CN110490390B - Distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory - Google Patents
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Abstract
The invention discloses a distributed photovoltaic multi-target optimization configuration method based on a multi-decision theory. The method comprises the following steps: (1) constructing a multi-objective optimization configuration model aiming at reducing node voltage deviation, node voltage harmonic distortion rate and system network loss and improving the static voltage stability of the power distribution network; (2) establishing a constraint equation of multi-objective optimization configuration, wherein the constraint conditions comprise system power flow constraint, voltage deviation constraint, power reverse transmission constraint and total access flow constraint; (3) obtaining comprehensive weight by utilizing an entropy weight method and a game theory combined weighting method; (4) and solving the established multi-objective optimization configuration model by using an improved particle swarm optimization algorithm to obtain an optimization configuration scheme of distributed photovoltaic access. According to the method, an optimization target is determined according to the influence of photovoltaic access on a power grid, the model is empowered in both objective and subjective aspects, and a global optimal solution is obtained through an improved particle swarm algorithm.
Description
Technical Field
The invention relates to a distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory, and belongs to the field of power operation and control.
Background
With the increasing severity of the two problems of energy crisis and climate warming, the global energy structure is facing a new transformation and upgrade. The development of renewable energy sources at the present stage of China mainly focuses on three aspects of photovoltaic power generation, wind power generation and hydroelectric power generation, and compared with wind power and hydropower, the photovoltaic power generation is slightly limited by geographical conditions, the capacity selection is more flexible, and the renewable energy sources have the greatest development potential in the new era.
The main development trend of photovoltaic power generation is photovoltaic power generation grid connection, but the power generation mode of a photovoltaic power supply is different from that of the traditional energy, the original structure of a power distribution network is changed by photovoltaic access, and certain negative influence is certainly caused on the power distribution network by large-scale grid connection. The output of the photovoltaic power supply has volatility and randomness, and the voltage fluctuation and voltage flicker of a power grid are easily caused; harmonic current can be generated when the photovoltaic inverter is frequently closed and the switching tube is opened, so that harmonic pollution is caused; the voltage level of a power distribution network can be increased by photovoltaic grid connection, and node voltage is easy to exceed the limit; the photovoltaic access capacity is too large, so that the power flow can flow reversely, and the stability of a power system is reduced.
The influence rules of photovoltaic access on the power distribution network are comprehensively and deeply researched and analyzed, and the photovoltaic access is optimally configured based on the rules, so that various indexes of the power distribution network are optimal as far as possible, and the method has important significance on the distributed photovoltaic access power distribution network.
Disclosure of Invention
The invention discloses a distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory, which is characterized in that the photovoltaic access has great influence on the voltage distribution, the voltage distortion, the static voltage stability and the system network loss of a power distribution network, a multi-objective optimization configuration model is constructed according to the four indexes, comprehensive weights are obtained by utilizing an entropy weight method and a game theory combined weighting method, and the multi-objective optimization configuration model is solved by utilizing an improved particle swarm optimization algorithm.
The specific method is realized by the following steps:
a distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory is characterized by comprising the following steps:
(1) constructing a multi-objective optimization configuration model aiming at reducing node voltage deviation, node voltage harmonic distortion rate and system network loss and improving the static voltage stability of the power distribution network;
after photovoltaic access, voltage drop in a line is reduced, the overall voltage level of the system is increased, and the possible voltage deviation of partial nodes exceeds the standard.
The node voltage deviation is expressed as the percentage of the difference between the actual voltage and the rated voltage of the node to the rated voltage and is determined by the formula (1); the system voltage deviation is expressed by the mean value of the voltage deviations of the nodes and is determined by the formula (2),
where U is the actual voltage at a node, U N Is the rated voltage, DeltaU, of the node i And n is the total number of nodes of the power distribution network system.
Frequent on-off actions of a switch tube in the photovoltaic inverter can inevitably generate harmonic current, so that the node voltage of the power distribution network is distorted. The node voltage harmonic distortion rate refers to a relative value of a root mean square value of each harmonic voltage and an effective value of fundamental voltage, and the voltage distortion rate of the node k is determined by a formula (3); the total voltage distortion rate of the system is expressed as the sum of the voltage distortion rates of all nodes and is determined by the formula (4),
wherein, THD k Is the voltage distortion rate of node k, THD is the total voltage distortion rate of the system, U i Is the effective value of the ith harmonic voltage, U 1 The effective value of the fundamental voltage is obtained, and n is the total number of nodes of the power distribution network system.
The index of the static voltage stability of the power distribution network reflects the distance between the current system voltage and the instability, and for the branch k, the static voltage stability index based on the existence of the tidal current equation solution is determined by a formula (5); the system voltage stability index is determined by the formula (6) by taking the maximum value of the static voltage stability index of each branch circuit,
VSI＝max{L 1 ,L 2 ,L 3 ,...,L n } (6)
wherein R and X are the resistance and reactance of branch k, P b And Q b Respectively absorbing active and reactive power, V, for the ends of branch k a Is the effective value of the voltage at the head end of the branch k.
The photovoltaic access changes the structure and the tide distribution of the power distribution network, and inevitably changes the current flowing through the branch, thereby having certain influence on the system network loss. The system loss is determined by equation (7),
wherein m is the total number of branches of the power distribution network system, G k Is the conductance of branch k, V i And V j The voltage amplitudes of the nodes at the two ends of the branch k are respectively theta i And theta j Respectively, its phase.
(2) Establishing a constraint equation of multi-objective optimization configuration, wherein the constraint conditions comprise system power flow constraint, voltage deviation constraint, power reverse transmission constraint, total access flow constraint, main transformer capacity limiting constraint and branch current limiting constraint;
and (3) system power flow constraint:
the power generated by the photovoltaic power supply in the power grid is matched with the sum of the load consumption power and the power among nodes in the line:
wherein,
active power and reactive power are respectively provided for the photovoltaic power supply at the node i;
respectively the active power and the reactive power consumed by the load at the node i; p ij And Q ij Respectively the active power and the reactive power flowing between the node i and the node j; u shape i Is the voltage amplitude of node i, θ ij Is the voltage phase angle difference between node i and node j, G ij And B ij Respectively the conductance and susceptance of the line between node i and node j.
And voltage deviation constraint:
the voltage of the node must not exceed its maximum and minimum voltage amplitudes:
U min ≤U i ≤U max (9)
wherein, U i Is the i-node voltage amplitude, U min 、U max Respectively, a lower limit and an upper limit of the node voltage amplitude.
Power back-off constraint:
the system cannot dump excess power to the large grid:
P T ≥0 (10)
wherein, P T Power delivered to the distribution network for the external grid.
Total access capacity constraint:
the distributed photovoltaic access capacity is limited by the self-installation capacity:
∑P DG ≤P DGmax (11)
wherein, P DGmax Is the maximum allowed photovoltaic power total capacity.
Main transformer capacity limiting constraint;
the main transformer cannot deliver power beyond a specified value.
S Ti ≤S Ti,max (12)
S Ti,max Is the maximum transmission power allowed by the transformer.
Branch current limiting constraint; each branch has its own maximum allowable current, and the actual operating current of the line cannot exceed the maximum allowable current in principle
I ij,min ≤I ij ≤I ij,max (13)
I ij,min And I ij,max The maximum and minimum allowed paths through the circuit between node i and node j, respectively.
(3) And obtaining the comprehensive weight by utilizing an entropy weight method and a game theory combined weighting method.
The entropy weight method is a method for objectively weighting multiple indexes, and the basic idea is to calculate the information entropy of each index according to the variation degree of each index and then calculate the objective weight of each index through the information entropy.
Constructing a multi-object and multi-index matrix:
for an index system with m objects, n indices, X ij The j-th index (i ═ 1,2,3, …, n) of the i-th object (i ═ 1,2,3, …, m).
Data normalization processing:
if the indicator is positive indicator, the first formula is selected, and if the indicator is negative indicator, the second formula is selected.
Calculating an index proportion matrix:
wherein, X' ij Is the specific gravity of the j-th index, determined by the formula (17),
calculating the entropy value of each index, the entropy value of the j index is determined by formula (18),
calculating the weight of each index, determined by formula (17),
in real life, not only the degree of susceptibility of each index, but also the importance of each index in an evaluation system are considered, and the importance depends on the subjective intention of a decision maker. The game theory combination weighting method is combined by the subjective weight and the objective weight determined by the entropy weight method, so that the evaluation system is more comprehensive and effective.
Assuming that the weights of n indexes are obtained by L methods, the weight vector obtained by the k method is:
ω k ＝(ω k1 ,ω k2 ,…,ω kn ),k＝(1,2,…,L) (20)
let the integrated weight be the linear combination of these L weight vectors:
by controlling alpha k To optimize ω such that ω should be associated with each ω k The distance between them is minimal:
derivation of equation (22) yields the optimization condition:
find (alpha) 1 ,α 2 ,…,α l ) Normalizing the vector to obtain a comprehensive weight vector omega * ：
(4) And solving the established multi-objective optimization configuration model by using an improved particle swarm optimization algorithm to obtain an optimization configuration scheme of distributed photovoltaic access.
The algorithm steps of the improved particle swarm optimization are as follows:
1) and reading parameters of the power distribution network, including the number of nodes, line impedance, load power and the like, and determining the access number of the photovoltaic power supplies and the upper limit of the access total capacity.
2) And determining a calculation formula of each index, solving the power flow by utilizing a forward-backward substitution algorithm, and determining the harmonic power flow by utilizing a decoupling method.
3) And determining a calculation formula of each constraint condition, and setting a penalty function.
4) Initializing a particle swarm, and setting the size of the swarm, the maximum iteration times, the initial position and the speed.
5) And calculating a fitness function value according to the particle position, namely the sum of the power distribution network operation comprehensive index F and the penalty function.
6) And individual extremum pbest i Comparing with global extreme value gbest, updating pbest i And gbest.
For the ith particle x i Randomly generating a 0-1 vector of length N
If it is
Then x is i,j And pbest i,j If the values of (1) are interchanged
Then exchange is not carried out to obtain new particle XP 1 And XP 2 . Also for x i And gbest to get XP 3 And XP 4 。
Pair XP 1 、XP 2 、XP 3 、XP 4 Respectively calculating the fitness, let f min ＝minf(XP j ) If f is min <f(pbest i ) Then pbest i ＝XP j (ii) a If f min <f (gbest), then gbest ═ XP j . Mixing pbest i And gbest participates in the next iteration as a new individual extremum and a new global extremum.
8-7) updating the particle velocity and position, the new velocity and position being determined by equations (26), (27), respectively.
Wherein,
and
respectively representing the velocity and position of the ith particle in the kth iteration,
represents the historical best solution, gbest, for the ith particle k A globally optimal solution is represented as a function of,
an average value representing the position of the particle; c. C 1 And c 2 The acceleration factors respectively represent the approaching trend of the particles to the individual extreme point and the global extreme point; rand 1 And rand 2 Is at [0,1 ]]Randomly generating an acceleration weight coefficient in the interval; ω is an inertial weight, which is a coefficient for maintaining the velocity at the previous time, and is determined by equation (28):
in the formula (28), ω is max And ω min The maximum value and the minimum value of the inertia weight respectively,k max k is the current iteration number.
8) And carrying out cross mutation on the updated particles.
When the variance of the population is below a set threshold, initializing the population according to equation (29):
wherein,
to reinitialize the seed group, the lower and upper expiration of the j-th dimension position are determined by equation (30):
in the formula (30), the first and second groups,
as the number of iterations increases from 1 to 0,
representing the lower and upper bounds, respectively, of the jth dimension of the particle.
9) Checking whether a termination condition (reaching the maximum iteration number or meeting the convergence precision error) is met, if so, terminating iteration and outputting an optimal solution; if not, go to step 5).
The invention has the following beneficial effects:
according to the method, a multi-objective optimization configuration model is constructed by negative influences caused after photovoltaic access to a power distribution network, wherein the negative influences include voltage deviation, voltage distortion, static voltage stability indexes and system network loss. The entropy weight method is used for objectively weighting each index, influence factors in actual life are considered, and a game theory combined weighting method is adopted to perfect an evaluation system. And solving the optimal solution of the objective function by using an improved particle swarm algorithm. According to the method, an optimization target is determined according to the influence of photovoltaic access on a power grid, the model is empowered in both objective and subjective aspects, and a global optimal solution is obtained through an improved particle swarm algorithm.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The photovoltaic access changes the original structure of the power distribution network, and the large-scale grid connection inevitably causes certain negative influence on the power distribution network. The output of the photovoltaic power supply has volatility and randomness, and the voltage fluctuation and voltage flicker of a power grid are easily caused; harmonic current can be generated when the photovoltaic inverter is frequently closed and the switching tube is opened, so that harmonic pollution is caused; the photovoltaic grid connection can increase the voltage level of a power distribution network, and the node voltage is easy to exceed the limit; the photovoltaic access capacity is too large, so that the power flow can flow reversely, and the stability of a power system is reduced.
The invention provides a distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory, which is characterized in that voltage deviation, voltage distortion rate, static voltage stability index and system network loss are used as optimization targets, and a multi-objective optimization configuration model is constructed; and obtaining comprehensive weights by utilizing an entropy weight method and a game theory combined weighting method, and solving the established multi-objective optimization configuration model by adopting an improved particle swarm optimization algorithm to obtain an optimization configuration scheme of distributed photovoltaic access.
As shown in fig. 1, a distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory is characterized by comprising the following steps:
(1) constructing a multi-objective optimization configuration model aiming at reducing node voltage deviation, node voltage harmonic distortion rate and system network loss and improving the static voltage stability of the power distribution network;
after photovoltaic access, voltage drop in a line is reduced, the overall voltage level of the system is increased, and the possible voltage deviation of partial nodes exceeds the standard.
The node voltage deviation is expressed as the percentage of the difference between the actual voltage of the node and the rated voltage to the rated voltage and is determined by the formula (1); the system voltage deviation is expressed by the mean value of the voltage deviations of the nodes and is determined by the formula (2),
where U is the actual voltage at a node, U N For the rated voltage, DeltaU, of the node i Is the voltage deviation of the i node, and n is the total number of nodes of the power distribution network system.
Frequent on-off actions of a switch tube in the photovoltaic inverter can inevitably generate harmonic current, so that the node voltage of the power distribution network is distorted. The node voltage harmonic distortion rate refers to a relative value of a root mean square value of each harmonic voltage and an effective value of fundamental voltage, and the voltage distortion rate of the node k is determined by a formula (3); the total voltage distortion rate of the system is expressed as the sum of the voltage distortion rates of the nodes, and is determined by formula (4),
wherein, THD k Is the voltage distortion rate of node k, THD is the total voltage distortion rate of the system, U i Is the effective value of the ith harmonic voltage, U 1 The effective value of the fundamental voltage is obtained, and n is the total number of nodes of the power distribution network system.
The index of the static voltage stability of the power distribution network reflects the distance between the current system voltage and the instability, and for the branch k, the static voltage stability index based on the existence of the tidal current equation solution is determined by a formula (5); the system voltage stability index is determined by the formula (6) by taking the maximum value of the static voltage stability index of each branch circuit,
VSI＝max{L 1 ,L 2 ,L 3 ,...,L n } (6)
wherein R and X are respectively the resistance and reactance of branch k, P b And Q b Respectively absorbing active and reactive power, V, for the ends of branch k a Is the effective value of the voltage at the head end of the branch k.
The photovoltaic access changes the structure and the tide distribution of the power distribution network, and inevitably changes the current flowing through the branch, thereby having certain influence on the system network loss. The system loss is determined by equation (7),
wherein m is the total number of branches of the power distribution network system, G k Is the conductance of branch k, V i And V j The voltage amplitudes of the nodes at the two ends of the branch k are respectively theta i And theta j Respectively, its phase.
(2) Establishing a constraint equation of multi-objective optimization configuration, wherein the constraint conditions comprise system power flow constraint, voltage deviation constraint, power reverse transmission constraint, total access flow constraint, main transformer capacity limiting constraint and branch current limiting constraint;
and (3) system power flow constraint:
the power generated by the photovoltaic power supply in the power grid is matched with the sum of the load consumption power and the power among nodes in the line:
wherein,
active power and reactive power are respectively provided for the photovoltaic power supply at the node i;
respectively the active power and the reactive power consumed by the load at the node i; p is ij And Q ij Respectively the active power and the reactive power flowing between the node i and the node j; u shape i Is the voltage amplitude of node i, θ ij Is the voltage phase angle difference between node i and node j, G ij And B ij Respectively the conductance and susceptance of the line between node i and node j.
And (4) voltage deviation constraint.
The voltage at the node cannot exceed its maximum and minimum voltage magnitudes:
U min ≤U i ≤U max (9)
wherein, U i Is the i-node voltage amplitude, U min 、U max Respectively, the lower limit and the upper limit of the node voltage amplitude.
And (4) power back-off constraint.
The system cannot dump excess power to the large grid:
P T ≥0 (10)
wherein, P T The power delivered to the distribution network for the external grid.
A total access capacity constraint.
The distributed photovoltaic access capacity is limited by the self-installation capacity:
∑P DG ≤P DGmax (11)
wherein, P DGmax Is the maximum photovoltaic power total capacity allowed to be accessed.
Main transformer capacity limiting constraint;
the power delivered by the main transformer cannot exceed a specified value.
S Ti ≤S Ti,max (12)
S Ti,max Is the maximum transmission power allowed by the transformer.
Branch current limiting constraint; each branch has its own maximum allowable current, and the actual operating current of the line cannot exceed the maximum allowable current in principle
I ij,min ≤I ij ≤I ij,max (13)
I ij,min And I ij,max The maximum and minimum allowed paths through the circuit between node i and node j, respectively.
(3) And obtaining the comprehensive weight by utilizing an entropy weight method and a game theory combined weighting method.
The entropy weight method is a method for objectively weighting multiple indexes, and the basic idea is to calculate the information entropy of each index according to the variation degree of each index and then calculate the objective weight of each index through the information entropy.
Constructing a multi-object and multi-index matrix:
for an index system with m objects, n indices, X ij The j-th index (i ═ 1,2,3, …, n) of the i-th object (i ═ 1,2,3, …, m).
Data normalization processing:
if the indicator is positive indicator, the first formula is selected, and if the indicator is negative indicator, the second formula is selected.
Calculating an index proportion matrix:
wherein, X ″ ij Is the specific gravity of the j-th index, determined by the formula (17),
calculating the entropy of each index, the entropy of the jth index being determined by equation (18),
calculating the weight of each index, determined by equation (19),
in real life, not only the degree of susceptibility of each index, but also the importance of each index in an evaluation system are considered, and the importance depends on the subjective intention of a decision maker. The game theory combination weighting method is combined by subjective weight and objective weight determined by the entropy weight method, so that the evaluation system is more comprehensive and effective.
Assuming that the weights of n indexes are obtained by L methods, the weight vector obtained by the kth method is:
ω k ＝(ω k1 ,ω k2 ,…,ω kn ),k＝(1,2,…,L) (20)
let the integrated weight be a linear combination of these L weight vectors:
by controlling alpha k To optimize ω such that ω should be associated with each ω k The distance between them is minimal:
derivation of equation (22) yields the optimization condition:
determine (alpha) 1 ,α 2 ,…,α l ) Normalizing the data to obtain the comprehensive weightWeight vector omega * ：
(4) And solving the established multi-objective optimization configuration model by using an improved particle swarm optimization algorithm to obtain an optimization configuration scheme of distributed photovoltaic access.
The algorithm steps of the improved particle swarm optimization are as follows:
1) and reading parameters of the power distribution network, including the number of nodes, line impedance, load power and the like, and determining the access number of the photovoltaic power supplies and the upper limit of the access total capacity.
2) And determining a calculation formula of each index, solving the power flow by utilizing a forward-backward substitution algorithm, and determining the harmonic power flow by utilizing a decoupling method.
3) And determining a calculation formula of each constraint condition, and setting a penalty function.
4) Initializing a particle swarm, and setting the size of the swarm, the maximum iteration times, the initial position and the speed.
5) And calculating a fitness function value according to the particle position, namely the sum of the comprehensive operation index F of the power distribution network and the penalty function.
6) And individual extremum pbest i Comparing with global extreme value gbest, updating pbest i And gbest.
For the ith particle x i Randomly generating a 0-1 vector of length N
If it is
Then x is i,j And pbest i,j If the values of (1) are interchanged
Then do not go intoExchanging to obtain new particle XP 1 And XP 2 . Also for x i And gbest to get XP 3 And XP 4 。
For XP 1 、XP 2 、XP 3 、XP 4 Respectively calculating the fitness, let f min ＝minf(XP j ) If f is min <f(pbest i ) Then pbest i ＝XP j (ii) a If f min <f (gbest), gbest ═ XP j . Mixing pbest i And gbest participates in the next iteration as a new individual extremum and a new global extremum.
8-7) updating the particle velocity and position, the new velocity and position being determined by equations (26), (27), respectively.
Wherein,
and
respectively representing the velocity and position of the ith particle in the kth iteration,
represents the historical best solution, gbest, for the ith particle k A globally optimal solution is represented as a function of,
an average value representing the position of the particle; c. C 1 And c 2 The acceleration factors respectively represent the approaching trend of the particles to the individual extreme point and the global extreme point; rand 1 And rand 2 Is at [0,1 ]]Randomly generating an acceleration weight coefficient in the interval; omega isThe inertial weight, which is the coefficient used to maintain the velocity at the previous time, is determined by equation (28):
in the formula (28), ω max And ω min Maximum and minimum values of the inertial weight, k max K is the current iteration number.
8) And carrying out cross mutation on the updated particles.
When the variance of the population is lower than a set threshold, initializing the population according to formula (29):
wherein,
to reinitialize the seed group, the lower and upper expiration of the j-th dimension position are determined by equation (30):
in the formula (28), the first and second groups of the functional groups are,
as the number of iterations increases from 1 to 0,
respectively representing the lower and upper dimension of the particle.
9) Checking whether a termination condition (reaching the maximum iteration number or meeting the convergence precision error) is met, if so, terminating iteration and outputting an optimal solution; if not, go to step 5).
Claims (8)
1. A distributed photovoltaic multi-objective optimization configuration method based on a multi-decision theory is characterized by comprising the following steps:
(1) constructing a multi-objective optimization configuration model aiming at reducing node voltage deviation, node voltage harmonic distortion rate and system loss and improving the static voltage stability of the power distribution network;
(2) establishing a constraint equation of multi-objective optimization configuration;
(3) obtaining comprehensive weight by utilizing an entropy weight method and a game theory combined weighting method;
(4) solving the established multi-target optimization configuration model by using an improved particle swarm optimization algorithm to obtain an optimization configuration scheme of distributed photovoltaic access;
the steps of improving the particle swarm algorithm in the step (4) are as follows:
4-1) reading parameters of the power distribution network, and determining the access number and the access total capacity upper limit of the photovoltaic power supplies;
4-2) determining a calculation formula of each index, solving the power flow by utilizing a forward-backward substitution algorithm, and determining the harmonic power flow by utilizing a decoupling method;
4-3) determining a calculation formula of each constraint condition, and setting a penalty function;
4-4) initializing a particle swarm, and setting the size of the swarm, the maximum iteration times, the initial position and the speed;
4-5) calculating a fitness function value according to the particle position, namely the sum of the comprehensive operation index F of the power distribution network and the penalty function;
4-6) and individual extremum pbest i Comparing with global extreme value gbest, updating pbest i And gbest;
for the ith particle x i Randomly generating a 0-1 vector of length N
If it is
Then x is i,j And pbest i,j If the values of (1) are interchanged
Then exchange is not carried out to obtain new particle XP 1 And XP 2 (ii) a Also for x i Operating with gbest to obtain XP 3 And XP 4 ；
Pair XP 1 、XP 2 、XP 3 、XP 4 Respectively calculating the fitness, let f min ＝minf(XP j ) If f is min <f(pbest i ) Then pbest i ＝XP j (ii) a If f min <f (gbest), then gbest ═ XP j (ii) a Mixing pbest i And the gbest is used as a new individual extreme value and a new global extreme value to participate in the next iteration;
4-7) updating the particle velocity and position, the new velocity and position being determined by the equations (26), (27), respectively;
wherein,
and
respectively representing the velocity and position of the ith particle in the kth iteration,
represents the historical best solution, gbest, for the ith particle k A global optimal solution is represented by a global optimal solution,
an average value representing the position of the particle; c. C 1 And c 2 Is an acceleration factor which respectively expresses the approaching of the particles to the individual extreme point and the global extreme pointThe magnitude of the recent trend; rand 1 And rand 2 Is at [0,1 ]]Randomly generating an acceleration weight coefficient in the interval; ω is the inertial weight, which is the coefficient used to maintain the velocity at the previous time, and is determined by equation (28):
in the formula (28), ω max And omega min Maximum and minimum values of the inertial weight, k max Is the maximum number of iterations, and k is the current number of iterations
4-8) carrying out cross variation on the updated particles;
when the variance of the population is below a set threshold, initializing the population according to equation (29):
wherein,
to reinitialize the lower and upper orders of the j-th dimension position of the seed group, the following equation (30) is used:
in the formula (28), the first and second groups,
as the number of iterations increases from 1 to 0,
respectively representing the lower dimension and the upper dimension of the particle;
4-9) checking whether a termination condition is met, the maximum iteration times are reached or the convergence precision error is met, if so, terminating iteration and outputting an optimal solution; if not, turning to the step 4-5).
2. The distributed photovoltaic multi-objective optimization configuration method based on the multi-decision theory as claimed in claim 1, wherein the node voltage deviation in the step (1) is expressed as a percentage of the difference between the actual node voltage and the rated node voltage to the rated node voltage, and is determined by formula (1); the system voltage deviation is expressed by the mean value of the voltage deviations of the nodes and is determined by the formula (2),
where U is the actual voltage at a node, U N Is the rated voltage, DeltaU, of the node i Is the voltage deviation of the i node, and n is the total number of nodes of the power distribution network system.
3. The distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory according to claim 1, characterized in that the node voltage harmonic distortion rate in step (1) refers to a relative value of a root mean square value of each subharmonic voltage and an effective value of a fundamental voltage, and the voltage distortion rate of a node k is determined by formula (3); the total voltage distortion rate of the system is expressed as the sum of the voltage distortion rates of the nodes, and is determined by formula (4),
wherein, THD k Is the voltage distortion rate of node k, THD is the total voltage distortion rate of the system, U i Is the effective value of the ith harmonic voltage, U 1 The effective value of the fundamental voltage is obtained, and n is the total number of nodes of the power distribution network system.
4. The distributed photovoltaic multi-objective optimization configuration method based on the multi-decision theory as claimed in claim 1, wherein the index of the static voltage stability of the power distribution network in the step (1) reflects the distance of the current system voltage distance instability, and for the branch k, the static voltage stability index based on the existence of the tidal current equation solution is determined by formula (5); the system voltage stability index is determined by the formula (6) by taking the maximum value of the static voltage stability index of each branch,
VSI＝max{L 1 ,L 2 ,L 3 ,...,L n } (6)
wherein R and X are respectively the resistance and reactance of branch k, P b And Q b Respectively absorbing active and reactive power, V, for the ends of branch k a Is the effective value of the voltage at the head end of the branch k.
5. The distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory as claimed in claim 1, wherein the system grid loss in the step (1) is determined by formula (7),
wherein m is the total number of branches of the power distribution network system, G k Is the conductance of branch k, V i And V j The voltage amplitudes of the nodes at the two ends of the branch k are respectively theta i And theta j Respectively, its phase.
6. The distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory according to claim 1, wherein the constraint conditions of the step (2) comprise:
system power flow constraint;
the power generated by the photovoltaic power supply in the power grid is matched with the sum of the load consumption power and the power among nodes in the line:
wherein,
active power and reactive power are respectively provided for the photovoltaic power supply at the node i;
respectively the active power and the reactive power consumed by the load at the node i; p ij And Q ij Respectively the active power and the reactive power flowing between the node i and the node j; u shape i Is the voltage amplitude of node i, θ ij Is the voltage phase angle difference between node i and node j, G ij And B ij Respectively the conductance and susceptance of the line between the node i and the node j;
voltage deviation constraint;
the voltage at the node cannot exceed its maximum and minimum voltage magnitudes:
U min ≤U i ≤U max (9)
wherein, U i Is the i-node voltage amplitude, U min 、U max Respectively the lower limit and the upper limit of the node voltage amplitude;
power back-off constraints;
the system cannot dump excess power to the large grid:
P T ≥0 (10)
wherein, P T For transmitting external power network to distribution networkThe power delivered;
a total access capacity constraint;
the distributed photovoltaic access capacity is limited by the self-installation capacity:
∑P DG ≤P DGmax (11)
wherein, P DGmax Is the maximum allowed total capacity of the accessed photovoltaic power supply;
main transformer capacity limiting constraint;
the power transmitted by the main transformer cannot exceed a specified value;
S Ti ≤S Ti,max (12)
S Ti,max is the maximum transmission power allowed by the transformer;
branch current limiting constraint; each branch has its maximum allowable current, and the actual operation current of the line can not exceed the maximum allowable current in principle
I ij,min ≤I ij ≤I ij,max (13)
I ij,min And I ij,max The maximum and minimum allowed paths through the circuit between node i and node j, respectively.
7. The distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory as claimed in claim 1, wherein the step (3) utilizes an entropy weight method to objectively weight multiple indexes, and the specific calculation steps are as follows:
7-1) constructing a multi-object and multi-index matrix:
for an index system with m objects, n indices, X ij The j-th index (i ═ 1,2,3, …, n) of the i-th object (i ═ 1,2,3, …, m);
7-2) data normalization processing:
if the index is a positive index, selecting a first formula, and if the index is a negative index, selecting a second formula;
7-3) the index specific gravity matrix is determined by equation (16),
wherein, X ″ ij Is the specific gravity of the j-th index, determined by the formula (17),
7-4) calculating the entropy value of each index, the entropy value of the jth index is determined by formula (18),
7-5) calculating the weight of each index, determined by formula (19),
8. the distributed photovoltaic multi-objective optimization configuration method based on multi-decision theory as claimed in claim 1, wherein the comprehensive weight in the step (3) is combined by subjective weight and objective weight determined by entropy weight method, and the calculation steps are as follows:
8-1) assuming that the weights of n indexes are obtained by L methods, the weight vector obtained by the k method is as follows:
ω k ＝(ω k1 ,ω k2 ,…,ω kn ),k＝(1,2,…,L) (20)
8-2) setting the integrated weight as the linear combination of the L weight vectors:
8-3) by controlling alpha k To optimize ω such that ω should be associated with each ω k The distance between them is minimal:
8-4) deriving the formula (22) to obtain the optimization condition:
8-5) obtaining (. alpha.) 1 ,α 2 ,…,α l ) Normalizing the vector to obtain a comprehensive weight vector omega * ：
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