CN112186765B - Modeling method of day-ahead scheduling model of unit combination decision - Google Patents

Modeling method of day-ahead scheduling model of unit combination decision Download PDF

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CN112186765B
CN112186765B CN202011110581.6A CN202011110581A CN112186765B CN 112186765 B CN112186765 B CN 112186765B CN 202011110581 A CN202011110581 A CN 202011110581A CN 112186765 B CN112186765 B CN 112186765B
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杨楠
王璇
李宏圣
黎索亚
叶迪
黄禹
董邦天
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China Three Gorges University CTGU
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Abstract

A modeling method of a day-ahead scheduling model of unit combination decision comprises the following steps: step 1, dividing a unit combination decision into a basic scene and a worst scene; step 2, modeling a day-ahead scheduling model in a basic scene by taking the uncertainty factor power predicted value as a basis, taking the minimum total system operation cost as a target and considering conventional constraint conditions in a deterministic environment; and 3, modeling a day-ahead scheduling model in the worst scene by taking the maximum fluctuation output of the uncertain power output as the basis and considering uncertain constraint conditions. The method divides the unit combination decision into a basic scene and a worst scene for modeling respectively, wherein the basic scene takes uncertainty factor power predicted value as a basis, takes the minimum total operation cost of the system as a target, and considers various conventional constraint conditions of the system in a deterministic environment, thereby ensuring the economy of the scheduling decision.

Description

Modeling method of day-ahead scheduling model of unit combination decision
Technical Field
The invention discloses a modeling method of a unit combination decision day-ahead scheduling model, and relates to the field of power system scheduling.
Background
Wind power and photovoltaic are pollution-free and green renewable energy sources, are widely distributed, have high energy density and are suitable for large-scale development, so that wind power and photovoltaic power generation technologies are highly valued by countries in the world. However, because the output of the power grid has the characteristics of randomness and volatility, the large-scale access to the power grid brings great challenges to the traditional scheduling method, and therefore, the research on the day-ahead scheduling method of the power system under the large-scale access of various new energy resources has important theoretical value and practical significance.
At present, a plurality of experts and scholars research the day-ahead scheduling problem of an electric power system under new energy access from different angles, but generally only a single uncertainty variable is considered, however, an actual electric power system comprises multiple uncertainty factors such as wind power output, photovoltaic output and load prediction error, and the existing day-ahead scheduling only considering single uncertainty is obviously difficult to guarantee the decision effectiveness and influence the economical efficiency of system operation. Therefore, considering the influence of multiple uncertainty factors in the scheduling problem has become a hot point for the research of experts in recent years.
Disclosure of Invention
Aiming at the defects of the existing method, the invention provides an improved robust scheduling method which comprehensively considers uncertainty and correlation of load, wind power and photovoltaic.
The technical scheme adopted by the invention is as follows:
a power system day-ahead robust scheduling method considering multiple uncertainties and correlations comprises the following steps:
1) the method comprises the following steps of (1) taking multiple random factors into consideration for day-ahead robust scheduling modeling;
2) solving a worst scenario;
3) solving the model by a Benders decomposition method;
in the step 1), firstly, the day-ahead robust scheduling modeling of multiple random factors is considered; then carrying out day-ahead scheduling modeling in a basic scene; then carrying out day-ahead scheduling modeling in an uncertain scene;
in the step 2), firstly, probability density function modeling of random factors is carried out, then samples are sampled, and then orthogonal transformation matrix derivation is carried out; then, solving a worst scene;
in the step 3), modeling of a UC main problem is firstly carried out, and then modeling of a safety sub-problem in a basic scene is carried out; and then modeling a safety sub-problem considering uncertainty.
In the step 1), multiple random factors comprise wind power, photovoltaic and load prediction error factors.
In the step 1), the unit combination decision is divided into a basic scene and a worst scene for modeling respectively.
The basic scenario is based on the uncertainty factor power predicted value, the minimum total operation cost of the system is taken as a target, and various conventional constraint conditions of the system in a deterministic environment are considered.
The worst scenario is based on the maximum fluctuation output of the uncertain power output, and the uncertain constraint condition is considered.
In step 2), the worst scene is sought, and then robustness check is performed by directly using the worst scene.
Firstly, probability density functions of wind power, photovoltaic and load are respectively constructed by utilizing nonparametric kernel density estimation, then, a Latin hypercube sampling is utilized to generate samples, finally, a Cholesky decomposition method is adopted to convert the random samples with correlation into mutually independent random samples, and the worst scene is determined on the basis of the mutually independent random samples.
If the number of load samples based on the historical data is n, constructing a probability density model of the load based on a non-parametric kernel density estimation method as follows:
Figure GDA0003630030690000021
in the formula, phi (P)d) Is a probability density function of the load; k (P)dL) is a kernel function; pdmIs the m-th sample value in the load sample, and l is the bandwidth.
Selecting a Gaussian function as a kernel function of the load probability density model, and solving the bandwidth l to obtain a probability density function phi (P) of the system loadd)。
Calculating the probability density function phi (P) of the wind power outputw) And a photovoltaic output probability density function phi (P)v). As shown in formula (2) and formula (3).
Figure GDA0003630030690000022
In the formula, phi (P)w) Is a probability density function of the load; k (P)wL) is a kernel function; pwmAnd l is the bandwidth, wherein the m is the sample value in the wind power output sample.
Figure GDA0003630030690000023
In the formula, phi (P)v) Is a probability density function of the load; k (P)vL) is a kernel function; pvmAnd l is the bandwidth, and is the mth sample value in the photovoltaic output sample.
Latin hypercube sampling is adopted for hierarchical sampling.
Let the sampling scale be N, Ym＝Fm(Xm) Denotes the m-th random variable XmThe specific sampling process of the probability density function of (1) is as follows: will be interval [0,1]The average is divided into N equal parts, the middle value of each subinterval is selected, and the sampling value is obtained through the inverse function of the middle value
Figure GDA0003630030690000036
And obtaining a sample matrix of all the random variables after sampling of all the random variables is completed.
The method comprises the steps of describing the correlation among loads, wind power and photovoltaic power generation by utilizing a correlation coefficient matrix, and setting a sample matrix obtained by Latin hypercube sampling as W ═ W1,w2,…wl]TThe matrix of correlation coefficients is Cw：
Figure GDA0003630030690000031
The elements of the matrix can be obtained by equation (5):
Figure GDA0003630030690000032
in the formula:
Figure GDA0003630030690000033
and
Figure GDA0003630030690000034
are respectively an input variable wiAnd wjStandard deviation of (d); cov(wi,wj) As an input variable wiAnd wjThe covariance of (a).
Correlation coefficient matrix CwIf it is a positive definite matrix, Cholesky decomposition may be performed on the coefficient matrix:
Cw＝GGT (6)
in the formula: g is a lower triangular matrix, in which the elements can be found by equation (7):
Figure GDA0003630030690000035
assuming an orthogonal matrix B, the input random variable W with correlation can be converted into an uncorrelated random variable Y:
Y＝BW (8)
correlation coefficient due to uncorrelated random variables YMatrix CYIs an identity matrix I, and thus:
CY＝ρ(Y,YT)＝ρ(BW,WTBT)＝Bρ(W,WT)BT＝BCWBT＝I (9)
further, it can be obtained from the formula (6):
CY＝BCWBT＝BGGTBT＝(BG)(BG)T＝I (10)
derived from the above equation:
B＝G-1 (11)
on the premise that the input uncertainty W having correlation is known, it can be changed to an uncorrelated random variable Y by orthogonal transformation matrix.
And converting the load, wind power and photovoltaic output matrixes with correlation into independent matrixes through the obtained orthogonal transformation matrix, eliminating the correlation among the independent matrixes, and further solving the worst scene through a worst scene linear superposition method.
The method comprises the following steps of when modeling of a day-ahead scheduling model of unit combination decision is carried out:
step 1, dividing a unit combination decision into a basic scene and a worst scene;
step 2, modeling a day-ahead scheduling model in a basic scene by taking the uncertainty factor power predicted value as a basis, taking the minimum total system operation cost as a target and considering conventional constraint conditions in a deterministic environment;
and 3, modeling a day-ahead scheduling model in the worst scene by taking the maximum fluctuation output of the uncertain power output as the basis and considering the uncertain constraint conditions.
When modeling a day-ahead scheduling model in a basic scene, an objective function and constraint conditions of the model are as follows:
1) determining an objective function containing fuel cost and unit start-stop cost of a conventional unit:
Figure GDA0003630030690000041
wherein:
Figure GDA0003630030690000042
in the formula:
Figure GDA0003630030690000043
the active output of the unit i at the moment t is represented;
Figure GDA0003630030690000044
representing the state of the unit i at the time t;
Figure GDA0003630030690000045
for the cost of starting up and stopping the machine, ai、bi、ciParameters of a generating cost function of the unit;
2) the constraints contained in the model are established as follows:
(1) system power balance constraint, under the condition of not counting network loss:
Figure GDA0003630030690000046
in the formula:
Figure GDA0003630030690000047
the predicted values of the wind power output, the load power and the photovoltaic power generation output at the moment t are obtained;
(2) and (3) output constraint of a conventional unit:
Figure GDA0003630030690000048
in the formula: pi minAnd Pi maxRespectively representing the maximum and minimum active output of the thermal power generating unit i;
(3) unit ramp rate constraint
Ascending and climbing rate constraint
Figure GDA0003630030690000049
Descent and climb rate constraint
Figure GDA00036300306900000410
In the formula: URi,DRiLimiting the climbing power of the conventional unit;
(4) conventional unit start-stop time constraints
Figure GDA00036300306900000411
Figure GDA00036300306900000412
In the formula:
Figure GDA00036300306900000413
for the on-off time, T, of the unit i at time Ton,iToff,iMinimum boot and downtime constraints;
(5) network security constraints
Figure GDA00036300306900000414
In the formula:
Figure GDA0003630030690000051
for maximum current constraints of the line, SFl,mA node power transfer factor; u (m), D (m), W (m) and V (m) are respectively the bus bar sets where the conventional unit, the load, the wind power and the photovoltaic are located.
And checking the day-ahead plan by using system constraint conditions in an uncertain environment.
When the day-ahead scheduling model under the worst scene is modeled, the constraint conditions in the established model are as follows:
(1) system power balance constraint, under the condition of not counting network loss:
Figure GDA0003630030690000052
in the formula:
Figure GDA0003630030690000053
and
Figure GDA0003630030690000054
actual values of wind power output, photovoltaic output and load under uncertain conditions;
(2) and (3) output constraint of a conventional unit:
Figure GDA0003630030690000055
in the formula:
Figure GDA0003630030690000056
the actual output of the conventional unit under the uncertain condition is obtained;
(3) and (3) restraining the climbing rate of the unit:
ascending and climbing rate constraint
Figure GDA0003630030690000057
Descending and climbing rate constraint
Figure GDA0003630030690000058
(4) Rotating reserve capacity constraint:
Figure GDA0003630030690000059
in the formula:
Figure GDA00036300306900000510
the rotary power machine set is used for standby in positive and negative rotation of a conventional machine set;
(5) network security constraints
Figure GDA00036300306900000511
In the formula:
Figure GDA00036300306900000512
for maximum current constraints of the line, SFl,mIs a node power transfer factor; u (m), D (m), W (m) and V (m) are respectively the bus bar sets where the conventional unit, the load, the wind power and the photovoltaic are located.
The above uncertainties include uncertainties that account for wind power, photovoltaic, and load prediction errors.
Solving the model by adopting a Benders decomposition method; decomposing an original problem into a main problem and two sub-problems, wherein the main problem is a UC decision main problem in a basic scene, and the two sub-problems are respectively a network security check sub-problem in the basic scene and a robust check sub-problem in a worst scene;
the method comprises the following steps: firstly, modeling a UC main problem; then, modeling a safety subproblem in a basic scene; then, modeling a safety subproblem considering uncertainty;
the method comprises the following specific steps:
1): UC Main problem modeling
The UC major problem includes the target function (1) and the constraint equations (3) through (9), as well as all the Benders cuts generated.
2): safety sub-problem modeling under basic scene
The network security syndrome problem under the basic scene is shown as formula (27), and the network security of the scheduling scheme is ensured by checking the load flow out-of-limit condition of the UC main problem.
Figure GDA0003630030690000061
Figure GDA0003630030690000062
Figure GDA0003630030690000063
vl,t≥0 (27)
In the formula: lambda1,l,t,λ2,l,tIs a dual variable of the network security constraint; v. ofl,tIs the relaxation variable.
Introducing a relaxation variable v into a subprobleml,tThe role of the method is to temporarily relieve the network security constraint by using a relaxation variable when the constraint condition cannot be met so as to ensure that the subproblem is always solved. V obtained if final optimizationl,tIf the maximum value is greater than the given safety threshold value, the optimal unit combination scheme obtained by the main problem cannot meet the network safety constraint, and therefore the Benders cut as follows needs to be returned:
Figure GDA0003630030690000064
3): uncertainty-aware safety sub-problem modeling
The safety check model under the uncertain scene is shown as a formula (29), and the safety check model is checked in the worst scene
Figure GDA0003630030690000065
And
Figure GDA0003630030690000066
whether the safety constraint can be met.
Figure GDA0003630030690000067
S.t.
Figure GDA0003630030690000068
Figure GDA0003630030690000069
Figure GDA0003630030690000071
Figure GDA0003630030690000072
Figure GDA0003630030690000073
Figure GDA0003630030690000074
Figure GDA0003630030690000075
0≤v1,lt,v2t,v3t (29)
In the formula:
Figure GDA0003630030690000076
and
Figure GDA0003630030690000077
the actual values of the unit output, the wind power output, the photovoltaic output and the load under the worst scene are obtained. Lambda1,it,λ2,it,μ1,it,μ2,it,η1,it,η2,itIs a dual variable of a rotation standby constraint, a unit capacity constraint and a climbing constraint.
And if the safety constraint cannot be met, returning to the Benders cut formula (30) to the main problem, wherein the main problem serves as a constraint condition, so that the unit combination and output scheme can be adaptively adjusted on the worst scene to meet the network safety constraint and the power balance.
Figure GDA0003630030690000078
Through the steps, the power system day-ahead robust scheduling considering multiple uncertainties and correlations is completed.
The invention has the following technical effects:
1) compared with the traditional method, on one hand, the method can effectively account for multiple uncertain factors and the correlation thereof, thereby improving the economical efficiency of system operation while ensuring the robustness of a scheduling decision scheme; on the other hand, the improved robust scheduling model effectively avoids solving the unit combination problem in a massive scene, and has higher solving efficiency.
2) The robust optimization method is improved by introducing a Cholesky decomposition method, so that the worst scene is directly determined without multi-scene load flow calculation, and the applicability and the solving efficiency of the robust optimization model are effectively improved.
Drawings
FIG. 1 is a block diagram of the overall modeling of the present invention;
FIG. 2 is a flow chart of a worst case scenario extraction of the present invention;
FIG. 3 is a block diagram of the overall algorithm concept of the present invention;
FIG. 4 illustrates wind and photovoltaic active power output curves according to an embodiment of the present invention;
FIG. 5 is a worst case comparison table at time 1;
FIG. 6 is a table of comparison results of scheduling costs from day ahead;
fig. 7 is a table comparing the calculated efficiencies.
Detailed Description
A power system day-ahead robust scheduling method considering multiple uncertainties and correlations comprises the following steps:
step 1: day-ahead scheduling modeling in basic scenarios
The method is based on a robust optimization thought, and a day-ahead scheduling model considering wind power, photovoltaic and load prediction error uncertainty is constructed. The method divides the unit combination decision into a basic scene and a worst scene for respectively modeling, wherein the basic scene takes uncertainty factor power prediction value as a basis, takes the minimum total operation cost of the system as a target, and simultaneously considers various conventional constraint conditions of the system in a deterministic environment, thereby ensuring the economy of the scheduling decision; in the worst scene, the maximum fluctuation output of the uncertain power output is taken as the basis, and the uncertain constraint condition is considered, so that the robustness of the decision scheme in the basic scene in the uncertain environment is ensured. The model block diagram is shown in fig. 1.
Step 1.1: day-ahead scheduling modeling in a basic scenario: including objective functions and constraints
1) Determining an objective function containing fuel cost and unit start-stop cost of a conventional unit:
Figure GDA0003630030690000081
wherein:
Figure GDA0003630030690000082
in the formula:
Figure GDA0003630030690000083
the active output of the unit i at the moment t is represented;
Figure GDA0003630030690000084
representing the state of the unit i at the time t;
Figure GDA0003630030690000085
for the cost of starting up and stopping the machine, ai、bi、ciIs a parameter of the generating cost function of the unit.
2) Constraints contained in the model are established, such as:
(1) system power balance constraint, under the condition of not counting network loss:
Figure GDA0003630030690000086
in the formula:
Figure GDA0003630030690000087
and the predicted values of the wind power output and the load power at the moment t and the photovoltaic power generation output are obtained.
(2) And (3) output constraint of a conventional unit:
Figure GDA0003630030690000088
in the formula: pi minAnd Pi maxAnd respectively representing the maximum and minimum active output of the thermal power generating unit i.
(3) Ramp rate restraint for unit
Ascending and climbing rate constraint
Figure GDA0003630030690000089
Descending and climbing rate constraint
Figure GDA00036300306900000810
In the formula: URi,DRiAnd limiting the climbing power of the conventional unit.
(4) Conventional unit start-stop time constraints
Figure GDA0003630030690000091
Figure GDA0003630030690000092
In the formula:
Figure GDA0003630030690000093
for the on-off time, T, of unit i at time Ton,iToff,iAre minimum boot and downtime constraints.
(5) Network security constraints
Figure GDA0003630030690000094
In the formula:
Figure GDA0003630030690000095
for maximum current constraints of the line, SFl,mIs the node power transfer factor. U (m), D (m), W (m) and V (m) are respectively the bus bar sets where the conventional unit, the load, the wind power and the photovoltaic are located.
Step 1.2: day-ahead scheduling modeling in uncertain scenes
The day-ahead unit combination and the unit output plan obtained in the basic scene should ensure the robustness of the system in the uncertain environment, so the day-ahead plan needs to be checked by using the system constraint conditions in the uncertain environment. It should be noted that in the actual calculation, the worst scenario may be first sought, and then the worst scenario may be directly utilized for robustness check.
Establishing constraints in the model:
(1) system power balance constraint, under the condition of not counting network loss:
Figure GDA0003630030690000096
in the formula:
Figure GDA0003630030690000097
and
Figure GDA0003630030690000098
the actual values of wind power output, photovoltaic output and load under uncertain conditions.
(2) The output constraint of the conventional unit is as follows:
Figure GDA0003630030690000099
in the formula:
Figure GDA00036300306900000910
the actual output of the conventional unit under the uncertain condition is realized.
(3) Unit ramp rate constraint
Ascending and climbing rate constraint
Figure GDA00036300306900000911
Descending and climbing rate constraint
Figure GDA00036300306900000912
(4) Rotational reserve capacity constraint
Figure GDA00036300306900000913
In the formula:
Figure GDA00036300306900000914
the device is used for the positive and negative rotation of the conventional unit for standby.
(5) Network security constraints
Figure GDA0003630030690000101
In the formula:
Figure GDA0003630030690000102
for maximum current constraints of the line, SFl,mIs the node power transfer factor. U (m), D (m), W (m) and V (m) are respectively the bus bar sets where the conventional unit, the load, the wind power and the photovoltaic are located.
Step 2: worst scenario solution
As can be seen from step 1, in the actual calculation, the worst scenario may be first sought, and then the worst scenario may be directly used for robustness check. Therefore, the invention provides a method for rapidly calculating the worst scene suitable for multiple correlation randomness factors based on the Cholesky decomposition theory. Firstly, probability density functions of wind power, photovoltaic and load are respectively constructed by utilizing nonparametric kernel density estimation, then, a Latin hypercube sampling is utilized to generate samples, finally, a Cholesky decomposition method is adopted to convert the random samples with correlation into mutually independent random samples, and the worst scene is determined on the basis of the mutually independent random samples.
Step 2.1: probability density function modeling of random factors
If the number of load samples based on the historical data is n, constructing a probability density model of the load based on a non-parametric kernel density estimation method as follows:
Figure GDA0003630030690000103
in the formula, phi (P)d) Is a probability density function of the load; k (P)dL) is a kernel function; pdmIs the m-th sample value in the load sample, and l is the bandwidth.
The invention selects a Gaussian function as a kernel function of the load probability density model and solves the bandwidth l to obtain the probability density function phi (P) of the system loadd)。
The probability density function phi (P) of the wind power output can be obtained by the same methodw) And a photovoltaic output probability density function phi (P)v). As shown in formula (17) and formula (18).
Figure GDA0003630030690000104
In the formula, phi (P)w) Is a probability density function of the load; k (P)wL) is a kernel function; p iswmAnd l is the bandwidth, wherein the m is the sample value in the wind power output sample.
Figure GDA0003630030690000105
In the formula, phi (P)v) Is a probability density function of the load; k (P)vL) is a kernel function; pvmAnd l is the bandwidth, wherein the value is the mth sample value in the photovoltaic output sample.
Step 2.2: sample sampling
Latin hypercube sampling is a hierarchical sampling method which has a sample memory function and can avoid the sampling of already appeared samples. Let the sampling scale be N, Ym＝Fm(Xm) Represents the m-th random variable XmIs calculated as a function of the probability density of (c). The specific sampling process is as follows: will be interval [0,1]Equally dividing the sampling value into N equal parts, selecting the middle value of each subinterval, and obtaining the sampling value through the inverse function of the middle value
Figure GDA0003630030690000111
And obtaining a sample matrix of all the random variables after sampling of all the random variables is completed.
Step 2.3: orthogonal transformation matrix derivation
The method comprises the steps of describing the correlation among loads, wind power and photovoltaic power generation by utilizing a correlation coefficient matrix, and setting a sample matrix obtained by Latin hypercube sampling as W ═ W1,w2,…wl]TThe matrix of correlation coefficients is Cw：
Figure GDA0003630030690000112
The elements of the matrix can be obtained by equation (20):
Figure GDA0003630030690000113
in the formula:
Figure GDA0003630030690000114
and
Figure GDA0003630030690000115
are respectively an input variable wiAnd wjStandard deviation of (d); cov(wi,wj) As an input variable wiAnd wjThe covariance of (a).
As can be seen by definition, the correlation coefficient matrix C of the present inventionwIf it is a positive definite matrix, Cholesky decomposition may be performed on the coefficient matrix:
Cw＝GGT (6)
in the formula: g is a lower triangular matrix in which the elements can be found by equation (22).
Figure GDA0003630030690000116
Assuming an orthogonal matrix B, the input random variable W with correlation can be converted into an uncorrelated random variable Y:
Y＝BW (8)
matrix C of correlation coefficients due to uncorrelated random variables YYIs an identity matrix I, and thus:
CY＝ρ(Y,YT)＝ρ(BW,WTBT)＝Bρ(W,WT)BT＝BCWBT＝I (9)
further, it can be obtained from the formula (21):
CY＝BCWBT＝BGGTBT＝(BG)(BG)T＝I (10)
derived from the above equation:
B＝G-1 (11)
on the premise that the input uncertainty W having correlation is known, it can be changed to an uncorrelated random variable Y by orthogonal transformation matrix.
Step 2.4: solving a worst scene;
and (3) converting the load, wind power and photovoltaic output matrixes with correlation into independent matrixes through the orthogonal transformation matrix obtained in the step (2.3), eliminating the correlation among the independent matrixes, and further obtaining the worst scene through a method of linear superposition of the worst scene. A worst case scenario retrieval flow diagram is shown in fig. 2.
And step 3: model solution
The invention provides a multistage decomposition algorithm based on Benders decomposition to solve a model.
The traditional Benders decomposition method generally decomposes an original problem into two primary and secondary problems, and decomposes the original problem into a main problem and two sub-problems in consideration of the particularity of the model of the invention, wherein the main problem is a main UC decision problem under a basic scene, and the two sub-problems are respectively as follows: the network safety checking sub-problem under the basic scene and the robust checking sub-problem under the worst scene. The whole frame is shown in figure 1.
Step 3.1: UC Main problem modeling
The main UC problem includes the objective function (1) and constraint equations (3-9) and all the generated Benders cuts.
Step 3.2: safety sub-problem modeling under basic scene
The network security syndrome problem under the basic scene is shown as formula (27), and the network security of the scheduling scheme is ensured by checking the load flow out-of-limit condition of the UC main problem.
Figure GDA0003630030690000121
Figure GDA0003630030690000122
Figure GDA0003630030690000124
vl,t≥0 (27)
In the formula: lambda [ alpha ]1,l,t,λ2,l,tIs a dual variable of the network security constraint; v. ofl,tIs the relaxation variable.
Introducing a relaxation variable v into a subprobleml,tThe role of the method is to temporarily relieve the network security constraint by using a relaxation variable when the constraint condition cannot be met so as to ensure that the subproblem is always solved. V obtained if final optimizationl,tIf the maximum value is greater than the given safety threshold value, the optimal unit combination scheme obtained by the main problem cannot meet the network safety constraint, and therefore the Benders cut as follows needs to be returned:
Figure GDA0003630030690000123
step 3.3: uncertainty-aware safety sub-problem modeling
The safety check model under the uncertain scene is shown as a formula (29), and the safety check model is checked in the worst scene
Figure GDA0003630030690000131
And
Figure GDA0003630030690000132
whether the safety constraint can be met.
Figure GDA0003630030690000133
S.t.
Figure GDA0003630030690000134
Figure GDA0003630030690000135
Figure GDA0003630030690000136
Figure GDA0003630030690000137
Figure GDA0003630030690000138
Figure GDA0003630030690000139
Figure GDA00036300306900001310
0≤v1,lt,v2t,v3t (29)
In the formula:
Figure GDA00036300306900001311
and
Figure GDA00036300306900001312
the actual values of the unit output, the wind power output, the photovoltaic output and the load under the worst scene are obtained. Lambda [ alpha ]1,it,λ2,it,μ1,it,μ2,it,η1,it,η2,itIs a dual variable of a rotation standby constraint, a unit capacity constraint and a climbing constraint.
And if the safety constraint cannot be met, returning to the Benders cut formula (30) to the main problem, wherein the main problem serves as a constraint condition, so that the unit combination and output scheme can be adaptively adjusted on the worst scene to meet the network safety constraint and the power balance.
Figure GDA00036300306900001313
And 4, step 4: establishing an operation mode;
in order to comparatively analyze the effectiveness and the correctness of the scheduling model established by the invention, the following two operation modes are established:
mode 1: robust day-ahead scheduling that accounts for multiple uncertainties but does not take correlation into account.
Mode 2: a robust day-ahead scheduling model that accounts for multiple uncertainties and their correlations.
In particular, the invention verifies the correctness of the proposed model with a modified IEEE-118 node system. The system comprises 54 conventional thermal power generating units, 3 wind power plants and 1 photovoltaic power station. The rated power of the wind power plant is respectively 100MW, 200MW and 250MW, and the wind power plant is positioned at nodes No. 5, 9 and 48; the capacity of the photovoltaic power station is 300MW and is positioned at the No. 20 node. The active power output curve of wind power and photovoltaic is shown in fig. 5. The positive rotation standby requirement of a conventional unit in the system is 8% of the maximum load of the system, and the negative rotation standby requirement is 2% of the minimum load of the system. The threshold values of the problem check values of the safety check sub-problems are all 10-3MWh. And adopting Latin hypercube sampling to sample the load, the wind power and the photovoltaic output 100 times per hour, and totaling 2400 groups of samples. The related calculations are all completed on an Intel core i5-4460 processor 3.20GHz, 8G memory computer, and Matlab and Cplex 12.5 are adopted to program and solve the example.
According to the worst scenario solution method of the present invention, the worst scenario comparison result of solving the uncertainty factors of mode 1 and mode 2 is shown in fig. 5.
As can be seen from fig. 5, if the probabilistic correlation between uncertainty factors is not considered, the worst scenario obtained by simple linear superposition is conservative, which will affect the economy of the future scheduling decision, and it can be seen from the precise calculation of the method herein that the worst scenario is actually impossible to occur due to the existence of the correlation between uncertainty factors.
The day-ahead scheduling schemes in mode 1 and mode 2 are calculated separately, and the results are shown in fig. 6.
As can be seen from fig. 6, compared to the conventional day-ahead scheduling method without considering the probability correlation of multiple uncertainty factors, the method proposed in the present invention reduces the day-ahead scheduling cost of the present example by about 38650 $. The method has the advantages that the method fully considers the probability correlation among wind power, photovoltaic and loads, and effectively avoids extreme scenes which are not possible to occur in the robustness checking process, so that the operation cost of the system is reduced while the robustness of the system is ensured by the day-ahead scheduling decision.
In order to compare the advantages of the method of the invention compared with the traditional method, the standard Benders decomposition method and the method of the invention are respectively adopted to simulate the same example, and the calculation efficiency is compared. The comparative results are shown in FIG. 7.
As can be seen from fig. 7: compared with the calculation efficiency, the method provided by the invention is remarkably improved, and the worst scene solving method based on Cholesky decomposition effectively avoids solving problems of unit combination and load flow calculation under a large number of scenes, so that the calculation efficiency is improved by 411.5%.
The present invention has been described in terms of the preferred embodiments, but the above embodiments are not intended to limit the present invention in any way, and all technical solutions obtained by substituting equivalents or equivalent variations fall within the scope of the technical solutions of the present invention.

Claims (8)

1. A modeling method of a day-ahead scheduling model of unit combination decision is characterized by comprising the following steps:
step 1, dividing a unit combination decision into a basic scene and a worst scene;
step 2, modeling a day-ahead scheduling model in a basic scene by taking the uncertainty factor power predicted value as a basis, taking the minimum total system operation cost as a target and considering conventional constraint conditions in a deterministic environment;
step 3, modeling a day-ahead scheduling model in a worst scene by taking the maximum fluctuation output of the uncertain power output as a basis and considering uncertain constraint conditions;
when modeling a day-ahead scheduling model in a basic scene, an objective function and constraint conditions of the model are as follows:
1) determining an objective function containing fuel cost and unit start-stop cost of a conventional unit:
Figure FDA0003630030680000011
wherein:
Figure FDA0003630030680000012
in the formula:
Figure FDA0003630030680000013
the active output of the unit i at the moment t is represented;
Figure FDA0003630030680000014
representing the state of the unit i at the time t;
Figure FDA0003630030680000015
for the cost of starting up and stopping the machine, ai、bi、ciParameters of a generating cost function of the unit;
2) the constraints contained in the model are established as follows:
(1) system power balance constraint, under the condition of not counting network loss:
Figure FDA0003630030680000016
in the formula:
Figure FDA0003630030680000017
the active output of the unit i at the moment t is represented;
Figure FDA0003630030680000018
the predicted values of the wind power output and the load power at the moment t and the photovoltaic power generation output are obtained;
(2) and (3) output constraint of a conventional unit:
Figure FDA0003630030680000019
in the formula: pi minAnd Pi maxRespectively representing the minimum active output and the maximum active output of the thermal power generating unit i;
(3) unit ramp rate constraint
Ascending and climbing rate constraint
Figure FDA00036300306800000110
Descending and climbing rate constraint
Figure FDA0003630030680000021
In the formula: pi minAnd Pi maxRespectively representing the minimum active output and the maximum active output of the thermal power generating unit i; URi,DRiLimiting the climbing power of the conventional unit;
Figure FDA0003630030680000022
the active output of the unit i at the moment t is represented;
(4) conventional unit start-stop time constraints
Figure FDA0003630030680000023
Figure FDA0003630030680000024
In the formula:
Figure FDA0003630030680000025
for the on-off time, T, of the unit i at time Ton,iToff,iFor minimum boot and shutdown timeBundling;
(5) network security constraints
Figure FDA0003630030680000026
In the formula:
Figure FDA0003630030680000027
for maximum current constraints of the line, SFl,mIs a node power transfer factor; u (m), D (m), W (m) and V (m) are respectively the bus bar sets where the conventional unit, the load, the wind power and the photovoltaic are located.
2. The modeling method for the day-ahead scheduling model of the unit combination decision as claimed in claim 1, wherein the day-ahead plan is checked using system constraints under an uncertainty environment.
3. The modeling method of the day-ahead scheduling model for unit combination decision according to claim 2, wherein when modeling the day-ahead scheduling model in the worst scenario, the constraint conditions in the established model are:
(1) system power balance constraint, under the condition of not counting network loss:
Figure FDA0003630030680000028
in the formula:
Figure FDA0003630030680000029
and
Figure FDA00036300306800000210
the actual values of the wind power output, the photovoltaic output and the load under the uncertain condition are obtained;
(2) and (3) output constraint of a conventional unit:
Figure FDA00036300306800000211
in the formula:
Figure FDA00036300306800000212
the actual output of the conventional unit under the uncertain condition is obtained; pi minAnd Pi maxRespectively representing the minimum active output and the maximum active output of the thermal power generating unit i;
(3) and (3) restraining the climbing rate of the unit:
ascending and climbing rate constraint
Figure FDA00036300306800000213
Descending and climbing rate constraint
Figure FDA0003630030680000031
In the formula, Pi minAnd Pi maxRespectively representing the minimum active output and the maximum active output of the thermal power generating unit i; URi,DRiLimiting the climbing power of the conventional unit;
(4) rotating reserve capacity constraint:
Figure FDA0003630030680000032
in the formula:
Figure FDA0003630030680000033
the rotary power generating set is used for standby in positive and negative rotation of a conventional set;
(5) network security constraints
Figure FDA0003630030680000034
In the formula:
Figure FDA0003630030680000035
for maximum current constraints of the line, SFl,mIs a node power transfer factor; u (m), D (m), W (m) and V (m) are bus sets where a conventional unit, a load, wind power and photovoltaic are located respectively;
Figure FDA0003630030680000036
and
Figure FDA0003630030680000037
the actual values of the wind power output, the photovoltaic output and the load under the uncertain conditions are obtained.
4. The method of modeling a day-ahead scheduling model for a unit portfolio decision of claim 1, wherein the uncertainty comprises uncertainty considering wind power, photovoltaic, and load prediction errors.
5. The modeling method of the day-ahead scheduling model of unit combination decision according to claim 4, characterized in that when solving the worst scenario, firstly, nonparametric kernel density estimation is used to respectively construct probability density functions of wind power, photovoltaic and load, then, Latin hypercube sampling is used to generate samples, and finally, Cholesky decomposition method is used to convert the random samples with correlation into mutually independent random samples, and the worst scenario is determined based on the random samples.
6. The modeling method of the unit combination decision day-ahead scheduling model according to claim 5, wherein if it is known that the number of load samples based on the historical data is n, the probability density model of the load constructed based on the non-parametric kernel density estimation method is:
Figure FDA0003630030680000038
in the formula, phi (P)d) Is a probability density function of the load; k (P)dL) is a kernel function; pdmIs the m-th sample value in the load sample, and l is the bandwidth.
7. The modeling method of the day-ahead scheduling model of the unit combination decision as claimed in claim 6, wherein: selecting a Gaussian function as a kernel function of the load probability density model, and solving the bandwidth l to obtain a probability density function phi (P) of the system loadd)。
8. The modeling method of the day-ahead scheduling model of the unit combination decision as claimed in claim 5 or 6, wherein: calculating the probability density function phi (P) of the wind power outputw) And a photovoltaic output probability density function phi (P)v) As shown in formula (2) and formula (3):
Figure FDA0003630030680000041
in the formula, phi (P)w) Is a probability density function of the load; k (P)wL) is a kernel function; p iswmThe m-th sample value in the wind power output sample is obtained, and l is the bandwidth;
Figure FDA0003630030680000042
in the formula, phi (P)v) Is a probability density function of the load; k (P)vL) is a kernel function; p isvmAnd l is the bandwidth, wherein the value is the mth sample value in the photovoltaic output sample.
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CN112186765A (en) 2021-01-05
CN112186766A (en) 2021-01-05

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