CN109980971B

CN109980971B - Three-level traction inverter control method considering potential balance and harmonic suppression

Info

Publication number: CN109980971B
Application number: CN201910167596.7A
Authority: CN
Inventors: 朱琴跃; 戴维; 谭喜堂; 解大波; 李朝阳
Original assignee: Tongji University
Current assignee: Tongji University
Priority date: 2019-03-06
Filing date: 2019-03-06
Publication date: 2020-04-28
Anticipated expiration: 2039-03-06
Also published as: CN109980971A

Abstract

The invention relates to a three-level traction inverter control method considering potential balance and harmonic suppression, which comprises the following steps: 1) constructing a mathematical model of the three-level inverter according to the working state of the three-level inverter; 2) calculating the output harmonic distortion rate of the level inverter; 3) calculating the midpoint potential fluctuation of the three-level inverter; 4) establishing constraint conditions by adopting a penalty function method, and constructing a multi-objective optimization model according to the harmonic distortion rate and the midpoint potential fluctuation; 5) and solving the multi-objective optimization model by adopting a PSO algorithm to finally obtain an optimal switching angle sequence. Compared with the prior art, the method has the advantages of strong applicability, practicability, safety and the like.

Description

Three-level traction inverter control method considering potential balance and harmonic suppression

Technical Field

The invention relates to the field of control of a three-level traction inverter, in particular to a control method of the three-level traction inverter considering potential balance and harmonic suppression.

Background

Compared with a two-level topological structure, the diode-clamped three-level traction inverter has been widely applied to high-speed motor train units by virtue of the advantages of flexible control, high output voltage level, low output harmonic content and the like, and gradually draws attention in the application of subway vehicles. However, due to the characteristics of the self topological structure, the inverter has the condition that the voltages of the upper and lower voltage-dividing capacitors on the direct current side are unbalanced when working, so that the midpoint potential fluctuates, the output voltage is distorted, the harmonic content is increased, and the working performance of the inverter is seriously influenced. Therefore, the neutral point potential balance control and the harmonic suppression of the three-level traction inverter are always the concerns of scholars at home and abroad, and how to give consideration to the neutral point potential balance control and the harmonic suppression is also the difficulty of the optimization control research of the inverter.

For a three-level traction inverter, the midpoint potential balance control target is to reduce the offset of the voltage of the direct-current side voltage-dividing capacitor and reduce the midpoint potential fluctuation amplitude; the main objective of harmonic suppression is to improve the output waveform quality and reduce the total harmonic distortion rate. The existing method mainly realizes single-target control on neutral potential balance control or harmonic suppression, and a control method combining the neutral potential balance control and the harmonic suppression has not been reported in documents.

At present, most of midpoint potential balance control strategies with better effects are control methods based on space vectors. Scholars such as ChoiUM and Bhat A propose that the neutral potential is balanced and controlled by adjusting the action time of the redundant small vector, the method can realize qualitative control, but the control precision is not high enough, and the generation of neutral potential fluctuation is not analyzed essentially. The students of the model wave, the cassie and the like use a modulation method based on a virtual space vector to enable the sum of output three-phase currents to be zero so as to realize the full-range control on the midpoint voltage, but the imbalance of the midpoint potential caused by approximate processing and accumulation effects in calculation cannot be solved. Aiming at the problem of harmonic suppression, the PWM method based on specific subharmonic elimination is widely concerned and applied. The method achieves the purpose of eliminating specific subharmonics by optimally selecting the switching time angle, and the core of the method lies in how to solve a nonlinear equation set related to the switching time angle. Although the traditional numerical solution method is simple in calculation and high in precision, the problems of excessive dependence on initial value selection, non-convergence and the like easily occur in the solution process. Therefore, related intelligent algorithms including genetic algorithms, swarm algorithms and particle swarm algorithms are gradually applied in recent years, the algorithms are simple in flow, complex parameters do not need to be set, and the method has great advantages in the aspects of nonlinear function optimization, multi-objective optimization and the like.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a control method of a three-level traction inverter considering midpoint potential balance and harmonic suppression.

The purpose of the invention can be realized by the following technical scheme:

a three-level traction inverter control method considering potential balance and harmonic suppression comprises the following steps:

1) constructing a mathematical model of the three-level inverter according to the working state of the three-level inverter;

2) calculating the output harmonic distortion rate of the level inverter;

3) calculating the midpoint potential fluctuation of the three-level inverter;

4) establishing constraint conditions by adopting a penalty function method, and constructing a multi-objective optimization model according to the harmonic distortion rate and the midpoint potential fluctuation;

5) and solving the multi-objective optimization model by adopting a PSO algorithm to finally obtain an optimal switching angle sequence.

In the step 2), the level inverter outputs the harmonic distortion f_THDThe calculation formula of (A) is as follows:

wherein, U_dcIs the DC side voltage, U, of a three-level inverter_L1Effective value of the fundamental wave of the load line voltage, α respectively_i(i 1., N) is the ith switching time angle that can be independently and optimally controlled in 1/4 cycles, N is the number of switching time angles that can be independently and optimally controlled in 1/4 cycles, K is the harmonic order, and K is the total harmonic order.

In the step 3), the midpoint potential fluctuation delta u is under the action of different vectors_cThe calculation formula of (A) is as follows:

wherein, U_dcIs the DC side voltage, k, of the three-level inverter_jIs an intermediate parameter, S_m、S_jThe switching states of m-phase and j-phase of the inverter respectively, tau is the dynamic time constant of the equivalent circuit, i_jThree-phase current, T is basic period, R is equivalent resistance of each phase load,

in the step 4), the objective function and the constraint condition of the multi-objective optimization model are respectively as follows:

min:f(x)＝f_THD

st:Δu_c＝0。

the step 5) specifically comprises the following steps:

501) after initializing parameters of the three-level traction inverter, randomly generating a switching angle sequence as initial particles, and initializing the positions and the speeds of the particles;

502) obtaining the positions of the individual optimal particles and the global optimal particles according to the fitness function value;

503) updating the speed and position of each particle in the population of particles;

504) acquiring the updated fitness function value of each particle, setting the fitness function value as a new individual optimal solution when the fitness function value in the current step is superior to the individual optimal solution in the previous step, and setting the individual optimal solution as a new global optimal solution when the individual optimal solution is superior to the previous global optimal solution;

505) when the iteration times reach the maximum iteration times, continuing to step 506), otherwise, returning to step 503);

506) and when the penalty term is zero, outputting the optimal solution as the optimal switch angle sequence, and otherwise, returning to the step 502).

Compared with the prior art, the invention has the following advantages:

firstly, the invention has simple requirement on the controlled object and strong adaptability, the design method provided by the invention only requires to know the corresponding parameters of the controlled object, namely the three-level inverter, and the parameters can be directly obtained from the controlled object without requiring the state of the object to be considerable, thereby greatly relaxing the requirement on the object and enhancing the applicability of the strategy of the invention.

The control strategy provided by the invention not only can effectively inhibit output current harmonic waves, but also can reduce the fluctuation amplitude of the midpoint potential to the maximum extent, improve the dynamic and steady-state performance of the inverter during operation, and enhance the practicability and safety of the strategy.

The invention does not need to increase the number of other devices, does not increase the control cost, has high cost performance, is easy to realize, is convenient to apply and has higher practical application value.

Drawings

FIG. 1 is a block diagram of the system of the present invention.

Fig. 2 is a diagram of a main circuit topology of a three-level inverter.

Fig. 3 is a simplified equivalent circuit diagram of an asynchronous motor.

Fig. 4 is a simplified equivalent circuit diagram of the asynchronous motor.

Fig. 5 is a diagram showing fluctuation of midpoint potential of the three-level inverter capacitor.

Fig. 6 is a diagram showing the output phase current waveform of the three-level inverter during resistive-inductive load.

Fig. 7 is a spectrum diagram of output phase current of the three-level inverter in the resistive-inductive load.

Fig. 8 is a diagram of a three-level inverter output line voltage waveform at the time of resistive-inductive load.

Fig. 9 is a spectrum diagram of output line voltage of the three-level inverter in the resistive-inductive load.

Fig. 10 is a waveform diagram of the output phase current of the three-level inverter when the motor is loaded.

Fig. 11 is a graph of the output phase current spectrum of a three-level inverter when the motor is loaded.

Fig. 12 is a graph of three-level inverter output line voltage waveforms at motor load.

Fig. 13 is a graph of the output line voltage spectrum of a three-level inverter when the motor is loaded.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments.

Examples

As shown in fig. 1, in this example, a three-level traction inverter optimization control system that combines midpoint potential balance control and harmonic suppression is mentioned, and the system mainly includes: the three-level traction inverter comprises a main circuit of a three-level traction inverter with a load, a harmonic distortion rate calculation module, a midpoint potential fluctuation calculation module and a multi-objective optimization control module. The output end of the inverter main circuit is connected with the harmonic distortion rate calculation module and the midpoint potential fluctuation calculation module, and outputs a switching time angle sequence in real time. The harmonic distortion rate calculation module and the midpoint potential fluctuation calculation module are used for calculating the corresponding harmonic distortion rate and midpoint potential fluctuation in real time and inputting the harmonic distortion rate and midpoint potential fluctuation to the multi-target optimization control module. And the multi-objective optimization control module outputs the optimized PWM control signal to the main circuit of the inverter so as to control the corresponding inverter to work.

The invention provides a midpoint potential balance control and harmonic suppression multi-objective optimization control method based on a particle swarm optimization algorithm according to a control system, which specifically comprises the following steps:

1. analyzing the working state of the three-level inverter and establishing a mathematical model thereof

In the three-level inverter topology shown in fig. 2, each phase of bridge arm includes four power switching tubes T_j1～T_j4(j ═ a, b, c). Analysis shows that the on-off conditions of four power switching tubes of each phase bridge arm of the inverter determine the switching state of the bridge arm: taking phase a as an example, when S_a1、S_a2Is on and S_a3、S_a4When the bridge arm is turned off, the switching state of the bridge arm is 'P'; when S is_a2、S_a3Is on and S_a1、S_a4When the bridge arm is turned off, the switching state of the bridge arm is O; when S is_a3、S_a4Is on and S_a1、S_a1When the bridge arm is turned off, the switch state of the bridge arm is 'N'. If the switching state of each phase bridge arm of the three-level inverter is defined as S_j(j ═ a, b, c) with values of 1, 0, -1, then when the dc side voltage is U_dcThe output phase voltages of three-phase bridge arms of the inverter can be respectively + U_dc/2、0、-U_dc/2。

2. Establishing a calculation model of the output harmonic distortion rate of the three-level inverter

The three-level inverter control strategy directly affects the harmonic magnitude of its output voltage current. Compared with a sinusoidal carrier PWM and space vector PWM modulation method, the random optimization PWM modulation method can enable the harmonic content of the output voltage or current waveform of the inverter to be the lowest. Through calculation, the total harmonic distortion rate of the load current is as follows:

in the formula of U_dcIs a DC side voltage of a three-level inverter, I_L1、U_L1Fundamental effective values of load line current and line voltage, α_i(i 1.., N) is the switching time angle that can be independently and optimally controlled in 1/4 cycles, and N is the number of the switching time angles.

As can be seen from the above equation (1), the total harmonic distortion of the current is represented by the switching time angle sequence X ═ α₁,α₂,...,α_N]It is decided that the correspondingly calculated total harmonic distortion of the current will be different for different sequences of switching instant angles.

The step 2 specifically comprises the following substeps:

(201) the harmonic content of the output voltage or current waveform of the inverter can be minimized by adopting a specific subharmonic elimination PWM method, and α can be independently controlled in the former 1/4 period₁～α_NN switching time angles are total, each time point can be obtained by calculation according to a certain optimization target and an optimization method, and the three-level inverter outputs a phase voltage u_jn(j ═ a, b, c) can be represented as:

(202) further, Fourier series expansion is performed on the phase voltage, and the output line voltage u of the three-level inverter can be obtained considering that the output line voltage does not contain third harmonic and multiple harmonic in a three-phase inverter system_LHas an effective value of the kth harmonic of:

(203) since the most critical factor that really determines and influences the system operation performance for most loads supplied by an inverter, particularly an alternating current asynchronous motor, is the load current, the harmonic suppression target variable of the invention is determined as the total harmonic distortion rate of the load current. The equivalent circuit of the asynchronous motor is shown in figure 3, wherein R_sIs stator resistance, X_sIs the fundamental wave reactance of the stator, X_mIs a fundamental mutual inductive reactance, X_rIs the fundamental reactance of the rotor, R_rIs the rotor resistance. Considering the slip s of the kth harmonic when the harmonic order is high_kSubstantially close to 1, and can therefore be simplified to FIG. 4Line analysis, from which the effective value of the line current I for the k-th harmonic can be derived_LkAnd line voltage effective value U_LkThe relationship between them is:

(204) according to the requirements of engineering application, the highest harmonic is taken as 50 times when the voltage or current harmonic distortion is calculated, and therefore the total harmonic distortion of the load current is obtained as follows:

3. Establishing a three-level inverter midpoint potential fluctuation calculation model

As can be seen from the above analysis of the operating principle of the three-level inverter, when the switching states of the legs of each phase of the inverter are "1", "0" and "-1", the corresponding output states are "P", "O" and "N", respectively, and the inverter can output 3 total output phases of the corresponding legs³Each state corresponds to a voltage vector, 27 states. According to its centering point current i_npThe voltage vectors can be divided into five types as shown in table 1.

TABLE 1 vector Classification

The three-phase current under different vector effects can be obtained as follows:

in the formula

From the above formulas, the midpoint potential fluctuation under different vector actions can be finally obtained as follows:

in the formula, τ and R are respectively the dynamic time constant of the corresponding equivalent circuit and the equivalent resistance of each phase load when different vectors act, and T is the size of the basic period.

Step 3 comprises the following substeps:

(301) in the main circuit shown in FIG. 2, let C be assumed₁＝C₂C, derived from kirchhoff's current law:

from this, the midpoint potential fluctuation Deltau can be obtained_cThe instantaneous expression of (c) is:

(302) assuming that three-phase voltage vectors can be respectively valued as 1, 0 and-1, the midpoint current i under the action of different voltage vectors can be induced_npThree-phase current i with a, b and c_jThe relationship between (j ═ a, b, c) is:

wherein S is_j＝1,0,-1。

By analyzing equivalent circuits under different vector actions, three-phase currents under different vector actions can be obtained as follows:

in the formula

(303) By combining the formulas (2), (3) and (4), the midpoint potential fluctuation delta u under the action of different vectors can be obtained_cComprises the following steps:

(304) As can be seen from equation (5), the magnitude of the midpoint potential fluctuation also corresponds to the switching time angle sequence X ═ α₁,α₂,...,α_N]In connection with this, Δ u at an arbitrary time t during actual operation of the inverter_cThe calculation process is as follows:

(3041) obtaining the three-phase switching state S of the inverter according to each switching time value of the switching time angle sequence X of the current time t_j(j ═ a, b, c), and the corresponding voltage vector;

(3042) reading three-phase current value i of inverter at last moment_j(t-1) to give i_j(0⁺) (j ═ a, b, c); based on the current voltage vector and the current voltage vector, calculating the current three-phase current value i according to the formula (4)_j(t) (j ═ a, b, c), and stored;

(3043) the total voltage fluctuation Delaut in one period T is calculated according to the above equation (5)_cThe magnitude of (c).

(4) And establishing constraint conditions by using a penalty function method according to the three-level inverter output harmonic distortion rate and the midpoint potential fluctuation mathematical model, and constructing a multi-objective optimization model.

The basic idea of the penalty function method in this step is to give a penalty to the unfeasible points that violate constraints or to the points that try to cross a boundary to escape a feasible domain, so that they are close to the feasible domain. The construction idea is to combine constraint functions to form a 'punishment' item, add the 'punishment' item on the original objective function to force the iteration point to approach the feasible domain, thereby changing the constraint optimization problem into an unconstrained problem to solve and process.

For constrained multi-objective optimization problems, it can be generally defined as:

min:f(x)＝(f₁(x),f₂(x),...,f_m(x))

wherein x is (x)₁,x₂,...,x_n) E.g. R is an n-dimensional decision variable; (x) ═ f₁(x),f₂(x),...,f_m(x) Is an objective function, comprising one or more objective functions; g (x), h (x) are inequality constraint and equality constraint, respectively.

Since inequality constraints can be interconverted with equality constraints, the new objective function with penalty function can be expressed as:

min:F(x,M)＝f(x)+Ma(x)

in the formula, M (M)>1) In order to be a penalty factor,

ma (x) is a penalty term for the penalty function.

According to the penalty function correlation theorem, for a certain determined M, the optimal solution of the new objective function F (x, M) finally obtained by solving according to the optimization method is the optimal solution of the original objective function F (x).

Therefore, the optimization model of the three-level traction inverter with both midpoint potential balance control and harmonic suppression is converted into an objective function min, F (X, M) is F_THD+MΔu_cAnd (6) solving.

(5) According to given parameters, a PSO algorithm is used for solving the multi-objective optimization model to obtain an optimal switching angle sequence X ═ α₁,α₂,...,α_N]。

The method for solving the multi-objective optimization model by using the PSO algorithm in the step specifically comprises the following steps:

(501) after the inverter parameters are initialized, randomly generating a switching angle sequence, and initializing the position and the speed of particles;

(502) calculating fitness function values of the mobile terminal, and finding out the optimal positions of individuals and the optimal positions of the whole situation;

(503) updating the speed and position of the particles;

(504) and calculating the updated fitness function value of each particle, setting the fitness function value as a new individual optimal solution if the fitness function value is superior to the previous individual optimal solution, and setting the individual optimal solution as a new global optimal solution if the individual optimal solution is superior to the previous global optimal solution.

(505) If the iteration times reach the maximum iteration times, continuing the next step, otherwise, returning to (503);

(506) if the penalty term is zero, outputting the optimal solution, otherwise, returning to the step (502);

(6) taking the actual parameters of the train of the sea-ground-rail second-size line as an example, a three-level inverter simulation model is built, and the corresponding parameters are set as follows: 190kW of inverter power, 0.86 of power factor and U of direct-current side input voltage_dc1500V, and the modulation ratio m is 0.72; in the PSO algorithm, the initial population number n is 40, and the maximum number of iterations M _axgen50, weight factor w₁＝0.7982，w₂0.2, learning factor c₁＝c₂1.4995; the switching time angle initial sequence is as follows:

X_i＝[0.5771 1.0437 1.1643 1.5466 1.5595 1.5650 1.5687 1.5695](rad)

the effectiveness of the invention will be described below in terms of both resistive inductive loads and motor loads.

(601) Inductance resistance load: assuming that the resistance R of the load is 8.64 Ω and the inductance L is 15.9mH, the switching time angle obtained through optimization calculation is: x_i＝[0.2904 1.4921 1.5284 1.5393 1.5555 1.5568 1.56381.5696](rad), the corresponding inverter input side capacitance midpoint potential fluctuation and inverter output voltage, current waveform diagram and spectrum distribution are shown in fig. 5-9.

As can be seen from FIG. 5, the peak value of the capacitor voltage is 6.7V, and the fluctuation coefficient ε_up0.89%; the wave valley value is-5.8V, and the fluctuation coefficient epsilon_down0.83%, and the fluctuation amplitude is about 0VDynamic and total fluctuation coefficient epsilon_total1.72%, thereby demonstrating the effectiveness of the proposed optimization control strategy.

6-9, the amplitude of fundamental frequency component of output phase current of the three-level inverter is 75.11A, THD is 1.87%; the amplitude of the fundamental frequency component of the output line voltage is 1053V, and the THD is 19.23%; the harmonics are mainly concentrated in the 7, 11, 13 and 19 orders. Therefore, the control strategy of the invention can optimize under lower switching frequency to obtain better switching time angle, and well improve the utilization rate and quality of voltage and current.

(602) And (3) motor load: the parameters of the load of the star-connected asynchronous traction motor are assumed as follows: the rated voltage is 1050V, the rated current is 132A, the rated rotating speed is 1500r/min, the rated power is 190KW, the rated frequency is 50Hz, the power factor is 0.85, the pole pair number is 4, the stator leakage inductance is 0.001511H, the rotor leakage inductance is 0.001511H, the stator and rotor mutual inductance is 0.04503H, the stator resistance is 0.111 omega, the rotor resistance is 0.099 omega, and the motor control mode adopts open loop control. The switching time angle sequence X obtained after optimization calculation_iSimilar to the resistive load, the inverter output voltage, the current waveform diagram and the frequency spectrum distribution obtained by the method are respectively shown in fig. 10, 11, 12 and 13.

As can be seen from fig. 10 to 13, the amplitude of the fundamental frequency component of the inverter output current when the motor is loaded is 64.69a, and the THD is 2.09%; the amplitude of the fundamental frequency component of the output voltage is 1022V, and the THD is 23.72 percent; the harmonics are mainly concentrated in 5, 13, 17, 19 orders. The harmonic content of the output voltage and the current of the inverter is slightly higher than the corresponding values under the resistance-inductance load, which is mainly caused by open-loop motor control and other modes, but the harmonic content of the output signal of the inverter based on the optimized control strategy is generally better than that of the traditional control strategy.

Claims

1. A three-level traction inverter control method considering potential balance and harmonic suppression is characterized by comprising the following steps:

2) computational level inversionThe harmonic distortion rate is output by the inverter, and the harmonic distortion rate f is output by the level inverter_THDThe calculation formula of (A) is as follows:

wherein, U_dcIs the DC side voltage, U, of a three-level inverter_L1Effective value of the fundamental wave of the load line voltage, α respectively_i(i 1., N) is the ith switching time angle which can be independently and optimally controlled in 1/4 periods, N is the number of the switching time angles which can be independently and optimally controlled in 1/4 periods, K is the harmonic frequency, and K is the total harmonic frequency;

3) calculating the midpoint potential fluctuation of the three-level inverter;

2. The method as claimed in claim 1, wherein the step 3) comprises a step of controlling the three-level traction inverter by considering the potential balance and harmonic suppression, wherein the midpoint potential fluctuation Δ u is obtained under different vector actions_cThe calculation formula of (A) is as follows:

wherein, U_dcIs the DC side voltage, k, of the three-level inverter_jIs an intermediate parameter, S_m、S_jThe switching states of m-phase and j-phase of the inverter respectively, tau is the dynamic time constant of the equivalent circuit, i_jThe three-phase current is shown, T is a basic period, and R is the equivalent resistance of each phase of load.

3. The method as claimed in claim 2, wherein in the step 4), the objective function and the constraint condition of the multi-objective optimization model are respectively:

min:f(x)＝f_THD

st:Δu_c＝0。

4. the method for controlling the three-level traction inverter considering the potential balance and the harmonic suppression as claimed in claim 1, wherein the step 5) specifically comprises the following steps: