CN109149981A - A kind of Multipurpose Optimal Method based on genetic algorithm suitable for MMC - Google Patents

Abstract

The invention discloses a multi-objective optimization method based on genetic algorithm suitable for MMC. On the premise that the current level of the switching device is not increased before and after optimization, the constraints on the bridge arm current before and after optimization are obtained. Based on the constraints and electrical parameters, the goal is to minimize the peak value of the modulation voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module. The algorithm obtains the Pareto solution set; taking the minimum peak value of the modulation voltage of the bridge arm or the minimum peak value of the capacitor voltage fluctuation of the sub-module as the priority target, the common mode voltage injection amount and the circulating current injection amount are determined from the Pareto solution set, and the multi-objective optimization is obtained. The bridge arm modulates the voltage; realizes the multi-objective optimization of MMC. In this application, the genetic algorithm is used to obtain the optimal common-mode voltage injection and circulating current injection, so that the MMC can be reasonably optimized.

Description

A Multi-objective Optimization Method Based on Genetic Algorithm for MMC

technical field

The invention belongs to the technical field of multi-level power electronic converters, and more particularly relates to a genetic algorithm-based multi-objective optimization method suitable for MMC.

Background technique

MMC (Modular Multilevel Converter) has gradually become the most promising converter topology for HVDC transmission systems due to its high modularity, easy expansion, and low output voltage harmonics. In recent years, the voltage level and capacity of high-voltage direct current transmission projects have continued to increase, which has put forward higher requirements for converters to improve output capacity and cost control.

The MMC-HVDC project currently in operation mainly adopts the half-bridge sub-module HBSM (Half-Bridge SM) topology, and the output capability is determined by the number of bridge arm sub-modules. The existing research achieves equivalent overmodulation by injecting common-mode voltage into the bridge arm voltage without increasing the number of MMC bridge arm sub-modules, and improves the output of the AC side of the converter. The sub-module capacitor is the core energy storage element of the converter, and is also the main manufacturing cost of the sub-module except for the switch tube. The design of the capacitor is determined by the voltage fluctuation rate of the capacitor under the steady-state operation of the converter. By controlling the circulating current in the bridge arm and injecting the circulating current, the fluctuation rate of the capacitor voltage can be effectively reduced to reduce the demand for the capacitance value of the capacitor.

However, the injection of common-mode voltage will affect the capacitor voltage fluctuation. Similarly, the injection of circulating current will change the bridge arm voltage and affect the effect of overmodulation. The internal coupling relationship between the two is complex, which limits the application of the optimization method in MMC to a certain extent.

SUMMARY OF THE INVENTION

In view of the above defects or improvement requirements of the prior art, the present invention provides a multi-objective optimization method based on genetic algorithm suitable for MMC, thereby solving the problems in the prior art that the injection of common mode voltage will affect the capacitor voltage fluctuation and the injection circulating current will Changing the bridge arm voltage affects the effect of overmodulation, which limits the technical problem of the application of the optimization method in MMC.

To achieve the above object, the present invention provides a genetic algorithm-based multi-objective optimization method suitable for MMC, including:

(1) Obtain electrical parameters, including: the rated power P of the MMC, the rated voltage U _dc of the DC side, the rated voltage U _c of the sub-module capacitor, and the modulation ratio m of the converter;

(2) According to the electrical parameters and the set maximum fluctuation rate ε of the capacitor voltage, the capacitance value required by the sub-module before optimization is obtained;

(3) On the premise that the current level of the switching device is not increased before and after optimization, the effective value of the bridge arm current during steady-state operation before optimization is calculated according to the electrical parameters, and then the constraints on the bridge arm current before and after optimization are obtained;

(4) Based on the constraints and electrical parameters, the Pareto solution set is obtained by using the genetic algorithm, aiming at the minimum peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module;

(5) Taking the minimum peak value of the modulation voltage of the bridge arm or the minimum peak value of the capacitor voltage fluctuation of the sub-module as the priority target, determine the injection amount of common mode voltage and circulating current injection amount from the Pareto solution set, and obtain the modulation voltage of the bridge arm after multi-objective optimization ;

(6) Adjust the bridge arm modulation voltage to the multi-objective optimized bridge arm modulation voltage obtained in step (5) to realize the multi-objective optimization of the MMC.

Further, the capacitance value required by the sub-module before optimization is:

Among them, I _m is the phase current amplitude of the AC side, ω is the AC output frequency, is the power factor angle.

Further, step (3) includes:

On the premise that the current level of the switching device is not increased before and after optimization, the RMS current of the bridge arm during steady-state operation before optimization is calculated according to the electrical parameters Among them, I _dc is the rated current of the DC side, I _m is the amplitude of the phase current of the AC side, and the circulating current injected into twice the fundamental frequency is optimized, and the effective value of the bridge arm current after optimization Among them, I _2m is the injected circulating current amplitude of twice the fundamental frequency, I′ _m is the optimized AC side phase current amplitude, and the constraints on the bridge arm current before and after the optimization include the bridge arm current during steady-state operation before the optimization. Arm current RMS and optimized bridge arm current RMS.

Further, step (4) includes:

(4-1) According to the constraints and electrical parameters, the initial solution set of the common-mode voltage injection amount and the circulating current injection amount is randomly established with the goal of minimizing the peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module;

(4-2) Calculate the peak value of the modulation voltage of the bridge arms and the peak value of the capacitor voltage fluctuation of the sub-module by using multiple initial solutions in the initial solution set, and calculate the difference between the peak value of the modulation voltage of each bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module and the target The fitness function is used to obtain the fitness values of multiple initial solutions in the initial solution set, and the Pareto solution set is selected from the initial solution set according to the fitness values;

(4-3) Crossover operation and mutation operation are performed on the initial solution set to generate a new solution set, and the new solution set is used to replace the initial solution set, and then step (4-2) is performed;

(4-4) Steps (4-2)-(4-3) are repeated until the maximum evolutionary algebra is reached, and the final Pareto solution set is obtained.

Further, the bridge arm modulation voltage after multi-objective optimization includes the upper and lower bridge arm modulation voltages up and u _n after the common mode voltage _is injected:

Among them, U _m ′ is the optimized AC side output voltage amplitude, U _m ′x ₁ is the sine component amplitude of the common mode voltage injection, U _m ′x ₂ is the cosine component amplitude of the common mode voltage injection, ω is the AC output frequency, and t is the running time of the MMC.

Further, the optimized AC side output voltage amplitude is:

U _m ′=kU _m

Among them, U _m is the output voltage amplitude of the AC side, and the equivalent modulation ratio u _pm is the minimum bridge arm modulation voltage peak value obtained by genetic algorithm.

In general, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

The introduction of common mode voltage injection into the bridge arm modulation voltage reduces the peak value of the bridge arm modulation voltage, and has the ability to increase the fundamental frequency output amplitude of the AC side when the number of bridge arm sub-modules remains unchanged; the introduction of the bridge arm current into the circulating current injection can effectively reduce the Capacitor voltage fluctuation peak value. Due to the internal coupling between the two optimization methods, the present invention introduces a multi-objective optimization genetic algorithm, taking into account the goals of improving the output capability of the AC side and reducing the voltage fluctuation rate of the capacitor, to obtain the optimal common-mode voltage injection and circulating current injection amount, so that the MMC can obtain Reasonable optimization. This solves the technical problems in the prior art that the injected common mode voltage will affect the capacitor voltage fluctuation, and the injected circulating current will change the bridge arm voltage and affect the effect of overmodulation, thereby limiting the application of the optimization method in the MMC.

Description of drawings

1 is a flowchart of a genetic algorithm-based multi-objective optimization method applicable to MMC provided by an embodiment of the present invention;

2 is a topology diagram of a three-phase modular multilevel converter provided by an embodiment of the present invention;

3 is a schematic diagram of a modulation voltage waveform of an upper bridge arm before and after common mode voltage injection according to an embodiment of the present invention;

4 is a schematic diagram of the current waveform of the upper bridge arm before and after circulating current injection according to an embodiment of the present invention;

5 is a flowchart of a genetic algorithm for multi-objective optimization provided by an embodiment of the present invention;

6 is a Pareto frontier diagram of a genetic algorithm result based on MATLAB multi-objective optimization provided in Embodiment 1 of the present invention;

Fig. 7 is the upper bridge arm modulation voltage waveform diagram based on MATLAB/Simulink simulation provided by Embodiment 1 of the present invention;

FIG. 8 is a waveform diagram of the capacitor voltage of a sub-module based on MATLAB/Simulink simulation provided by Embodiment 1 of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

As shown in Figure 1, a multi-objective optimization method based on genetic algorithm suitable for MMC, including:

(1) Obtain electrical parameters, including: the rated power P of the MMC, the rated voltage U _dc of the DC side, the rated voltage U _c of the sub-module capacitor, and the modulation ratio m of the converter; specifically, regardless of the redundancy of the sub-module, the obtained Calculation of electrical parameters for the number of half-bridge MMC bridge arm sub-modules

(2) Calculate the unoptimized AC side phase current amplitude according to the electrical parameters According to the electrical parameters and the maximum fluctuation rate ε of the capacitor voltage, the capacitor value required by the sub-module before optimization is obtained:

Among them, I _m is the phase current amplitude of the AC side, ω is the AC output frequency, is the power factor angle.

(3) On the premise that the current level of the switching device is not increased before and after optimization, the effective value of the bridge arm current during steady-state operation before optimization is calculated according to the electrical parameters, and then the constraints on the bridge arm current before and after optimization are obtained; The power balance on the AC and DC sides of the converter, the current on the DC side is The circulating current is completely suppressed before optimization, and the RMS current of the bridge arm during steady-state operation By optimizing the circulating current injected with twice the fundamental frequency, the injected currents of the upper and lower arms are:

Among them, x ₃ is the amplitude of the sine component of the circulating current injected with twice the fundamental frequency, and x ₄ is the amplitude of the cosine component of the circulating current injected with twice the fundamental frequency.

RMS value of bridge arm current after optimization where I _2m is the injected circulating current amplitude, I _′m is the optimized AC side phase current amplitude, and the constraints on the bridge arm current before and after the optimization include the RMS current of the bridge arm current during steady-state operation before the optimization and the optimized The rms value of the rear arm current.

(4) Based on the constraints and electrical parameters, the Pareto solution set is obtained by using the genetic algorithm, aiming at the minimum peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module;

(5) Taking the minimum peak value of the modulation voltage of the bridge arm or the minimum peak value of the capacitor voltage fluctuation of the sub-module as the priority target, determine the injection amount of common mode voltage and circulating current injection amount from the Pareto solution set, and obtain the modulation voltage of the bridge arm after multi-objective optimization ;

(6) Adjust the bridge arm modulation voltage to the multi-objective optimized bridge arm modulation voltage obtained in step (5), so that the output of the MMC AC side is maximized under the bridge arm current constraint, and the capacitor voltage fluctuation rate is maximized. reduce to achieve multi-objective optimization of MMC.

As shown in Figure 2, each phase of the three-phase MMC is composed of two identical upper and lower bridge arms, each bridge arm contains N sub-modules, the sub-modules are connected in cascade, and the upper and lower bridge arms are connected by a bridge The arm inductors are connected, and the connection point is the output point of the AC side. The sub-module includes two IGBTs, two anti-parallel diodes and a capacitor.

Figure 3 is a schematic diagram of the modulation voltage waveform of the upper arm before and after common mode voltage injection, and Figure 4 is a schematic diagram of the current waveform of the upper arm before and after circulating current injection; it can be seen that the peak value of the modulation voltage of the bridge arm decreases after the injection of the common mode voltage. When the sub-module of the bridge arm remains unchanged, the amplitude of the fundamental frequency output voltage on the AC side can be increased to achieve equivalent over-modulation.

Figure 5 is a flowchart of the genetic algorithm for multi-objective optimization. Genetic algorithm has unique advantages in solving multi-variable, multi-constraint, multi-peak (valley) value, nonlinear and discrete problems. The objective optimization method is suitable for the multi-objective optimization considering the minimum bridge arm modulation voltage peak value and the minimum capacitor voltage fluctuation peak value. Genetic algorithm makes the next generation group closer to the optimal solution as a whole by performing a series of seed selection, crossover and mutation for the first generation group according to the optimization goal. The present invention introduces Pareto sorting in the selection operator to form a genetic algorithm of multi-objective optimization, including:

(4-1) According to the constraints and electrical parameters, the initial solution set of the common-mode voltage injection amount and the circulating current injection amount is randomly established with the goal of minimizing the peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module;

(4-2) Calculate the peak value of the modulation voltage of the bridge arms and the peak value of the capacitor voltage fluctuation of the sub-module by using multiple initial solutions in the initial solution set, and calculate the difference between the peak value of the modulation voltage of each bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module and the target The fitness function is used to obtain the fitness values of multiple initial solutions in the initial solution set, and the Pareto solution set is selected from the initial solution set according to the fitness values;

(4-3) Crossover operation and mutation operation are performed on the initial solution set to generate a new solution set, and the new solution set is used to replace the initial solution set, and then step (4-2) is performed;

(4-4) Steps (4-2)-(4-3) are repeated until the maximum evolutionary algebra is reached, and the final Pareto solution set is obtained.

Further, the bridge arm modulation voltage after multi-objective optimization includes the upper and lower bridge arm modulation voltages up and u _n after the common mode voltage _is injected:

Among them, U _m ′ is the optimized AC side output voltage amplitude, U _m ′x ₁ is the sine component amplitude of the common mode voltage injection, U _m ′x ₂ is the cosine component amplitude of the common mode voltage injection, ω is the AC output frequency, and t is the running time of the MMC.

Further, the optimized AC side output voltage amplitude is:

U _m ′=kU _m

Among them, U _m is the output voltage amplitude of the AC side, and the equivalent modulation ratio u _pm is the minimum bridge arm modulation voltage peak value obtained by genetic algorithm.

Example 1

This example is used to illustrate that the modulation voltage and capacitor voltage fluctuations of the bridge arm can be effectively reduced by injecting common-mode voltage and circulating current, and the optimal injection amount of the two can be quickly found by genetic algorithm to achieve multi-objective optimization. For a clearer explanation, the following analysis is performed:

The above bridge arm is taken as an example, the switch function of the bridge arm is:

The bridge arm current after injecting the circulating current is:

Considering the unity power factor, the capacitor current can be obtained from the product of the bridge arm switching function and the bridge arm current:

i _cp =S _p ·I _rp

Combining the above formula, the relationship between the sub-module capacitor voltage fluctuation and the common mode voltage and circulating current injection is as follows:

The main parameters of this example are shown in Table 1:

Table 1

According to the above analysis, I _r = 6.93A before optimization, the bridge arm inductance value is designed according to the circulating current injection not exceeding 20% of the bridge arm current fundamental amplitude, and the common mode voltage injection is designed not to exceed 20% of the AC output voltage, then The multi-objective optimization problem is:

min Δu _cp (x ₁ , x ₂ , x ₃ , x ₄ )

min u _p (x ₁ , x ₂ , x ₃ , x ₄ )

The multi-objective genetic algorithm is implemented using the global optimization toolbox in MATLAB. Figure 6 is the result diagram of the genetic algorithm based on the multi-objective optimization of MATLAB. The Pareto optimal frontier can be obtained from the algorithm results. In this frontier, two optimization objectives are considered. The _{optimal solution} set of and circulation injection The given values of the bridge arm modulation voltage and circulating current are obtained by multi-objective optimization.

A simulation model is built in MATLAB/Simulink, and the common-mode voltage injection and circulating current injection obtained by the multi-objective optimization genetic algorithm are added to the MMC before optimization. The modulation voltage of the bridge arm is shown in Figure 7. It can be seen that the modulation voltage of the bridge arm The peak decreases after injection, which is consistent with the algorithm results.

Given the circulating current injection amount in the circulating current suppressor, the capacitor voltage fluctuation is suppressed by changing the waveform of the bridge arm current. The capacitor voltage fluctuation is shown in Figure 8. It can be seen that the capacitor voltage fluctuates around the rated voltage, and the fluctuation mainly includes the fundamental frequency component. and the double frequency component, the maximum fluctuation decreases after injection, which is basically consistent with the algorithm result.

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (6)

1. a kind of multi-objective optimization method based on genetic algorithm applicable to MMC, is characterized in that, comprises: (1) Obtain electrical parameters, including: the rated power P of the MMC, the rated voltage U _dc of the DC side, the rated voltage U _c of the sub-module capacitor, and the modulation ratio m of the converter; (2) According to the electrical parameters and the set maximum fluctuation rate ε of the capacitor voltage, the capacitance value required by the sub-module before optimization is obtained; (3) On the premise that the current level of the switching device is not increased before and after optimization, the effective value of the bridge arm current during steady-state operation before optimization is calculated according to the electrical parameters, and then the constraints on the bridge arm current before and after optimization are obtained; (4) Based on the constraints and electrical parameters, the Pareto solution set is obtained by using the genetic algorithm, aiming at the minimum peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module; (5) Taking the minimum peak value of the modulation voltage of the bridge arm or the minimum peak value of the capacitor voltage fluctuation of the sub-module as the priority target, determine the injection amount of common mode voltage and circulating current injection amount from the Pareto solution set, and obtain the modulation voltage of the bridge arm after multi-objective optimization ; (6) Adjust the bridge arm modulation voltage to the multi-objective optimized bridge arm modulation voltage obtained in step (5) to realize the multi-objective optimization of the MMC. 2. a kind of multi-objective optimization method based on genetic algorithm that is applicable to MMC as claimed in claim 1, is characterized in that, the required capacitance value of submodule before described optimization is: Among them, I _m is the phase current amplitude of the AC side, ω is the AC output frequency, is the power factor angle. 3. a kind of multi-objective optimization method based on genetic algorithm suitable for MMC as claimed in claim 1 or 2, is characterized in that, described step (3) comprises: On the premise that the current level of the switching device is not increased before and after optimization, the RMS current of the bridge arm during steady-state operation before optimization is calculated according to the electrical parameters Among them, I _dc is the rated current of the DC side, I _m is the amplitude of the phase current of the AC side, and the circulating current injected into twice the fundamental frequency is optimized, and the effective value of the bridge arm current after optimization Among them, I _2m is the injected circulating current amplitude of twice the fundamental frequency, I′ _m is the optimized AC side phase current amplitude, and the constraints on the bridge arm current before and after the optimization include the bridge arm current during steady-state operation before the optimization. Arm current RMS and optimized bridge arm current RMS. 4. a kind of multi-objective optimization method based on genetic algorithm suitable for MMC as claimed in claim 1 or 2, is characterized in that, described step (4) comprises: (4-1) According to the constraints and electrical parameters, the initial solution set of the common-mode voltage injection amount and the circulating current injection amount is randomly established with the goal of minimizing the peak value of the modulated voltage of the bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module; (4-2) Calculate the peak value of the modulation voltage of the bridge arms and the peak value of the capacitor voltage fluctuation of the sub-module by using multiple initial solutions in the initial solution set, and calculate the difference between the peak value of the modulation voltage of each bridge arm and the peak value of the capacitor voltage fluctuation of the sub-module and the target The fitness function is used to obtain the fitness values of multiple initial solutions in the initial solution set, and the Pareto solution set is selected from the initial solution set according to the fitness values; (4-3) Crossover operation and mutation operation are performed on the initial solution set to generate a new solution set, and the new solution set is used to replace the initial solution set, and then step (4-2) is performed; (4-4) Steps (4-2)-(4-3) are repeated until the maximum evolutionary algebra is reached, and the final Pareto solution set is obtained. 5. a kind of multi-objective optimization method based on genetic algorithm suitable for MMC as claimed in claim 1 or 2, is characterized in that, the bridge arm modulation voltage after described multi-objective optimization comprises the upper, Lower arm modulation voltage _{up, u n :} Among them, U _m ′ is the optimized AC side output voltage amplitude, U _m ′x ₁ is the sine component amplitude of the common mode voltage injection, U _m ′x ₂ is the cosine component amplitude of the common mode voltage injection, ω is the AC output frequency, and t is the running time of the MMC. 6. a kind of multi-objective optimization method based on genetic algorithm suitable for MMC as claimed in claim 5, is characterized in that, described optimized AC side output voltage amplitude is: U _m ′=kU _m Among them, U _m is the output voltage amplitude of the AC side, and the equivalent modulation ratio u _pm is the minimum bridge arm modulation voltage peak value obtained by genetic algorithm.