CN110212799B - Passive backstepping control method for suppressing circulating current in modular multilevel converters - Google Patents

Abstract

The invention relates to a passive backstepping control method for restraining circular current of a modular multilevel converter, which comprises the following steps: s1, obtaining a PCHD model of MMC circulation according to the single-phase equivalent circuit of the MMC and based on an orthodefinite quadratic energy function; s2, constructing a PCHD model-based MMC circulating current suppression passive backstepping controller; s3, inputting the double frequency actual value and the reference value of the circulating current into an MMC circulating current restraining passive backstepping controller to output circulating current voltage compensation quantity; and S4, carrying out carrier phase shift modulation on the circulating current voltage compensation quantity, and controlling the on-off of a switch tube in the MMC submodule through the modulation wave to achieve the purpose of circulating current inhibition. Compared with the prior art, the PCHD model-based passive control and the back-stepping method are organically combined, the overall stability can be guaranteed, the rapid dynamic response can be realized, the control law is simple in operation, free of singular points, strong in robustness and obvious in circulation restraining effect.

Description

Passive backstepping control method for suppressing circulating current in modular multilevel converters

technical field

The invention relates to the field of modularized multilevel converter control, in particular to a passive backstepping control method for suppressing the circulating current of the modularized multilevel converter.

Background technique

At present, Modular multilevel converter (MMC) is widely used in grid-connected system of distributed power supply. The mathematical model of MMC is simple. By controlling the on and off of switches in each sub-module of MMC, The switching of the output voltage can be realized, but since the MMC contains multiple sub-modules, with the switching in and out of each sub-module, it is difficult to achieve a complete balance of the capacitor voltage in the sub-modules, resulting in unbalanced voltages between the bridge arms, thereby forming a circulating current.

In order to suppress the circulation generated during the operation of MMC, the traditional vector control method does not start from the perspective of energy, and cannot effectively control the nonlinear nature of MMC. Once there is uncertainty disturbance, the traditional vector control will face disturbance immunity and robustness. Although the existing nonlinear control methods solve the problem of nonlinear control to a certain extent, there are shortcomings in energy optimization, the energy loss of the system is too large, and its transient performance is poor, and the adjustment time is too long. long and slow dynamic response.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a passive backstepping control method for suppressing the circulating current of the modular multilevel converter in order to overcome the above-mentioned defects of the prior art.

The object of the present invention can be achieved through the following technical solutions: a passive backstepping control method for suppressing the circulating current of a modular multilevel converter, comprising the following steps:

S1. According to the single-phase equivalent circuit of MMC, and based on the positive definite quadratic energy function, the PCHD model of MMC circulation is obtained;

S2. Adopt passive control and backstepping control theory to construct a passive backstepping controller for MMC circulation suppression based on PCHD model;

S3. Input the double frequency actual value and reference value of the circulating current into the MMC circulating current suppression passive backstep controller to output the circulating current voltage compensation amount;

S4. Perform carrier phase shift modulation on the circulating current voltage compensation amount to generate a modulated wave, and control the on and off of the switch tube in the MMC sub-module through the modulated wave, so as to achieve the purpose of circulating current suppression.

Further, the step S1 specifically includes the following steps:

S11. According to the single-phase equivalent circuit of MMC, the dynamic equation of circulation under the dq rotating coordinate system is obtained;

S12, select the state variables, input and output variables respectively, and based on the positive definite quadratic energy function, perform an equivalent transformation on the circulation dynamic equation to obtain the PCHD model of the MMC circulation.

Further, the circulation dynamic equation in the step S11 is specifically:

Among them, ω ₀ is the fundamental angular frequency, L _m is the bridge arm inductance, R _m is the bridge arm resistance, i _cird and i _cirq are the actual value of the d-axis component and the actual value of the q-axis component of the double frequency of the three-phase circulating current, respectively, u _cird and u _cirq are the d-axis compensation amount and the q-axis compensation amount of the three-phase circulating voltage, respectively, d is the differential operator, and t is the time.

Further, the state variables, input and output variables in the step S12 are specifically:

where x is the state variable, u is the input variable, y is the output variable, x1 and _x2 are the d _- axis and q-axis components of the state variable, respectively, and u1 and u2 are the d _- axis and q _- axis components of the input variable, respectively Axis components, y ₁ and y ₂ are the d-axis and q-axis components of the output variable, respectively;

The positive definite quadratic energy function is specifically:

Among them, H(x) is the energy originally stored in the MMC circulation nonlinear system;

The PCHD model of the MMC circulation is specifically:

为状态变量x对时间的微分，J(x)为互联矩阵，R(x)为阻尼矩阵，g(x)为端口矩阵。in,

is the differential of the state variable x with respect to time, J(x) is the interconnection matrix, R(x) is the damping matrix, and g(x) is the port matrix.

Further, the step S2 specifically includes the following steps:

S21, define the state variable error, and set the expected energy function of the MMC circulating closed-loop control system;

S22, combining the PCHD model of the MMC circulation and the expected energy function, obtain the state equation of the MMC circulation closed-loop system;

S23, according to the state equation of the MMC circulation closed-loop system, determine the constraint conditions of the passive control law, and obtain the MMC circulation suppression passive control law based on the PCHD model;

S24. Based on the backstepping control theory, by equivalently transforming the circulation dynamic equation, and defining the progressive tracking error, the MMC circulation suppression backstepping control law is obtained;

S25, combining the MMC circulation suppression passive control law and the MMC circulation suppression backstepping control law to construct an MMC circulation suppression passive backstepping controller.

Further, the expected energy function in the step S21 is specifically:

x*=[x ₁ ^* x ₂ ^* ]

x _e = xx ^*

和

分别为期望平衡点的d轴分量和q轴分量。where H _d (x) is the desired energy, H _a (x) is the energy injected into the system by introducing state feedback control, x _e is the state variable error, D is the inductance matrix, x* is the desired equilibrium point,

and

are the d-axis and q-axis components of the desired equilibrium point, respectively.

Further, the state equation of the MMC circulation closed-loop system in the step S22 is specifically:

J _d (x)=J(x)+J _a (x)

R _d (x)=R(x)+R _a (x)

Among them, J _d (x) is the desired interconnection matrix of the system, R _d (x) is the desired damping matrix of the system, and Ja (x) and R _{a (} x) are the injected dissipation matrix and damping matrix, respectively.

Further, the constraints of the passive control law in the step S23 are specifically:

Choose the injected dissipation matrix to be 0:

Ja( _x )=0

That is:

u=g ^-1 (x)[(J _d (x)-R _d (x))D x-(J _d (x)-R _d (x))D x ^* -(J(x)- R(x))D x]

=g ^-1 (x)[-R _d (x)D x-(J(x)-R _d (x))D x ^* +R(x)D x]

=g ^-1 (x)[-R _a (x)D·x-(J(x)-R _d (x))D·x ^* ]

The specific passive control law of MMC circulation suppression based on PCHD model is:

Among them, u ¹ _cird and u ¹ _cirq are the d-axis compensation amount and q-axis compensation amount of the passive control circulating current voltage, respectively, i ^* _cird and i ^* _cirq are the d-axis component reference value and q of the double frequency of the three-phase circulating current, respectively The reference value of the axis component, r _a1 and r _a2 are the injected positive damping parameters, that is, the injected damping matrix

Further, the equivalent transformation of the circulation dynamic equation in the step S24 is:

x ₁ =L _m i _cird

x ₂ =L _m i _cirq

a ₂ =2ω ₀

Among them, a ₁ and a ₂ are equivalent transformation coefficients;

The progressive tracking error is:

where e ₁ and e ₂ are the progressive tracking errors of i _cird and i _cirq , respectively,

The specific control law of MMC circulation suppression backstepping is:

Among them, u ² _cird and u ² _cirq are the d-axis compensation amount and the q-axis compensation amount of the back-step control circulating voltage, respectively, and k ₁ and k ₂ are both back-step control parameters.

Further, in the step S3, the compensation amount of the circulating current voltage is specifically:

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

1. The present invention passively controls the MMC circulation based on the PCHD model. Through the shaping of the energy function, the energy function can achieve the minimum value at the desired equilibrium point, optimize the input and output energy of the control system, and reduce the energy loss. Input and output mapping to ensure the global asymptotic stability of the system.

2. The present invention adopts the backstep control theory, and cancels the nonlinear term in the first derivative of the Lyapunov function by retaining the nonlinear term, so as to satisfy the Lyapunov stability theorem, and at the same time, the linear quantity is introduced to effectively improve the transient performance of the control closed-loop system , the fast tracking of the double frequency component of the circulating current under internal and external disturbances is realized.

3. The present invention combines passive backstepping control to suppress MMC circulating current, has simple control operation, short adjustment time, strong robustness, and has stronger stability and faster response speed under uncertain disturbance conditions.

Description of drawings

Fig. 1 is the method flow schematic diagram of the present invention;

Fig. 2 is the single-phase equivalent circuit diagram of MMC;

3 is a block diagram of the passive backstepping control block diagram of the MMC circulating current suppression based on the PCHD model of the present invention;

Fig. 4a is the DC side current waveform of MMC in the embodiment;

Fig. 4b is the current waveform of the upper and lower arms of phase a of the MMC in the embodiment;

Fig. 4c is a phase upper and lower bridge arm sub-module capacitor voltage waveforms of MMC in the embodiment;

Fig. 4d is the three-phase interphase circulating current waveform of MMC in the embodiment;

Fig. 4e is the interphase double frequency circulating current waveform of MMC in the embodiment;

Fig. 4f is the three-phase voltage waveform of the AC side of the MMC in the embodiment;

FIG. 4g is the three-phase current waveform on the AC side of the MMC in the embodiment.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

As shown in Figure 1, a passive backstepping control method for suppressing the circulating current of a modular multilevel converter includes the following steps:

S1. According to the single-phase equivalent circuit of MMC, and based on the positive definite quadratic energy function, the PCHD model of MMC circulation is obtained;

S2. Adopt passive control and backstepping control theory to construct a passive backstepping controller for MMC circulation suppression based on PCHD model;

S3. Input the double frequency actual value and reference value of the circulating current into the MMC circulating current suppression passive backstep controller to output the circulating current voltage compensation amount;

S4. Perform carrier phase shift modulation on the circulating current voltage compensation amount to generate a modulated wave, and control the on and off of the switch tube in the MMC sub-module through the modulated wave, so as to achieve the purpose of circulating current suppression.

Wherein, the method steps specifically include the following processes:

According to the single-phase equivalent circuit diagram of the modular multi-level converter shown in Figure 2, the dynamic equation of the circulation in the dq rotating coordinate system can be obtained:

In the formula, ω ₀ is the fundamental angular frequency, L _m is the bridge arm inductance, R _m is the bridge arm resistance, i _cird and i _cirq are the actual value of the d-axis component and the actual value of the q-axis component of the double frequency of the three-phase circulating current, respectively. , u _cird and u _cirq are the d-axis compensation and q-axis compensation of the three-phase circulating voltage, respectively, d is the differential operator, and t is the time;

Select the state variable x, the input variable u, and the output variable y as:

In the formula, x is the state variable, u is the input variable, y is the output variable, x ₁ and x ₂ are the d-axis and q-axis components of the state variable, respectively, and u ₁ and u ₂ are the d-axis and d-axis components of the input variable. q-axis component, y ₁ and y ₂ are the d-axis and q-axis components of the output variable, respectively;

Design a positive definite quadratic energy function:

Equivalently transform the circulation dynamic equation (1) in the dq rotating coordinate system to obtain the MMC circulation PCHD model:

为互联矩阵，

为阻尼矩阵，

为端口矩阵；In the formula,

is the interconnection matrix,

is the damping matrix,

is the port matrix;

The dissipation inequality can be obtained from equations (3) and (4):

The left side of equation (5) is the increment of the entire MMC circulation system, the right side is the external supply energy, the mapping u→x is strictly passive for the output, and the system satisfies the passive condition;

According to the system control performance objectives, the expected equilibrium point of the MMC circulation system is set as:

Define the state variable error x _e =xx ^* , set the expected energy function of the MMC circulation closed-loop control system:

H(x)为MMC环流非线性系统中原存储的能量，H_a(x)为通过引入状态反馈控制所注入系统的能量；In the formula,

H(x) is the energy originally stored in the MMC circulation nonlinear system, and H _a (x) is the energy injected into the system by introducing state feedback control;

The derivatives of H(x), H _a (x), and H _d (x) with respect to x are respectively

From equations (4) and (7), the state equation of the MMC circulation closed-loop system can be obtained as:

In the formula, J _d (x)=J(x)+J _a (x) is the desired interconnection matrix of the system, R _d (x)=R(x)+R _a (x) is the desired damping matrix of the system, J _a (x) and R _a (x) are the injected dissipation matrix and damping matrix, respectively;

Simultaneously Equation (3) and Equation (9), the state feedback control law can be obtained to satisfy the partial differential equation shown in Equation (10)

The desired interconnection matrix and damping matrix need to satisfy equations (11) and (12), respectively:

使得控制律简易可行且系统收敛速率可控，Choose J _a (x) = 0,

The control law is simple and feasible and the system convergence rate is controllable,

Simultaneous equations (8) and (10) can be obtained

From equation (13), the passive control law of MMC circulation suppression under PCHD model can be obtained as:

In the formula, u ¹ _cird and u ¹ _cirq are the d-axis compensation amount and q-axis compensation amount of the passive control circulating voltage, respectively, i ^* _cird and i ^* _cirq are the reference value of the d-axis component of the double frequency of the three-phase circulating current and q-axis component reference value, r _a1 and r _a2 are both injected positive damping parameters;

On the basis of the passive control of MMC circulation, backstep control is added, the nonlinear term of the MMC circulation system is retained in the control strategy, and the dynamic response performance of the closed-loop system is improved.

Equation (1) can be equivalently transformed into

In the formula, a ₁ and a ₂ are equivalent transformation coefficients;

The progressive tracking error of i _cird and i _cirq is defined as

The asymptotic tracking error derivative is

In order to achieve the system control objectives e ₁ → 0 and e ₂ → 0, the Lyapunov function is defined as

Combining Equation (16), Equation (17), and Equation (18), the first derivative of the Lyapunov function can be obtained as

忽略状态变量参考值的微分项

和

设计MMC环流抑制反步控制律为Since the expected equilibrium point of the MMC circulation system is

Ignore the derivative term of the state variable reference value

and

The design of the MMC circulation suppression backstepping control law is

In the formula, u ² _cird and u ² _cirq are the d-axis compensation amount and the q-axis compensation amount of the back-step control circulating voltage, respectively, and k ₁ and k ₂ are both back-step control parameters;

Simultaneous equations (20) and (14), it can be deduced that the circulating current voltage compensation output by the MMC circulating current suppression passive backstep controller is:

That is:

From this, the control block diagram of the MMC circulating current suppression passive backstepping controller is shown in Figure 3. The output circulating current voltage compensation (u _cird , u _cirq ) is input into the carrier phase-shift modulation module to generate modulated waves and send them accordingly It is given to the sub-modules of the bridge arms of each phase of the MMC, and then the working states of the switch tubes in the sub-modules of the bridge arms of each phase of the MMC are controlled to realize the suppression of the circulating current of each phase of the MMC.

A modular multilevel converter and a simulation model of circulating current suppression are built in MATLAB/Simulink to verify the effectiveness of the circulating current suppression of the present invention. The simulation parameters of this embodiment are shown in Table 1.

Table 1 Simulation parameters

Simulation model parameters Numerical value Number of submodules n/piece twenty four Submodule capacitance C/mF 2 Bridge arm inductance Lm/mH 5 Bridge arm resistance Rm/Ω 5 AC side rated voltage u_k/V 220 AC system frequency f/Hz 50 DC side voltage U_dc/V 650 AC side inductance L/mH 1 AC side resistance R/mΩ 100

Under the steady-state operation of the MMC system, the circulating current suppression passive backstep control method based on the PCHD model is used for the simulation test: the simulation time is set to 0.5s, and the circulating current suppression passive backstepping control is started at t=0.4s. The simulation results are as follows: shown in Figures 4a to 4g.

From the analysis of Figure 4a, it can be seen that the passive backstep circulating current suppression method effectively reduces the DC side power ripple and improves the system stability;

From the analysis of Figure 4b, it can be seen that when the circulating current suppression is not used, the current of the upper arm of the a-phase is distorted due to the existence of the double-frequency negative sequence circulating current component; Mainly DC component and fundamental frequency component, which are close to ideal sine wave, and the waveform quality is improved;

It can be seen from the analysis in Figure 4c that the suppression of the double frequency negative sequence component significantly reduces the DC capacitance and the voltage fluctuation of the sub-module capacitor;

It can be seen from the analysis in Fig. 4d that the actual values (i _cird , i _cirq ) of the double-frequency negative-sequence dq-axis components can quickly track the reference value of the given circulating current double-frequency component

From the analysis in Fig. 4e, it can be seen that the three-phase circulating current waveform has obvious double frequency characteristics before t=0.4s. After the passive backstep control of the circulating current suppression is started, the three-phase circulating current fluctuates at the DC component, which is consistent with the theoretical analysis results. Passive backstepping circulation suppression strategy, the double frequency circulation component is effectively suppressed, and the circulation suppression effect is obvious;

From the analysis of Fig. 4f and Fig. 4g, it can be seen that the external characteristics of the AC side output are not affected after the MMC circulating current is suppressed, and the system runs smoothly.

Claims (8)

1. a passive backstepping control method for suppressing the circulating current of a modular multilevel converter, is characterized in that, comprises the following steps: S1. According to the single-phase equivalent circuit of MMC, and based on the positive definite quadratic energy function, the PCHD model of MMC circulation is obtained; S2. Adopt passive control and backstepping control theory to construct a passive backstepping controller for MMC circulation suppression based on PCHD model; S3. Input the double frequency actual value and reference value of the circulating current into the MMC circulating current suppression passive backstep controller to output the circulating current voltage compensation amount; S4. Perform carrier phase shift modulation on the circulating current voltage compensation amount to generate a modulated wave, and control the on and off of the switch tube in the MMC sub-module through the modulated wave, so as to achieve the purpose of circulating current suppression; The step S2 specifically includes the following steps: S21, define the state variable error, and set the expected energy function of the MMC circulating closed-loop control system; S22, combining the PCHD model of the MMC circulation and the expected energy function, obtain the state equation of the MMC circulation closed-loop system; S23. Determine the constraints of the passive control law according to the state equation of the MMC circulation closed-loop system, and obtain the MMC circulation suppression passive control law based on the PCHD model, wherein the constraints of the passive control law are specifically:

J _d (x)=J(x)+J _a (x) Among them, H(x) is the original energy stored in the MMC circulation nonlinear system, J(x) is the interconnection matrix, R(x) is the damping matrix, g(x) is the port matrix, H _d (x) is the expected energy, H _a (x) is the energy injected into the system by introducing state feedback control, x _e is the state variable error, D is the inductance matrix, x* is the desired equilibrium point, J _d (x) is the desired interconnection matrix of the system, R _d (x) is the expected damping matrix of the system, J _a (x) and _Ra (x) are the injected dissipation matrix and damping matrix, respectively, and the injected dissipation matrix is selected as 0: Ja( _x )=0 That is: u=g ^-1 (x)[(J _d (x)-R _d (x))D x-(J _d (x)-R _d (x))D x ^* -(J(x)- R(x))D x] =g ^-1 (x)[-R _d (x)D x-(J(x)-R _d (x))D x ^* +R(x)D x] =g ^-1 (x)[-R _a (x)D·x-(J(x)-R _d (x))D·x ^* ] The specific passive control law of MMC circulation suppression based on PCHD model is:

Among them, u ¹ _cird and u ¹ _cirq are the d-axis compensation amount and q-axis compensation amount of the passive control circulating current voltage, respectively, i ^* _cird and i ^* _cirq are the d-axis component reference value and q of the double frequency of the three-phase circulating current, respectively The reference value of the shaft component, ω ₀ is the fundamental angular frequency, L _m is the bridge arm inductance, R _m is the bridge arm resistance, i _cird and i _cirq are the actual value of the d-axis component and the q-axis component of the double frequency of the three-phase circulating current, respectively The actual value, r _a1 and r _a2 are the injected positive damping parameters, that is, the injected damping matrix

S24. Based on the backstepping control theory, by equivalently transforming the circulation dynamic equation, and defining the progressive tracking error, the MMC circulation suppression backstepping control law is obtained; S25, combining the MMC circulation suppression passive control law and the MMC circulation suppression backstepping control law to construct an MMC circulation suppression passive backstepping controller. 2. The passive backstepping control method for suppressing the circulating current of the modular multilevel converter according to claim 1, wherein the step S1 specifically comprises the following steps: S11. According to the single-phase equivalent circuit of MMC, the dynamic equation of circulation under the dq rotating coordinate system is obtained; S12, select state variables, input and output variables respectively, and based on the positive definite quadratic energy function, perform equivalent transformation on the circulation dynamic equation to obtain the PCHD model of the MMC circulation. 3. a kind of passive backstepping control method for suppressing the circulating current of modularized multilevel converter according to claim 2, is characterized in that, in described step S11, the dynamic equation of circulating current is specifically:

Among them, ω ₀ is the fundamental angular frequency, L _m is the bridge arm inductance, R _m is the bridge arm resistance, i _cird and i _cirq are the actual value of the d-axis component and the actual value of the q-axis component of the double frequency of the three-phase circulating current, respectively, u _cird and u _cirq are the d-axis compensation amount and the q-axis compensation amount of the three-phase circulating voltage, respectively, d is the differential operator, and t is the time. 4. a kind of passive backstepping control method for suppressing the circulating current of modularized multilevel converter according to claim 3, is characterized in that, in described step S12, state variable, input and output variable are specifically:

where x is the state variable, u is the input variable, y is the output variable, x1 and _x2 are the d _- axis and q-axis components of the state variable, respectively, and u1 and u2 are the d _- axis and q _- axis components of the input variable, respectively Axis components, y ₁ and y ₂ are the d-axis and q-axis components of the output variable, respectively; The positive definite quadratic energy function is specifically:

Among them, H(x) is the energy originally stored in the MMC circulation nonlinear system; The PCHD model of the MMC circulation is specifically:

in,

is the differential of the state variable with respect to time, J(x) is the interconnection matrix, R(x) is the damping matrix, and g(x) is the port matrix. 5. The passive backstepping control method for suppressing the circulating current of the modular multilevel converter according to claim 4, wherein the expected energy function in the step S21 is specifically:

x*=[x ₁ ^* x ₂ ^* ] x _e = xx ^* where H _d (x) is the desired energy, H _a (x) is the energy injected into the system by introducing state feedback control, x _e is the state variable error, D is the inductance matrix, x* is the desired equilibrium point,

and

are the d-axis and q-axis components of the desired equilibrium point, respectively. 6. a kind of passive backstepping control method for suppressing modularized multilevel converter circulating current according to claim 5, is characterized in that, in described step S22, the state equation of MMC circulating current closed-loop system is specifically:

J _d (x)=J(x)+J _a (x) R _d (x)=R(x)+R _a (x) Among them, J _d (x) is the desired interconnection matrix of the system, R _d (x) is the desired damping matrix of the system, and Ja (x) and R _{a (} x) are the injected dissipation matrix and damping matrix, respectively. 7. a kind of passive backstepping control method for suppressing the circulating current of modularized multilevel converter according to claim 6, is characterized in that, in described step S24, the dynamic equation of circulating current is equivalently transformed into:

x ₁ =L _m i _cird x ₂ =L _m i _cirq

a ₂ =2ω ₀ Among them, a ₁ and a ₂ are equivalent transformation coefficients; The progressive tracking error is:

where e ₁ and e ₂ are the progressive tracking errors of i _cird and i _cirq , respectively, The specific control law of MMC circulation suppression backstepping is:

Among them, u ² _cird and u ² _cirq are the d-axis compensation amount and the q-axis compensation amount of the back-step control circulating voltage, respectively, and k ₁ and k ₂ are both back-step control parameters. 8. The passive backstepping control method for suppressing the circulating current of the modular multilevel converter according to claim 7, wherein the circulating current voltage compensation amount in the step S3 is specifically:

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