CN108964142B - Multi-objective optimization method of railway power regulator considering voltage fluctuation of power supply arm - Google Patents

Multi-objective optimization method of railway power regulator considering voltage fluctuation of power supply arm Download PDF

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CN108964142B
CN108964142B CN201810425389.2A CN201810425389A CN108964142B CN 108964142 B CN108964142 B CN 108964142B CN 201810425389 A CN201810425389 A CN 201810425389A CN 108964142 B CN108964142 B CN 108964142B
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power supply
power
particle
supply arm
voltage fluctuation
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CN108964142A (en
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罗培
杨维民
马茜
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Xiangtan University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H02J3/1871—Methods for planning installation of shunt reactive power compensators
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

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Abstract

The invention discloses a railway power regulator multi-objective optimization method considering voltage fluctuation of power supply arms, which introduces a power supply arm voltage fluctuation index by analyzing the reason that RPC compensation current aggravates voltage fluctuation of two power supply arms, takes the power supply arm voltage fluctuation and RPC compensation capacity as optimization targets, provides an RPC multi-objective optimization design method, adopts a particle swarm multi-objective optimization algorithm to obtain a mathematical model for system optimization, and can effectively reduce the compensation capacity of a railway power regulator and relieve the voltage fluctuation of the two power supply arms as much as possible on the premise of meeting various electric energy quality effects.

Description

Multi-objective optimization method of railway power regulator considering voltage fluctuation of power supply arm
Technical Field
The invention relates to a railway power regulator, in particular to a railway power regulator multi-objective optimization method considering voltage fluctuation of a power supply arm.
Background
At present, the electrified railway of China advances into a 'high-speed era', which mainly shows high speed and heavy load, and the safety and the reliability of the train are also paid unprecedented attention. Problems of negative sequence, voltage fluctuation and the like caused by the coupling mode of a transformer in a traction power supply system, single-phase traction load fluctuation and the like bring hidden dangers to the safety and stability of a public power grid and a train.
At present, in order to improve the quality of electric energy of electrified railways, scholars at home and abroad propose various compensation devices. When a reactive Compensator (Static Var Compensator, SVC) or a Static Var Generator (SVG) is applied to an electrified railway, negative sequence current can be suppressed, but active power between two power supply arms cannot be balanced. In order to comprehensively manage the problems of negative sequence, reactive Power and the like in a traction Power supply system, a Japanese scholars provides a Railway Power Regulator (RPC), and the Railway Power regulator has good application prospect. The document 'novel electric railway power quality management system' researches a control strategy of RPC, adopts a complete compensation mode to compensate a traction power supply system, and can enable the negative sequence current of a three-phase power grid side to be close to 0 and the power to reach 1.
In the document of 'railway power quality control system capacity optimization design', the minimum compensation capacity of a railway power Regulator (RPC) is used as a target function, a power quality parameter is used as a constraint condition, a capacity optimization compensation coefficient is used as a decision variable, and a differential evolution algorithm (DE) is adopted to obtain a global optimal solution of the compensation coefficient and a target minimum value of the compensation capacity. By adopting a single-target optimization compensation mode to compensate the traction power supply system, the compensation capacity of the RPC can be reduced on the premise of meeting various power quality indexes.
The above method has the following drawbacks:
1. when a railway power Regulator (RPC) adopts a complete compensation mode, the voltage fluctuation of two power supply arms is large due to large compensation current, the required compensation capacity is large, the cost is high, and the popularization and the application of the RPC are influenced.
2. When the railway power Regulator (RPC) adopts a single-target optimization compensation mode, the compensation capacity of the RPC can be reduced, and the influence of compensation current on the voltages of the two power supply arms is not considered, so that the two power supply arms have larger voltage fluctuation. The influence process of the compensation current on the voltage of the power supply arm is as follows:
fig. 1 is a system vector diagram before compensation. In FIG. 1, the primary-side phase voltage of a V/V transformer is used
Figure GDA0001839113680000021
For the sake of reference,
Figure GDA0001839113680000022
the voltages of the alpha and beta power supply arms respectively,
Figure GDA0001839113680000023
the current of the alpha and beta power supply arms respectively,
Figure GDA0001839113680000024
load currents of the two power supply arms alpha and beta, thetaα，θβIs the power factor angle of the two power supply arms. Without being provided with
Figure GDA0001839113680000025
Before the compensation, the compensation is carried out,
Figure GDA0001839113680000026
taking the alpha power supply arm as an example, the alpha arm current is applied
Figure GDA0001839113680000027
At supply arm voltage
Figure GDA0001839113680000028
Direction decomposition into active components
Figure GDA0001839113680000029
And a reactive component
Figure GDA00018391136800000210
Active current component
Figure GDA00018391136800000211
Resistance component R in the winding of a V/V transformerαTo form a pressure drop, by
Figure GDA00018391136800000212
Indicates, direction and
Figure GDA00018391136800000213
the same is true. Likewise, reactive current component
Figure GDA00018391136800000214
Inductance component L in winding of V/V transformerαWill also form a pressure drop, using
Figure GDA00018391136800000215
It shows that the inductor voltage leads the current by 90 deg., so
Figure GDA00018391136800000216
In a direction of
Figure GDA00018391136800000217
The same is true. In the voltage component
Figure GDA00018391136800000218
And
Figure GDA00018391136800000219
under the combined action of the two voltage sources, the voltage fluctuation of the alpha arm is formed
Figure GDA00018391136800000220
Indicating that the port voltage of the alpha supply arm is
Figure GDA00018391136800000221
The alpha supply arm port is therefore under-voltage. Similarly, the beta supply arm also has a voltage component
Figure GDA00018391136800000222
And
Figure GDA00018391136800000223
voltage fluctuation of beta arm
Figure GDA00018391136800000224
Indicates, direction and
Figure GDA00018391136800000225
the port voltage of the beta power supply arm is equal to
Figure GDA00018391136800000226
The beta supply arm port is therefore under-voltage.
FIG. 2 is a vector diagram of a system after RPC is fully compensated, the RPC transfers active power from a beta arm to an alpha arm, and performs reactive power compensation on two power supply arms,
Figure GDA00018391136800000227
and the currents of the two power supply arms after compensation are shown. As can be seen from FIG. 3, after compensation, θα＝-30°，θ β30 deg. compared with the current of alpha arm before compensation
Figure GDA00018391136800000228
Active component of
Figure GDA00018391136800000229
Is reduced, i.e.
Figure GDA00018391136800000230
Compensated supply arm voltage ripple component
Figure GDA00018391136800000231
Is reduced, i.e.
Figure GDA00018391136800000232
Also, after compensation, the α -arm current
Figure GDA00018391136800000233
Reactive component of
Figure GDA00018391136800000234
And
Figure GDA00018391136800000235
in the opposite direction, so
Figure GDA00018391136800000236
Direction and
Figure GDA00018391136800000237
the direction is opposite. Because of the inductive reactance component ω L of the equivalent impedance of the V/V transformerαGreater than the impedance component RαSo that the voltage fluctuation value of the alpha arm
Figure GDA00018391136800000238
And
Figure GDA00018391136800000239
the direction is opposite, and the port voltage of the alpha power supply arm is
Figure GDA00018391136800000240
Therefore, the port of the alpha power supply arm is in an overvoltage state; similarly, compensated beta arm current
Figure GDA00018391136800000241
Active component of
Figure GDA00018391136800000242
The size of the material is increased to be larger,
Figure GDA00018391136800000243
also becomes larger, beta arm current
Figure GDA00018391136800000244
Reactive component of
Figure GDA00018391136800000245
As well as to be larger, as well,
Figure GDA00018391136800000246
and also becomes larger. As can be seen from FIG. 3, after the compensation is completed, the voltage fluctuation amount of the alpha arm
Figure GDA00018391136800000247
And
Figure GDA00018391136800000248
the direction of the power supply is opposite, and the port of the alpha power supply arm is in an overvoltage state; amount of voltage fluctuation of beta arm
Figure GDA00018391136800000249
And
Figure GDA00018391136800000250
the direction is the same, and than the fluctuation before the compensation is more serious, beta supply arm port is in the undervoltage state. If the two power supply arms work in the state for a long time, the safe operation of the train is not facilitated.
Therefore, the compensation current of the RPC, whether it is a full compensation or a single target optimization compensation, will cause large fluctuations in the voltages of the two supply arms.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a multi-objective optimization method of the railway power regulator considering the voltage fluctuation of the power supply arms aiming at the defects of the prior art, so that the compensation capacity of the railway power regulator is effectively reduced and the voltage fluctuation of the two power supply arms is relieved on the premise of ensuring the comprehensive electric energy quality control effect of the railway power regulator. In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a multi-objective optimization method for a railway power regulator considering voltage fluctuation of a power supply arm comprises the following steps:
1) obtaining load power sampling value P of two power supply arms of railway power regulatorαL、QαL、PβL、QβL(ii) a Wherein, PαL、QαLRespectively the active power and the reactive power of the alpha-phase power supply arm; pβL、QβLActive power and reactive power of a beta-phase power supply arm are respectively provided;
2) sampling the load power value PαL、QαL、PβL、QβLSubstituting into the objective optimization model:
Figure GDA0001839113680000031
wherein, the lambda is the transfer degree of the active power of the railway power regulator; thetaα，θβPower factor angles of an alpha-phase power supply arm and a beta-phase power supply arm are respectively set;
Figure GDA0001839113680000032
Uiindicating the rated voltage value, DeltaU, of the i-phase supply armiThe voltage fluctuation value of the i-phase power supply arm is represented, and mu represents the voltage fluctuation degree of the two normalized power supply arms; scFor the compensation capacity of the railway power conditioner,
Figure GDA0001839113680000041
3) initializing three dimensions of particles in the particle swarm, wherein the three dimensions respectively represent the transfer degree lambda of the active power of the railway power regulator, and the power factor angle theta of an alpha phase power supply arm and a beta phase power supply armα，θβ(ii) a Setting the size of a particle population and the number of iterations;
4) initializing a particle swarm, randomly generating an initial value position x and a velocity v, and generating an initial individual optimal position P of the particlebestAs an initial value, a global optimal solution set GbestIs empty;
5) the particle values (. lamda.,. theta.) are measuredα，θβ) Substituting into the target optimization model, obtaining the objective function value under the constraint condition, and putting the non-dominated solution into GbestPerforming the following steps;
6) updating the three-dimensional position and three-dimensional velocity of the particle, updating the optimal position P of the particlebestAnd global optimal solution set Gbest)；
7) Judging whether the iteration times are reached, and if so, executing the step 8); if not, returning to the step 4);
8) outputting an optimal compromise solution (lambda)*，θα *，θβ *)；
9) Will (lambda)*，θα *，θβ *) Substituting into the following formula to obtain the command value (P) of RPC compensation power* αc,Q* αc,P* βc,Q* βC)：
Figure GDA0001839113680000042
Wherein, Pαc、QαcRespectively representing active power and reactive power of an alpha-phase power supply arm; pβc、QβcRespectively representing active power and reactive power of a beta-phase power supply arm;
10) and (6) ending.
In step 6), the optimal position P of the particlesbestThe updating method comprises the following steps: if the current position dominates PbestThen P isbestUpdating the current particle position; if P isbestDominating the current particle, PbestAnd keeping the same, and randomly selecting one of the two if the two have no dominance relation.
In step 6), Gbest(i) The updating method comprises the following steps: if any GbestIf the current particle is not dominated, the current particle is added to a Pareto front edge and stored; if the current particle dominates a certain solution of the Pareto front, the current particle replaces the vector to be added to the Pareto front and stored; if G isbestThe presence vector dominates the current particle, and the particle is not stored to the Pareto front.
In step 8), the solution with the maximum satisfaction is the optimal compromise solution, and the satisfaction value u solving formula is as follows:
Figure GDA0001839113680000051
wherein m is the number of objective functions;
Figure GDA0001839113680000052
is the membership value, f, of the ith objective functionkIs the k-th objective function; f. ofk max，fk minThe k-th objective function is a maximum value and a minimum value, respectively. In the invention, k is 1 or 2; u (1) represents. mu. and u (2) represents Sc. Compared with the prior art, the invention has the beneficial effects that: the invention analyzes the reason that RPC compensation current aggravates voltage fluctuation of two power supply arms, introduces the voltage fluctuation index of the power supply arms, takes the voltage fluctuation index of the power supply arms and the RPC compensation capacity as optimization targets, provides an RPC multi-objective optimization design method, and adopts a particle swarm multi-objective optimization algorithm to solve system optimizationThe mathematical model ensures that the compensation capacity of the railway power regulator can be effectively reduced and the voltage fluctuation of the two power supply arms can be relieved as much as possible on the premise of meeting various electric energy quality effects.
Drawings
FIG. 1 is a system vector diagram before compensation;
FIG. 2 is a diagram of RPC fully compensated backward vectors;
FIG. 3 is a topological diagram of an RPC device;
FIG. 4 is an equivalent electrical model of two power supply arms;
FIG. 5 is a flow chart of the method of the present invention.
Detailed Description
The topology of the RPC compensation device is shown in fig. 3. Comprising a V/V transformer, a step-down transformer (T)α、Tβ) Single phase Voltage Source Converter (VSC)α、VSCβ) A DC capacitor (C) and a series reactor (L)α、Lβ) And (4) forming. The left power supply arm in the figure is defined as an alpha power supply arm, and the right power supply arm is defined as a beta power supply arm. The RPC realizes active power transfer and reactive power compensation of the two power supply arms through two back-to-back VSCs, so that the electric energy quality of the traction power supply system is controlled.
In order to obtain the mathematical relationship between the voltage fluctuation values of the two power supply arms and the RPC compensation current, an equivalent electrical model of the two power supply arms is established as shown in fig. 4. I isαL、IβLThe load current of the two power supply arms. In FIG. 4, RPC is equivalent to a current source Iαcp、IβcpAnd a variable LC series impedance Lαc、CαcAnd Lβc、Cβc. The active power transferred by the current source is IαcpAnd IβcpAnd the transferred active currents are equal, i.e. Iαcp＝-Iβcp. LC series impedance provides inductive or capacitive reactive power compensation of IαcqAnd Iβcq。LαAnd RαThe inductance component and the resistance component of the equivalent impedance of the V/V traction transformer on the two supply arms, respectively.
In fig. 4, according to kirchhoff's current theorem, there are:
Figure GDA0001839113680000061
IαLp、IαLqrespectively represent the load current IαLActive and reactive components of; i isβLp、IβLqRespectively representing the load current IβLActive and reactive components. From the above analysis, it is known that the reason for the voltage fluctuation is that the active and reactive components in the two supply arm currents are at RαAnd LαCaused by the pressure drop, Δ U, as can be obtained from FIG. 4αAnd Δ UβThe expression of (a) is:
Figure GDA0001839113680000062
in the formula (2), | IαI and IβI represents the effective value of the current of the alpha and beta power supply arms respectively, thetaα，θβThe power factor angle of the two power supply arms is known from formula (1):
Figure GDA0001839113680000063
and defining lambda as the transfer degree of the RPC active power. λ represents the active current of the RPC transfer compared to the difference between the active currents of the two supply arms when the active currents of the two supply arms are unbalanced, i.e.:
Figure GDA0001839113680000064
substituting the formula (4) and the formula (3) into the formula (2) to obtain the voltage fluctuation values of the two traction power supply arms as follows:
Figure GDA0001839113680000065
by PαL、QαL，PβL、QβLRespectively showing the loads of alpha and beta power supply armsPower and reactive power, so equation (5) is expressed in terms of power as:
Figure GDA0001839113680000066
(one) objective function
(1) Optimization objective 1: the power supply arm voltage fluctuation ensures that the two power supply arms supply power normally, and prevents the influence of too low or too high voltage on the safe operation of the train. In order to quantitatively represent the fluctuation situation of two traction power supply arms, the power supply arm voltage fluctuation index is introduced, and the index is defined as shown in formula (9):
Figure GDA0001839113680000071
in the formula of UiIndicating the rated voltage value, DeltaU, of the i-phase supply armiRepresenting the voltage fluctuation value of the i-phase power supply arm. And mu represents the voltage fluctuation degree of the two power supply arms after normalization. By definition, the smaller μ, the smaller the voltage fluctuation of the two supply arms, and the closer the voltage of the two supply arms is to the rated value.
(2) Optimization objective 2: the RPC compensation capacity reduces the compensation capacity and can reduce the cost of the device under the condition of meeting various electric energy quality indexes.
The compensation power of the RPC to the alpha and beta power supply arms comprises active power and reactive power, and can be known from formula (1):
Figure GDA0001839113680000072
in the formula Pαc、Qαc，Pβc、QβcRespectively represents the active power and the reactive power compensated by the two power supply arms of alpha and beta, so the compensation capacity S of the RPCcComprises the following steps:
Figure GDA0001839113680000073
from the equations (6) and (11), it can be seen that the objective functions μ and ScAre all related to λ, θα，θβIs measured.
(II) constraint Condition
(1) Power factor
According to the national standard, the power factor PF of the three-phase power grid measured at the high-voltage metering point of the traction grid is required to be not less than 0.9. In the case of a three-phase load imbalance, the three-phase grid power factor is calculated from equation (12), i.e.
Figure GDA0001839113680000074
By Uα、UβFor reference, according to the energy balance principle, it is known that:
Figure GDA0001839113680000075
delta P represents active power transferred by RPC, and the constraint condition that the system power factor can be obtained by substituting formula (4) and formula (13) into formula (12) is
Figure GDA0001839113680000081
(2) Degree of voltage unbalance
According to the regulation of GB/T15543 'electric energy quality three-phase voltage unbalance', if the positive sequence impedance and the negative sequence impedance of a common connection Point (PCC) are equal, the negative sequence voltage unbalance degree at the PCC caused by a traction load is as follows:
Figure GDA0001839113680000082
while
Figure GDA0001839113680000083
Wherein U isABRated voltage (kV) at the side of a three-phase power grid; k is the turn ratio of the V/V traction transformer; i-is the negative sequence current of the three-phase power grid; skThree-phase short-circuit capacity (MV. A) for common connection point, and epsilonuLess than or equal to 1.3 percent. The primary side negative sequence current calculation formula of the V/V traction transformer is as follows:
Figure GDA0001839113680000084
according to the cosine theorem, the effective value of the negative sequence current is:
Figure GDA0001839113680000085
substituting the formulas (16) and (18) into the formula (15) to obtain
Figure GDA0001839113680000086
The power and current have the following relationship:
Figure GDA0001839113680000087
in the formula Sα，SβThe apparent power of the arm is supplied to alpha and beta. The constraint condition for obtaining the system voltage unbalance degree by substituting the formula (20) into the formula (19) is as follows:
Figure GDA0001839113680000091
in summary, the RPC multi-objective optimization model is:
Figure GDA0001839113680000092
(III) multi-objective optimization algorithm based on particle swarm optimization and fuzzy membership
When the multi-target problem is solved, because each target has mutual exclusivity, the global optimal solution is often not unique, and a solution set containing a plurality of elements exists.
PbestThe individual optimal positions are selected according to the pareto dominance relationship. If the current position dominates PbestThen P isbestUpdating the current particle position; if P isbestDominating the current particle, PbestAnd keeping the same, and randomly selecting one of the two if the two have no dominance relation.
GbestAnd selecting and storing the global optimal position solution set according to the dominance relation between the Pareto front edge and the current particles. If any Gbest(i) None dominates the current particle, the current particle is added to the Pareto front and stored. If the current particle dominates a certain solution of the Pareto front, the current particle replaces the vector to be added to the Pareto front and stored; if G isbest(i) The presence vector dominates the current particle, and the particle is not stored to the Pareto front. Herein, G is collected at solution by the dynamic dense distance of particlesbest(i) And selecting a population global optimal solution.
The dense distance represents the density of a particle with its surrounding particles, and can be used to describe the uniformity of the solution, particle xiDense distance I (x)i) Comprises the following steps:
Figure GDA0001839113680000101
where m is the number of objective functions, fj(xi) Denotes the particle xiThe jth objective function value of (1); f. ofj max，fj minRespectively representing the maximum and minimum of the jth objective function.
Defining a fuzzy membership function:
Figure GDA0001839113680000102
wherein u (i) is an objective function fmMembership value of fiIs the ith objective function; f. ofi max，fi minThe maximum and minimum values of the ith objective function, respectively. If u (i) is 1, it means that a certain function is completely satisfied, and if u (i) is 0, it means that a certain function is completely not satisfied.
And for the Pareto solution set, solving the normalized satisfaction value according to the formula (25), wherein the solution with the maximum satisfaction is the optimal compromise solution.
Figure GDA0001839113680000103
In the formula: u is the normalized satisfaction value and m is the number of the optimization objective functions.
When the RPC is adopted to carry out multi-objective optimization compensation on the traction power supply system, the steps are as follows:
1. through sampling, active power and reactive power P of alpha and beta power supply arms are obtainedαL、QαL，PβL、QβL
2. Substituting the sampled values into an equation (22) to obtain the constraint conditions and the objective function of the multi-objective optimization compensation
3. Three dimensions of particles in the initialized particle swarm respectively represent the transfer degree lambda of RPC active power and the power factor angle theta of two power supply armsα，θβ。
4. Setting the size of particle population and the number of iterations
5. Initializing a particle swarm, randomly generating an initial value position x and a velocity v, and generating an initial individual optimal position P of the particlebestAs an initial value, a global optimal solution set GbestIs empty
6. The particle values (. lamda.,. theta.) are measuredα，θβ) In the formula (22), an objective function value under a constraint condition is obtained. Put non-dominant solution into Gbest(i) In
7. Updating the three-dimensional position and three-dimensional velocity of the particle, and updating the optimal position P of the particle according to the method in (III)bestUpdating the optimal particle position G according to the method in (III)best(i)。
8. And judging whether the iteration times are met. If yes, executing step 9; if not, executing the step 5.
9. According to the method (III), an optimal compromise solution (lambda) is output*，θα *，θβ *)
10. Will (lambda)*，θα *，θβ *) In the formula (10), the command value (P) of RPC compensation power is obtained* αc,Q* αc,P* βc,Q* βC)
11. End up
The specific flow is shown in fig. 5.

Claims (4)

1. A multi-objective optimization method for a railway power regulator considering voltage fluctuation of a power supply arm is characterized by comprising the following steps:
1) obtaining load power sampling value P of two power supply arms of railway power regulatorαL、QαL、PβL、QβL(ii) a Wherein, PαL、QαLRespectively the active power and the reactive power of the alpha-phase power supply arm; pβL、QβLActive power and reactive power of a beta-phase power supply arm are respectively provided;
2) sampling the load power value PαL、QαL、PβL、QβLSubstituting into the objective optimization model:
Figure FDA0002920471540000011
wherein, the lambda is the transfer degree of the active power of the railway power regulator; thetaα，θβPower factor angles of an alpha-phase power supply arm and a beta-phase power supply arm are respectively set;
Figure FDA0002920471540000012
Uiindicating the rated voltage value, DeltaU, of the i-phase supply armiRepresenting the voltage fluctuation value of the i-phase power supply arm, and mu representing normalizationThe voltage fluctuation degree of the two power supply arms; scFor the compensation capacity of the railway power conditioner,
Figure FDA0002920471540000013
Skthree-phase short circuit capacity of a public connection point;
3) initializing three dimensions of particles in the particle swarm, wherein the three dimensions respectively represent the transfer degree lambda of the active power of the railway power regulator, and the power factor angle theta of an alpha phase power supply arm and a beta phase power supply armα，θβ(ii) a Setting the particle swarm scale and the iteration times;
4) initializing a particle swarm, randomly generating an initial value position x and a velocity v, and generating an initial individual optimal position P of the particlebestAs an initial value, a global optimal solution set GbestIs empty;
5) the particle values (. lamda.,. theta.) are measuredα，θβ) Substituting into the target optimization model, obtaining the objective function value under the constraint condition, and putting the non-dominated solution into GbestPerforming the following steps;
6) updating the three-dimensional position and three-dimensional velocity of the particle, updating the optimal position P of the particlebestAnd global optimal solution set Gbest；
7) Judging whether the iteration times are reached, and if so, executing the step 8); if not, returning to the step 4);
8) outputting an optimal compromise solution (lambda)*，θα *，θβ *)；λ*，θα *，θβ *Respectively correspond to lambda and thetaα，θβThe optimal compromise solution of (a);
9) will (lambda)*’ θα *’ θβ *) Substituting the following formula to obtain the command value (P) of the compensation power of the railway power regulator* αc,Q* αc,P* βc,Q* βC)：
Figure FDA0002920471540000021
Wherein, Pαc、QαcRespectively representing active power and reactive power of an alpha-phase power supply arm; pβc、QβcRespectively representing active power and reactive power of a beta-phase power supply arm; p* αc,Q* αcRespectively representing an active power instruction value and a reactive power instruction value of an alpha-phase power supply arm; p* βc,Q* βCRespectively representing the active power instruction value and the reactive power instruction value of the beta-phase power supply arm;
10) and (6) ending.
2. The method for multi-objective optimization of railway power regulators considering voltage fluctuation of power supply arms as claimed in claim 1, wherein in step 6), the optimal particle position PbestThe updating method comprises the following steps: if the current position dominates PbestThen P isbestUpdating the current particle position; if P isbestDominating the current particle, PbestAnd keeping the same, and randomly selecting one of the two if the two have no dominance relation.
3. The method for multi-objective optimization of railway power regulators considering voltage fluctuation of power supply arms as claimed in claim 1, wherein in step 6), G isbestThe updating method comprises the following steps: if any GbestIf the current particle is not dominated, the current particle is added to a Pareto front edge and stored; if the current particle dominates a certain solution of the Pareto front, the current particle replaces the solution to be added to the Pareto front and stored; if G isbestThe presence vector dominates the current particle, and the particle is not stored to the Pareto front.
4. The method for multi-objective optimization of the railway power regulator considering the voltage fluctuation of the power supply arm as claimed in claim 1, wherein in the step 8), the solution with the maximum satisfaction degree is the optimal compromise solution, and the satisfaction degree u solving formula is as follows:
Figure FDA0002920471540000031
wherein m is the number of objective functions;
Figure FDA0002920471540000032
u (k) is the membership value of the kth objective function, fkIs the k-th objective function;
Figure FDA0002920471540000033
the k-th objective function is a maximum value and a minimum value, respectively.
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