CN111030110A - Robust cooperative scheduling method for electric power-natural gas coupling system considering electric power conversion gas consumption wind power - Google Patents

Robust cooperative scheduling method for electric power-natural gas coupling system considering electric power conversion gas consumption wind power Download PDF

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CN111030110A
CN111030110A CN201911387565.9A CN201911387565A CN111030110A CN 111030110 A CN111030110 A CN 111030110A CN 201911387565 A CN201911387565 A CN 201911387565A CN 111030110 A CN111030110 A CN 111030110A
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张亚超
郑峰
黄张浩
林佳壕
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Abstract

The invention relates to a robust collaborative scheduling method of an electric power-natural gas coupling system considering electric power conversion and wind power consumption, and establishes a two-stage robust scheduling model of the electric power-natural gas coupling system considering wind power output uncertainty. Firstly, establishing a day-ahead scheduling model of a first stage of an electric-gas coupling system by combining a wind power output reference prediction scene; then, constructing a second-stage real-time scheduling model of the electric-gas coupling system under the wind power output uncertain set; and finally, converting the double-layer optimization problem with the min-max structure into a single-layer optimization problem to solve by combining a main and sub problem solving frame and a column constraint generation method. The method can be applied to the scheduling decision making of the power-natural gas coupling system comprising the power-to-gas conversion device and the wind turbine generator, and is beneficial to improving the effectiveness and reliability of the scheduling scheme under the uncertain operation environment.

Description

Robust cooperative scheduling method for electric power-natural gas coupling system considering electric power conversion gas consumption wind power
Technical Field
The invention relates to the technical field of collaborative optimization scheduling of an electric power-natural gas coupling system, in particular to a robust collaborative scheduling method of the electric power-natural gas coupling system considering electric power conversion and wind power consumption.
Background
At present, for theoretical research on optimal scheduling of a power-natural gas coupling system considering wind power uncertainty, a random planning method and an interval optimization method are mainly used. The two solving methods aiming at the optimization problem containing the uncertainty have the defects. In addition, the random planning method generates a large amount of wind power output original scene sets, the time cost for directly carrying out modeling calculation is too high, and the decision risk consideration is possibly insufficient by adopting scene subtraction. On the other hand, the interval optimization method obtains a scheduling decision expressed in the form of an interval number, and is difficult to be directly used in actual engineering.
Disclosure of Invention
In view of the above, the invention aims to provide a robust cooperative scheduling method for a power-natural gas coupling system considering electricity, gas and wind power consumption, a robust optimization model is constructed, and a scheduling decision obtained by using the robust optimization model can improve the effectiveness and reliability of a scheduling scheme in an uncertain operation environment.
The invention is realized by adopting the following scheme: a robust cooperative scheduling method for a power-natural gas coupling system considering electricity to gas and wind power consumption comprises the following steps:
step S1: establishing a day-ahead scheduling objective function of the power-natural gas coupling system in a first stage under a wind power output reference scene; respectively constructing an electric power system operation constraint, a natural gas network operation constraint and a coupling operation constraint of the electric power system and the natural gas system;
step S2: constructing a real-time scheduling objective function of a second stage of the power-natural gas coupling system under the wind power output uncertainty set; respectively constructing the operation constraints and the coupling constraints of the electric power and natural gas networks at the second stage;
step S3: combining the first-stage and second-stage scheduling models constructed in the steps S1 and S2 to form a two-stage robust scheduling model of the power-natural gas coupling system, and converting the two-stage robust scheduling model into a main problem and a sub problem by using a main and sub problem solving framework;
step S4: converting the double-layer optimization sub-problem with the max-min form in the step S3 into a single-layer linear optimization problem by combining a dual theory and an extreme point method, and establishing an iterative solution flow of the robust scheduling model in the step S3 by adopting a column constraint generation method;
step S5: and (3) solving the two-stage robust scheduling model in the step S3 by using a CPLEX solver under the Matlab platform and by using the iterative solving process in the step S4 to obtain a robust scheduling scheme of the two-stage robust scheduling model, so as to realize robust cooperative scheduling of the power-natural gas coupled system.
Further, the step S1 specifically includes the following steps:
step S11, establishing a day-ahead scheduling objective function of the first stage of the power-natural gas coupling system under the wind power output reference scene as follows:
Figure BDA0002342393600000021
in the formula, function f1An objective function representing a first stage operating cost; t is the total scheduling time period number; cfuelIs the fuel price;
Figure BDA0002342393600000031
the price of the upper/lower standby capacity of the unit i;
Figure BDA0002342393600000032
up/down reserve capacity price for electric gas (Powertogas, PtG) equipment j;
Figure BDA0002342393600000033
the power of the unit i in the time period t under a reference scene;
Figure BDA0002342393600000034
the output of an electrical switching device, namely PtG device j, in a reference scene in a time period t;
Figure BDA0002342393600000035
the up/down spare capacity is provided for the unit i in the t time period;
Figure BDA0002342393600000036
upper/lower spare capacity for PtG device j for time period t;
Figure BDA0002342393600000037
representing the on/off cost of the unit i in the time period t; fiThe power generation cost function of the unit i is obtained;
step S12, establishing the first stage electric power system operation constraint conditions as follows:
Figure BDA0002342393600000038
in the formula, PimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set; pjmaxPtG maximum output of device j;
Figure BDA0002342393600000039
the on/off duration of the unit i to the time period t-1;
Figure BDA00023423936000000310
minimum on/off duration for unit i;
Figure BDA00023423936000000311
the up/down climbing rate of the unit i;
Figure BDA00023423936000000312
is PtGThe up/down ramp rate of device j; i, j and k are serial numbers of the generator set, the PtG equipment and the wind power plant which are connected with the node h in sequence;
Figure BDA00023423936000000313
the predicted output of the wind power plant j in the time period t is obtained;
Figure BDA00023423936000000314
the injected power for node h at time period t; k is a radical oflhThe sensitivity factor of the line l to the node h; f. oflmaxIs the maximum transmission power of line l;
step S13, establishing the operation constraint conditions of the natural gas system in the first stage as follows:
Figure BDA0002342393600000041
in the formula, QstThe air supply flow is the air supply flow of the air source s in the time period t; qsmax/QsminThe upper limit/lower limit of the air supply quantity of the air source; pietPressure for gas network node e at time period t; piemax/πeminUpper/lower pressure limits for gas network node e; q. q.smn(t)The average flow through the pipe mn at the time t; cmnIs the pipeline comprehensive coefficient; l ismn(t)Storing the pipeline mn for t time period;
Figure BDA0002342393600000042
the input/output flow of the pipeline mn in the t period; gamma-shapedcThe compression coefficient of the air compressor; egtThe gas storage quantity of the gas storage device g in the time period t is obtained;
Figure BDA0002342393600000043
the input/output flow of the gas storage device in the time period t; egmax/EgminThe maximum/minimum gas storage amount of the gas storage device; qgmax/QgminMaximum/minimum gas flow rate of the gas storage device;
Figure BDA0002342393600000044
represents the air load of node e during time period t;
Figure BDA0002342393600000045
the gas consumption of the gas unit i is a time period t;
and step S14, establishing the coupling operation constraint of the electric power system and the natural gas system in the first stage as follows:
Figure BDA0002342393600000051
in the formula, HHV is the high calorific value of natural gas;
Figure BDA0002342393600000052
representing the number set of gas turbine units,. tau. energy conversion coefficient ηPtGConversion efficiency for the PtG device;
Figure BDA0002342393600000053
representing PtG a set of device numbers;
Figure BDA0002342393600000054
the upper limit/lower limit of the gas consumption of the gas unit in the period i and the period t;
Figure BDA0002342393600000055
is PtG upper/lower limit of the gas production of the device.
Further, the step S2 specifically includes the following steps:
step S21, establishing a real-time scheduling objective function of the second stage of the power-natural gas coupling system under the uncertain wind power output set as follows:
Figure BDA0002342393600000056
in the formula, the outer layer max is used for identifying the worst scene of the real-time output of the wind power; the inner-layer min is used for seeking the minimum value of the real-time scheduling cost in the worst wind power scene;
Figure BDA0002342393600000057
representing the actual output of the wind farm k in a time period t; cwindAnd CloadPunishment cost coefficients of wind abandonment and load abandonment are respectively; n is a radical ofwAnd NhRespectively the number of wind power plants and the number of load nodes;
Figure BDA0002342393600000058
representing the air curtailment quantity of the wind power plant k in the period t;
Figure BDA0002342393600000059
representing the involuntary load abandoning amount of the load node h in the period t;
Figure BDA00023423936000000510
adjusting the price for the upper/lower standby of the unit i;
Figure BDA00023423936000000511
adjust the price for the up/down standby of PtG device j;
Figure BDA00023423936000000512
adjusting output force for the up/down adjustment of the unit i in the t period;
Figure BDA0002342393600000061
adjust out force up/down for t period PtG device j;
step S22: the power system operation constraint conditions for establishing the second stage of the power-natural gas coupling system are as follows:
Figure BDA0002342393600000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002342393600000063
the actual injected power for node h during time t.
Step S23: establishing natural gas system operation constraint of a second stage of the electric power-natural gas coupling system and coupling operation constraint of the electric power system and the natural gas system, wherein variables to be solved under a natural gas system reference scene are expressed as follows:
Figure BDA0002342393600000064
when the gas consumption of the gas unit is
Figure BDA0002342393600000065
PtG the equipment gas production is
Figure BDA0002342393600000066
In extreme conditions, the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure BDA0002342393600000067
similarly, when the gas consumption of the gas unit is
Figure BDA0002342393600000068
PtG the equipment gas production is
Figure BDA0002342393600000069
In the extreme case of (3), the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure BDA0002342393600000071
further, the step S3 specifically includes the following steps:
step S31: representing a first-stage decision variable and a natural gas system decision variable of an electric power system in the electric power-natural gas coupled system by using a vector X, and representing a second-stage decision variable of the electric power system by using a vector Y, so that a two-stage robust scheduling model of the electric power-natural gas coupled system is represented as follows:
Figure BDA0002342393600000072
in the formula, c, b, d and h are coefficient vectors, and A, G, E, M is a coefficient matrix;
step S32: the above double-layer optimization model with the max-min form is converted into the following main problem MP and sub problem SP:
Figure BDA0002342393600000073
Figure BDA0002342393600000074
further, the step S4 specifically includes the following steps:
step S41: combining the dual theory, the subproblem SP in formula (12) is transformed into the following single-layer optimization problem:
Figure BDA0002342393600000081
in the formula, mu is a decision variable of a dual problem;
step S42: combining an extreme point method, converting bilinear terms in the target function of the formula (13), and converting vectors
Figure BDA0002342393600000082
Middle element
Figure BDA0002342393600000083
Element mu in sum vector mudProduct of (2)
Figure BDA0002342393600000084
The following transformations were carried out:
Figure BDA0002342393600000085
in the formula (I), the compound is shown in the specification,
Figure BDA0002342393600000086
and
Figure BDA0002342393600000087
β as auxiliary continuous variable0，β+And β-Is an auxiliary binary integer variable; m is a sufficiently large positive number;
step S43: and establishing a solving flow of the main problem and the subproblems by adopting a column constraint generation method.
Further, the step S43 specifically includes the following steps:
step S431: setting the upper and lower bound initial values L of the optimization problemb＝-∞，UbInfinity, +,; the initial iteration number K is 0; the maximum gap between the upper and lower boundaries is epsilon;
step S432: solving the main problem MP of the formula (11) to obtain the optimal solution
Figure BDA0002342393600000088
And updates the upper bound of the optimization problem to:
Figure BDA0002342393600000089
step S433: solving the dual problem of the sub-problem SP shown in the formula (13), wherein X in the objective function is the one obtained in the step S432
Figure BDA00023423936000000810
The optimal solution of the formula (13) is obtained
Figure BDA00023423936000000811
The optimum value is
Figure BDA00023423936000000812
The lower bound is updated as:
Figure BDA00023423936000000813
step S434: if U is presentb-LbIf the value is less than or equal to epsilon, the iteration process is terminated, and the obtained optimal decision result is
Figure BDA00023423936000000814
Otherwise add an auxiliary variable YK+1And the corresponding constraint conditional expressions (15) to the main question MP, update the iteration number K to K +1, and return to step S432.
Figure BDA0002342393600000091
Compared with the prior art, the invention has the following beneficial effects:
the invention adopts the electricity-to-gas technology and the gas turbine as the coupling elements to promote the energy bidirectional flow and the deep coupling between the power system and the natural gas system, provides a new way for the consumption of renewable energy sources, and establishes the two-stage robust scheduling model of the power-natural gas coupling system on the basis of the way, thereby being beneficial to improving the effectiveness and the reliability of scheduling decision.
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FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a diagram of the configuration of the reserve capacity of the unit in consideration of the operation constraint of the air grid according to the embodiment of the present invention.
Fig. 3 is a diagram of the configuration of the reserve capacity of the unit in consideration of the operation constraint of the gas grid and the electric-to-gas conversion according to the embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the embodiment provides a robust cooperative scheduling method for a power-natural gas coupling system considering electricity to gas to consume wind power, which includes the following steps:
step S1: establishing a day-ahead scheduling objective function of the power-natural gas coupling system in a first stage under a wind power output reference scene; respectively constructing an electric power system operation constraint, a natural gas network operation constraint and a coupling operation constraint of the electric power system and the natural gas system;
step S2: constructing a real-time scheduling objective function of a second stage of the power-natural gas coupling system under the wind power output uncertainty set; respectively constructing the operation constraints and the coupling constraints of the electric power and natural gas networks at the second stage;
step S3: combining the first-stage and second-stage scheduling models constructed in the steps S1 and S2 to form a two-stage robust scheduling model of the power-natural gas coupling system, and converting the two-stage robust scheduling model into a main problem and a sub problem by using a main and sub problem solving framework;
step S4: converting the double-layer optimization sub-problem with the max-min form in the step S3 into a single-layer linear optimization problem by combining a dual theory and an extreme point method, and establishing an iterative solution flow of the robust scheduling model in the step S3 by adopting a column constraint generation method;
step S5: and (3) solving the two-stage robust scheduling model in the step S3 by using a CPLEX solver under the Matlab platform and by using the iterative solving process in the step S4 to obtain a robust scheduling scheme of the two-stage robust scheduling model, so as to realize robust cooperative scheduling of the power-natural gas coupled system.
In this embodiment, the step S1 specifically includes the following steps:
step S11, establishing a day-ahead scheduling objective function of the first stage of the power-natural gas coupling system under the wind power output reference scene as follows:
Figure BDA0002342393600000101
in the formula, function f1Represents the firstAn objective function of phase operating cost; t is the total scheduling time period number; cfuelIs the fuel price;
Figure BDA0002342393600000111
the price of the upper/lower standby capacity of the unit i;
Figure BDA0002342393600000112
up/down reserve capacity price for electric gas (Powertogas, PtG) equipment j;
Figure BDA0002342393600000113
the power of the unit i in the time period t under a reference scene;
Figure BDA0002342393600000114
the output of an electrical switching device, namely PtG device j, in a reference scene in a time period t;
Figure BDA0002342393600000115
the up/down spare capacity is provided for the unit i in the t time period;
Figure BDA0002342393600000116
upper/lower spare capacity for PtG device j for time period t;
Figure BDA0002342393600000117
representing the on/off cost of the unit i in the time period t; fiThe power generation cost function of the unit i is obtained;
step S12, establishing the first stage electric power system operation constraint conditions as follows:
Figure BDA0002342393600000118
in the formula, PimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set; pjmaxPtG maximum output of device j;
Figure BDA0002342393600000119
the on/off duration of the unit i to the time period t-1;
Figure BDA00023423936000001110
minimum on/off duration for unit i;
Figure BDA00023423936000001111
the up/down climbing rate of the unit i;
Figure BDA00023423936000001112
PtG uphill/downhill speed for device j; i, j and k are serial numbers of the generator set, the PtG equipment and the wind power plant which are connected with the node h in sequence;
Figure BDA00023423936000001113
the predicted output of the wind power plant j in the time period t is obtained;
Figure BDA0002342393600000121
the injected power for node h at time period t; k is a radical oflhThe sensitivity factor of the line l to the node h; f. oflmaxIs the maximum transmission power of line l;
step S13, establishing the operation constraint conditions of the natural gas system in the first stage as follows:
Figure BDA0002342393600000122
in the formula, QstThe air supply flow is the air supply flow of the air source s in the time period t; qsmax/QsminThe upper limit/lower limit of the air supply quantity of the air source; pietPressure for gas network node e at time period t; piemax/πeminUpper/lower pressure limits for gas network node e; q. q.smn(t)The average flow through the pipe mn at the time t; cmnIs the pipeline comprehensive coefficient; l ismn(t)Storing the pipeline mn for t time period;
Figure BDA0002342393600000123
the input/output flow of the pipeline mn in the t period; gamma-shapedcThe compression coefficient of the air compressor; egtThe gas storage quantity of the gas storage device g in the time period t is obtained;
Figure BDA0002342393600000124
the input/output flow of the gas storage device in the time period t; egmax/EgminThe maximum/minimum gas storage amount of the gas storage device; qgmax/QgminMaximum/minimum gas flow rate of the gas storage device;
Figure BDA0002342393600000125
represents the air load of node e during time period t;
Figure BDA0002342393600000126
the gas consumption of the gas unit i is a time period t;
and step S14, establishing the coupling operation constraint of the electric power system and the natural gas system in the first stage as follows:
Figure BDA0002342393600000131
in the formula, HHV is the high calorific value of natural gas;
Figure BDA0002342393600000132
representing the number set of gas turbine units,. tau. energy conversion coefficient ηPtGConversion efficiency for the PtG device;
Figure BDA0002342393600000133
representing PtG a set of device numbers;
Figure BDA0002342393600000134
the upper limit/lower limit of the gas consumption of the gas unit in the period i and the period t;
Figure BDA0002342393600000135
is PtG upper/lower limit of the gas production of the device.
In this embodiment, the step S2 specifically includes the following steps:
step S21, establishing a real-time scheduling objective function of the second stage of the power-natural gas coupling system under the uncertain wind power output set as follows:
Figure BDA0002342393600000136
in the formula, the outer layer max is used for identifying the worst scene of the real-time output of the wind power; the inner-layer min is used for seeking the minimum value of the real-time scheduling cost in the worst wind power scene;
Figure BDA0002342393600000137
representing the actual output of the wind farm k in a time period t; cwindAnd CloadPunishment cost coefficients of wind abandonment and load abandonment are respectively; n is a radical ofwAnd NhRespectively the number of wind power plants and the number of load nodes;
Figure BDA0002342393600000138
representing the air curtailment quantity of the wind power plant k in the period t;
Figure BDA0002342393600000139
representing the involuntary load abandoning amount of the load node h in the period t;
Figure BDA00023423936000001310
adjusting the price for the upper/lower standby of the unit i;
Figure BDA00023423936000001311
adjust the price for the up/down standby of PtG device j;
Figure BDA00023423936000001312
adjusting output force for the up/down adjustment of the unit i in the t period;
Figure BDA0002342393600000141
adjust out force up/down for t period PtG device j;
step S22: the power system operation constraint conditions for establishing the second stage of the power-natural gas coupling system are as follows:
Figure BDA0002342393600000142
in the formula (I), the compound is shown in the specification,
Figure BDA0002342393600000143
the actual injected power for node h during time t.
Step S23: establishing natural gas system operation constraint of a second stage of the electric power-natural gas coupling system and coupling operation constraint of the electric power system and the natural gas system, wherein variables to be solved under a natural gas system reference scene are expressed as follows:
Figure BDA0002342393600000144
when the gas consumption of the gas unit is
Figure BDA0002342393600000145
PtG the equipment gas production is
Figure BDA0002342393600000146
In extreme conditions, the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure BDA0002342393600000147
similarly, when the gas consumption of the gas unit is
Figure BDA0002342393600000148
PtG the equipment gas production is
Figure BDA0002342393600000149
In the extreme case of (3), the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure BDA0002342393600000151
in this embodiment, the step S3 specifically includes the following steps:
step S31: representing a first-stage decision variable and a natural gas system decision variable of an electric power system in the electric power-natural gas coupled system by using a vector X, and representing a second-stage decision variable of the electric power system by using a vector Y, so that a two-stage robust scheduling model of the electric power-natural gas coupled system is represented as follows:
Figure BDA0002342393600000152
in the formula, c, b, d and h are coefficient vectors, and A, G, E, M is a coefficient matrix;
step S32: the above double-layer optimization model with the max-min form is converted into the following main problem MP and sub problem SP:
Figure BDA0002342393600000153
Figure BDA0002342393600000154
in this embodiment, the step S4 specifically includes the following steps:
step S41: combining the dual theory, the subproblem SP in formula (12) is transformed into the following single-layer optimization problem:
Figure BDA0002342393600000161
in the formula, mu is a decision variable of a dual problem;
step S42: combining an extreme point method, converting bilinear terms in the target function of the formula (13), and converting vectors
Figure BDA0002342393600000162
Middle element
Figure BDA0002342393600000163
Element mu in sum vector mudProduct of (2)
Figure BDA0002342393600000164
The following transformations were carried out:
Figure BDA0002342393600000165
in the formula (I), the compound is shown in the specification,
Figure BDA0002342393600000166
and
Figure BDA0002342393600000167
β as auxiliary continuous variable0，β+And β-Is an auxiliary binary integer variable; m is a sufficiently large positive number;
step S43: and establishing a solving flow of the main problem and the subproblems by adopting a column constraint generation method.
In this embodiment, the step S43 specifically includes the following steps:
step S431: setting the upper and lower bound initial values L of the optimization problemb＝-∞，UbInfinity, +,; the initial iteration number K is 0; the maximum gap between the upper and lower boundaries is epsilon;
step S432: solving the main problem MP of the formula (11) to obtain the optimal solution
Figure BDA0002342393600000168
And updates the upper bound of the optimization problem to:
Figure BDA0002342393600000169
step S433: solving the dual problem of the sub-problem SP shown in the formula (13), wherein X in the objective function is the one obtained in the step S432
Figure BDA00023423936000001610
The optimal solution of the formula (13) is obtained
Figure BDA00023423936000001611
The optimum value is
Figure BDA00023423936000001612
The lower bound is updated as:
Figure BDA00023423936000001613
step S434: if U is presentb-LbIf the value is less than or equal to epsilon, the iteration process is terminated, and the obtained optimal decision result is
Figure BDA00023423936000001614
Otherwise add an auxiliary variable YK+1And the corresponding constraint conditional expressions (15) to the main question MP, update the iteration number K to K +1, and return to step S432.
Figure BDA0002342393600000171
Preferably, in this embodiment, the two-stage robust optimization problem can be converted into a single-layer mixed integer linear programming problem by the derivation, and a CPLEX solver is used to solve the problem.
Preferably, the robust optimization collaborative scheduling model of the power-natural gas coupled system established in the embodiment is beneficial to improving the effectiveness and reliability of scheduling decisions.
Preferably, the present embodiment performs test example simulation in an MATLAB environment, and performs model solution by using a CPLEX solver. The modeling solution flow is shown in figure 1.
The two-stage robust model of the embodiment takes the minimum sum of the operation costs of the pre-dispatching stage and the re-dispatching stage of the power system as an objective function, and includes the operation constraint of the power system, the operation constraint of the natural gas system and the coupling operation constraint condition of the system.
According to a specific example of the embodiment, the two-stage robust optimization method is applied to an improved IEEE-24 node power system and a 12-node natural gas system for verification, wherein G1-G3 are gas generating sets, G4-G10 are thermal generating sets, and a node 19 is connected to the wind generating sets.
In this embodiment, the following three scheduling scenarios are constructed:
scenario 1: the method comprises the following steps of (1) performing two-stage robust scheduling on the power system without considering the operation constraint of a gas network;
scenario 2: two-stage robust scheduling of the electrical coupling system considering the operation constraint of the air network;
scenario 3: an electrically coupled system two-stage robust scheduling that takes into account the gas grid operating constraints and the PtG technique.
The simulation results are shown in table 1:
table 1 simulation results for different scheduling scenarios
Figure BDA0002342393600000172
Figure BDA0002342393600000181
Analysis of the simulation results obtained by the different methods in table 1 shows that: scenario 2, which accounts for the operating constraints of the gas network, has an increased operating cost in both the first and second phases compared to scenario 1, while scenario 3, which has access to PtG equipment, has a significantly lower total operating cost for robust scheduling decisions compared to scenario 2. The cooperative scheduling of the power-natural gas coupled system taking the electric-to-gas technology into consideration provided by the embodiment is proved to be capable of obtaining a scheduling decision with more excellent performance.
Fig. 2 is the configuration of the upper and lower reserve capacities of the unit under the robust scheduling decision in consideration of the operation constraint of the gas network in the scenario 2, and fig. 3 is the configuration of the upper and lower reserve capacities of the unit under the robust scheduling decision in consideration of the operation constraint of the gas network and the power-to-gas conversion in the scenario 3. As can be seen from fig. 2 and 3, PtG equipment can provide as much lower spare capacity as possible after the electrical switching technology is adopted, and spare capacity configuration required to be provided by a unit is reduced, so that a more superior scheduling scheme is obtained.
The main process realized by the embodiment comprises the establishment of a robust cooperative scheduling model of the two-stage power-natural gas coupling system and a conversion and solving method of the model.
According to the method, a first-stage mathematical model taking the day-ahead operation cost of the electric power-natural gas coupling system in a reference prediction scene as an objective function and a second-stage mathematical model taking the real-time operation cost of the wind power uncertain set coupling system as the objective function are established, and the electric-gas coupling system is optimally scheduled by taking the minimum total operation cost of two stages as a target.
In the aspect of model conversion and solution, the double-layer optimization problem containing uncertain quantity is converted into a single-layer optimization problem to be solved by combining a dual theory, an extreme point method and a column constraint generation method, so that an optimal decision scheme of the power-natural gas coupling system in the worst wind power output scene is found.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (6)

1. A robust cooperative scheduling method for a power-natural gas coupling system considering electricity to gas and wind power consumption is characterized by comprising the following steps: the method comprises the following steps:
step S1: establishing a day-ahead scheduling objective function of the power-natural gas coupling system in a first stage under a wind power output reference scene; respectively constructing an electric power system operation constraint, a natural gas network operation constraint and a coupling operation constraint of the electric power system and the natural gas system;
step S2: constructing a real-time scheduling objective function of a second stage of the power-natural gas coupling system under the wind power output uncertainty set; respectively constructing the operation constraints and the coupling constraints of the electric power and natural gas networks at the second stage;
step S3: combining the first-stage and second-stage scheduling models constructed in the steps S1 and S2 to form a two-stage robust scheduling model of the power-natural gas coupling system, and converting the two-stage robust scheduling model into a main problem and a sub problem by using a main and sub problem solving framework;
step S4: converting the double-layer optimization sub-problem with the max-min form in the step S3 into a single-layer linear optimization problem by combining a dual theory and an extreme point method, and establishing an iterative solution flow of the robust scheduling model in the step S3 by adopting a column constraint generation method;
step S5: and (3) solving the two-stage robust scheduling model in the step S3 by using a CPLEX solver under the Matlab platform and by using the iterative solving process in the step S4 to obtain a robust scheduling scheme of the two-stage robust scheduling model, so as to realize robust cooperative scheduling of the power-natural gas coupled system.
2. The robust cooperative scheduling method of the power-natural gas coupled system considering electricity to gas to consume wind power of claim 1, wherein:
the step S1 specifically includes the following steps:
step S11, establishing a day-ahead scheduling objective function of the first stage of the power-natural gas coupling system under the wind power output reference scene as follows:
Figure FDA0002342393590000021
in the formula, function f1An objective function representing a first stage operating cost; t is the total scheduling time period number; cfuelIs the fuel price;
Figure FDA0002342393590000022
the price of the upper/lower standby capacity of the unit i;
Figure FDA0002342393590000023
the up/down reserve capacity price for the electrical to gas device j;
Figure FDA0002342393590000024
the power of the unit i in the time period t under a reference scene;
Figure FDA0002342393590000025
the output of an electrical switching device, namely PtG device j, in a reference scene in a time period t;
Figure FDA0002342393590000026
the up/down spare capacity is provided for the unit i in the t time period;
Figure FDA0002342393590000027
upper/lower spare capacity for PtG device j for time period t;
Figure FDA0002342393590000028
representing the on/off cost of the unit i in the time period t; fiThe power generation cost function of the unit i is obtained;
step S12, establishing the first stage electric power system operation constraint conditions as follows:
Figure FDA0002342393590000029
in the formula, PimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set; pjmaxPtG maximum output of device j;
Figure FDA00023423935900000210
the on/off duration of the unit i to the time period t-1;
Figure FDA00023423935900000211
minimum on/off duration for unit i;
Figure FDA00023423935900000212
the up/down climbing rate of the unit i;
Figure FDA0002342393590000031
PtG uphill/downhill speed for device j; i, j and k are serial numbers of the generator set, the PtG equipment and the wind power plant which are connected with the node h in sequence;
Figure FDA0002342393590000032
the predicted output of the wind power plant j in the time period t is obtained;
Figure FDA0002342393590000033
the injected power for node h at time period t; k is a radical oflhFor line l pairs of nodesh, a sensitivity factor; f. oflmaxIs the maximum transmission power of line l;
step S13, establishing the operation constraint conditions of the natural gas system in the first stage as follows:
Figure FDA0002342393590000034
in the formula, QstThe air supply flow is the air supply flow of the air source s in the time period t; qsmax/QsminThe upper limit/lower limit of the air supply quantity of the air source; pietPressure for gas network node e at time period t; piemax/πeminUpper/lower pressure limits for gas network node e; q. q.smn(t)The average flow through the pipe mn at the time t; cmnIs the pipeline comprehensive coefficient; l ismn(t)Storing the pipeline mn for t time period;
Figure FDA0002342393590000035
the input/output flow of the pipeline mn in the t period; gamma-shapedcThe compression coefficient of the air compressor; egtThe gas storage quantity of the gas storage device g in the time period t is obtained;
Figure FDA0002342393590000036
the input/output flow of the gas storage device in the time period t; egmax/EgminThe maximum/minimum gas storage amount of the gas storage device; qgmax/QgminMaximum/minimum gas flow rate of the gas storage device;
Figure FDA0002342393590000041
represents the air load of node e during time period t;
Figure FDA0002342393590000042
the gas consumption of the gas unit i is a time period t;
and step S14, establishing the coupling operation constraint of the electric power system and the natural gas system in the first stage as follows:
Figure FDA0002342393590000043
in the formula, HHV is the high calorific value of natural gas;
Figure FDA0002342393590000044
representing the number set of gas turbine units,. tau. energy conversion coefficient ηPtGConversion efficiency for the PtG device;
Figure FDA0002342393590000045
representing PtG a set of device numbers;
Figure FDA0002342393590000046
the upper limit/lower limit of the gas consumption of the gas unit in the period i and the period t;
Figure FDA0002342393590000047
is PtG upper/lower limit of the gas production of the device.
3. The robust cooperative scheduling method of the power-natural gas coupled system considering electricity to gas to consume wind power of claim 2, wherein: the step S2 specifically includes the following steps:
step S21, establishing a real-time scheduling objective function of the second stage of the power-natural gas coupling system under the uncertain wind power output set as follows:
Figure FDA0002342393590000048
in the formula, the outer layer max is used for identifying the worst scene of the real-time output of the wind power; the inner-layer min is used for seeking the minimum value of the real-time scheduling cost in the worst wind power scene;
Figure FDA0002342393590000049
representing the actual output of the wind farm k in a time period t; cwindAnd CloadPunishment cost coefficients of wind abandonment and load abandonment are respectively; n is a radical ofwAnd NhRespectively the number of wind power plants and the number of load nodes;
Figure FDA0002342393590000051
representing the air curtailment quantity of the wind power plant k in the period t;
Figure FDA0002342393590000052
representing the involuntary load abandoning amount of the load node h in the period t;
Figure FDA0002342393590000053
adjusting the price for the upper/lower standby of the unit i;
Figure FDA0002342393590000054
adjust the price for the up/down standby of PtG device j;
Figure FDA0002342393590000055
adjusting output force for the up/down adjustment of the unit i in the t period;
Figure FDA0002342393590000056
adjust out force up/down for t period PtG device j;
step S22: the power system operation constraint conditions for establishing the second stage of the power-natural gas coupling system are as follows:
Figure FDA0002342393590000057
in the formula (I), the compound is shown in the specification,
Figure FDA0002342393590000058
the actual injected power for node h during time t.
Step S23: establishing natural gas system operation constraint of a second stage of the electric power-natural gas coupling system and coupling operation constraint of the electric power system and the natural gas system, wherein variables to be solved under a natural gas system reference scene are expressed as follows:
Figure FDA0002342393590000059
when the gas consumption of the gas unit is
Figure FDA00023423935900000510
PtG the equipment gas production is
Figure FDA00023423935900000511
In extreme conditions, the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure FDA0002342393590000061
similarly, when the gas consumption of the gas unit is
Figure FDA0002342393590000062
PtG the equipment gas production is
Figure FDA0002342393590000063
In the extreme case of (3), the operation constraint which the natural gas system needs to satisfy is the same as the formula (3), the coupling operation constraint of the power system and the natural gas system is the same as the formula (4), and only the decision variable G in the coupled operation constraint is requiredbThe following variables were substituted:
Figure FDA0002342393590000064
4. the robust cooperative scheduling method of the power-natural gas coupled system considering electricity to gas to consume wind power of claim 1, wherein: the step S3 specifically includes the following steps:
step S31: representing a first-stage decision variable and a natural gas system decision variable of an electric power system in the electric power-natural gas coupled system by using a vector X, and representing a second-stage decision variable of the electric power system by using a vector Y, so that a two-stage robust scheduling model of the electric power-natural gas coupled system is represented as follows:
Figure FDA0002342393590000065
in the formula, c, b, d and h are coefficient vectors, and A, G, E, M is a coefficient matrix;
step S32: the above double-layer optimization model with the max-min form is converted into the following main problem MP and sub problem SP:
Figure FDA0002342393590000066
Figure FDA0002342393590000071
5. the robust cooperative scheduling method of the power-natural gas coupled system considering electricity to gas to consume wind power of claim 1, wherein: the step S4 specifically includes the following steps:
step S41: combining the dual theory, the subproblem SP in formula (12) is transformed into the following single-layer optimization problem:
Figure FDA0002342393590000072
in the formula, mu is a decision variable of a dual problem;
step S42: combining an extreme point method, converting bilinear terms in the target function of the formula (13), and converting vectors
Figure FDA0002342393590000073
Middle element
Figure FDA0002342393590000074
Element mu in sum vector mudProduct of (2)
Figure FDA0002342393590000075
The following transformations were carried out:
Figure FDA0002342393590000076
in the formula (I), the compound is shown in the specification,
Figure FDA0002342393590000077
and
Figure FDA0002342393590000078
β as auxiliary continuous variable0，β+And β-Is an auxiliary binary integer variable; m is a sufficiently large positive number;
step S43: and establishing a solving flow of the main problem and the subproblems by adopting a column constraint generation method.
6. The robust cooperative scheduling method of the power-natural gas coupled system considering electricity to gas to consume wind power of claim 5, wherein: the step S43 specifically includes the following steps:
step S431: setting the upper and lower bound initial values L of the optimization problemb＝-∞，UbInfinity, +,; the initial iteration number K is 0; the maximum gap between the upper and lower boundaries is epsilon;
step S432: solving the main problem MP of the formula (11) to obtain the optimal solution
Figure FDA0002342393590000081
And updates the upper bound of the optimization problem to:
Figure FDA0002342393590000082
step S433: solving the dual problem of the sub-problem SP shown in the formula (13), wherein X in the objective function is the one obtained in the step S432
Figure FDA0002342393590000083
The optimal solution of the formula (13) is obtained
Figure FDA0002342393590000084
The optimum value is
Figure FDA0002342393590000085
The lower bound is updated as:
Figure FDA0002342393590000086
step S434: if U is presentb-LbIf the value is less than or equal to epsilon, the iteration process is terminated, and the obtained optimal decision result is
Figure FDA0002342393590000087
Otherwise add an auxiliary variable YK+1And the corresponding constraint conditional expressions (15) to the main question MP, update the iteration number K to K +1, and return to step S432.
Figure FDA0002342393590000088
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