specific steps:
4-1) constructing a target function of a power trading unified clearing model of a power market in the day before, wherein the expression is as follows:
Figure FDA0003061510980000012
wherein i is the number of the unit, nGThe total number of the units in the system; t is a time interval number;
Figure FDA0003061510980000013
representing the power generation output of the ith unit in the t time period during the r iteration,
Figure FDA0003061510980000014
the power generation output of the ith unit in the t period is
Figure FDA0003061510980000015
The cost of operation;
Figure FDA0003061510980000016
the starting cost of the ith unit in the t time period;
Figure FDA0003061510980000017
the shutdown cost of the ith unit in the t time period;
cost of starting up
Figure FDA0003061510980000018
Wherein
Figure FDA0003061510980000019
The single starting cost of the ith unit;
Figure FDA00030615109800000110
the state of the startup and shutdown of the ith unit in the t time interval during the r iteration is represented as a variable of 0 and 1,
Figure FDA00030615109800000111
the unit is shown to be in a starting state,
Figure FDA00030615109800000112
indicating the unit is in a shutdown state
Figure FDA00030615109800000113
4-2) determining constraint conditions of the unified clearing model of the electric power trade of the electric power market in the day before, wherein the constraint conditions are as follows:
4-2-1) energy balance constraints:
Figure FDA00030615109800000114
wherein k is the number of the node;
Figure FDA00030615109800000115
the load demand of the kth node in the t period;
Figure FDA00030615109800000116
at the t-th in the day-ahead power market for the r-th iteration0Time period pair k0Node pointA bid amount of the virtual bid performed;
4-2-2) rotational standby constraint:
Figure FDA0003061510980000021
wherein the content of the first and second substances,
Figure FDA0003061510980000022
the maximum allowable output of the ith unit; r isreserveThe load reserve rate of the system;
4-2-3) restraining the upper limit and the lower limit of the output of the machine set:
Figure FDA0003061510980000023
wherein the content of the first and second substances,
Figure FDA0003061510980000024
the minimum allowable output of the ith unit;
4-2-4) maximum climbing rate constraint of the unit:
Figure FDA0003061510980000025
Figure FDA0003061510980000026
wherein the content of the first and second substances,
Figure FDA0003061510980000027
the maximum allowable climbing speed for climbing under the ith unit,
Figure FDA0003061510980000028
the maximum allowable climbing speed of the climbing on the ith unit is obtained;
4-2-5) minimum continuous on-off time constraint of the unit:
Figure FDA0003061510980000029
Figure FDA00030615109800000210
wherein the content of the first and second substances,
Figure FDA00030615109800000211
for the minimum allowed continuous boot time of the ith unit,
Figure FDA00030615109800000212
the minimum allowable continuous shutdown time of the ith unit is obtained; when t is less than or equal to 0,
Figure FDA00030615109800000213
4-2-6) maximum active power flow constraint of the power transmission line:
Figure FDA00030615109800000214
Figure FDA00030615109800000215
wherein j is the serial number of the line;
Figure FDA00030615109800000216
the maximum allowable active power flow of the jth power transmission line; pj,kThe method comprises the steps that the jth row and kth column elements of a power transmission distribution factor matrix in a direct current power flow model of a power transmission system are defined;
5) solving the power trading unified clearing model of the power market in the day before established in the step 4) and judging: if there is an optimal solution, the system will,then obtaining the unified clearing result of the power trading of the power market in the day before the r iteration
Figure FDA00030615109800000217
And
Figure FDA00030615109800000218
entering step 6); if no optimal solution exists, jumping to the step 16);
6) obtained by solving in the step 4)
Figure FDA0003061510980000031
Substituting the current power market power trading unified clearing model in the step 4) to obtain a current power market safety constraint economic dispatching SCED model; the method comprises the following specific steps:
6-1) constructing an objective function of the SCED model of the day-ahead power market, wherein the expression is as follows:
Figure FDA0003061510980000032
6-2) determining the constraint conditions of the SCED model of the power market at the day before, wherein the constraint conditions are as follows:
6-2-1) energy balance constraints:
Figure FDA0003061510980000033
6-2-2) restraining the upper and lower limits of the unit output:
Figure FDA0003061510980000034
Figure FDA0003061510980000035
6-2-3) maximum climbing rate constraint of the unit:
Figure FDA0003061510980000036
Figure FDA0003061510980000037
Figure FDA0003061510980000038
Figure FDA0003061510980000039
6-2-4) maximum active power flow constraint of the power transmission line:
Figure FDA00030615109800000310
Figure FDA00030615109800000311
7) converting the SCED model of the day-ahead power market established in the step 6) into a linear programming model in a standard form, wherein the expression is as follows:
Figure FDA00030615109800000312
wherein A is a constraint condition coefficient matrix, and each row in the constraint condition coefficient matrix A corresponds to each constraint condition in the formulas (11) to (17); b(r)Is a constraint right-end constant vector at the time of the r-th iteration, cTIs a target function value coefficient vector, lb is a variable lower limit vector, ub is a variable upper limit vector; x is the number of(r)The model variable vector at the r iteration is;
8) and (3) judging the value of r: if r is 0, go to step 9); if r ≠ 0, then proceed to step 10);
9) when r is 0, make the bid amount
Figure FDA0003061510980000041
And (12) and (17) are updated, the expressions (11), (13), (14), (15) and (16) are kept unchanged, and the future electric power market SCED model at the moment is derived in a standard form, wherein the expressions are as follows:
Figure FDA0003061510980000042
wherein, b*As bid amount
Figure FDA0003061510980000043
Constraint conditions of time right-hand constant vectors;
10) solving the standard form of the SCED model of the day-ahead electric power market shown in the formula (18) by a simplex method and judging: if no feasible solution exists, the step 5) is returned again, and the current projection quantity is solved again
Figure FDA0003061510980000044
On-off state of each unit
Figure FDA0003061510980000045
If a feasible solution exists, obtaining a clear result x of the r-th iteration of the SCED model of the power market in the day before(r)Wherein x is(r)The partial variable with the value of 0 is the non-base variable, the partial variable with the value of 0 is the base variable, x is(r)The line number sets of the middle base variable and the non-base variable are respectively marked as
Figure FDA0003061510980000046
11) According to node electricity price formula
Figure FDA0003061510980000047
Solving node electricity prices of all time periods of all nodes of system in the nth iteration
Figure FDA0003061510980000048
Wherein λt,(r)Is a dual variable of the constraint (12),
Figure FDA0003061510980000049
the upper bound dual variable and the lower bound dual variable of the constraint conditions (16) and (17) respectively; at this time, j is the amount of no bid in the r-th iteration0Cost difference of line node
Figure FDA00030615109800000410
12) In the constraint condition coefficient matrix A, a base variable row number set is selected
Figure FDA00030615109800000411
The corresponding columns form a submatrix B(r)(ii) a Calculating the influence coefficient vector delta b of the virtual bid on the right constant vector b of the constraint condition(r)＝(B(r))-1(b*-b(0))；
13) Solving inequality
Figure FDA00030615109800000412
Obtaining bid amount
Figure FDA00030615109800000413
Feasible projection scalar interval
Figure FDA00030615109800000414
Figure FDA00030615109800000415
Respectively throwing scalar quantities under the condition of keeping node price difference unchanged during the r-th iteration
Figure FDA00030615109800000416
The lower limit and the upper limit of allowable variation of (2);
14) updating a projection quantity
Figure FDA00030615109800000417
Epsilon is less than 0.01 so that the bid amount
Figure FDA00030615109800000418
Is greater than
Figure FDA00030615109800000419
15) Let r be r +1, model variables in equations (11) to (17)
Figure FDA00030615109800000420
Returning to the step 7) again;
16) completing iteration, recording all feasible projection quantity intervals in each iteration process
Figure FDA00030615109800000421
With corresponding node price difference Δ p(r)(ii) a In bid amount
Figure FDA00030615109800000422
And obtaining a step-shaped curve of the influence of the virtual bid on the node price difference of the electric power market in the day before by taking the node price difference as a dependent variable, and ending the method.
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