CN110739687B - Power system distribution robust scheduling method considering wind power high-order uncertainty - Google Patents
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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
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 xiDividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsetsAndif it is notThe sample set is divided into M subsets with equal number of elements; otherwise, beforeThe number of elements contained in each subset is K, and the number of elements contained in the Mth subset is KThe following random variables were constructed:
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);
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 conditionsWherein 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 methodThe upper and lower bounds of (a) and (b) are respectively; building a data setWhich comprisesA mutually different element, zjTo representThe j-th smallest element; is defined as followsA face body:
in the formula, indexSatisfy the requirement ofThe 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 valueThe upper and lower bounds of the probability density value are respectivelyAndobtained by solving the following linear programming problem:
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
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:
wherein,the fuel price for unit i;andrespectively representing the starting cost and the stopping cost of the unit i in a time period t;representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;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;for wind farmsw predicted contribution at time t; l isdtElectrical load for user d during time period t;minimum start-up/shut-down time for unit i;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;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
Wherein,the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
in the formula,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 asThe following model was established:
wherein, L'btRepresenting the net load predicted value on the bus b;for actual output from wind powerThe relevant uncertainty is expressed as follows:
further, the step S4 specifically includes the following steps:
step S41: and (3) fuzzy set construction: amount of uncertaintyThe sample set at time period t is defined asIts fuzzy set is as follows:
for the same reason, for the uncertain quantityConstructing a corresponding fuzzy set to obtain the fuzzy set of the 2-dimensional uncertain quantity:
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy setThe following distribution robust opportunity constraints:
in the formula, gamma1/γ2Representing the allowable load shedding/wind shedding probability of the system;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:
in the formula, n1And n2Respectively being adjustable boundariesAndin 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:
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
in the formula, eta is,andsequentially 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:
wherein L istAnd UtIs represented as follows:
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 xiDividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsetsAndif it is notThe sample set is divided into M subsets with equal number of elements; otherwise, beforeThe number of elements contained in each subset is K, and the number of elements contained in the Mth subset is KThe following random variables were constructed:
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);
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 conditions1,2, …, 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 methodThe upper and lower bounds of (a) and (b) are respectively; building a data setWhich comprisesA mutually different element, zjTo representMiddle j smallAn element of (1); the following polyhedrons are defined:
in the formula, indexSatisfy the requirement ofThe 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 valueThe upper and lower bounds of the probability density value are respectivelyAndobtained by solving the following linear programming problem:
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
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:
wherein,the fuel price for unit i;andrespectively representing the starting cost and the stopping cost of the unit i in a time period t;representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;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;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;minimum start-up/shut-down time for unit i;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;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
Wherein,the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
in the formula,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 asThe following model was established:
wherein, L'btRepresenting the net load predicted value on the bus b;for actual output from wind powerThe relevant uncertainty is expressed as follows:
in this embodiment, the step S4 specifically includes the following steps:
step S41: and (3) fuzzy set construction: amount of uncertaintyThe sample set at time period t is defined asThe fuzzy set construction method according to step S1 can obtain the fuzzy set as follows:
for the same reason, for the uncertain quantityConstructing a corresponding fuzzy set to obtain the fuzzy set of the 2-dimensional uncertain quantity:
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy setThe following distribution robust opportunity constraints:
in the formula, gamma1/γ2Representing the allowable load shedding/wind shedding probability of the system;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:
in the formula, n1And n2Respectively being adjustable boundariesAndin 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:
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
in the formula, eta is,andsequentially 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:
wherein L istAnd UtIs represented as follows:
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
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 xiDividing the data into subsets with the number of elements being K, and defining the following two parameters related to the number of the subsetsAndif it is notThe sample set is divided into M subsets with equal number of elements; otherwise, beforeThe number of elements contained in each subset is K, and the Mth subset contains elementsThe number of elements isThe following random variables were constructed:
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);
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 conditionsWherein 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 methodThe upper and lower bounds of (a) and (b) are respectively; building a data setWhich comprisesA mutually different element, zjRepresenting an ascending ordered set of samplesThe middle index is an element of j; the following polyhedrons are defined:
in the formula, indexSatisfy the requirement ofThe 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 valueThe upper and lower bounds of the probability density value are respectivelyAndobtained by solving the following linear programming problem:
And solving a fuzzy set of the uncertain quantity xi under the confidence level 1-alpha as follows:
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:
wherein,the fuel price for unit i;andrespectively representing the starting cost and the stopping cost of the unit i in a time period t;representing the up/down spare capacity price of the unit i; pitOutputting the reference force of the unit i in the time period t;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;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;minimum start-up/shut-down time for unit i;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;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
Wherein,the actual output of the wind power in the re-dispatching stage; introducing the following regulation strategy of unit power:
in the formula,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 asThe following model was established:
wherein, L'btRepresenting the net load predicted value on the bus b;for actual output from wind powerThe relevant uncertainty is expressed as follows:
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 uncertaintyThe sample set at time period t is defined asIts fuzzy set is as follows:
for the same reason, for the uncertain quantityConstructing corresponding fuzzy set to obtain the 2-dimensional uncertainty
step S42: distribution robust opportunity constraint: converting the constraint condition containing uncertain quantity in the formula (9) into a fuzzy setThe following distribution robust opportunity constraints:
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:
in the formula, n1And n2Respectively being adjustable boundaries tφAndin 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:
step S45: the inner-layer maximization problem in the rescheduling phase objective function is represented as follows:
in the formula, eta is,andsequentially 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:
wherein L istAnd UtIs represented as follows:
equations (17) - (18) are the deterministic mixed integer linear programming problem.
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