CN110571863B - Distributed power supply maximum acceptance capacity evaluation method considering flexibility of power distribution network - Google Patents

Distributed power supply maximum acceptance capacity evaluation method considering flexibility of power distribution network Download PDF

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CN110571863B
CN110571863B CN201910723284.XA CN201910723284A CN110571863B CN 110571863 B CN110571863 B CN 110571863B CN 201910723284 A CN201910723284 A CN 201910723284A CN 110571863 B CN110571863 B CN 110571863B
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刘伟生
刘志清
王飞
郑志杰
张晓磊
吴奎华
杨慎全
刘钊
刘淑莉
李昭
崔灿
邓少治
王延朔
张雯
黄亦昕
代琼丹
刘欣怡
杨莉
林振智
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
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State Grid Corp of China SGCC
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Abstract

The invention relates to a distributed power supply maximum receiving capacity evaluation method considering the flexibility of a power distribution network. And constructing a distributed power supply maximum acceptance capacity multi-target evaluation model considering the flexibility of the power distribution network by taking the maximization of the on-line power in a day, the minimization of voltage deviation and the maximization of the line capacity margin as targets. And solving the multi-target optimization model by adopting a comprehensive learning particle swarm optimization algorithm. Leading-edge solutions with optimal joint equilibrium values in a pareto solution set obtained by introducing a hybrid strategy Nash equilibrium selection algorithm are used as the maximum acceptance capacity of the distributed power supply, so that the benefits of all objective functions can be better considered. The example simulation result shows that the flexibility can be fully considered through the indexes, and the receiving capacity of the distributed power supply of the power distribution network can be effectively evaluated.

Description

Distributed power supply maximum acceptance capacity evaluation method considering flexibility of power distribution network
Technical Field
The invention relates to the field of power systems, in particular to a distributed power supply maximum acceptance capacity evaluation method considering the flexibility of a power distribution network.
Background
At present, the development mode of relying on traditional energy sources such as fossil energy is gradually changed into the development mode of utilizing renewable new energy sources such as wind power, photovoltaic energy, nuclear energy and the like all over the world. In a power distribution network, with the reform of the power market in China, Distributed wind power Generation and photovoltaic power Generation develop rapidly, the permeability of a Distributed Generation (DG) of the power distribution network is improved continuously, and when the capacity of the Distributed power in the traditional medium-voltage and low-voltage power distribution networks reaches a higher proportion (namely, high permeability), certain difficulties exist in realizing power balance and safe operation of the power distribution network and ensuring power supply reliability and power quality of users. On one hand, the distributed power supply is connected to the power distribution network, so that the environmental benefit is improved, the network loss is reduced and the voltage quality of the power distribution network is improved while the energy supply shortage is relieved; on the other hand, due to the randomness and the volatility of the distributed power supply, the problems of power quality, relay protection, flexibility and the like caused by the access of the power distribution network affect the safe and reliable operation of the system. The volatility, the intermittence and the difficult predictability of the renewable energy aggravate the volatility of net load of a power distribution network under the access of a high-permeability DG, and cause the problems of low operation efficiency, large investment and the like of power distribution equipment. The flexibility of the power distribution network is improved, the adverse effect of high-permeability DG access is effectively reduced, and the method is a research hotspot at home and abroad in recent years.
At present, safety and economy are mainly considered in a distributed power supply admission capacity evaluation model at home and abroad, further evaluation on flexibility is lacked, the consideration is not comprehensive enough, and a distributed power supply maximum admission capacity evaluation method which comprehensively considers the flexibility of a power distribution network is not discovered for a while.
Disclosure of Invention
The invention mainly solves the technical problem of the evaluation of the maximum admission capacity of a distributed power supply in consideration of the flexibility of a power distribution network, and provides a distributed power supply maximum admission capacity evaluation method in consideration of the flexibility of the power distribution network.
The invention adopts the following technical scheme:
a distributed power supply maximum admission capacity evaluation method considering the flexibility of a power distribution network comprises the following steps:
1) constructing a distributed power supply maximum acceptance capacity multi-target evaluation model considering the flexibility of a power distribution network by taking the maximum on-line power, the minimum voltage deviation and the maximum line capacity margin in a day as targets;
2) solving the multi-target optimization model by adopting a comprehensive learning particle swarm optimization algorithm;
3) leading edge solutions with optimal joint equilibrium values in a pareto solution set obtained by introducing a hybrid strategy Nash equilibrium selection algorithm are the maximum acceptance capacity of the distributed power supply.
In the above technical solution, further, step 1) specifically includes:
maximizing the on-line electricity quantity in a day, namely the actual consumption F of the distribution network to the distributed energy sources in the operation scheduling period taking the day as a unitDG(ii) a The expression is as follows:
Figure BDA0002157994490000021
in the formula: t is a time interval number; t is the number of time periods in the daily scheduling cycle; omegaPVThe method comprises the steps of collecting distributed photovoltaic power generation nodes; omegaWFThe method comprises the steps of collecting distributed wind power generation nodes;
Figure BDA0002157994490000022
and
Figure BDA0002157994490000023
actual power of distributed photovoltaic and wind power generation of the node i in a scheduling time period t is respectively; delta t is the unit scheduling time interval length;
the voltage deviation is minimized, and along with the access of a large number of distributed power supplies of the power distribution network, the voltage fluctuation of the power distribution network can be caused, namely, the voltage deviation delta U% is introduced, and the expression is as follows:
Figure BDA0002157994490000024
in the formula: omeganodeIs a set of all nodes; pL,i,tLoad of a node i in a scheduling time period t; i isk,tCurrent for branch k at scheduling time t;
Figure BDA0002157994490000031
a nominal voltage for node i during a scheduled time period t;
the capacity margin of the line is maximized, a large number of novel loads and DGs of the power distribution network are connected, the fluctuation and randomness of net loads are increased, and the local blockage of the line is easily caused. The difference between the maximum value of the allowable transmission capacity of the distribution line and the actual value of the transmission capacity of the line at a certain moment is used as the line capacity margin FLMCExpressed as:
Figure BDA0002157994490000032
in the formula: fLMC,k,tThe capacity margin of the kth distribution line is a scheduling time t; i isk,t,maxIs the maximum transmission current of line k; fLMC,k,tGenerally referring to the line margin at the moment corresponding to the load peak, FLMC,k,tNot less than 0 indicates that the line margin is sufficient and can adapt to the load power fluctuation FLMC,k,t<0 indicates insufficient line margin and line blocking may occur.
The constraint condition of the multi-target evaluation model comprises the following steps:
considering system power flow constraint, a power distribution network containing distributed power supplies is developed into a bidirectional power flow network from a traditional unidirectional power flow network, and an active power flow balance model and a reactive power flow balance model need to be established by considering a power flow direction:
Figure BDA0002157994490000033
Figure BDA0002157994490000034
wherein the content of the first and second substances,
Figure BDA0002157994490000035
Figure BDA0002157994490000036
in the formula: pij,tAnd Qij,tRespectively the active power and the reactive power which flow through the branches i-j in the time interval t; vi,tThe voltage amplitude of node i in time period t; n is the total number of the branch circuits of the power distribution network; gijAnd BijRespectively corresponding elements of the node admittance matrix; thetaij,tIs a power factor angle; omegaLineA power distribution network branch set is formed;
Figure BDA0002157994490000037
and
Figure BDA0002157994490000038
respectively the net power and the reactive power of the node i in the scheduling time period t;
Figure BDA0002157994490000039
and
Figure BDA00021579944900000310
actual active power and reactive power of the node i in the scheduling time period t are respectively;
Figure BDA00021579944900000311
and
Figure BDA00021579944900000312
respectively injecting active power and reactive power into a node i for a superior power grid in a scheduling time period t;
Figure BDA0002157994490000041
and
Figure BDA0002157994490000042
wind power generation, photovoltaic power generation and active power of the loss load at a scheduling time t node i are respectively carried out;
Figure BDA0002157994490000043
and
Figure BDA0002157994490000044
wind power generation, photovoltaic power generation and load loss reactive power at a scheduling time t node i are respectively;
considering node voltage constraints, the node voltage amplitude at any time needs to meet the safe operation requirement, and the following formula is obtained:
Ui,min≤Ui,t≤Ui,max(i∈Ωnode)
in the formula: u shapei,minAnd Ui,maxThe lowest and highest voltage amplitudes of node i, respectively;
considering branch load constraints:
|Pij,t|≤Sij(i,j∈Ωnode)
in the formula: sijIs the power limit flowing through branch i-j;
considering the output constraint of the distributed power supply, the actual output of the distributed power supply is constrained by the maximum wind abandon rate and the light abandon rate:
Figure BDA0002157994490000045
in the formula: thetaWFAnd thetaPVRespectively the maximum wind abandoning rate and the maximum light abandoning rate allowed by the system;
Figure BDA0002157994490000046
and
Figure BDA0002157994490000047
respectively representing the maximum output of wind power and photovoltaic power at the node i in the scheduling time t;
considering the loss of load constraint:
Figure BDA0002157994490000048
in the formula: λ is the maximum load loss rate;
Figure BDA0002157994490000049
load loss power of a node i in a scheduling time period t;
considering the power purchase constraint of the power supply node:
Figure BDA00021579944900000410
in the formula:
Figure BDA00021579944900000411
the power purchasing power of the power supply node i in the scheduling time period t is obtained; omegaGIs a set of power supply nodes.
Further, in the step 2), a multi-objective optimization model is solved by adopting a comprehensive learning particle swarm algorithm, the positions and the speeds of the particles are updated through the global optimal positions and the self optimal positions of the particles, the self optimal positions of the particles are updated according to the pareto domination relation, pareto non-inferior solutions meeting requirements in an iteration process of external archive storage are adopted, and the global optimal solutions are updated for two randomly extracted particles in a binary tournament mode; the updating process is as follows:
1) speed update of particle swarm
The particle swarm algorithm is comprehensively learned, and the particle speed is updated through the self optimal positions and the global optimal positions of all the particles; namely:
Figure BDA0002157994490000051
in the formula:
Figure BDA0002157994490000052
and
Figure BDA0002157994490000053
the d-th item velocity of the ith particle of the t +1 th generation and the t-th generation respectively;
Figure BDA0002157994490000054
the position of the d item of the ith particle of the t generation represents the decision variable value of the d node in the ith distributed power supply access scheme; omega (t) is an inertia coefficient of the t generation, and is used for balancing the global and local searching capability of the particles; c. C1、c2And c3Is an acceleration constant; rdIs [0, 1]]A random number over the interval;
Figure BDA0002157994490000055
the position of the ith particle in the t-th generation global optimal position g is the d-th position of the ith particle;
Figure BDA0002157994490000056
and
Figure BDA0002157994490000057
respectively the d-th item positions of the r-th particle and the i-th particle in the self optimal position p of the t generation, wherein r is randomly generated and represents the learning to the optimal positions of other particles; hdRepresenting the d-th element in H, wherein H is a binary sequence and stops updating for a certain number of times N when p stops updatingPThen, the binary sequence H needs to be updated, and ω (t) is updated for each generation, and the updating expression is:
Figure BDA0002157994490000058
in the formula: omegamaxAnd ωminRespectively the maximum value and the minimum value of the inertia coefficient; n is a radical ofGIs the maximum iteration number;
after the speed update, the particle position update strategy is:
Figure BDA0002157994490000059
in the formula:
Figure BDA00021579944900000510
the d-th position of the ith particle of the t +1 th generation;
2) updating of self-optimum position p
Updating the self optimal position p of each generation of particles according to the pareto domination relationship so as to avoid the target preference of the multi-target optimization problem, and defining the updating strategy of the self optimal position p of the t +1 generation as follows:
Figure BDA0002157994490000061
in the formula:
Figure BDA0002157994490000062
to represent
Figure BDA0002157994490000063
Dominating
Figure BDA0002157994490000064
Namely, the three item scalar values of the ith distributed power supply access scheme corresponding to the newly generated particles of the t +1 th generation are all superior to the three item scalar values of the ith distributed power supply access scheme corresponding to the optimal particles of the t th generation;
Figure BDA0002157994490000065
to represent
Figure BDA0002157994490000066
Dominating
Figure BDA0002157994490000067
If the two are not dominant, then a random number R is generateddIf R isd<0.5, then
Figure BDA0002157994490000068
3) External archive QeAnd update of the global optimal position g
Solving maximum admission capacity of distributed power supplyIn the case of the multi-objective optimization problem, an external archive Q is usedeStoring the distributed power access scheme meeting the requirements in the iterative process: if new scheme and QeThe original distributed power access schemes do not dominate each other, or dominate QeSome of the access schemes in (1), then add the new scheme to QeAnd removing QeThe original distributed power access scheme governed by the new scheme; if the newly generated distributed power supply access scheme is subjected to QeIf a certain distributed power supply access scheme in the system is dominant, the new scheme is refused to join the Qe(ii) a When Q iseThe number of the schemes exceeds the file size CmaxThen, Q is calculatedeThe congestion distance between schemes in (1), reserve front CmaxA distributed power access scheme with the largest congestion distance;
defining ith distributed power supply access scheme g of global optimal position giThe updating principle is as follows: from QeSelecting two particles randomly, and selecting the better one as g by adopting a binary tournament modei。
Further, the particle velocity is constrained to be between the intervals [0,0.2] in the present invention.
Further, leading edge solutions with optimal joint equilibrium values in a pareto solution set obtained by a hybrid strategy Nash equilibrium selection algorithm are introduced in the step 3 and serve as the maximum admission capacity of the distributed power supply;
pareto frontier solution set obtained by comprehensive learning particle swarm optimization algorithm is stored in QeIn the method, an optimal compromise solution needs to be picked out from an external archive as the final maximum admission capacity of the distributed power supply, three optimization targets are regarded as non-cooperative decision participants by virtue of the thought of a game theory, objective function values in a pareto frontier can be modeled by action sets of the decision participants, and the optimal compromise solution is obtained by solving an optimization problem of joint probability distribution in a frontier action set space, specifically:
firstly, carrying out normalization processing on an objective function to solve the problem of inconsistency of a plurality of objective dimensions, and then establishing a multi-objective non-cooperative equilibrium decision model based on a mixed strategy Nash equilibrium, wherein the expression is as follows:
Figure BDA0002157994490000071
in the formula:
Figure BDA0002157994490000073
an equalization solution representing the ith target; y isijSolving an equalization value for the ith target for the jth leading edge; u. ofiAn ith target function expectation value upper limit; omegaiFor the importance weight of the ith target, the invention adopts an entropy weight method to solve omegaiA value of (d); f. ofijSolving a normalized function value for the ith target for the jth leading edge; sobIs the number of objective functions; sesThe number of pareto frontier solutions in the external file; the leading edge solution with the best joint equilibrium value represents the joint action of the decision participant corresponding to the highest reward, i.e. the best compromise solution:
Figure BDA0002157994490000072
the technical scheme provided by the invention has the beneficial effects that:
the maximum admitting ability evaluation model of the distributed power supply considering the flexibility of the power distribution network, which is provided by the invention, aims at maximizing the on-line power in a day, minimizing the voltage deviation and maximizing the line capacity margin, can fully consider the flexibility and effectively evaluate the admitting ability of the distributed power supply of the power distribution network.
Drawings
Fig. 1 is a schematic flow chart of a distributed power supply maximum admission capacity evaluation method considering flexibility of a power distribution network.
FIG. 2 is a network topology of a distribution network in a region in an embodiment of the invention;
FIG. 3 is a typical output scenario of wind power and photovoltaic at each scheduling period in an example of the present invention;
FIG. 4 is a graph of a distributed power supply grid power objective function;
FIG. 5 is a graph of a node voltage fluctuation objective function;
FIG. 6 is a line capacity margin objective function curve;
FIG. 7 is a graph of an external archive solution set objective function distribution;
FIG. 8 is a relation between the grid-connected electricity quantity of the distributed power supply and node voltage fluctuation;
FIG. 9 is a graph of node voltage fluctuation versus line capacity margin;
FIG. 10 is a relationship between the power on the grid and the line capacity margin of the distributed power supply;
fig. 11 shows access capacities of nodes DG of the optimal compromise solution for access of the distributed power supply of the power distribution network.
Detailed Description
For better understanding of the objects, technical solutions and effects of the present invention, the present invention will be further described with reference to fig. 1.
The invention discloses a distributed power supply maximum acceptance capacity evaluation method considering the flexibility of a power distribution network, which comprises the following detailed steps:
step 1, constructing a distributed power supply maximum receiving capacity multi-target evaluation model considering the flexibility of a power distribution network;
the method comprises the following steps of establishing a multi-objective function of a distributed power supply maximum acceptance evaluation model considering the flexibility of a power distribution network, wherein the multi-objective function comprises the following steps:
the maximum online electric quantity is considered, and the actual consumption of the distributed energy source by the power distribution network in the operation scheduling period taking day as a unit is reflected by the online electric quantity in day from the whole power distribution system. When the load demand in the scheduling period of the system is fixed, the electricity purchasing quantity of the power distribution network from a superior power grid can be minimized by maximizing the on-line electricity quantity in the day, and the demand on the electricity outside the system is reduced, so that the flexible resources such as distributed power supplies and the like can be utilized to the maximum, the consumption of renewable energy sources is promoted, and the economical efficiency of the operation of the power distribution network is improved. The mathematical expression is:
Figure BDA0002157994490000091
in the formula: t is the time interval number(ii) a T is the number of time periods in the daily scheduling cycle; omegaPVThe method comprises the steps of collecting distributed photovoltaic power generation nodes; omegaWFThe method comprises the steps of collecting distributed wind power generation nodes;
Figure BDA0002157994490000092
and
Figure BDA0002157994490000093
distributing photovoltaic and wind power generation actual power for the node i in a scheduling time period t respectively; Δ t is a unit scheduling period length.
The voltage deviation is minimized, the voltage fluctuation is an important index of the power distribution network, the voltage fluctuation of the power distribution network can be caused along with the access of a large number of distributed power supplies of the power distribution network, the voltage fluctuation can cause the instability of the system, and the instability and even the disconnection of the system can be caused under severe conditions. Therefore, it is necessary to consider the voltage deviation in the objective function of the distributed power supply receptivity evaluation, so as to embody the stability of the power distribution network. The expression is as follows,
Figure BDA0002157994490000094
in the formula: omeganodeIs a set of all nodes; pL,i,tLoad of a node i in a scheduling time period t; i isk,tCurrent for branch k at scheduling time t;
Figure BDA0002157994490000095
is the nominal voltage of node i during the scheduled time period t.
The capacity margin of the line is maximized, a large number of novel loads and DGs of the power distribution network are connected, the fluctuation and randomness of net loads are increased, and the local blockage of the line is easily caused. The capacity margin of the line is used as a flexibility index for evaluating the acceptance capacity of the distributed power supply, and the flexible adequacy of the distribution line is reflected. The line capacity margin refers to the maximum allowable transmission capacity in the difference ratio of the maximum allowable transmission capacity of the distribution line to the actual transmission capacity of the line at a certain moment, and embodies the upward flexibility of the distribution line to load fluctuation. The expression is as follows:
Figure BDA0002157994490000096
in the formula: fLMC,k,tThe capacity margin of the kth distribution line is a scheduling time t; i isk,t,maxIs the maximum transmission current of line k; fLMC,k,tGenerally referring to the line margin at the moment corresponding to the load peak, FLMC,k,tNot less than 0 indicates that the line margin is sufficient and can adapt to the load power fluctuation FLMC,k,t<0 indicates insufficient line margin and line blocking may occur.
The method comprises the following steps of establishing a constraint condition of a distributed power supply maximum acceptance capability evaluation model considering the flexibility of a power distribution network, wherein the constraint condition comprises the following steps:
considering system power flow constraint, a power distribution network containing distributed power supplies is developed into a bidirectional power flow network from a traditional unidirectional power flow network, and an active power flow balance model and a reactive power flow balance model need to be established by considering a power flow direction:
Figure BDA0002157994490000101
Figure BDA0002157994490000102
wherein the content of the first and second substances,
Figure BDA0002157994490000103
Figure BDA0002157994490000104
in the formula: pij,tAnd Qij,tRespectively the active power and the reactive power which flow through the branches i-j in the time interval t; vi,tThe voltage amplitude of node i in time period t; n is the total number of the branch circuits of the power distribution network; gijAnd BijRespectively corresponding elements of the node admittance matrix；θij,tIs a power factor angle; omegaLineA power distribution network branch set is formed;
Figure BDA0002157994490000105
and
Figure BDA0002157994490000106
respectively the net power and the reactive power of the node i in the scheduling time period t;
Figure BDA0002157994490000107
and
Figure BDA0002157994490000108
actual active power and reactive power of the node i in the scheduling time period t are respectively;
Figure BDA0002157994490000109
and
Figure BDA00021579944900001010
respectively injecting active power and reactive power into a node i for a superior power grid in a scheduling time period t;
Figure BDA00021579944900001011
and
Figure BDA00021579944900001012
wind power generation, photovoltaic power generation and active power of the loss load at a scheduling time t node i are respectively carried out;
Figure BDA00021579944900001013
and
Figure BDA00021579944900001014
wind power generation, photovoltaic power generation and load loss reactive power at a scheduling time t node i are respectively.
Considering node voltage constraints, the node voltage amplitude at any time needs to meet the safe operation requirement, and the following formula is obtained:
Ui,min≤Ui,t≤Ui,max(i∈Ωnode) (8)
in the formula: u shapei,minAnd Ui,maxRespectively, the lowest and highest voltage amplitudes of node i.
Considering branch load constraints:
|Pij,t|≤Sij(i,j∈Ωnode) (9)
in the formula: sijIs the power limit flowing through branch i-j.
Considering the output constraint of the distributed power supply, the actual output of the distributed power supply is constrained by the maximum wind abandon rate and the light abandon rate:
Figure BDA0002157994490000111
in the formula: thetaWFAnd thetaPVRespectively the maximum wind abandoning rate and the maximum light abandoning rate allowed by the system;
Figure BDA0002157994490000112
and
Figure BDA0002157994490000113
and the maximum output of the wind power and the photovoltaic power of the node i in the scheduling time t is respectively.
Considering the loss of load constraint:
Figure BDA0002157994490000114
in the formula: λ is the maximum load loss rate;
Figure BDA0002157994490000115
the node i loses load power for the scheduling period t.
Considering the power purchase constraint of the power supply node:
Figure BDA0002157994490000116
in the formula:
Figure BDA0002157994490000117
the power purchasing power of the power supply node i in the scheduling time period t is obtained; omegaGIs a set of power supply nodes.
Step 2, solving the multi-target optimization model by adopting a comprehensive learning particle swarm optimization algorithm;
the particle swarm optimization algorithm is an intelligent algorithm which randomly generates an initial particle swarm, integrates the self and global information of population particles, evaluates the distance between the particles and an optimal point by using a fitness function, moves each particle to the optimal point according to the self information and the information trend obtained from the population, and obtains an optimal solution through repeated iteration optimization. The algorithm is easy to realize and is a random and parallel optimization algorithm. The evaluation problem solved here is a multi-objective optimization problem, and the comprehensive learning particle swarm optimization algorithm is proposed to solve the problem while ensuring the diversity of the obtained pareto non-inferior solution and avoiding the pareto non-inferior solution from falling into local optimization. The comprehensive learning particle swarm optimization algorithm (CLPSO algorithm) adopts a comprehensive learning strategy to update the speed and the position of the particles, so that the problem of dimension explosion caused by the traditional mathematical solving method can be prevented. The particle swarm optimization is comprehensively learned to update the positions and the speeds of the particles through the global optimal positions and the self optimal positions of the particles, the self optimal positions of the particles are updated according to the pareto domination relation, pareto non-inferior solutions meeting requirements in an external archive storage iteration process are adopted, and the global optimal solutions are updated for two randomly extracted particles in a binary tournament mode. The updating process is as follows:
1) speed update of particle swarm
The particle swarm algorithm is comprehensively learned, and the particle speed is updated through the self optimal position and the global optimal position of all the particles. Namely:
Figure BDA0002157994490000121
in the formula:
Figure BDA0002157994490000122
and
Figure BDA0002157994490000123
the d-th item velocity of the ith particle of the t +1 th generation and the t-th generation respectively;
Figure BDA0002157994490000124
the position of the d item of the ith particle of the t generation represents the decision variable value of the d node in the ith distributed power supply access scheme; omega (t) is an inertia coefficient of the t generation, and is used for balancing the global and local searching capability of the particles; c. C1、c2And c3Is an acceleration constant; rdIs [0, 1]]A random number over the interval;
Figure BDA0002157994490000125
the position of the ith particle in the t-th generation global optimal position g is the d-th position of the ith particle;
Figure BDA0002157994490000126
and
Figure BDA0002157994490000127
respectively the d-th item positions of the r-th particle and the i-th particle in the self optimal position p of the t generation, wherein r is randomly generated and represents the learning to the optimal positions of other particles; hdRepresenting the d-th element in H, wherein H is a binary sequence and stops updating for a certain number of times N when p stops updatingPThen, the binary sequence H needs to be updated. Each generation of ω (t) is updated, and the updating expression is as follows:
Figure BDA0002157994490000128
in the formula: omegamaxAnd ωminRespectively the maximum value and the minimum value of the inertia coefficient; n is a radical ofGIs the maximum number of iterations.
After the speed update, the particle position update strategy is:
Figure BDA0002157994490000129
in the formula:
Figure BDA00021579944900001210
is the d-th position of the ith particle of the t +1 th generation.
In the overall learning particle swarm algorithm, if the speed of a particle is too fast, a globally optimal solution may be missed, and if the speed of the particle is too slow, a locally optimal solution is likely to be trapped, so that a maximum speed v is definedmaxTo limit the velocity of the particles. The invention constrains the speed to the interval 0,0.2]In the meantime.
2) Updating of self-optimum position p
The CLPSO algorithm updates the self optimal position p of each generation of particles according to the pareto domination relationship so as to avoid the target preference of the multi-target optimization problem, and an updating strategy of the self optimal position p of the t +1 generation is defined as follows:
Figure BDA0002157994490000131
in the formula:
Figure BDA0002157994490000132
to represent
Figure BDA0002157994490000133
Dominating
Figure BDA0002157994490000134
Namely, the three item scalar values of the ith distributed power supply access scheme corresponding to the newly generated particles of the t +1 th generation are all superior to the three item scalar values of the ith distributed power supply access scheme corresponding to the optimal particles of the t th generation;
Figure BDA0002157994490000135
to represent
Figure BDA0002157994490000136
Dominating
Figure BDA0002157994490000137
If the two are not dominant, then a random number R is generateddIf R isd<0.5, then
Figure BDA0002157994490000138
3) External archive QeAnd update of the global optimal position g
When solving the multi-objective optimization problem of the maximum receiving capacity of the distributed power supply, an external archive Q is adoptedeStoring the distributed power access scheme meeting the requirements in the iterative process: if new scheme and QeThe original distributed power access schemes do not dominate each other, or dominate QeSome of the access schemes in (1), then add the new scheme to QeAnd removing QeThe original distributed power access scheme governed by the new scheme; if the newly generated distributed power supply access scheme is subjected to QeIf a certain distributed power supply access scheme in the system is dominant, the new scheme is refused to join the Qe. When Q iseThe number of the schemes exceeds the file size CmaxThen, Q is calculatedeThe congestion distance between schemes in (1), reserve front CmaxAnd the distributed power access scheme with the largest congestion distance.
Defining ith distributed power supply access scheme g of global optimal position giThe updating principle is as follows: from QeSelecting two particles randomly, and selecting the better one as g by adopting a binary tournament modei。
And 3, introducing a leading edge solution with an optimal joint equilibrium value in a pareto solution set obtained by a hybrid strategy Nash equilibrium selection algorithm, and taking the leading edge solution as the maximum admission capacity of the distributed power supply.
Pareto frontier solution set obtained by comprehensive learning particle swarm optimization algorithm is stored in QeAnd finally, picking out an optimal compromise solution from an external file to serve as the final maximum receiving capacity of the distributed power supply. However, the weight determination method in the linear weighting method or the fuzzy inference method is greatly influenced by the preference of the decision maker. Therefore, three optimization targets can be set by the idea of game theoryThe objective function values in the pareto frontier can be modeled with the action sets of the decision participants, and the optimal compromise solution is obtained by solving the optimization problem of joint probability distribution in frontier action set space.
Firstly, carrying out normalization processing on an objective function, solving the problem of inconsistency of a plurality of objective dimensions, and then establishing a multi-objective non-cooperative equilibrium decision model based on a mixed strategy Nash equilibrium, wherein the expression is as follows:
Figure BDA0002157994490000141
in the formula:
Figure BDA0002157994490000143
an equalization solution representing the ith target; y isijSolving an equalization value for the ith target for the jth leading edge; u. ofiAn ith target function expectation value upper limit; omegaiFor the importance weight of the ith target, the invention adopts an entropy weight method to solve omegaiA value of (d); f. ofijSolving a normalized function value for the ith target for the jth leading edge; sobIs the number of objective functions; sesThe number of pareto frontier solutions in the external file. The leading edge solution with the best joint equilibrium value represents the joint action of the decision participant corresponding to the highest reward, i.e. the best compromise solution:
Figure BDA0002157994490000142
the practical application of the present invention will be explained below by taking an actual 20kV distribution network in a certain area as an example.
The power distribution network comprises 2 110kV nodes (node 1 and node 53, indicated by orange solid points) and 53 20kV load nodes, the total active load of the system is 272.85MW, 53 lines are shared, the topological diagram of the power distribution network frame is shown in figure 2, and the dotted line is a connecting line in the system. Setting the voltage fluctuation range of the system node i at the scheduling time t as
Figure BDA0002157994490000151
Node 41 is a distributed wind power generation access node and nodes 2-40 and 42-55 are distributed photovoltaic access nodes.
Considering the uncertainty of the output of the distributed power supply, the calculation example generates 3 distributed wind power generation typical output scenes and 4 distributed photovoltaic power generation typical output scenes based on measured data, each scene is divided into 8 scheduling time periods, and the per-unit output curve of each scheduling time period is shown in fig. 3.
The basic parameter settings of the overall learning particle swarm algorithm used are as follows:
number of particles 30, acceleration factor c1、c2And c3Are all 1.494, the inertia weight is updated according to the formula (15), and omega is takenmax＝0.7，ωminThe maximum number of iterations is 100, 0.2. 4-6 are three objective function convergence graphs in the process of solving the maximum receiving capacity of the multi-objective distributed power supply. As can be seen from FIG. 4, the particle swarm optimization algorithm has a fast index optimization speed from generation 1 to generation 30, and reaches a solution very close to the optimal solution after generation 40, and the algorithm converges at generation 100.
And obtaining a distributed power supply maximum receiving capacity external archive solution set through a comprehensive learning particle swarm algorithm, and carrying out normalization processing on the objective function values of all decision schemes. According to the characteristic of multi-objective optimization, in order to visually display the distribution condition of three objective functions corresponding to each external archive solution, a three-dimensional objective function space pareto frontier solution set is drawn as shown in fig. 7. As can be seen from fig. 7, each external archive solution is distributed on the pareto optimal front edge, and the distance between each external archive solution is large, and the congestion degree is low, which indicates that the external archive solution set obtained by the CLPSO algorithm contains various decision schemes that fully consider that the three objective functions provided herein dominate each other, thereby ensuring that the optimal compromise solution can fully balance the benefits of each objective function, and achieving comprehensive optimization.
The weights of the three objective functions calculated by the entropy weight method are respectively 0.1745, 0.3003 and 0.5252, and the line capacity margin index weight is higher than other indexes, which shows that in the multi-objective power distribution network distributed power supply receptivity evaluation model provided by the invention, the line capacity margin index variability is larger and the provided information amount is more. Therefore, when a hybrid strategy nash equilibrium decision is made according to the index weight, the flexibility of the power distribution network frame is fully considered, the normalized target values of the external archive solution (the optimal compromise solution, namely, red square marks in fig. 6) with the highest combined equilibrium value are (0.889, 0.829, 1.000), and table 1 shows the target function values and DG access capacity values of the decision scheme of the three single target optimal boundary solutions and the optimal compromise solution in the external archive solution. As can be seen from fig. 7 and table 1, the optimal compromise solution is simultaneously the optimal solution of the line capacity margin, the optimal line capacity objective function value of the DG access decision scheme is higher, and the function values of the other two objectives are also higher, so that it is reasonable to select the distributed power access decision scheme as the optimal compromise solution.
Table 1 scheme of single target optimal boundary solution and optimal compromise solution
Figure BDA0002157994490000161
The correlation analysis of the three objective functions of the model provided by the invention is performed by selecting different distributed power supply access schemes generated in the overall learning particle swarm optimization process, as shown in fig. 8-10.
As can be seen from fig. 8 to fig. 10, in each distributed power access scheme, there is no obvious linear correlation between the normalized target function values of each index. The function values of three targets in each scheme are in a region with dense distribution, the node voltage fluctuation target function values are intensively distributed in [0.1, 0.3], and the line capacity margin target function values are intensively distributed in [0.7, 1], because each particle is gradually converged in the optimization process of the CLPSO algorithm, and the target function values of the particles are continuously close to the optimum in the iteration process. In order to prevent the particle swarm optimization result from falling into local optimization, particle mutation operation is executed in the optimization process, namely the DG access capacity of a certain node in the DG access scheme is randomly changed. In the DG access scheme that adopts the mutation operation, the optimal power flow calculation result is significantly changed, and the variation of each objective function value is large, which is represented as a discrete point in fig. 8 to 10.
The access capacity of each node of the optimal power distribution network distributed power supply access solution obtained by the power distribution network distributed power supply admission capacity evaluation method is shown in fig. 11.
The capacities of distributed power supplies connected to the node 7 and the node 21 are 3390.6kW and 2528.6kW respectively, the two nodes are located at the initial ends of branch circuits of the power distribution network, the active power flow flowing through the circuits ( circuits 5, 6, 20 and 21) connected with the two nodes is large, the two nodes are adjacent to the power supply nodes, the voltage drop of the nodes is small, and voltage support does not need to be provided by means of DGs. Thus, the distributed power capacity accessed by node 7 and node 21 is smaller for an increased line capacity margin target value.
The distributed power supply maximum acceptance evaluation model considering the flexibility of the power distribution network is explained through the example analysis result of the planned region in a certain domestic city, the flexibility can be fully considered by taking the maximization of the on-line electricity quantity in a day, the minimization of the voltage deviation and the maximization of the line capacity margin as the targets, and the acceptance of the distributed power supply of the power distribution network can be effectively evaluated.

Claims (5)

1. A distributed power supply maximum acceptance capacity assessment method considering the flexibility of a power distribution network is characterized by comprising the following steps:
1) constructing a distributed power supply maximum acceptance capacity multi-target evaluation model considering the flexibility of a power distribution network by taking the maximum on-line power, the minimum voltage deviation and the maximum line capacity margin in a day as targets;
2) solving the multi-target optimization model by adopting a comprehensive learning particle swarm optimization algorithm;
3) leading-edge solutions with optimal joint equilibrium values in a pareto solution set obtained by introducing a hybrid strategy Nash equilibrium selection algorithm, wherein the leading-edge solutions are the maximum acceptance capacity of the distributed power supply;
the step 1) specifically comprises the following steps:
maximizing the on-line electricity quantity in a day, namely, maximizing the distribution of the distribution network pair in the operation scheduling period taking the day as a unitActual consumption of energy FDG(ii) a The expression is as follows:
Figure FDA0002684951900000011
in the formula: t is a time interval number; t is the number of time periods in the daily scheduling cycle; omegaPVThe method comprises the steps of collecting distributed photovoltaic power generation nodes; omegaWFThe method comprises the steps of collecting distributed wind power generation nodes;
Figure FDA0002684951900000012
and
Figure FDA0002684951900000013
actual power of distributed photovoltaic and wind power generation of the node i in a scheduling time period t is respectively; delta t is the unit scheduling time interval length;
the voltage deviation is minimized, and along with the access of a large number of distributed power supplies of the power distribution network, the voltage fluctuation of the power distribution network can be caused, namely, the voltage deviation delta U% is introduced, and the expression is as follows:
Figure FDA0002684951900000014
in the formula: omeganodeIs a set of all nodes; pL,i,tLoad of a node i in a scheduling time period t; i isk,tCurrent for branch k at scheduling time t;
Figure FDA0002684951900000026
a nominal voltage for node i during a scheduled time period t;
maximizing the capacity margin of the line, accessing a large number of novel loads and DGs of the power distribution network, increasing the fluctuation and randomness of net loads, easily causing local blockage of the line, and taking the difference value between the maximum value of the allowable transmission capacity of the power distribution line and the actual value of the transmission capacity of the line at a certain moment as the ratio of the difference value to the maximum value of the allowable transmission capacity, namely the capacity margin F of the lineLMCExpressed as:
Figure FDA0002684951900000021
in the formula: fLMC,k,tThe capacity margin of the kth distribution line is a scheduling time t; i isk,t,maxIs the maximum transmission current of line k; fLMC,k,tGenerally referring to the line margin at the moment corresponding to the load peak, FLMC,k,tNot less than 0 indicates that the line margin is sufficient and can adapt to the load power fluctuation FLMC,k,t<0 indicates insufficient line margin and line blocking may occur.
2. The distributed power supply maximum acceptance assessment method considering the flexibility of the power distribution network according to claim 1, wherein the constraint conditions of the multi-objective assessment model constructed in the step 1) comprise:
considering system power flow constraint, a power distribution network containing distributed power supplies is developed into a bidirectional power flow network from a traditional unidirectional power flow network, and an active power flow balance model and a reactive power flow balance model need to be established by considering a power flow direction:
Figure FDA0002684951900000022
Figure FDA0002684951900000023
wherein the content of the first and second substances,
Figure FDA0002684951900000024
Figure FDA0002684951900000025
in the formula: pij,tAnd Qij,tAre respectively a period of timet flows through the active and reactive powers of the branches i-j; vi,tThe voltage amplitude of node i in time period t; n is the total number of the branch circuits of the power distribution network; gijAnd BijRespectively corresponding elements of the node admittance matrix; thetaij,tIs a power factor angle; omegaLineA power distribution network branch set is formed;
Figure FDA0002684951900000031
and
Figure FDA0002684951900000032
respectively the net power and the reactive power of the node i in the scheduling time period t;
Figure FDA0002684951900000033
and
Figure FDA0002684951900000034
actual active power and reactive power of the node i in the scheduling time period t are respectively;
Figure FDA0002684951900000035
and
Figure FDA0002684951900000036
respectively injecting active power and reactive power into a node i for a superior power grid in a scheduling time period t;
Figure FDA0002684951900000037
and
Figure FDA0002684951900000038
wind power generation, photovoltaic power generation and active power of the loss load at a scheduling time t node i are respectively carried out;
Figure FDA0002684951900000039
and
Figure FDA00026849519000000310
respectively at the scheduling period tWind power generation, photovoltaic power generation and load loss reactive power of the node i;
considering node voltage constraints, the node voltage amplitude at any time needs to meet the safe operation requirement, and the following formula is obtained:
Ui,min≤Ui,t≤Ui,max(i∈Ωnode)
in the formula: u shapei,minAnd Ui,maxThe lowest and highest voltage amplitudes of node i, respectively;
considering branch load constraints:
|Pij,t|≤Sij(i,j∈Ωnode)
in the formula: sijIs the power limit flowing through branch i-j;
considering the output constraint of the distributed power supply, the actual output of the distributed power supply is constrained by the maximum wind abandon rate and the light abandon rate:
Figure FDA00026849519000000311
in the formula: thetaWFAnd thetaPVRespectively the maximum wind abandoning rate and the maximum light abandoning rate allowed by the system;
Figure FDA00026849519000000312
and
Figure FDA00026849519000000313
respectively representing the maximum output of wind power and photovoltaic power at the node i in the scheduling time t;
considering the loss of load constraint:
Figure FDA00026849519000000314
in the formula: λ is the maximum load loss rate;
Figure FDA0002684951900000041
load loss power of a node i in a scheduling time period t;
considering the power purchase constraint of the power supply node:
Figure FDA0002684951900000042
in the formula:
Figure FDA0002684951900000043
the power purchasing power of the power supply node i in the scheduling time period t is obtained; omegaGIs a set of power supply nodes.
3. The distributed power supply maximum acceptance evaluation method considering the flexibility of the power distribution network according to claim 1, wherein in the step 2), a comprehensive learning particle swarm algorithm is adopted to solve the multi-objective optimization model, the positions and the speeds of the particles are updated through the global optimal positions and the self optimal positions of the particles, the self optimal positions of the particles are updated according to the pareto domination relationship, the pareto non-inferior solutions meeting the requirements in the iteration process of external archive storage are adopted, and the global optimal solutions are updated for two randomly extracted particles in a binary tournament mode; the updating process is as follows:
1) speed update of particle swarm
The particle swarm algorithm is comprehensively learned, and the particle speed is updated through the self optimal positions and the global optimal positions of all the particles; namely:
Figure FDA0002684951900000044
in the formula:
Figure FDA0002684951900000045
and
Figure FDA0002684951900000046
the d-th item velocity of the ith particle of the t +1 th generation and the t-th generation respectively;
Figure FDA0002684951900000047
the position of the d item of the ith particle of the t generation represents the decision variable value of the d node in the ith distributed power supply access scheme; omega (t) is an inertia coefficient of the t generation, and is used for balancing the global and local searching capability of the particles; c. C1、c2And c3Is an acceleration constant; rdIs [0, 1]]A random number over the interval;
Figure FDA0002684951900000048
the position of the ith particle in the t-th generation global optimal position g is the d-th position of the ith particle;
Figure FDA0002684951900000051
and
Figure FDA0002684951900000052
respectively the d-th item positions of the r-th particle and the i-th particle in the self optimal position p of the t generation, wherein r is randomly generated and represents the learning to the optimal positions of other particles; hdRepresenting the d-th element in H, wherein H is a binary sequence and stops updating for a certain number of times N when p stops updatingPThen, the binary sequence H needs to be updated, and ω (t) is updated for each generation, and the updating expression is:
Figure FDA0002684951900000053
in the formula: omegamaxAnd ωminRespectively the maximum value and the minimum value of the inertia coefficient; n is a radical ofGIs the maximum iteration number;
after the speed update, the particle position update strategy is:
Figure FDA0002684951900000054
in the formula:
Figure FDA0002684951900000055
the d-th position of the ith particle of the t +1 th generation;
2) updating of self-optimum position p
Updating the self optimal position p of each generation of particles according to the pareto domination relationship so as to avoid the target preference of the multi-target optimization problem, and defining the updating strategy of the self optimal position p of the t +1 generation as follows:
Figure FDA0002684951900000056
in the formula:
Figure FDA0002684951900000057
to represent
Figure FDA0002684951900000058
Dominating
Figure FDA0002684951900000059
Namely, the three item scalar values of the ith distributed power supply access scheme corresponding to the newly generated particles of the t +1 th generation are all superior to the three item scalar values of the ith distributed power supply access scheme corresponding to the optimal particles of the t th generation;
Figure FDA00026849519000000510
to represent
Figure FDA00026849519000000511
Dominating
Figure FDA00026849519000000512
If the two are not dominant, then a random number R is generateddIf R isd<0.5, then
Figure FDA00026849519000000513
3) External archive QeAnd update of the global optimal position g
When solving the multi-objective optimization problem of the maximum receiving capacity of the distributed power supply, an external archive Q is adoptedeStoring the distributed power access scheme meeting the requirements in the iterative process: if new scheme and QeThe original distributed power access schemes do not dominate each other, or dominate QeSome of the access schemes in (1), then add the new scheme to QeAnd removing QeThe original distributed power access scheme governed by the new scheme; if the newly generated distributed power supply access scheme is subjected to QeIf a certain distributed power supply access scheme in the system is dominant, the new scheme is refused to join the Qe(ii) a When Q iseThe number of the schemes exceeds the file size CmaxThen, Q is calculatedeThe congestion distance between schemes in (1), reserve front CmaxA distributed power access scheme with the largest congestion distance;
defining ith distributed power supply access scheme g of global optimal position giThe updating principle is as follows: from QeSelecting two particles randomly, and selecting the better one as g by adopting a binary tournament modei。
4. The distributed power supply maximum capacity evaluation method considering flexibility of a power distribution network according to claim 3, wherein the particle speed is constrained to be between intervals [0,0.2 ].
5. The distributed power supply maximum admission capacity evaluation method considering the flexibility of the power distribution network according to claim 1, characterized in that a leading edge solution with an optimal joint equalization value in a pareto solution set obtained by introducing a hybrid strategy nash equalization selection algorithm is used as the maximum admission capacity of the distributed power supply in step 3;
pareto frontier solution set obtained by comprehensive learning particle swarm optimization algorithm is stored in QeIn the method, an optimal compromise solution needs to be picked out from an external archive as the final maximum admission capacity of the distributed power supply, three optimization targets are regarded as non-cooperative decision participants by virtue of the thought of the game theory, the objective function value in the pareto frontier can be modeled by the action set of the decision participants, and the decision participants are solved by solvingSolving the optimization problem of joint probability distribution in the front edge action set space to obtain the optimal compromise solution, which specifically comprises the following steps:
firstly, carrying out normalization processing on an objective function to solve the problem of inconsistency of a plurality of objective dimensions, and then establishing a multi-objective non-cooperative equilibrium decision model based on a mixed strategy Nash equilibrium, wherein the expression is as follows:
Figure FDA0002684951900000071
Figure FDA0002684951900000072
yij≥0,i＝1,2,...,Sob,j＝1,2,...,Ses
Figure FDA0002684951900000073
in the formula:
Figure FDA0002684951900000074
an equalization solution representing the ith target; y isijSolving an equalization value for the ith target for the jth leading edge; u. ofiAn ith target function expectation value upper limit; omegaiFor the importance weight of the ith target, the invention adopts an entropy weight method to solve omegaiA value of (d); f. ofijSolving a normalized function value for the ith target for the jth leading edge; sobIs the number of objective functions; sesThe number of pareto frontier solutions in the external file; the leading edge solution with the best joint equilibrium value represents the joint action of the decision participant corresponding to the highest reward, i.e. the best compromise solution:
Figure FDA0002684951900000075
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