CN110689209A - Method for synchronously optimizing wind power tolerance interval and expected generating cost of unit - Google Patents

Method for synchronously optimizing wind power tolerance interval and expected generating cost of unit Download PDF

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CN110689209A
CN110689209A CN201911048031.3A CN201911048031A CN110689209A CN 110689209 A CN110689209 A CN 110689209A CN 201911048031 A CN201911048031 A CN 201911048031A CN 110689209 A CN110689209 A CN 110689209A
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蓝超凡
王文睿
余涛
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Abstract

The invention discloses a method for synchronously optimizing a wind power tolerance interval and expected power generation cost of a unit, which comprises the following steps of: step S1, acquiring data; step S2, obtaining a lower triangular matrix according to the Nataf transformation principle; step S3, forming a sampling matrix Z according to a three-point estimation method; step S4, available output sampling values are inversely transformed through Nataf; step S5, obtaining an actual output value of the unit through an affine correction process; step S6, constructing an objective function of the text model; step S7, eliminating the nonlinear term; step S8, calculating the actual output of the unit; step S9, a target function is embossed; step S10, solving a text model; and step S11, carrying out Monte Carlo simulation by using the correction model to obtain the wind curtailment quantity and the readjusted output of the unit for responding to wind power fluctuation. The method takes the expected value of the power generation cost corresponding to the wind power fluctuation as an economic target, and reflects a minimization model of the actual power generation cost.

Description

Method for synchronously optimizing wind power tolerance interval and expected generating cost of unit
Technical Field
The invention relates to the field of wind power robust interval scheduling of a power system, in particular to a method for synchronously optimizing a wind power allowable interval and expected power generation cost of a unit.
Background
According to statistics, the total installed wind power of China reaches 1.2 hundred million KW by 2020, and simultaneously, along with the increase of the wind power grid-connected quantity, the uncertainty problem caused by the intermittent and random characteristics of wind energy to the operation of a power grid is increasingly prominent. At present, methods for processing wind power uncertainty in a power grid scheduling problem mainly include random planning and robust optimization. Different from random planning, robust optimization does not need a large number of random scenes, the calculated amount is greatly reduced, and meanwhile the reliability of the system for responding to wind power fluctuation can be strictly guaranteed, so that the method is widely applied.
Existing robust economic Dispatch models and existing literature ([ Li Shi, Wu Wen, Zyming. Disable robust Interval economic Dispatch (one) mode of Dispatch and mathematical model [ J ]. Power System Automation, 2014,38(20):33-39.DOI:10.7500/AEPS20131123001 ] ], [ Li Shi, Wu Wen, Zyming. Disable robust Interval economic Dispatch (two) uncertain set construction and conservative Regulation [ J ]. Power System Automation, 2014,38(21):32-38.DOI:10.7500/AEPS20140515001 ] and [ LI Z, WU W, Zhang B, Adjjus Robusu Real-able Power Disch move With Large-Scale Wind turbine — cutter Wired Power station [ J ]. IEEE operation on, Transactions on, Enj 12, Eng stand, Power park strategy [ J ] No. 6, Syage, 2017,41(05): 1451-1463), on the premise of ensuring the safe operation of the system, the day-ahead ground-state power generation cost of the unit is often taken as an economic target, and the power generation cost of the system for dealing with wind power fluctuation in the actual scheduling process is not optimized, so that the economy of the system cannot be fully reflected.
Disclosure of Invention
Based on the above, the present application provides a method for synchronously optimizing a wind power tolerance interval and a desired power generation cost of a unit. The method is based on nonlinear term relaxation treatment, and can solve the problem of nonlinear terms introduced for improving the wind power absorption capacity, namely the wind power bearing coefficient of the unit; the non-convexity introduced by taking the expected power generation cost of the model as a target can be solved through a convex-concave process, the solving speed of the optimization task is obviously improved, the maximization of a wind power allowable interval is guaranteed, meanwhile, the expected power generation cost value corresponding to wind power fluctuation is taken as an economic target, and the minimum model of the actual power generation cost is reflected.
The invention is realized by at least one of the following technical schemes.
A method for synchronously optimizing wind power tolerance interval and expected generating cost of a unit comprises the following steps:
step S1, acquiring data;
s2, obtaining a correlation coefficient matrix rho of a standard normal distribution variable from the data obtained in the step S1 according to a Nataf transformation principle, and thus obtaining a lower triangular matrix B;
step S3, forming a sampling matrix Z for each time section t according to a three-point estimation method;
s4, mapping a standard normal sampling matrix Z into an original probability distribution space of the wind power plant through Nataf inverse transformation to obtain an available output sampling value of the wind power plant k;
step S5, comparing the relation between the available wind power output sampling value and the allowable interval to obtain an actual output value of the wind power plant, and further obtaining the actual output value of the unit through affine correction;
s6, constructing an expected power generation cost as an economic target by adopting the actual output value of the unit obtained in S5, and constructing a target function of the model together with a wind power punishment item;
step S7, eliminating the nonlinear term;
step S8, calculating the actual output of the unit;
step S9, a target function is embossed;
step S10, solving an objective function of the text model;
s11, carrying out Monte Carlo simulation by using the correction model to obtain the wind curtailment amount and the readjusted output of the unit for dealing with wind power fluctuation;
and step S12, controlling the actual output of the unit by the unit according to the calculated readjusted output, so that the expected value of the power generation cost is smaller, and the optimal economic benefit is achieved.
Further, the data acquired at step S1 includes: installed capacity of generator, position and rated power of wind power plant, maximum load in 24 time sections and wind power punishment item for wind power ground state output PW,k,tTracking expected wind power output PWF,k,tWind power allowable interval
Figure BDA0002254606310000031
And tracking wind power prediction interval
Figure BDA0002254606310000032
First penalty factor for the resulting deviationAnd a second penalty factor
Figure BDA0002254606310000034
The method comprises the steps of convergence tolerance, a correlation coefficient matrix rho of the wind power plant, generator set parameters, loads and wind power plant prediction data, wherein subscript W points to wind power output to be solved, subscript WF points to known wind power prediction output parameters, k indicates the wind power plant, and t indicates a time section.
Further, step S3 specifically includes: for each time section t, according to the three-point estimation method, there is NWA wind farm in an independent standard normal space
Figure BDA0002254606310000035
k＝1,...,NW2N in the form of 1,2WA sampling vector Zk,mThereby forming a sampling matrix
Figure BDA0002254606310000036
The number of rows and columns of the sampling matrix Z is NW×(2NW+1), wherein:
Figure BDA0002254606310000037
for intermediate quantities introduced, the indices are not equal to k and the values are all taken to be 0, Zk,mM-th sampling vector, vector Z, pointing to the k-th wind farm3All the elements of (A) are taken as 0; at the same time, Zk,1Element z in (1)k,1And the weights are respectively taken as
Figure BDA0002254606310000038
And 1/6; zk,2Element z in (1)k,2And the weights are respectively taken as
Figure BDA0002254606310000039
And 1/6; z3The weight of (1/N) is taken asW-1/3。
Further, step S4 includes: mapping the standard normal sampling matrix Z to the original probability distribution space of the wind power plant through Nataf inverse transformation to obtain an available output sampling value of the wind power plant k
Figure BDA00022546063100000310
The formula is as follows:
Y＝BZ
Figure BDA00022546063100000311
in the formula, Y is NW×(2NW+1) two-dimensional normal distribution correlation matrix, yk,uThe sampled value of the wind field k in the u column vector of the matrix Y, phi (-) is the cumulative distribution function of the standard normal distribution,
Figure BDA00022546063100000312
and B represents a lower triangular matrix which is an inverse function of the cumulative distribution function of the wind farm k on the time section t.
Further, step S5 includes: comparing the relation between the available output sampling value of the wind power and the allowable interval to obtain the actual output value of the wind power plant
Figure BDA0002254606310000041
And then obtaining the reality of the unit n through affine correctionForce output value
Figure BDA0002254606310000042
The specific formula is as follows:
Figure BDA0002254606310000043
Figure BDA0002254606310000044
wherein: the subscript G points to the variable to be solved or known parameter, Ω, of the generator setWFor the set of all wind farms, PG,n,tIs the ground state output, alpha, of the unit nn,k,tThe assumed coefficient of the unit n to the output fluctuation of the wind power plant k is P because the prediction interval is wider and the lower limit of the allowable interval is smaller than the lower limit of the prediction intervalW,k,tRepresenting the wind power basic state output, wherein only the available wind power output needs to be compared
Figure BDA0002254606310000045
And upper limit of allowable interval
Figure BDA0002254606310000046
The relationship (2) of (c).
Further, in step S6, the objective function of the text model is:
Figure BDA0002254606310000047
Figure BDA0002254606310000048
wherein: omegaTAnd ΩGRespectively, the set of all time sections and all generator sets, Cn(. to) is a cost function of power generation for the unit n, which is a quadratic function, MW,k,tIs a wind power penalty term, wherein
Figure BDA0002254606310000049
Is a wind power allowable areaThe lower limit of the interval between the two,
Figure BDA00022546063100000410
is the upper limit of the wind power allowable interval,P WF，k，tthe lower limit of the wind power prediction interval is set,
Figure BDA00022546063100000412
the lower limit of the wind power prediction interval is set,
Figure BDA00022546063100000413
further, step S7 specifically includes: eliminating wind power bearing coefficient alpha of a setn,k,tThe non-linear terms appearing for the variables are specifically formulated as follows:
Figure BDA00022546063100000414
Figure BDA0002254606310000051
wherein, the subscript GW points to the variable to be solved of the generator set for responding the output fluctuation of the wind power plant,and
Figure BDA0002254606310000053
the reserve capacities borne by the unit n for coping with the maximum positive and negative fluctuation of the wind farm k respectively,and
Figure BDA0002254606310000055
respectively providing an upper limit and a lower limit of allowable output of the unit n for dealing with wind power fluctuation;
due to the introduction of the wind power bearing coefficient alphan,k,tAfter being used as a variable, before optimization, the quasi-steady-state power distribution transfer factor of the wind power field k to the transmission section l in the power flow constraint is difficult to judgeSeed of Japanese apricot
Figure BDA0002254606310000056
So that there will still be a non-linear term, to eliminate the non-linear term in the flow constraint, the following relaxation process is adopted:
Figure BDA0002254606310000057
Figure BDA0002254606310000058
wherein:
Figure BDA0002254606310000059
and
Figure BDA00022546063100000510
respectively representing the minimum and maximum values of the influence of the wind farm k on the branch transmission power during the fluctuation within the tolerance interval, one of which is fixed at three endpoints
Figure BDA00022546063100000511
Namely obtaining the lower limit, the upper limit and the ground state value of the wind power allowable interval; gl,n、gl,k、gl,iThe power distribution transfer factors P of the unit n, the wind power plant k and the load node i to the line l are respectivelyD,i,tIs the total load of the load node i, ΩDFor the set of all the load nodes,
Figure BDA00022546063100000512
andT lrespectively, the upper limit and the lower limit of the power flow of the line l.
Further, step S8 is to calculate the actual output of the unit as follows:
the actual output of the unit n is described as:
Figure BDA0002254606310000061
Figure BDA0002254606310000062
wherein:
Figure BDA0002254606310000063
representing the actual force output value of the unit obtained through an affine correction process;
Figure BDA0002254606310000064
and
Figure BDA0002254606310000065
wind power bearing coefficients of the set for dealing with positive and negative fluctuation of wind power;
the affine correction process is as follows: to be provided with
Figure BDA0002254606310000066
And
Figure BDA0002254606310000067
as affine factors, the actual output of the unit after the wind power positive and negative fluctuation is corrected
Figure BDA0002254606310000068
Expressed as the amount of fluctuation of the wind power in the formula (1)
Figure BDA0002254606310000069
The affine relationship of (1).
Because the nonlinear term of multiplication of the wind power positive and negative fluctuation bearing coefficient and the wind power unbalance exists in the formula, the text model is difficult to solve the actual output of the unit, and the formula is subjected to approximate processing for further eliminating the nonlinear term:
Figure BDA00022546063100000610
Figure BDA00022546063100000611
Figure BDA00022546063100000612
wherein:
Figure BDA00022546063100000613
and PW0,k,tAnd respectively obtaining the wind power allowable interval and the ground state output which are obtained by the traditional robust interval scheduling model.
Further, in step S9, the objective function f is a non-convex function, and is mainly composed of a difference between two convex functions, and the objective function f is described as:
in the formula (I), the compound is shown in the specification,
Figure BDA0002254606310000072
the remaining part of the objective function f except for the reduced convex function, i.e., the objective function f in step S6 is removedThe remainder of (a); a isnAs a function of the cost of electricity generation CnCoefficient of quadratic term of (·).
Solving the objective function f by adopting a Convex-Concave process (CCP), and firstly, carrying out linear approximation on a reduced item in the objective function by using a first-order Taylor formula to obtain an objective function expression fsNamely:
wherein: s is the current number of iterations,
Figure BDA0002254606310000075
and
Figure BDA0002254606310000076
and the actual output of the CCP for the last iteration and the current iteration of the CCP is obtained.
The CCP continuously iterates through a first-order Taylor formula to enable the optimization result to gradually approach to an optimal point, and when the optimization results of the last two times meet the following convergence requirements, the CCP converges to an optimal solution of a target function f:
|fs-fs-1|≤ε|fs|
wherein: ε represents a convergence tolerance.
Further, step S10 is to solve the model by using CPLEX software.
Further, step S11 specifically includes: monte Carlo simulation is carried out by utilizing the correction model to obtain the abandoned air volume
Figure BDA0002254606310000077
Readjusting output delta p of harmonic generator set for wind power fluctuationGW,n,k；
In the correction model, the capital letters or the quantities with subscripts t are constants or solved variables of the text model, and the small letters or the quantities without subscripts t are variables to be solved in the correction model;
Figure BDA0002254606310000078
for simulating wind power sampling values in a scene, pWF,kThe wind power available output of the current simulation scene on the time section t is as follows:
the correction model only simulates a single time section t of each simulation scene, and the objective function of the model is as follows:
Figure BDA0002254606310000081
wherein: p is a radical ofG,n、pW,kAnd pD,iRespectively the actual output of the unit, the actual output of the wind power and the actual value of the residual load, m1And m2Respectively, wind curtailment and load shedding penalty coefficient, m1＝a、m2＝10a，PD,i,tThe total load capacity of the load node i;
the constraints of the correction model include:
Figure BDA0002254606310000082
Figure BDA0002254606310000083
ΔpGD,n,i＝αn(pD,i-PD,i,t)ΔpGD,n,i≤0
Figure BDA0002254606310000085
Figure BDA0002254606310000086
wherein: alpha is alphanIs the bearing coefficient, delta p, of the power unbalance quantity generated by the unit after the tangential loadGW,n,kThe amount of power unbalance, delta p, born by the unit to cope with wind power fluctuationGD,n,iThe amount of the power unbalance borne by the unit after load shedding,
Figure BDA0002254606310000087
and
Figure BDA0002254606310000088
respectively the remaining positive and negative rotation reserve capacities,andP G，n，trespectively the maximum output force and the minimum output force of the machine set,
Figure BDA00022546063100000811
and
Figure BDA00022546063100000812
respectively positive and negative rotation reserve capacities,
Figure BDA00022546063100000813
andthe rotating standby requirements in the day ahead are respectively; pD,iExpressed as the total load capacity of the load node i;
for robust interval scheduling, there are
Figure BDA0002254606310000092
Wherein:and
Figure BDA0002254606310000094
and wind power bearing coefficients for wind power allowable interval upper limit and wind power positive and negative fluctuation of the unit are obtained.
Furthermore, while the maximization of the wind power allowable interval is ensured, a power generation cost expected value corresponding to wind power fluctuation is taken as an economic target, a minimization model of actual power generation cost is reflected, a wind power bearing coefficient of an AGC unit is taken as a variable to be optimized, meanwhile, a wind power available output sampling matrix is formed based on a three-point estimation method of Nataf inverse transformation, the expected power generation cost is constructed as the economic target, and the synchronous optimization of the wind power allowable interval and the expected power generation cost is realized on the model;
further, in a solving algorithm based on nonlinear term relaxation processing and a convex-concave process, the wind power bearing coefficient of an AGC unit is eliminated through relaxation processing and approximate calculation as a variable and a nonlinear term introduced when the unit actually outputs power is calculated;
further, in a solving algorithm based on nonlinear term relaxation processing and a convex-concave process, for non-convexity introduced by taking expected power generation cost as a target, a convex-concave process is adopted for iterative processing, and finally, the solving process is completely converted into a quadratic programming problem.
The method for synchronously optimizing the wind power allowable interval and the expected generating cost of the unit is based on a three-point estimation method of Nataf inverse transformation, the actual generating cost expected value under wind power fluctuation is taken as an economic target, and synchronous optimization of the wind power allowable interval and the expected generating cost is realized on the basis of a model. The provided solving algorithm based on the nonlinear term relaxation processing and the convex-concave process can solve the nonlinear term introduced for improving the wind power absorption capacity, and obviously improves the solving speed of the optimization task through the non-convexity introduced by taking the expected power generation cost of a convex-concave process solving model as a target.
Compared with the prior art, the method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit has the following advantages and effects:
(1) compared with the traditional robust interval scheduling method, the wind power robust estimation method provided by the invention takes the expected value of the power generation cost as an economic target, and reduces the power generation cost in the actual scheduling process on the premise of ensuring that the wind power consumption effect is consistent with the traditional robust interval scheduling.
(2) According to the method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit, which is designed by the invention, the expected value of the power generation cost optimized by the described model is basically close to the actual expected value of the power generation cost, and the method can be considered to truly reflect the power generation cost in the actual scheduling process.
(3) The method and the model provided by the invention can keep consistent wind power consumption effect with the existing robust interval scheduling model and have the same robustness.
(4) According to the method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit, the method and the model provided by the invention can truly reflect the minimization of the power generation cost in the actual scheduling process, and have good adaptability to wind power prediction intervals with different wind power available output and fluctuation ranges under different probability distributions.
Drawings
FIG. 1 is a flowchart illustrating a method for synchronously optimizing a wind power tolerance interval and a desired power generation cost of a unit according to this embodiment;
fig. 2a is a machine set performance diagram of the conventional robust interval scheduling with higher cost in this embodiment;
fig. 2b is a diagram illustrating the unit performance of the conventional robust interval scheduling with low cost according to the embodiment;
FIG. 3a is a diagram illustrating the operation of the present embodiment of the present invention with higher cost;
FIG. 3b is a diagram illustrating the operation of the present embodiment with a lower cost by using the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit is shown in FIG. 1. The method starts from a traditional robust interval scheduling model, constructs an optimization model for the system power generation cost when wind power fluctuation is responded in the actual scheduling process, and further solves the minimization problem that the actual power generation cost is reflected by taking the power generation cost expected value corresponding to the wind power fluctuation as an economic target while the maximization of a wind power allowable interval is ensured. The method comprises the following steps:
step S1, obtaining installed capacity of a generator, position and rated power of a wind power plant, maximum load in 24 time sections and wind power basic state output P in wind power punishment itemsW,k,tTracking expected wind power output PWF,k,tWind power allowable interval
Figure BDA0002254606310000111
And tracking wind power prediction interval
Figure BDA0002254606310000112
First penalty factor for the resulting deviation
Figure BDA0002254606310000113
And a second penalty factor
Figure BDA0002254606310000114
Convergence tolerance, a correlation coefficient matrix rho of the wind power plant, generator set parameters, load and wind power plant prediction data, wherein N isWThe subscript W points to wind power output to be solved, the subscript WF points to known wind power prediction output parameters, k indicates a wind power plant, and t indicates time.
This example uses the IEEE 118 power network as an example of a simulation. The generator set comprises 34 generators, the total installed capacity is 4600MW, wherein the units No. 6-8, No. 10-13, No. 15-16 and No. 28-29 are AGC units; the 5 wind power plants are respectively positioned at nodes 12, 54, 61, 77 and 100 of the network, and the rated power is respectively 100, 200, 300, 400 and 400 MW; the maximum load in 24 time sections was 4500 MW; in the wind power punishment item
Figure BDA0002254606310000115
The convergence tolerance ε is set to 10-7In the calculation example, the midpoint of the wind power prediction interval is assumed as expected output, and the correlation coefficient matrix rho of the wind power plant covering the prediction interval with the probability of 99.9% for the available output of the wind power is as follows:
Figure BDA0002254606310000116
genset parameters, as shown in table 1:
TABLE 1 Generator set parameters
Figure BDA0002254606310000117
Figure BDA0002254606310000121
Load and wind farm forecast data, as shown in table 2:
TABLE 2 load and wind farm forecast data
Figure BDA0002254606310000131
Step S2, obtaining a correlation coefficient matrix rho of the standard normal distribution variable according to the Nataf transformation principle0To thereby obtain ρ0A lower triangular matrix B;
converting the correlation coefficient matrix rho of the step S1 into a correlation coefficient matrix rho by utilizing the Nataf transformation principle0。
Step S3, forming a sampling matrix Z for each time section t according to a three-point estimation method; for each time section t, according to the three-point estimation method, there is NWA wind farm in an independent standard normal space
Figure BDA0002254606310000141
Formal structure 2NWA sampling vector Zk,mThereby forming a sampling matrix
Figure BDA0002254606310000142
The number of rows and columns of the sampling matrix Z is NW×(2NW+1) of vector Z3All the elements of (A) are taken as 0, and simultaneously, Zk,1Element z in (1)k,1And the weights are respectively taken as
Figure BDA0002254606310000143
And 1/6; zk,2Element z in (1)k,2And the weights are respectively taken asAnd 1/6; z3The weight of (1/N) is taken asW-1/3。
S4, mapping the standard normal sampling matrix Z to the original probability distribution space of the wind power plant through Nataf inverse transformation to obtain an available output sampling value of the wind power plant k
Figure BDA0002254606310000145
Y＝BZ
Figure BDA0002254606310000146
In the formula, Y is NW×(2NW+1) two-dimensional normal distribution correlation matrix, yk,uThe sampled value of the wind field k in the u column vector of the matrix Y, phi (-) is the cumulative distribution function of the standard normal distribution,
Figure BDA0002254606310000147
and B represents a lower triangular matrix which is an inverse function of the cumulative distribution function of the wind farm k on the time section t.
Step S5, comparing the relation between the available output sampling value of the wind power and the allowable interval to obtain the actual output value of the wind power plant
Figure BDA0002254606310000148
And then obtaining the actual output value of the unit n through an affine correction process
Figure BDA0002254606310000149
As shown in the following equation:
Figure BDA00022546063100001410
Figure BDA00022546063100001411
wherein: the subscript G points to the variable to be solved or known parameter, Ω, of the generator setWFor the set of all wind farms, PG,n,tIs the ground state output, alpha, of the unit nn,k,tThe assumed coefficient of the unit n to the output fluctuation of the wind power plant k is P because the prediction interval is wider and the lower limit of the allowable interval is smaller than the lower limit of the prediction intervalW,k,tRepresenting the wind power basic state output, wherein only the available wind power output needs to be comparedAnd upper limit of allowable interval
Figure BDA0002254606310000152
The relationship (2) of (c).
Step S6, taking the expected power generation cost as an economic target, and forming an objective function of the text model together with the wind power penalty term
Figure BDA0002254606310000153
Figure BDA0002254606310000154
Figure BDA0002254606310000155
Wherein: omegaTAnd ΩGRespectively, the set of all time sections and all generator sets, Cn(. to) is a cost function of power generation for the unit n, which is a quadratic function, MW,k,tAnd a wind power penalty item.
And step S7, elimination of the nonlinear term. Eliminating the nonlinear term of the outgoing line in the previous step, and performing the following processing:
Figure BDA0002254606310000156
Figure BDA0002254606310000157
wherein, the subscript GW points to the variable to be solved of the generator set for responding the output fluctuation of the wind power plant,
Figure BDA0002254606310000158
and
Figure BDA0002254606310000159
handling wind farm k max respectively borne by unit nThe spare capacity of the positive and negative fluctuations,
Figure BDA00022546063100001510
andrespectively providing an upper limit and a lower limit of allowable output of the unit n for dealing with wind power fluctuation;
due to difficulty in judging before optimizing
Figure BDA0002254606310000161
And thus there will still be non-linear terms. To eliminate the non-linear terms in the equations, the following relaxation process is adopted:
Figure BDA0002254606310000162
Figure BDA0002254606310000163
in the formula (I), the compound is shown in the specification,andextreme values representing the influence of the fluctuations of the wind farm k in the tolerance interval on the branch transmission power, which are fixed at three terminals
Figure BDA0002254606310000166
Obtaining the lower limit, the upper limit and the ground state value of the wind power allowable interval; gl,n、gl,k、gl,iThe power distribution transfer factors P of the unit n, the wind power plant k and the load node i to the line l are respectivelyD,i,tIs the total load of the load node i, ΩDFor the set of all the load nodes,
Figure BDA0002254606310000167
andT lupper limit of power flow for line lAnd a lower limit.
And step S8, approximate calculation of the actual output of the unit. The actual capacity of the unit can be described as:
Figure BDA0002254606310000169
Figure BDA00022546063100001610
wherein:representing the actual force output value of the unit obtained through an affine correction process;
Figure BDA00022546063100001612
and
Figure BDA00022546063100001613
and the wind power bearing coefficient of the unit for dealing with positive and negative fluctuation of wind power is obtained.
Because the nonlinear term of multiplication of the wind power positive and negative fluctuation bearing coefficient and the wind power unbalance exists in the above formula, the model is difficult to solve the actual output of the unit, and the above formula is subjected to approximate processing for further eliminating the nonlinear term:
the above equation is approximated:
Figure BDA0002254606310000171
Figure BDA0002254606310000172
Figure BDA0002254606310000173
in the formula (I), the compound is shown in the specification,
Figure BDA0002254606310000174
and PW0，k，tAnd respectively obtaining the wind power allowable interval and the ground state output which are obtained by the traditional robust interval scheduling model.
And step S9, the target function is convex. The objective function f is a non-convex function, which essentially consists of the difference of two convex functions, which can be described as:
Figure BDA0002254606310000176
in the formula (I), the compound is shown in the specification,
Figure BDA0002254606310000177
the remaining part of the objective function f except for the reduced convex function, i.e., the objective function f in step S6 is removed
Figure BDA0002254606310000178
The remainder of (a); a isnAs a function of the cost of electricity generation CnCoefficient of quadratic term of (·).
Based on this characteristic of the objective function, a Convex-Concave process (CCP) may be used for the solution. Firstly, linear approximation is carried out on the reduced terms in the objective function by using a first-order Taylor formula to obtain an objective function expression fsNamely:
Figure BDA0002254606310000181
wherein: s is the current number of iterations,
Figure BDA0002254606310000182
and
Figure BDA0002254606310000183
and the actual output of the CCP for the last iteration and the current iteration of the CCP is obtained.
The CCP is iterated continuously through a first-order Taylor formula, so that the optimization result gradually approaches to an optimal point. When the last two optimization results are close enough, the CCP converges to the optimal solution of the objective function f.
And step S10, solving the model. The model is completely converted into a quadratic programming problem, and CPLEX software can be adopted for solving.
Step S11, Monte Carlo simulation is carried out by utilizing the correction model to calculate the air curtailment quantity
Figure BDA0002254606310000184
Readjusting output delta p of harmonic generator set for wind power fluctuationGW,n,k。
Figure BDA0002254606310000185
For simulating wind power sampling values in a scene, pWF,kAnd the available wind power output of the current simulation scene on the time section t. For a single time slice t of each simulated scene, the correction model is as follows:
the correction model only simulates a single time section t of each simulation scene, and the objective function of the model is as follows:
Figure BDA0002254606310000186
wherein: p is a radical ofG,n、pWF,kAnd pD,iRespectively the actual output of the unit, the actual output of the wind power and the actual value of the residual load, m1And m2Respectively, wind curtailment and load shedding penalty coefficient, m1＝a、m2＝10a，PD,i,tThe total load capacity of the load node i;
the constraints of the correction model include:
Figure BDA0002254606310000187
Figure BDA0002254606310000191
ΔpGD,n,i＝αn(pD,i-PD,i,t)ΔpGD,n,i≤0
Figure BDA0002254606310000192
Figure BDA0002254606310000193
wherein: alpha is alphanIs the bearing coefficient, delta p, of the power unbalance quantity generated by the unit after the tangential loadGW,n,kThe amount of power unbalance, delta p, born by the unit to cope with wind power fluctuationGD,n,iThe amount of the power unbalance borne by the unit after load shedding,
Figure BDA0002254606310000194
andrespectively the remaining positive and negative rotation reserve capacities,
Figure BDA0002254606310000196
andP G，n，trespectively the maximum output force and the minimum output force of the machine set,and
Figure BDA0002254606310000199
respectively for the solved positive and negative rotation reserve capacity,and
Figure BDA00022546063100001911
the rotating standby requirements in the day ahead are respectively;
for robust interval scheduling, there are
Figure BDA00022546063100001912
Figure BDA00022546063100001913
Wherein:
Figure BDA00022546063100001914
and
Figure BDA00022546063100001915
the method is used for solving the upper limit of the wind power allowable interval and the amount of power unbalance born by the unit for dealing with positive and negative fluctuation of wind power.
And step S12, the unit controls the actual output according to the calculated readjusted output, so that the expected value of the power generation cost is smaller, and the optimal economic benefit is achieved.
Through the steps, the maximum wind power allowable interval is guaranteed, meanwhile, the expected value of the power generation cost corresponding to wind power fluctuation is used as an economic target, a minimum model of the actual power generation cost is reflected, and meanwhile, the wind power allowable interval and the expected power generation cost of the unit are synchronously optimized.
Comparing fig. 2a, fig. 2b, fig. 3a and fig. 3b, it can be known that, compared with the conventional robust interval scheduling, the method mostly transfers the spare capacity tracking the downward fluctuation of wind power to the AGC set with lower cost, and thus it can be known that the method optimizes the process of upward adjustment of the AGC (automatic Generation control) set with lower cost in the actual scheduling, thereby achieving the optimization of the wind power allowable interval and the optimization of the power Generation cost at the same time.
The above examples are merely illustrative of the embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims (10)

1. A method for synchronously optimizing a wind power tolerance interval and expected power generation cost of a unit is characterized by comprising the following steps:
step S1, acquiring data;
s2, obtaining a correlation coefficient matrix rho of a standard normal distribution variable from the data obtained in the step S1 according to a Nataf transformation principle, and thus obtaining a lower triangular matrix B;
step S3, forming a sampling matrix Z for each time section t according to a three-point estimation method;
s4, mapping a standard normal sampling matrix Z into an original probability distribution space of the wind power plant through Nataf inverse transformation to obtain an available output sampling value of the wind power plant k;
step S5, comparing the relation between the available wind power output sampling value and the allowable interval to obtain an actual output value of the wind power plant, and further obtaining the actual output value of the unit through affine correction;
s6, constructing an expected power generation cost as an economic target by adopting the actual output value of the unit obtained in S5, and constructing a target function of the model together with a wind power punishment item;
step S7, eliminating the nonlinear term;
step S8, calculating the actual output of the unit;
step S9, a target function is embossed;
step S10, solving an objective function of the text model;
s11, carrying out Monte Carlo simulation by using the correction model to obtain the wind curtailment amount and the readjusted output of the unit for dealing with wind power fluctuation;
and step S12, controlling the actual output of the unit by the unit according to the calculated readjusted output.
2. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit according to claim 1, wherein the data obtained in the step S1 comprises: installed capacity of generator, position and rated power of wind power plant, maximum load in 24 time sections and wind power punishment item for wind power ground state output PW,k,tTracking expected wind power output PWF,k,tWind power allowable interval
Figure FDA0002254606300000011
And tracking wind power prediction interval
Figure FDA0002254606300000021
First penalty factor for the resulting deviation
Figure FDA0002254606300000022
And a second penalty factorThe method comprises the steps of convergence tolerance, a correlation coefficient matrix rho of the wind power plant, generator set parameters, loads and wind power plant prediction data, wherein subscript W points to wind power output to be solved, subscript WF points to known wind power prediction output parameters, k indicates the wind power plant, and t indicates a time section.
3. The method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit according to claim 1, wherein the step S3 specifically comprises: for each time section t, according to the three-point estimation method, there is NWA wind farm in an independent standard normal space
Figure FDA0002254606300000024
k＝1,...,NW2N in the form of 1,2WA sampling vector Zk,mThereby forming a sampling matrix
Figure FDA0002254606300000025
The number of rows and columns of the sampling matrix Z is NW×(2NW+1), wherein:
Figure FDA0002254606300000026
for intermediate quantities introduced, the indices are not equal to k and the values are all taken to be 0, Zk,mM-th sampling vector, vector Z, pointing to the k-th wind farm3All the elements of (A) are taken as 0; at the same time, Zk,1In (1)Element zk,1And the weights are respectively taken as
Figure FDA0002254606300000027
And 1/6; zk,2Element z in (1)k,2And the weights are respectively taken as
Figure FDA0002254606300000028
And 1/6; z3The weight of (1/N) is taken asW-1/3。
4. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit according to claim 1, wherein the step S4 comprises: mapping the standard normal sampling matrix Z to the original probability distribution space of the wind power plant through Nataf inverse transformation to obtain an available output sampling value of the wind power plant kThe formula is as follows:
Y＝BZ
in the formula, Y is NW×(2NW+1) two-dimensional normal distribution correlation matrix, yk,uThe sampled value of the wind field k in the u column vector of the matrix Y, phi (-) is the cumulative distribution function of the standard normal distribution,
Figure FDA00022546063000000211
and B represents a lower triangular matrix which is an inverse function of the cumulative distribution function of the wind farm k on the time section t.
5. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit according to claim 1, wherein the step S5 comprises: comparing the relation between the available output sampling value of the wind power and the allowable interval to obtain the actual output value of the wind power plant
Figure FDA0002254606300000031
And then obtaining the actual output value of the unit n through affine correction
Figure FDA0002254606300000032
The specific formula is as follows:
Figure FDA0002254606300000033
Figure FDA0002254606300000034
wherein: the subscript G points to the variable to be solved or known parameter, Ω, of the generator setWFor the set of all wind farms, PG,n,tIs the ground state output, alpha, of the unit nn,k,tThe assumed coefficient of the unit n to the output fluctuation of the wind power plant k is P because the prediction interval is wider and the lower limit of the allowable interval is smaller than the lower limit of the prediction intervalW,k,tRepresenting the wind power basic state output, wherein only the available wind power output needs to be compared
Figure FDA0002254606300000035
And upper limit of allowable interval
Figure FDA0002254606300000036
The relationship (2) of (c).
6. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit according to claim 1, wherein in step S6, the objective function of the model is as follows:
Figure FDA0002254606300000037
Figure FDA0002254606300000038
wherein: omegaTAnd ΩGRespectively, the set of all time sections and all generator sets, Cn(. to) is a cost function of power generation for the unit n, which is a quadratic function, MW,k,tIs a wind power penalty term, whereinThe lower limit of the wind power allowable interval is,
Figure FDA00022546063000000310
is the upper limit of the wind power tolerance interval, PWF,k,tThe lower limit of the wind power prediction interval is set,the lower limit of the wind power prediction interval is set,
Figure FDA00022546063000000312
7. the method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit according to claim 1, wherein the step S7 specifically comprises: eliminating wind power bearing coefficient alpha of a setn,k,tThe non-linear terms appearing for the variables are specifically formulated as follows:
Figure FDA0002254606300000041
Figure FDA0002254606300000042
wherein, the subscript GW points to the variable to be solved of the generator set for responding the output fluctuation of the wind power plant,
Figure FDA0002254606300000043
and
Figure FDA0002254606300000044
the reserve capacities borne by the unit n for coping with the maximum positive and negative fluctuation of the wind farm k respectively,
Figure FDA0002254606300000045
and
Figure FDA0002254606300000046
respectively providing an upper limit and a lower limit of allowable output of the unit n for dealing with wind power fluctuation;
due to the introduction of the wind power bearing coefficient alphan,k,tAfter being used as a variable, before optimization, the quasi-steady-state power distribution transfer factor of the wind power field k to the transmission section l in the power flow constraint is difficult to judge
Figure FDA0002254606300000047
So that there will still be a non-linear term, to eliminate the non-linear term in the flow constraint, the following relaxation process is adopted:
Figure FDA0002254606300000048
Figure FDA0002254606300000049
wherein:
Figure FDA00022546063000000410
and
Figure FDA00022546063000000411
respectively representing the minimum and maximum values of the influence of the wind farm k on the branch transmission power during the fluctuation within the tolerance interval, one of which is fixed at three endpoints
Figure FDA00022546063000000412
Namely obtaining the lower limit, the upper limit and the ground state value of the wind power allowable interval; gl,n、gl,k、gl,iThen the unit n, the wind power field k and the load node i are respectively aligned with the linePower distribution transfer factor, P, of way lD,i,tIs the total load of the load node i, ΩDFor the set of all the load nodes,
Figure FDA0002254606300000051
andT lrespectively, the upper limit and the lower limit of the power flow of the line l.
8. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit according to claim 1, wherein the step S8 is implemented by calculating the actual output of the unit as follows:
the actual output of the unit n is described as:
Figure FDA0002254606300000052
Figure FDA0002254606300000053
wherein:
Figure FDA0002254606300000054
representing the actual force output value of the unit obtained through an affine correction process;
Figure FDA0002254606300000055
and
Figure FDA0002254606300000056
wind power bearing coefficients of the set for dealing with positive and negative fluctuation of wind power;
the affine correction process is as follows: to be provided with
Figure FDA0002254606300000057
And
Figure FDA0002254606300000058
as affine factors, the wind power positive and negative fluctuation of the unit is correctedActual force after
Figure FDA0002254606300000059
Expressed as the amount of fluctuation of the wind power in the formula (1)
Figure FDA00022546063000000510
The affine relationship of (1);
because the nonlinear term of multiplication of the wind power positive and negative fluctuation bearing coefficient and the wind power unbalance exists in the formula, the text model is difficult to solve the actual output of the unit, and the formula is subjected to approximate processing for further eliminating the nonlinear term:
Figure FDA00022546063000000511
Figure FDA0002254606300000061
Figure FDA0002254606300000062
wherein:
Figure FDA0002254606300000063
and PW0,k,tAnd respectively obtaining the wind power allowable interval and the ground state output which are obtained by the traditional robust interval scheduling model.
9. The method for synchronously optimizing the wind power allowable interval and the expected power generation cost of the unit according to claim 1, wherein in step S9, the objective function f is a non-convex function, and is mainly composed of the difference between two convex functions, and the objective function f is described as:
Figure FDA0002254606300000064
in the formula (I), the compound is shown in the specification,the remaining part of the objective function f except for the reduced convex function, i.e., the objective function f in step S6 is removed
Figure FDA0002254606300000066
The remainder of (a); a isnAs a function of the cost of electricity generation CnCoefficient of quadratic term of (·);
solving the objective function f by adopting a Convex-Concave process (CCP), and firstly, carrying out linear approximation on a reduced item in the objective function by using a first-order Taylor formula to obtain an objective function expression fsNamely:
Figure FDA0002254606300000067
wherein: s is the current number of iterations,
Figure FDA0002254606300000068
and
Figure FDA0002254606300000069
actual output of the set for the last iteration and the current iteration of the CCP
The CCP continuously iterates through a first-order Taylor formula to enable the optimization result to gradually approach to an optimal point, and when the optimization results of the last two times meet the following convergence requirements, the CCP converges to an optimal solution of a target function f:
|fs-fs-1|≤ε|fs|
wherein: ε represents a convergence tolerance.
10. The method for synchronously optimizing the wind power tolerance interval and the expected power generation cost of the unit as claimed in claim 1, wherein step S10 is to solve the model by using CPLEX software;
step S11 specifically includes: monte Carlo simulation is carried out by utilizing the correction model to obtain the abandoned air volume
Figure FDA0002254606300000071
Readjusting output delta p of harmonic generator set for wind power fluctuationGW,n,k；
In the correction model, the capital letters or the quantities with subscripts t are constants or solved variables of the text model, and the small letters or the quantities without subscripts t are variables to be solved in the correction model;
Figure FDA0002254606300000072
for simulating wind power sampling values in a scene, pWF,kThe wind power available output of the current simulation scene on the time section t is as follows:
the correction model only simulates a single time section t of each simulation scene, and the objective function of the model is as follows:
Figure FDA0002254606300000073
wherein: p is a radical ofG,n、pW,kAnd pD,iRespectively the actual output of the unit, the actual output of the wind power and the actual value of the residual load, m1And m2Respectively, wind curtailment and load shedding penalty coefficient, m1＝a、m2＝10a，PD,i,tThe total load capacity of the load node i;
the constraints of the correction model include:
Figure FDA0002254606300000074
Figure FDA0002254606300000075
Figure FDA0002254606300000081
ΔpGD,n,i＝αn(pD,i-PD,i,t)ΔpGD,n,i≤0
Figure FDA0002254606300000082
Figure FDA0002254606300000083
wherein: alpha is alphanIs the bearing coefficient, delta p, of the power unbalance quantity generated by the unit after the tangential loadGW,n,kThe amount of power unbalance, delta p, born by the unit to cope with wind power fluctuationGD,n,iThe amount of the power unbalance borne by the unit after load shedding,
Figure FDA0002254606300000084
and
Figure FDA0002254606300000085
respectively the remaining positive and negative rotation reserve capacities,
Figure FDA0002254606300000086
andP G,n,trespectively the maximum output force and the minimum output force of the machine set,
Figure FDA0002254606300000087
and
Figure FDA0002254606300000088
respectively positive and negative rotation reserve capacities,
Figure FDA0002254606300000089
andthe rotating standby requirements in the day ahead are respectively; pD,iExpressed as the total load capacity of the load node i;
for robust interval scheduling, there are
Figure FDA00022546063000000812
Wherein:and
Figure FDA00022546063000000814
and wind power bearing coefficients for wind power allowable interval upper limit and wind power positive and negative fluctuation of the unit are obtained.
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