CN110661258B - Flexible resource distributed robust optimization method for power system - Google Patents

Flexible resource distributed robust optimization method for power system Download PDF

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CN110661258B
CN110661258B CN201910935575.5A CN201910935575A CN110661258B CN 110661258 B CN110661258 B CN 110661258B CN 201910935575 A CN201910935575 A CN 201910935575A CN 110661258 B CN110661258 B CN 110661258B
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CN110661258A (en
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罗松林
罗煜
司徒友
陈威洪
张鑫
李敬光
刘树安
宋想富
陈守滨
吴伟东
周娟
邱泽坚
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Guangdong Power Grid Co Ltd
Dongguan Power Supply Bureau of Guangdong Power Grid Co Ltd
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Dongguan Power Supply Bureau of Guangdong Power Grid Co Ltd
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses a distributed robust optimization method for flexible resources of an electric power system, which comprises the steps of obtaining cost expectation and constraint conditions of each power supply energy in the electric power system, and establishing a flexible resource robust optimization model; converting the flexible resource robust optimization model into a plurality of single-target optimization problems by adopting a dual method; and solving a plurality of single-target optimization problems to obtain a power system flexible resource distributed robust optimization scheme. The distributed robust optimization method for the flexibility resources of the power system, provided by the invention, can solve the problems existing in the flexibility resource optimization in the prior art, achieves the aim of minimizing the total cost, and meanwhile, can reduce the calculation burden, protect the data privacy and improve the system stability.

Description

Flexible resource distributed robust optimization method for power system
Technical Field
The invention relates to the technical field of power systems, in particular to a flexible resource distributed robust optimization method for a power system.
Background
To solve the serious environmental problems caused by the heavy use of fossil fuels and to meet the growing energy demand in an environmentally friendly manner, the current solution is to couple a large proportion of renewable energy into the power system. However, renewable energy sources such as wind energy and photovoltaic power generation have uncertain and unpredictable properties that pose significant challenges to the scheduling and operation of power systems. Therefore, there is a pressing need for schedulable flexible resources, such as traditional generators, energy storage systems, and deferrable loads, to maintain power supply-demand balance between fluctuating renewable energy power generation and time-varying load demands.
The existing research results show that the economy and stability of accessing a large-scale renewable energy system can be improved to a certain extent through reasonable flexible resource optimization, but the existing optimization means mostly focus on deterministic optimization and centralized optimization. The problem of deterministic optimization is that the characteristics of uncertainty, strong volatility and the like of renewable energy sources cannot be considered in optimization, so that the problem of unbalanced supply and demand is easily caused in an actual situation, and larger economic loss is caused; centralized optimization may be computationally burdensome because of the large amount of information that needs to be gathered from all distributed generator sets and loads, and moreover, when the power system is large in scale, real-time communication becomes inconvenient and difficult with centralized optimization methods.
Disclosure of Invention
The invention provides a distributed robust optimization method for flexible resources of a power system, which aims to overcome the defects of the prior art.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the embodiment of the invention provides a distributed robust optimization method for flexible resources of a power system, which comprises the following steps:
acquiring cost expectation and constraint conditions of each power supply energy in the power system, and establishing a flexible resource robust optimization model;
converting the flexible resource robust optimization model into a plurality of single-target optimization problems by adopting a dual method;
and solving a plurality of single-target optimization problems to obtain a power system flexible resource distributed robust optimization scheme.
Further, in the distributed robust optimization method for the flexible resources of the power system, the robust optimization model for the flexible resources is as follows:
Figure BDA0002221492400000021
s.t.D(X)＝0；
E(X)≤0；
wherein the content of the first and second substances,
Figure BDA0002221492400000022
the method comprises the following steps:
Figure BDA0002221492400000023
Ω includes:
Figure BDA0002221492400000024
Δ t is the time interval, and Rgi is the ramp speed of the conventional unit i;
s.t. d (x) 0 includes:
Figure BDA0002221492400000031
and
Figure BDA0002221492400000032
e (X). ltoreq.0 comprises:
Figure BDA0002221492400000033
Figure BDA0002221492400000034
and
Figure BDA0002221492400000035
further, in the distributed robust optimization method for the flexible resources of the power system, the step of converting the robust optimization model for the flexible resources into a plurality of single-target optimization problems by using a dual method includes:
converting the flexible resource robust optimization model into an equivalent Lagrangian dual problem:
Figure BDA0002221492400000036
where L can be decomposed into several different single-target optimization problems Li:
Figure BDA0002221492400000037
Xi＝[x1i，x2i，…，xMi]T。
further, in the distributed robust optimization method for flexible resources of an electric power system, the step of solving the plurality of single-target optimization problems to obtain the distributed robust optimization scheme for flexible resources of the electric power system includes:
solving a plurality of the single-target optimization problems according to the following distributed computing process to obtain a power system flexible resource distributed robust optimization scheme:
initializing, and enabling K to be 0;
the iterative calculation is performed using the following formula:
Figure BDA0002221492400000041
Figure BDA0002221492400000042
Figure BDA0002221492400000043
Figure BDA0002221492400000044
Figure BDA0002221492400000045
the projection is performed using the following formula:
Xi∈Ω,λi≥0,μi∈R；
Figure BDA0002221492400000046
wherein, PΩIs a projection function;
information exchange is performed based on the following formula:
Xk+1＝Pf(W)Xk+1
＝(a0I+a1W+a2W2+...+adWd)Xk+1；
λk+1＝Pf(W)λk+1；
μk+1＝Pf(W)μk+1；
judging whether the following stopping condition formula is met or not; if yes, the solution is ended:
Figure BDA0002221492400000051
where K is a non-negative integer and a non-negative constant, to define the iteration accuracy.
Further, in the distributed robust optimization method for flexible resources of an electric power system, after the step of solving the plurality of single-target optimization problems to obtain the distributed robust optimization scheme for flexible resources of an electric power system, the method further includes:
and performing optimized scheduling on the power system according to the power system flexible resource distributed robust optimization scheme.
The distributed robust optimization method for the flexibility resources of the power system, provided by the embodiment of the invention, can solve the problems of flexibility resource optimization in the prior art, achieves the aim of minimizing the total cost, and can reduce the calculation burden, protect the data privacy and improve the system stability.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a flow chart diagram of a method for robust optimization of flexibility resource distribution of an electric power system according to an embodiment of the present invention;
FIG. 2 is a flowchart of a distributed robust optimization method for providing flexible scheduling according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
Example one
Referring to fig. 1, a flow diagram of a method for robust optimization of flexible resources of an electrical power system in a distributed manner according to an embodiment of the present invention is shown. The method specifically comprises the following steps:
s101, obtaining cost expectation and constraint conditions of each power supply energy in the power system, and establishing a flexible resource robust optimization model;
s102, converting the flexible resource robust optimization model into a plurality of single-target optimization problems by adopting a dual method;
specifically, step S102 further includes:
converting the flexible resource robust optimization model into an equivalent Lagrangian dual problem:
Figure BDA0002221492400000061
where L can be decomposed into several different single-target optimization problems Li:
Figure BDA0002221492400000062
Xi＝[x1i，x2i，…，xMi]T。
s103, solving the single-target optimization problems to obtain a power system flexible resource distributed robust optimization scheme.
Specifically, step S103 further includes:
solving a plurality of the single-target optimization problems according to the following distributed computing process to obtain a power system flexible resource distributed robust optimization scheme:
initializing, and enabling K to be 0;
the iterative calculation is performed using the following formula:
Figure BDA0002221492400000063
Figure BDA0002221492400000071
Figure BDA0002221492400000072
Figure BDA0002221492400000073
Figure BDA0002221492400000074
the projection is performed using the following formula:
Xi∈Ω,λi≥0,μi∈R；
Figure BDA0002221492400000075
wherein, PΩIs a projection function;
information exchange is performed based on the following formula:
Xk+1＝Pf(W)Xk+1
＝(a0I+a1W+a2W2+...+adWd)Xk+1；
λk+1＝Pf(W)λk+1；
μk+1＝Pf(W)μk+1；
judging whether the following stopping condition formula is met or not; if yes, the solution is finished, if not, K is equal to K +1, and the step of iterative computation is returned:
Figure BDA0002221492400000076
where K is a non-negative integer and a non-negative constant, to define the iteration accuracy.
Preferably, after step S103, the method further includes:
and performing optimized scheduling on the power system according to the power system flexible resource distributed robust optimization scheme.
The specific implementation steps are as follows:
flexible resource robust optimization modeling
The active power of the power system should satisfy the following relations at any time:
Figure BDA0002221492400000081
where Pgi represents the power output (MW) of a conventional generator; pei represents the output power (MW) of the energy storage system; pri represents a curtailed power (MW) of the renewable energy source; pdli represents the delayable load (MW); ptpi represents the junctor power exchange (MW) with other areas; pli and Primax are load demand and renewable energy power output at maximum power point tracking (MP1923888PT mode); ploss, ij is the power loss (MW) on the transmission line
The transmission line power loss can be calculated as:
Figure BDA0002221492400000082
in an ac transmission power system, the voltage level Vi is close to 1.0p.u., and the voltage angle difference θ ij between two connecting busbars is close to zero. Therefore, (2) can be simplified to:
Figure BDA0002221492400000083
renewable energy and load requirements are considered to be two sources of uncertainty. gi and ei are the extra power output of the conventional generator and energy storage system to compensate for renewable energy generation and load demand prediction errors, and the equation constraints are as follows:
Figure BDA0002221492400000091
wherein, Δ ri is a renewable energy power generation prediction error, and Δ li is a load demand prediction error.
Typically, short term prediction errors of renewable energy generation and load demand are limited. In view of this, ellipsoids may be used to define the uncertainty, as follows:
Figure BDA0002221492400000092
wherein, η1And η2In the interval [0,1]In is used forQuantize robustness level by adjusting η1And η2Can be traded off between risk and economy, particularly η1And η2The larger the value of (A), the more conservative the result is, the lower the risk is, η1And η2The smaller the value of (A), the more economical the result obtained and the greater the risk.
The objective function is to minimize the sum of the cost expectations of all units in the power system:
Figure BDA0002221492400000093
the cost expectation of a conventional generator can be expressed as a quadratic function, as follows:
Figure BDA0002221492400000101
of these, agi, bgi and cgi are cost factors for conventional generators.
Uncertainty delta r of generating capacity of renewable energyiAnd load demand uncertainty Δ liHas a mean value of zero. Renewable energy generation is related to load demand. Thus, according to (4), E (g)i) Equal to zero, E (g)i 2) Is equal to σ gi 2。
Figure BDA0002221492400000102
Wherein Λ is Δ riAnd Δ liThe covariance matrix of (2).
Also, the cost of the energy storage system is expected to be written as:
Figure BDA0002221492400000103
wherein, aeiIs the cost factor of the energy storage system.
Typically, renewable energy power generation operates in MP1923888PT mode. However, in order to satisfy the power balance under the power system constraint, it is sometimes necessary to reduce the amount of renewable energy generation. Therefore, fri (pri) is used to penalize the renewable energy generation curtailment:
Figure BDA0002221492400000104
fdli(Pdli) Deferrable load cost expectation in the form of a quadratic function:
Figure BDA0002221492400000111
wherein, adliIs a cost factor.
ftpi(Ptpi) Is the tie line power cost:
Figure BDA0002221492400000112
wherein a istpiIs a cost factor.
The blocking constraints of the transmission line are as follows:
Figure BDA0002221492400000113
wherein LPijFor the power flowing on the lines i-j,
Figure BDA0002221492400000114
is the upper limit, xijReactance of power transmission circuit: considering uncertain parameters, the power transmission line tide should satisfy the line blocking constraint:
Figure BDA0002221492400000115
Figure BDA0002221492400000116
Figure BDA0002221492400000117
all power output constraints are as follows:
Figure BDA0002221492400000118
Figure BDA0002221492400000119
Figure BDA0002221492400000121
where Δ t is the time interval, RgiIs the climbing speed of the traditional unit i.
Robust optimization with equality and inequality constraints can be summarized in the form:
Figure BDA0002221492400000122
Figure BDA0002221492400000123
Figure BDA0002221492400000124
where Ω is the domain of X and M is the sum of the number of all the independent variables.
Due to any uncertainty in the parameter ξr,ζlThese constraints should be satisfied, and therefore, the worst case uncertainty set of ellipsoids needs to be considered to eliminate these constraints. According to (5), (21) can be obtained by the Cauchy inequality:
Figure BDA0002221492400000125
thus, the combination (21), (4) can be written as (22):
Figure BDA0002221492400000126
with uncertain parameter ξr,ξlInequality (14) of (a) can be written as:
Figure BDA0002221492400000127
Figure BDA0002221492400000131
from the cauchy inequality and the ellipsoid uncertainty set, one can obtain (25):
Figure BDA0002221492400000132
to this end, the uncertainty parameter in the optimization problem (20) is eliminated and can be written as follows:
Figure BDA0002221492400000133
s.t.D(X)＝0…………(26b)；
E(X)≤0…………(26c)；
wherein Ω comprises (19); (26b) comprises (1) and (22); (26c) comprising (23), (24) and (25).
(II) distributed robust optimization method
In order to prevent oscillation and improve convergence speed, the step size of the distributed robust optimization method provided by the patent is adaptively adjusted along with iteration. In addition, the method also uses a polynomial filter to accelerate the convergence speed of the consistency algorithm.
The lagrangian dual problem of problem (26) is as follows:
Figure BDA0002221492400000134
each argument is managed by an independent agent, so L can be decomposed into M different LiAs follows:
Figure BDA0002221492400000141
wherein, Xi＝[x1i，x2i，…，xMi]T。
Thereafter, each L is reduced by gradient descentiAnd (4) minimizing. The falling or rising gradient being LiFor xii,，λiAnd muiThe partial derivatives of (a) are updated at each iteration. x is the number ofij(j ≠ i) is not updated by agent i (29) - (33) exhibits the update rules of the proposed distributed robust optimization method, wherein αi kIs x in the k-th iterationiβ is λiAnd muiShould select the appropriate αi kBecause of αi kToo great may result in divergence, αi kToo little will result in too slow convergence, and thus, based on the line search method, αi kDetermined by (33) since (33) is αi kBy solving for
Figure BDA0002221492400000142
The adaptive step size α is easily obtainedi k+1。
Figure BDA0002221492400000143
Figure BDA0002221492400000144
Figure BDA0002221492400000145
Figure BDA0002221492400000146
Figure BDA0002221492400000147
The argument has its upper and lower limits, which should be projected into the following ranges:
Xi∈Ω,λi≥0,μi∈R
…………(34)；
Figure BDA0002221492400000151
wherein P isΩIs a projection function.
The distributed robust optimization method provided by the invention is based on a consistency algorithm, and realizes information exchange between each intelligent agent and adjacent intelligent agents. In a communication network, two different agents are defined as being adjacent if there is a direct connection between them. W is a dual random matrix representing network information exchange weights. w is aijFor the elements of column i and row j of W, the calculation is as follows:
Figure BDA0002221492400000152
wherein n isiIs a neighboring agent of agent i, NiA set of neighboring agents of agent i.
The communication network adopts a ring structure because it is the simplest topology that satisfies the "N-1" rule and can withstand random failures of any communication line. In order to accelerate the convergence speed of the consistency algorithm, a polynomial filter is introduced in the information exchange process. It has been demonstrated that the convergence speed increases with decreasing absolute value of the second largest eigenvalue of W, which can be considered a consistently converging performance indicator. pf is a polynomial filter of order d, defined as follows:
Pf(W)＝a0I+a1W+a2W2+...+adWd…………(37)；
since W can be written as Qdiag (λ W) QT, where diag (λ W) diagonal matrix whose diagonal elements are eigenvalues of W, (37) can be written as:
Pf(W)＝Pf(Qdiag(λW)QT)
＝a0I+a1(Qdiag(λW)QT)+...+ad(Qdiag(λW)dQT)
＝QPf(diag(λW))QT…………(38)；
meaning that the eigenvalues of W can be changed by polynomial filtering. Therefore, a is reasonably selected0～adThe absolute value of the second largest eigenvalue of W can be reduced, improving the convergence speed of the consistency algorithm.
Hermite interpolation is a method for calculating a0～adThe simple method comprises the following steps:
Pf(a)＝0,Pf(1)＝1,Pf(i)(a)＝1,i＝1,...,d-1,
…………(39)；
wherein i is the order of derivation, and the eigenvalue span of W is [ a,1 ].
(40) - (42) is for the argument matrix X (X ═ X)1，X2，…，XM]) The lagrange multiplier matrices mu and lambda propose an update protocol based on a consistency algorithm. (40) Indicating that the system exchanged d times information at the kth iteration, thus yielding Xk+1，WXk+1，W2Xk+1，…，WdXk+1Their linear combination is the output result of the k-th iteration.
Xk+1＝Pf(W)Xk+1
＝(a0I+a1W+a2W2+...+adWd)Xk+1…………(40)；
λk+1＝Pf(W)λk+1
…………(41)；
μk+1＝Pf(W)μk+1
…………(42)；
The stop conditions were designed as follows:
Figure BDA0002221492400000171
where K is a non-negative integer and is a small non-negative constant that defines the iteration accuracy. A flow chart of a distributed robust optimization method for flexible resource scheduling is shown in fig. 2.
The distributed robust optimization method for the flexibility resources of the power system, provided by the embodiment of the invention, can solve the problems of flexibility resource optimization in the prior art, achieves the aim of minimizing the total cost, and can reduce the calculation burden, protect the data privacy and improve the system stability.
The above embodiments are merely to illustrate the technical solutions of the present invention, and not to limit the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (4)

1. A distributed robust optimization method for flexible resources of a power system is characterized by comprising the following steps:
acquiring cost expectation and constraint conditions of each power supply energy in the power system, and establishing a flexible resource robust optimization model;
converting the flexible resource robust optimization model into a plurality of single-target optimization problems by adopting a dual method;
solving a plurality of single-target optimization problems to obtain a power system flexible resource distributed robust optimization scheme;
the flexible resource robust optimization model is as follows:
Figure FDA0002625516270000011
s.t. D(X)＝0；
E(X)≤0；
wherein the content of the first and second substances,
Figure FDA0002625516270000012
the method comprises the following steps:
Figure FDA0002625516270000013
Ω includes:
Figure FDA0002625516270000014
Figure FDA0002625516270000015
Δ t is the time interval, and Rgi is the ramp speed of the conventional unit i;
s.t. d (x) 0 includes:
Figure FDA0002625516270000021
and
Figure FDA0002625516270000022
e (X). ltoreq.0 comprises:
Figure FDA0002625516270000023
Figure FDA0002625516270000024
and
Figure FDA0002625516270000025
wherein, PgiRepresents the power output of a conventional generator; peiRepresenting the output power of the energy storage system; priRepresents a reduced power of renewable energy; pdliRepresenting a deferrable load; ptpiRepresenting other areasExchanging the power of the tie line; pliAnd PrimaxLoad demand and renewable energy power output under maximum power point tracking; ploss,ijIs the power loss on the transmission line; giAnd eiIs the additional power output of the traditional generator and energy storage system; Δ riError of prediction for renewable energy power generation, Δ liPredicting error for load demand η1And η2In the interval [0,1]For quantifying the robustness level; f. ofriFor penalizing renewable energy generation curtailment; f. ofeiRepresenting an energy storage system cost function; f. ofgiRepresenting a conventional generator cost function; f. ofdliA deferrable load cost expectation that is a quadratic function; f. oftpiIs the tie line power cost;
Figure FDA0002625516270000026
is the upper limit of the power flowing on line i-j; zetar,ζlAre uncertain parameters.
2. The distributed robust optimization method for flexible resources of an electric power system according to claim 1, wherein the step of transforming the robust optimization model for flexible resources into a plurality of single-target optimization problems by using a dual method comprises:
converting the flexible resource robust optimization model into an equivalent Lagrangian dual problem:
Figure FDA0002625516270000031
where L can be decomposed into several different single-target optimization problems Li:
Figure FDA0002625516270000032
Xi＝[x1i，x2i，…，xMi]T。
3. the distributed robust optimization method for flexibility resources of an electric power system according to claim 1, wherein the step of solving the plurality of single-objective optimization problems to obtain the distributed robust optimization scheme for flexibility resources of an electric power system includes:
solving a plurality of the single-target optimization problems according to the following distributed computing process to obtain a power system flexible resource distributed robust optimization scheme:
initializing, and enabling k to be 0;
the iterative calculation is performed using the following formula:
Figure FDA0002625516270000033
Figure FDA0002625516270000034
Figure FDA0002625516270000035
Figure FDA0002625516270000036
Figure FDA0002625516270000037
the projection is performed using the following formula:
Xi∈Ω,λi≥0,μi∈R；
Figure FDA0002625516270000041
wherein, PΩIs a projection function;
information exchange is performed based on the following formula:
Xk+1＝Pf(W)Xk+1
＝(a0I+a1W+a2W2+...+adWd)Xk+1；
λk+1＝Pf(W)λk+1；
μk+1＝Pf(W)μk+1；
judging whether the following stopping condition formula is met or not; if yes, the solution is ended:
Figure FDA0002625516270000042
where k is a non-negative integer and a non-negative constant to define the iteration accuracy αi kIs x in the k-th iterationiβ is λiAnd muiThe iteration step size of (2); pf is a polynomial filter of order d; w is a double random matrix representing network information exchange weights; pli and Primax are load demand and renewable energy power output under maximum power point tracking; ploss, ij is the power loss on the transmission line; fri is used to penalize renewable energy power generation reduction; fei represents an energy storage system cost function; fgi represents a conventional generator cost function; fdli is the deferrable load cost expectation in the form of a quadratic function; ftpi is the tie-line power cost; Ω is the domain of X and M is the sum of the number of all independent variables;
Figure FDA0002625516270000043
is the upper limit of the power flowing on line i-j; zetar,ζlAre uncertain parameters.
4. The distributed robust optimization method for flexibility resources of an electric power system according to claim 1, further comprising, after the step of solving a plurality of the single-objective optimization problems to obtain a distributed robust optimization scheme for flexibility resources of an electric power system, the following steps:
and performing optimized scheduling on the power system according to the power system flexible resource distributed robust optimization scheme.
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