CN110739687B - Power system distribution robust scheduling method considering wind power high-order uncertainty - Google Patents

Power system distribution robust scheduling method considering wind power high-order uncertainty Download PDF

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CN110739687B
CN110739687B CN201911016650.4A CN201911016650A CN110739687B CN 110739687 B CN110739687 B CN 110739687B CN 201911016650 A CN201911016650 A CN 201911016650A CN 110739687 B CN110739687 B CN 110739687B
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张亚超
郑峰
叶韬
陈一强
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Abstract

The invention relates to a power system distribution robust scheduling method considering wind power high-order uncertainty, and establishes a power system distribution robust optimal scheduling model considering wind power probability distribution uncertainty. Firstly, aiming at the uncertain quantity of wind power output, constructing a fuzzy set based on the confidence coefficient of a probability density function; then, establishing a two-stage distribution robust scheduling model of the power system by combining a dual-factor affine adjustable strategy; and finally, converting the min-max structure optimization problem containing the uncertainty into a deterministic mixed integer linear programming problem by combining dual theory and robust equality conversion and solving the problem. The method can be applied to the scheduling plan formulation of the wind power-containing power system, and is beneficial to improving the flexibility of the standby configuration of the schedulable unit.

Description

Power system distribution robust scheduling method considering wind power high-order uncertainty
Technical Field
The invention relates to the technical field of power system distribution robust optimization scheduling, in particular to a power system distribution robust scheduling method considering wind power high-order uncertainty.
Background
At present, theoretical research on a scheduling method of a wind power system mainly includes a stochastic programming method and a robust optimization method. The two methods for solving the optimization problem containing the uncertain parameters have limitations to a certain degree. The stochastic programming method based on the probabilistic scene set needs to presuppose the probability distribution characteristic of the wind power, the rationality of the stochastic programming method is difficult to effectively prove, and the inaccuracy of historical sample data causes the uncertainty of the wind power probability distribution. In addition, a large number of wind power discrete scene sets are generated by the stochastic programming method, the time complexity of direct modeling calculation is too high, and the decision risk is not considered enough when a scene reduction method is used for obtaining the simplified scene set modeling. On the other hand, the robust optimization method only constructs an uncertain set according to upper and lower boundary parameters of a predicted value and seeks an optimal decision in the worst scene, and calculation is easy to achieve.
Disclosure of Invention
In view of the above, the present invention provides a power system distribution robust scheduling method considering wind power high-order uncertainty, and a dual factor affine adjustment strategy enables a unit to more flexibly configure its upper/lower spare capacity, so as to implement a higher scheduling decision for a decision variable in a pre-scheduling stage within its feasible domain.
The invention is realized by adopting the following scheme: a power system distribution robust scheduling method considering wind power high-order uncertainty comprises the following steps:
step S1: carrying out interval estimation on the wind power output probability density value according to the acquired wind power output historical data; establishing a linear programming problem to solve a wind power probability density confidence band, and constructing a fuzzy set for describing high-order uncertainty of wind power output;
step S2: establishing a target function and an operation constraint condition of a pre-dispatching stage of the power system on the basis of a day-ahead predicted value of wind power output and by taking the generation cost, the startup and shutdown cost and the reserve capacity cost of a unit under a wind power reference scene as optimization targets;
step S3: utilizing the wind power output fuzzy set constructed in the step S1, introducing a double-factor-based affine-adjustable unit output adjustment strategy, taking the unit adjustment cost and the wind abandoning load abandoning penalty cost in the re-dispatching stage as optimization targets, and establishing a re-dispatching stage target function containing uncertainty and an operation constraint condition;
step S4: converting the objective function containing uncertain quantity and the constraint condition in the step S3 into a deterministic mixed integer linear programming problem by combining the structural characteristics and the robust equation pair of the fuzzy set generated in the step S1;
step S5: and solving the mixed integer linear programming problem in the step S4 by adopting a CPLEX solver under a Matlab platform to obtain a distributed robust scheduling scheme, so as to improve the operation decision flexibility of the power system and the wind power energy consumption level thereof.
Further, the step S1 specifically includes the following steps:
and step S11, according to the obtained wind power output historical data, performing interval estimation on the wind power output probability density numerical value, namely constructing random variables with the same distribution: aiming at a sample set containing N random variables and arranged in ascending order and used for uncertain quantity xi
Figure BDA0002246054670000021
Dividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsets
Figure BDA0002246054670000031
And
Figure BDA0002246054670000032
if it is not
Figure BDA0002246054670000033
The sample set is divided into M subsets with equal number of elements; otherwise, before
Figure BDA0002246054670000034
The number of elements contained in each subset is K, and the number of elements contained in the Mth subset is K
Figure BDA0002246054670000035
The following random variables were constructed:
Figure BDA0002246054670000036
in the formula, F represents a cumulative distribution function of the uncertainty ξ; the random variables have the same distribution as the random variable Δ i defined by the formula (2);
Figure BDA0002246054670000037
wherein gamma (A, B) represents a random variable with parameters of A, B obeying gamma distribution;
let constant c-(alpha) and c+(α), satisfying constraint conditions
Figure BDA0002246054670000038
Wherein α is a predetermined significance level, c-(alpha) and c+(alpha) values are obtained by sampling estimation according to the formula (2);
step S12, polyhedron is established: the original sample set in step S11 is obtained by Devrroye-Wise method
Figure BDA0002246054670000039
The upper and lower bounds of (a) and (b) are respectively; building a data set
Figure BDA00022460546700000310
Which comprises
Figure BDA00022460546700000311
A mutually different element, zjTo represent
Figure BDA00022460546700000312
The j-th smallest element; is defined as followsA face body:
Figure BDA0002246054670000041
in the formula, index
Figure BDA0002246054670000042
Satisfy the requirement of
Figure BDA0002246054670000043
The vector beta is composed of a probability density function value of the uncertain quantity xi; wherein rows 1-2 in equation (3) indicate unimodal properties of the probability density function; the behavior 3-4 in the formula (3) is an equivalent of the constraint condition in the step S11; lines 5-6 in the formula (3) show that the integral value of the probability density function of the uncertain quantity xi of p (xi) is 1 and the value is not negative;
and step S13, solving the confidence band of the probability density function: when the uncertainty xi takes on the value
Figure BDA0002246054670000044
The upper and lower bounds of the probability density value are respectively
Figure BDA0002246054670000045
And
Figure BDA0002246054670000046
obtained by solving the following linear programming problem:
Figure BDA0002246054670000047
in the formula, index
Figure BDA0002246054670000048
Satisfy the requirement of
Figure BDA0002246054670000049
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
Figure BDA00022460546700000410
in the formula,
Figure BDA00022460546700000411
representing all non-negative lux measure function spaces.
Further, the specific contents of establishing the objective function and the operation constraint condition of the power system pre-dispatching stage in step S2 are as follows:
Figure BDA0002246054670000051
wherein,
Figure BDA0002246054670000052
the fuel price for unit i;
Figure BDA0002246054670000053
and
Figure BDA0002246054670000054
respectively representing the starting cost and the stopping cost of the unit i in a time period t;
Figure BDA0002246054670000055
representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;
Figure BDA0002246054670000056
the up/down spare capacity is provided for the unit i in the time period t; fiRepresenting the cost function of the power generation of the unit i, wherein Fi(Pit)＝ai(Pit)2+biPit+ci，ai、bi、ciThe power generation cost coefficient of the unit i is obtained;
Figure BDA0002246054670000057
for wind farmsw predicted contribution at time t; l isdtElectrical load for user d during time period t;
Figure BDA0002246054670000058
minimum start-up/shut-down time for unit i;
Figure BDA0002246054670000059
the starting-up/stopping duration time of the unit i to the time period t-1 is obtained; i isitRepresenting the starting and stopping state of the unit i in a time period t; pimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set;
Figure BDA00022460546700000510
the upward/downward climbing speed of the unit i; k is a radical oflbThe sensitivity factor of the line l to the bus b; f. oflIs the maximum transmission power of line i.
Further, the specific steps of establishing the rescheduling phase objective function containing the uncertainty and the operation constraint condition in step S3 are as follows:
step S31: a dual factor affine tunable strategy: first, the net load of the power system is predicted
Figure BDA00022460546700000511
Wherein,
Figure BDA00022460546700000512
the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
Figure BDA0002246054670000061
in the formula,
Figure BDA0002246054670000062
adjusting factors for the unit i in the rescheduling stage in the upward/downward direction of the time period t;
step (ii) ofS32: rescheduling phase mathematical model: defining the adjustable output range of the unit in the time period t as
Figure BDA0002246054670000063
The following model was established:
Figure BDA0002246054670000064
wherein, L'btRepresenting the net load predicted value on the bus b;
Figure BDA0002246054670000065
for actual output from wind power
Figure BDA0002246054670000066
The relevant uncertainty is expressed as follows:
Figure BDA0002246054670000067
further, the step S4 specifically includes the following steps:
step S41: and (3) fuzzy set construction: amount of uncertainty
Figure BDA0002246054670000068
The sample set at time period t is defined as
Figure BDA0002246054670000069
Its fuzzy set is as follows:
Figure BDA00022460546700000610
in the formula,
Figure BDA00022460546700000611
the upper/lower limit values of the sample values;
for the same reason, for the uncertain quantity
Figure BDA00022460546700000612
Constructing a corresponding fuzzy set to obtain the fuzzy set of the 2-dimensional uncertain quantity:
Figure BDA0002246054670000071
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy set
Figure BDA0002246054670000072
The following distribution robust opportunity constraints:
Figure BDA0002246054670000073
in the formula, gamma1/γ2Representing the allowable load shedding/wind shedding probability of the system;
Figure BDA0002246054670000074
the index sets of all the generator sets;
step S43: constructing the following linear programming problem, and solving the adjustable output range of the unit:
Figure BDA0002246054670000075
in the formula, n1And n2Respectively being adjustable boundaries
Figure BDA0002246054670000076
And
Figure BDA0002246054670000077
in ascending order of sample set phitThe index value of (1);
step S44: on the basis of obtaining the adjustable output range of the unit, converting the distributed robust opportunity constraint condition into a corresponding robust corresponding form:
Figure BDA0002246054670000081
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
Figure BDA0002246054670000082
in the formula, eta is,
Figure BDA0002246054670000083
and
Figure BDA0002246054670000084
sequentially are dual variables corresponding to the constraint conditions in the step (16);
defined by the dual theory and fuzzy set, the dual problem of the above formula is as follows:
Figure BDA0002246054670000085
wherein L istAnd UtIs represented as follows:
Figure BDA0002246054670000086
equations (17) - (18) are the deterministic mixed integer linear programming problem.
Compared with the prior art, the invention has the following beneficial effects:
the fuzzy set constructed by adopting the probability density confidence band of the uncertainty not only fuses the probability distribution statistical information of historical sample data, but also fully considers the uncertainty of the probability distribution of the uncertainty, and the establishment of a system scheduling model based on the uncertainty is favorable for enhancing the effectiveness of decision making.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic diagram of output set values of each unit when the distributed robust optimization method using the single affine adjustable strategy according to the embodiment of the present invention is adopted.
Fig. 3 illustrates an upper and lower standby configuration of a unit using a single affine adjustable strategy according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of output set values of each unit when the distributed robust optimization method using the dual affine adjustable strategy is adopted in the embodiment of the present invention.
Fig. 5 shows the upper and lower standby configurations of the unit when the dual affine adjustable strategy is adopted 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.
The embodiment provides a power system distribution robust scheduling method considering wind power high-order uncertainty, which comprises the following steps:
step S1: carrying out interval estimation on the wind power output probability density value according to the acquired wind power output historical data; establishing a linear programming problem to solve a wind power probability density confidence band, and constructing a fuzzy set for describing high-order uncertainty of wind power output;
step S2: establishing a target function and an operation constraint condition of a pre-dispatching stage of the power system on the basis of a day-ahead predicted value of wind power output and by taking the generation cost, the startup and shutdown cost and the reserve capacity cost of a unit under a wind power reference scene as optimization targets;
step S3: utilizing the wind power output fuzzy set constructed in the step S1, introducing a double-factor-based affine-adjustable unit output adjustment strategy, taking the unit adjustment cost and the wind abandoning load abandoning penalty cost in the re-dispatching stage as optimization targets, and establishing a re-dispatching stage target function containing uncertainty and an operation constraint condition;
step S4: converting the objective function containing uncertain quantity and the constraint condition in the step S3 into a deterministic mixed integer linear programming problem by combining the structural characteristics and the robust equation pair of the fuzzy set generated in the step S1;
step S5: and solving the mixed integer linear programming problem in the step S4 by adopting a CPLEX solver under a Matlab platform to obtain a distributed robust scheduling scheme, so as to improve the operation decision flexibility of the power system and the wind power energy consumption level thereof.
In this embodiment, the step S1 specifically includes the following steps:
and step S11, according to the obtained wind power output historical data, performing interval estimation on the wind power output probability density numerical value, namely constructing random variables with the same distribution: aiming at a sample set containing N random variables and arranged in ascending order and used for uncertain quantity xi
Figure BDA0002246054670000111
Dividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsets
Figure BDA0002246054670000112
And
Figure BDA0002246054670000113
if it is not
Figure BDA0002246054670000114
The sample set is divided into M subsets with equal number of elements; otherwise, before
Figure BDA0002246054670000115
The number of elements contained in each subset is K, and the number of elements contained in the Mth subset is K
Figure BDA0002246054670000116
The following random variables were constructed:
Figure BDA0002246054670000117
in the formula, F represents a cumulative distribution function of the uncertainty ξ; the random variables have the same distribution as the random variable Δ i defined by the formula (2);
Figure BDA0002246054670000118
wherein gamma (A, B) represents a random variable with parameters of A, B obeying gamma distribution;
let constant c-(alpha) and c+(α), satisfying constraint conditions
Figure BDA00022460546700001110
1,2, …, M } ≧ 1-alpha; wherein α is a predetermined significance level, c- (α) and c+(alpha) values are obtained by sampling estimation according to the formula (2);
step S12, polyhedron is established: the original sample set in step S11 is obtained by Devrroye-Wise method
Figure BDA0002246054670000119
The upper and lower bounds of (a) and (b) are respectively; building a data set
Figure BDA0002246054670000121
Which comprises
Figure BDA0002246054670000122
A mutually different element, zjTo represent
Figure BDA0002246054670000123
Middle j smallAn element of (1); the following polyhedrons are defined:
Figure BDA0002246054670000124
in the formula, index
Figure BDA0002246054670000125
Satisfy the requirement of
Figure BDA0002246054670000126
The vector beta is composed of a probability density function value of the uncertain quantity xi; wherein rows 1-2 in equation (3) indicate unimodal properties of the probability density function; the behavior 3-4 in the formula (3) is an equivalent of the constraint condition in the step S11; lines 5-6 in the formula (3) show that the integral value of the probability density function of the uncertain quantity xi of p (xi) is 1 and the value is not negative;
and step S13, solving the confidence band of the probability density function: when the uncertainty xi takes on the value
Figure BDA0002246054670000127
The upper and lower bounds of the probability density value are respectively
Figure BDA0002246054670000128
And
Figure BDA0002246054670000129
obtained by solving the following linear programming problem:
Figure BDA00022460546700001210
in the formula, index
Figure BDA00022460546700001211
Satisfy the requirement of
Figure BDA00022460546700001212
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
Figure BDA00022460546700001213
in the formula,
Figure BDA00022460546700001214
representing all non-negative lux measure function spaces.
In this embodiment, the specific contents of establishing the objective function and the operation constraint condition in the pre-dispatching stage of the power system in step S2 are as follows:
Figure BDA0002246054670000131
wherein,
Figure BDA0002246054670000132
the fuel price for unit i;
Figure BDA0002246054670000133
and
Figure BDA0002246054670000134
respectively representing the starting cost and the stopping cost of the unit i in a time period t;
Figure BDA0002246054670000135
representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;
Figure BDA0002246054670000136
the up/down spare capacity is provided for the unit i in the time period t; fiRepresenting the cost function of the power generation of the unit i, wherein Fi(Pit)＝ai(Pit)2+biPit+ci，ai、bi、ciThe power generation cost coefficient of the unit i is obtained;
Figure BDA0002246054670000137
the predicted output of the wind power plant w in the time period t is obtained; l isdtElectrical load for user d during time period t;
Figure BDA0002246054670000138
minimum start-up/shut-down time for unit i;
Figure BDA0002246054670000139
the starting-up/stopping duration time of the unit i to the time period t-1 is obtained; i isitRepresenting the starting and stopping state of the unit i in a time period t; pimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set;
Figure BDA00022460546700001310
the upward/downward climbing speed of the unit i; k is a radical oflbThe sensitivity factor of the line l to the bus b; f. oflIs the maximum transmission power of line i.
In this embodiment, the specific steps of establishing the rescheduling phase objective function and the operation constraint condition containing the uncertainty in step S3 are as follows:
step S31: a dual factor affine tunable strategy: first, the net load of the power system is predicted
Figure BDA00022460546700001311
Wherein,
Figure BDA00022460546700001312
the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
Figure BDA0002246054670000141
in the formula,
Figure BDA0002246054670000142
adjusting factors for the unit i in the rescheduling stage in the upward/downward direction of the time period t;
step S32: rescheduling phase mathematical model: defining the adjustable output range of the unit in the time period t as
Figure BDA0002246054670000143
The following model was established:
Figure BDA0002246054670000144
wherein, L'btRepresenting the net load predicted value on the bus b;
Figure BDA0002246054670000145
for actual output from wind power
Figure BDA0002246054670000146
The relevant uncertainty is expressed as follows:
Figure BDA0002246054670000147
in this embodiment, the step S4 specifically includes the following steps:
step S41: and (3) fuzzy set construction: amount of uncertainty
Figure BDA0002246054670000148
The sample set at time period t is defined as
Figure BDA0002246054670000149
The fuzzy set construction method according to step S1 can obtain the fuzzy set as follows:
Figure BDA00022460546700001410
in the formula,
Figure BDA00022460546700001411
the upper/lower limit values of the sample values;
for the same reason, for the uncertain quantity
Figure BDA00022460546700001412
Constructing a corresponding fuzzy set to obtain the fuzzy set of the 2-dimensional uncertain quantity:
Figure BDA00022460546700001413
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy set
Figure BDA0002246054670000151
The following distribution robust opportunity constraints:
Figure BDA0002246054670000152
in the formula, gamma1/γ2Representing the allowable load shedding/wind shedding probability of the system;
Figure BDA0002246054670000153
the index sets of all the generator sets;
step S43: constructing the following linear programming problem, and solving the adjustable output range of the unit:
Figure BDA0002246054670000154
in the formula, n1And n2Respectively being adjustable boundaries
Figure BDA0002246054670000155
And
Figure BDA0002246054670000156
in ascending order of sample set phitThe index value of (1);
step S44: on the basis of obtaining the adjustable output range of the unit, converting the distributed robust opportunity constraint condition into a corresponding robust pair equation:
Figure BDA0002246054670000161
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
Figure BDA0002246054670000162
in the formula, eta is,
Figure BDA0002246054670000163
and
Figure BDA0002246054670000164
sequentially are dual variables corresponding to the constraint conditions in the step (16);
defined by the dual theory and fuzzy set, the dual problem of the above formula is as follows:
Figure BDA0002246054670000165
wherein L istAnd UtIs represented as follows:
Figure BDA0002246054670000166
equations (17) - (18) are the deterministic mixed integer linear programming problem.
Preferably, in this embodiment, the above derivation can convert the min-max structure optimization problem with uncertainty into a deterministic single-layer mixed integer linear programming problem, and a CPLEX solver is used to solve the problem.
Preferably, the fuzzy set constructed by the probability density confidence band of the uncertainty is used for not only fusing the probability distribution statistical information of the historical sample data, but also fully considering the uncertainty of the probability distribution of the uncertainty, and establishing a system scheduling model on the basis of the uncertainty is favorable for enhancing the effectiveness of decision making.
The embodiment can combine the advantages of the stochastic programming method and the traditional robust optimization method, and the scheduling decision of the embodiment can effectively reduce the conservatism of the traditional robust optimization method.
Compared with the existing research adopting a single-factor affine adjustment strategy, the double-factor affine adjustment strategy provided by the embodiment enables the unit to more flexibly configure the upper/lower spare capacity of the unit, and further realizes that the decision variables in the pre-scheduling stage seek superior scheduling decisions in the range of the feasible domain of the decision variables.
Preferably, the present embodiment performs a test example simulation in an MATLAB environment, and performs a model solution using a CPLEX software package. The modeling solution flow is shown in figure 1.
The two-stage distribution robust model of the embodiment takes the minimum sum of the operation cost and the spare capacity cost of the unit in the pre-dispatching stage of the power system and the adjustment cost, the wind abandoning cost and the load abandoning cost of the unit in the re-dispatching stage as an objective function, and comprises operation constraint conditions such as unit output limit, minimum start-stop time limit, unit climbing rate and rotation spare constraint, transmission line power flow limit, system power balance and the like.
According to a specific example of the embodiment, the distribution robust optimization method based on the uncertainty fuzzy set is applied to an improved IEEE-24 node system for verification, wherein G1-G3 are gas turbines, G4-G10 are thermal power turbines, and nodes 5 and 19 are respectively connected to wind power turbines.
The distributed robust optimization method, the stochastic programming method and the conventional robust optimization method of the present embodiment are compared, and the results are shown in table 1:
TABLE 1 comparison of results of different uncertainty optimization methods
Figure BDA0002246054670000181
The methods in table 1 are in sequence: SP-S represents a random planning method considering a single-factor affine adjustable strategy; SP-D represents a stochastic programming method considering a dual-factor affine adjustable strategy: DRO-S represents a distributed robust optimization method considering a single-factor affine adjustable strategy; DRO-D represents the distributed robust optimization method of the invention considering the dual factor affine adjustable strategy.
Analysis of the simulation results obtained by the different methods in table 1 shows that: the total running cost of the RO is the largest, the conservatism of RO scheduling decisions is reduced to a certain extent by distributed robust optimization methods DRO-S and DRO-D, the running cost of the random planning methods SP-S and SP-D is the lowest, but the decision effectiveness is questioned. From the analysis, the distributed robust optimization method can combine the advantages of the traditional robust optimization method and the random planning method, so that the conservative property of the traditional robust decision is reduced, and the decision effectiveness is ensured.
As can be known from the stochastic programming method considering two different affine adjustable strategies, when the dual-factor affine adjustable strategy provided by this embodiment is adopted, the total operation cost of the scheduling decision is reduced by 8930.19 $. As for the distributed robust optimization method considering different affine adjustable strategies, the total operation cost is reduced by 8078.37 $whenthe double-factor affine adjustable strategy is adopted. Therefore, compared with a single-factor affine adjustable strategy, the double-factor affine adjustable strategy can improve the flexibility of unit planned output and spare capacity configuration, and proves that the double-factor affine adjustable strategy provided by the embodiment can obtain a scheduling decision with better performance.
As can be seen from fig. 2 to 5, when the dual-factor affine adjustable strategy is adopted, the upper and lower standby configurations of each unit are more flexible, so that a scheduling decision can obtain a more superior scheduling scheme in a larger feasible domain range.
The main processes realized by the embodiment comprise the construction of an uncertain quantity fuzzy set, the establishment of a two-stage power system distribution robust scheduling model and a conversion and solving method of the model.
The embodiment constructs a fuzzy set of the uncertainty probability density function based on a confidence band of the uncertainty probability density function, and represents the high-order uncertainty of the uncertainty. On the basis, a pre-dispatching stage mathematical model taking the generating cost and the spare capacity cost of the unit as objective functions in a reference prediction scene and a re-dispatching stage mathematical model taking the adjusting cost and the wind abandoning load abandoning cost of the unit as objective functions in the worst scene distribution are established, and the optimal dispatching is carried out on the power system with the wind power by taking the lowest total operating cost of the two stages as a target.
In the aspect of model conversion and solution, the embodiment provides an affine adjustable strategy based on dual factors to distribute the output of the unit in the re-scheduling stage, and converts the re-scheduling stage objective function containing uncertain quantity and constraint conditions into a deterministic mixed integer linear programming problem to solve by combining a special structure and a robust equality of a fuzzy set.
According to the method, a high-order uncertainty of the wind power output is characterized by a wind power output fuzzy set based on a probability density function confidence band through a large amount of historical sample data, and on the basis, a two-stage distribution robust scheduling mathematical model of the power system is built to find an optimal decision scheme under the worst scene distribution.
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 (5)

1. A power system distribution robust scheduling method considering wind power high-order uncertainty is characterized by comprising the following steps:
the method comprises the following steps:
step S1: carrying out interval estimation on the wind power output probability density value according to the acquired wind power output historical data; establishing a linear programming problem to solve a wind power probability density confidence band, and constructing a fuzzy set for describing high-order uncertainty of wind power output;
step S2: establishing a target function and an operation constraint condition of a pre-dispatching stage of the power system on the basis of a day-ahead predicted value of wind power output and by taking the generation cost, the startup and shutdown cost and the reserve capacity cost of a unit under a wind power reference scene as optimization targets;
step S3: utilizing the wind power output fuzzy set constructed in the step S1, introducing a double-factor-based affine-adjustable unit output adjustment strategy, taking the unit adjustment cost and the wind abandoning load abandoning penalty cost in the re-dispatching stage as optimization targets, and establishing a re-dispatching stage target function containing uncertainty and an operation constraint condition;
step S4: converting the objective function containing uncertain quantity and the constraint condition in the step S3 into a deterministic mixed integer linear programming problem by combining the structural characteristics and the robust equation pair of the fuzzy set generated in the step S1;
step S5: and solving the mixed integer linear programming problem in the step S4 by adopting a CPLEX solver under a Matlab platform to obtain a distributed robust scheduling scheme, so as to improve the operation decision flexibility of the power system and the wind power energy consumption level thereof.
2. The power system distribution robust scheduling method considering wind power high-order uncertainty according to claim 1, characterized in that: the step S1 specifically includes the following steps:
and step S11, according to the obtained wind power output historical data, performing interval estimation on the wind power output probability density numerical value, namely constructing random variables with the same distribution: aiming at a sample set containing N random variables and arranged in ascending order and used for uncertain quantity xi
Figure FDA0003010901320000021
Dividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsets
Figure FDA0003010901320000022
And
Figure FDA0003010901320000023
if it is not
Figure FDA0003010901320000024
The sample set is divided into M subsets with equal number of elements; otherwise, before
Figure FDA0003010901320000025
The number of elements contained in each subset is K, and the Mth subset contains elementsThe number of elements is
Figure FDA0003010901320000026
The following random variables were constructed:
Figure FDA0003010901320000027
in the formula, F represents a cumulative distribution function of the uncertainty ξ; the random variables have the same distribution as the random variable Δ i defined by the formula (2);
Figure FDA0003010901320000028
wherein gamma (A, B) represents a random variable with parameters of A, B obeying gamma distribution;
let constant c-(alpha) and c+(α), satisfying constraint conditions
Figure FDA0003010901320000029
Wherein α is a predetermined significance level, c-(alpha) and c+(alpha) values are obtained by sampling estimation according to the formula (2);
step S12, polyhedron is established: the original sample set in step S11 is obtained by Devrroye-Wise method
Figure FDA00030109013200000210
The upper and lower bounds of (a) and (b) are respectively; building a data set
Figure FDA00030109013200000211
Which comprises
Figure FDA00030109013200000212
A mutually different element, zjRepresenting an ascending ordered set of samples
Figure FDA00030109013200000213
The middle index is an element of j; the following polyhedrons are defined:
Figure FDA0003010901320000031
in the formula, index
Figure FDA0003010901320000032
Satisfy the requirement of
Figure FDA0003010901320000033
The vector beta is composed of a probability density function value of the uncertain quantity xi; wherein rows 1-2 in equation (3) indicate unimodal properties of the probability density function; the behavior 3-4 in the formula (3) is an equivalent of the constraint condition in the step S11; lines 5-6 in the formula (3) show that the integral value of the probability density function of the uncertain quantity xi of p (xi) is 1 and the value is not negative;
and step S13, solving the confidence band of the probability density function: when the uncertainty xi takes on the value
Figure FDA0003010901320000034
The upper and lower bounds of the probability density value are respectively
Figure FDA0003010901320000035
And
Figure FDA0003010901320000036
obtained by solving the following linear programming problem:
Figure FDA0003010901320000037
in the formula, index
Figure FDA0003010901320000038
Satisfy the requirement of
Figure FDA0003010901320000039
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
Figure FDA00030109013200000310
in the formula,
Figure FDA00030109013200000311
representing all non-negative lux measure function spaces.
3. The power system distribution robust scheduling method considering wind power high-order uncertainty according to claim 2, characterized in that: the specific contents of establishing the objective function and the operation constraint condition of the pre-dispatching stage of the power system in the step S2 are as follows:
Figure FDA0003010901320000041
wherein,
Figure FDA0003010901320000042
the fuel price for unit i;
Figure FDA0003010901320000043
and
Figure FDA0003010901320000044
respectively representing the starting cost and the stopping cost of the unit i in a time period t;
Figure FDA0003010901320000045
representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;
Figure FDA0003010901320000046
providing for unit i at time tUp/down spare capacity of (c); fiRepresenting the cost function of the power generation of the unit i, wherein Fi(Pit)＝ai(Pit)2+biPit+ci，ai、bi、ciThe power generation cost coefficient of the unit i is obtained;
Figure FDA0003010901320000047
the predicted output of the wind power plant w in the time period t is obtained; l isdtElectrical load for user d during time period t;
Figure FDA0003010901320000048
minimum start-up/shut-down time for unit i;
Figure FDA0003010901320000049
the starting-up/stopping duration time of the unit i to the time period t-1 is obtained; i isitRepresenting the starting and stopping state of the unit i in a time period t; pimaxAnd PiminThe upper limit and the lower limit of the output of the unit i are respectively set;
Figure FDA00030109013200000410
the upward/downward climbing speed of the unit i; k is a radical oflbThe sensitivity factor of the line l to the bus b; f. oflIs the maximum transmission power of line i.
4. The power system distribution robust scheduling method considering wind power high-order uncertainty according to claim 3, characterized in that: the specific steps of establishing the rescheduling stage objective function containing the uncertainty and the operation constraint condition in the step S3 are as follows:
step S31: a dual factor affine tunable strategy: first, the net load prediction error of the power system is expressed as
Figure FDA00030109013200000411
Wherein,
Figure FDA00030109013200000412
the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
Figure FDA0003010901320000051
in the formula,
Figure FDA0003010901320000052
adjusting factors for the unit i in the rescheduling stage in the upward/downward direction of the time period t;
step S32: rescheduling phase mathematical model: defining the adjustable output range of the unit in the time period t as
Figure FDA0003010901320000053
The following model was established:
Figure FDA0003010901320000054
wherein, L'btRepresenting the net load predicted value on the bus b;
Figure FDA0003010901320000055
for actual output from wind power
Figure FDA0003010901320000056
The relevant uncertainty is expressed as follows:
Figure FDA0003010901320000057
5. the power system distribution robust scheduling method considering wind power high-order uncertainty according to claim 4, characterized in that: the step S4 specifically includes the following steps:
step (ii) ofS41: and (3) fuzzy set construction: amount of uncertainty
Figure FDA0003010901320000058
The sample set at time period t is defined as
Figure FDA0003010901320000059
Its fuzzy set is as follows:
Figure FDA00030109013200000510
in the formula,
Figure FDA00030109013200000511
the upper/lower limit values of the sample values;
for the same reason, for the uncertain quantity
Figure FDA00030109013200000512
Constructing corresponding fuzzy set to obtain the 2-dimensional uncertainty
Figure FDA0003010901320000061
Fuzzy sets of (1):
Figure FDA0003010901320000062
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy set
Figure FDA0003010901320000063
The following distribution robust opportunity constraints:
Figure FDA0003010901320000064
in the formula, gamma1/γ2Representing the allowable load shedding/wind shedding probability of the system; i is an index set of all generator sets;
step S43: constructing the following linear programming problem, and solving the adjustable output range of the unit:
Figure FDA0003010901320000065
in the formula, n1And n2Respectively being adjustable boundaries tφAnd
Figure FDA0003010901320000066
in ascending order of sample set phitThe index value of (1);
step S44: on the basis of obtaining the adjustable output range of the unit, converting the distributed robust opportunity constraint condition into a corresponding robust pair equation:
Figure FDA0003010901320000071
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
Figure FDA0003010901320000072
Figure FDA0003010901320000073
in the formula, eta is,
Figure FDA0003010901320000074
and
Figure FDA0003010901320000075
sequentially are dual variables corresponding to the constraint conditions in the step (16);
defined by the dual theory and fuzzy set, the dual problem of the above formula is as follows:
Figure FDA0003010901320000076
wherein L istAnd UtIs represented as follows:
Figure FDA0003010901320000077
Figure FDA0003010901320000078
equations (17) - (18) are the deterministic mixed integer linear programming problem.
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