CN111211701B - A sensor-less model predictive control method for three-phase voltage source rectifier - Google Patents
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- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
- H02M7/02—Conversion of AC power input into DC power output without possibility of reversal
- H02M7/04—Conversion of AC power input into DC power output without possibility of reversal by static converters
- H02M7/12—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M7/21—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M7/217—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M7/219—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only in a bridge configuration
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Abstract
一种三相电压源型整流器的少传感器模型预测控制方法，包括如下步骤：1)获得三相电网电压的A相电压、三相电流，三相相位信息；2)建立B相电路的数学模型，将B相电压展开为傅里叶级数，取B相电流和B相电压展开的傅里叶级数的每一项系数作为状态变量，并结合相位信息设计状态观测器，计算得到B相电压的估计值；3)仿照步骤2，计算得到C相电压的估计值；4)结合得到的三相电压和三相电流，根据三相电压源型PWM整流器的拓扑建立其数学模型，利用一阶前向欧拉近似将该数学模型离散化得到电流的预测方程；5)设计价值函数，通过比较价值函数在不同开关状态下的值，选出最优的开关状态实现电流的控制。本发明降低应用成本，增强适应环境的能力。
A sensor-less model predictive control method for a three-phase voltage source type rectifier, comprising the following steps: 1) obtaining A-phase voltage, three-phase current, and three-phase phase information of a three-phase grid voltage; 2) establishing a mathematical model of a B-phase circuit , expand the B-phase voltage into a Fourier series, take each coefficient of the Fourier series expanded by the B-phase current and the B-phase voltage as a state variable, and design a state observer combined with the phase information to calculate the B-phase The estimated value of the voltage; 3) following step 2, calculate the estimated value of the C-phase voltage; 4) combine the obtained three-phase voltage and three-phase current, establish its mathematical model according to the topology of the three-phase voltage source type PWM rectifier, and use a The first-order forward Euler approximation discretizes the mathematical model to obtain the prediction equation of the current; 5) Design the value function, and select the optimal switch state to control the current by comparing the value of the value function in different switching states. The invention reduces the application cost and enhances the ability to adapt to the environment.
Description
Technical Field
The invention relates to the field of control of power electronic converters, in particular to a few-sensor model prediction control method of a three-phase voltage source type rectifier.
Background
In recent years, power electronics technology has been developed at a high speed, a rectifier has attracted attention as an important converter, the rectifier can convert alternating current into direct current, and the rectifier is widely applied to conversion of a grid-connected power system, particularly wind power generation, a micro-grid, a distributed power generation system and the like. Among various types of rectifiers, a three-phase voltage source type PWM rectifier has become a research focus of the rectifier with advantages of simple structure, high efficiency, reliability, convenient control, high energy storage efficiency, and the like. Generally speaking, to realize the control of the rectifier, information of the voltage and current of the power grid needs to be obtained, which requires the use of sensors for acquisition, and the use of sensors increases hardware cost and is not strong in adaptability to the environment. In addition, in the area with weak power grid, the condition of power grid voltage distortion is also common.
Disclosure of Invention
The invention mainly aims to realize the current control of a rectifier of a few-voltage sensor under the condition of power grid voltage distortion so as to obtain low-distortion input current, low-ripple direct current side voltage and unit/adjustable power factor, and provides a few-sensor model prediction control method of a three-phase voltage source type rectifier.
The invention adopts the following technical scheme:
a few-sensor model predictive control method of a three-phase voltage source type rectifier is characterized by comprising the following steps:
1) the method comprises the steps that A phase voltage and three-phase current of three-phase power grid voltage are obtained through a sensor, phase information of the A phase voltage is detected through a phase-locked loop, and frequency information of B, C two-phase voltage is the same as the A phase;
2) establishing a mathematical model of the B-phase circuit, expanding the B-phase voltage into a Fourier series, taking each term coefficient of the B-phase current and the Fourier series expanded by the B-phase voltage as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the B-phase voltage by using the information obtained by the observer;
3) establishing a mathematical model of the C-phase circuit, expanding the C-phase voltage into a Fourier series, taking each term coefficient of the Fourier series after the C-phase current and the C-phase voltage are expanded as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the C-phase voltage by using the information obtained by the observer;
4) combining the three-phase voltage and the three-phase current obtained in the steps, establishing a mathematical model of the three-phase voltage source type PWM rectifier according to the topology of the three-phase voltage source type PWM rectifier, and discretizing the mathematical model of the rectifier by utilizing first-order forward Euler approximation to obtain a prediction equation of the current;
5) and designing a cost function, and selecting an optimal switching state to realize current control by comparing values of the cost function in different switching states.
Preferably, the B-phase voltage is expanded into a fourier series, specifically as follows:
wherein ebIs the phase of B phase voltage, theta is the phase, a0Represents ebA direct current component ofiAnd biRepresents ebN represents ebThe highest order of the harmonic orders contained.
Preferably, the mathematical model is established according to the topology of the three-phase voltage source type PWM rectifier, and the mathematical model is as follows:
wherein eaIs the voltage of the A-phase,
is an estimate of the C-phase voltage,
is an estimate of the B-phase voltage, ia，ib、icPhase A current, phase B current and phase C current, R and L are the filter inductance and equivalent impedance of the rectifier interface circuit, Uao＝SaUdc+Uno，Ubo＝SbUdc+Uno，Uco＝ScUdc+Uno,UdcRepresenting the DC-side bus voltage of the rectifier, UnoRepresenting the voltage between the negative pole of the capacitor on the DC side and the midpoint of the three-phase supply, Sa、Sb、ScIs a switch of a rectifier.
Preferably, the prediction equation of the current is as follows:
wherein T iss＝5e-5Is the sampling period.
Preferably, the cost function is as follows:
wherein
A, B, C reference values of the three-phase current, respectively, the optimum switching state being the combination of switches which minimizes J。
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
1. the invention reduces the use of voltage sensors, and compared with the traditional rectifier control method, the invention reduces the cost of the rectifier in practical application and enhances the environment-adaptive capacity of the rectifier.
2. The observer can also be used for solving the problem that the power grid voltage is distorted, namely when the power grid voltage is unbalanced and contains harmonic waves or fundamental frequency fluctuation, the observer provided by the invention can still be used for detecting the power grid voltage, so that the current control is realized, and the effects of sinusoidal input current, low ripple direct current side voltage and unit or adjustable power factor are obtained.
Drawings
Fig. 1 is a topology of a three-phase voltage source type PWM rectifier.
Fig. 2 is a control block diagram of the low sensor approach proposed by the present invention.
Fig. 3 is a flowchart of a program used in the control method of the present invention.
Fig. 4 is a comparison of the B-phase voltage reconstructed using the B-phase observer and the B-phase true voltage.
Fig. 5 is a comparison of the reconstructed C-phase voltage and the C-phase real voltage using a C-phase observer.
Fig. 6, 7, and 8 show A, B, C three-phase currents.
Fig. 9 is harmonic distortion (THD) of three-phase current.
Fig. 10 is the output voltage of the rectifier, i.e. the voltage across the load.
Wherein: e.g. of the typea、eb、ecFor the input three-phase AC voltage, R and L are respectively resistance and filter inductance, Sa、Sb、Sc、
Is a switch of a rectifier, SiAnd
the switch states of (2) are opposite. C is a DC side filter capacitor, RLIs the load impedance.
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
Referring to fig. 2 and 3, a method for predictive control of a three-phase voltage source type rectifier using a few-sensor model,
1) the method comprises the steps of obtaining A-phase voltage and three-phase current of three-phase power grid voltage by using a sensor, wherein the three-phase current comprises the A-phase current, the B-phase current and the C-phase current, and obtaining phase information theta of the A-phase voltage by using a phase-locked loop (PLL), wherein the frequency of the two phases of B, C is the same as that of the A-phase.
2) Establishing a mathematical model of the B-phase circuit, expanding the B-phase voltage into a Fourier series, taking each term coefficient of the B-phase current and the Fourier series expanded by the B-phase voltage as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the B-phase voltage by using the information obtained by the observer. The method comprises the following specific steps:
performing Fourier series decomposition on the B-phase voltage:
a0represents ebA direct current component ofiAnd biRepresents ebN represents ebThe highest order of the harmonic orders contained.
A mathematical model of the B-phase circuit is constructed from the topology of the rectifier (see fig. 1) as follows:
r and L are the resistance and filter inductance of the rectifier interface circuit, respectively.
Taking the state variable as X ═ X1,x2,x3,x4,...,x2n+1,x2n+2]T＝[ib,a0,a1,b1,...,an,bn]TThe following state observer is designed by combining the formula (2) and is used for estimating the coefficient of each term after Fourier decomposition of the phase voltage of the B phase
Wherein L is0,La0,La1,Lb1,…,Lan,LbnAre all constants greater than zero. "^" represents the estimated value of the variable, the estimated value of the B-phase voltage reconstructed using the observer is:
3) performing Fourier series decomposition on the C-phase voltage, establishing a mathematical model of the C-phase circuit, taking each term coefficient of the Fourier series after the C-phase current and the C-phase voltage are expanded as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the C-phase voltage by using the information obtained by the observer
4) And combining the three-phase voltage and the three-phase current obtained in the steps, establishing a mathematical model of the three-phase voltage source type PWM rectifier according to the topology of the three-phase voltage source type PWM rectifier, and discretizing the mathematical model of the rectifier by utilizing first-order forward Euler approximation to obtain a prediction equation of the current. The method comprises the following specific steps:
obtained in conjunction with an observer
And
topology based on three-phase voltage source type rectifier(FIG. 1) to obtain:
wherein, Uao＝SaUdc+Uno，Ubo＝SbUdc+Uno，Uco＝ScUdc+Uno，UdcRepresenting the DC-side bus voltage of the rectifier, UnoRepresenting the voltage between the negative pole of the capacitor on the DC side and the midpoint of the three-phase supply, Sa、SbAnd ScThe combinations of values of (A) are shown in Table 1.
TABLE 1
From equation (5) to obtain UnoThe calculation formula of (a) is as follows:
discretizing the formula (5) by utilizing a first-order forward Euler approximation to obtain a prediction formula of the three-phase current, wherein the prediction formula is as follows:
wherein T iss＝5e-5Is a sampling period, under different switch states, the current prediction value under each switch combination is calculated according to a formula (7),
5) and designing a cost function, and selecting an optimal switching state to realize current control by comparing values of the cost function in different switching states.
The design cost function is as follows:
In order to verify the feasibility of the method proposed by the present invention, the following is a result of simulation of the algorithm by the simulation software MATLAB/SIMULINK, where the simulation parameters are shown in table 2, and T issRepresenting the sampling period.
TABLE 2
The three-phase voltage used by the simulation is balanced and free of harmonic before 2.5s, the three-phase voltage contains harmonic and is unbalanced after 2.5s, and fig. 4 and 5 respectively show the comparison between B, C two-phase voltage and the real value thereof and the error curve between the real value and the observed value, which are observed by an observer, and as can be seen from the graphs, the observer provided by the invention can well detect B, C two-phase voltage. Fig. 6 is a comparison of the a-phase current and its reference current and the error curve therebetween, and fig. 7 and 8 are comparisons between currents of B, C two phases and their reference currents, respectively. It can be seen that the current of each phase can be well tracked with the reference current, the dynamic response is fast, the accuracy is high, fig. 9 shows the harmonic distortion rate (THD) of the three-phase current, and it can be seen from the graph that after 2.5s, namely even under the condition of the grid voltage distortion, the THD of the three-phase current can be lower than 4% by using the method, which also verifies the feasibility of the control method provided by the present invention. FIG. 10 is a DC voltage U output by the rectifierdcAs can be seen from the figure, UdcThe voltage of the power grid can be stabilized to a certain value under the condition of voltage distortion of the power grid, and the transition time of the voltage can be influenced by the filter capacitor C on the direct current side.
The simulation result verifies the feasibility of the less-sensor control method of the three-phase voltage source type PWM rectifier provided by the invention. The observer provided by the invention can detect the voltages of other two phases according to the voltage information of one phase in the three-phase power grid voltage, thereby reducing the use of voltage sensors, being capable of normally working even if the three-phase voltage contains harmonic waves or is unbalanced, and having good robustness.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.
Claims (3)
1. A few-sensor model predictive control method of a three-phase voltage source type rectifier is characterized by comprising the following steps:
1) the method comprises the steps that A phase voltage and three-phase current of three-phase power grid voltage are obtained through a sensor, phase information of the A phase voltage is detected through a phase-locked loop, and frequency information of B, C two-phase voltage is the same as the A phase;
2) establishing a mathematical model of the B-phase circuit, expanding the B-phase voltage into a Fourier series, taking each term coefficient of the B-phase current and the Fourier series expanded by the B-phase voltage as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the B-phase voltage by using the information obtained by the observer;
3) establishing a mathematical model of the C-phase circuit, expanding the C-phase voltage into a Fourier series, taking each term coefficient of the Fourier series after the C-phase current and the C-phase voltage are expanded as a state variable, designing a state observer by combining the phase information obtained in the step 1), and calculating to obtain an estimated value of the C-phase voltage by using the information obtained by the observer;
4) combining the three-phase voltage and the three-phase current obtained in the steps, establishing a mathematical model of the three-phase voltage source type PWM rectifier according to the topology of the three-phase voltage source type PWM rectifier, and discretizing the mathematical model of the rectifier by utilizing first-order forward Euler approximation to obtain a prediction equation of the current, wherein the mathematical model is as follows:
wherein eaIs the voltage of the A-phase,
is an estimate of the C-phase voltage,
is an estimate of the B-phase voltage, ia，ib、icPhase A current, phase B current and phase C current, R and L are the filter inductance and equivalent impedance of the rectifier interface circuit, Uao＝SaUdc+Uno，Ubo＝SbUdc+Uno，Uco＝ScUdc+Uno,UdcRepresenting the DC-side bus voltage of the rectifier, UnoRepresenting the voltage between the negative pole of the capacitor on the DC side and the midpoint of the three-phase supply, Sa、Sb、ScA switch that is a rectifier;
the prediction equation of the current is as follows:
wherein T iss＝5e-5Is the sampling period;
5) and designing a cost function, and selecting an optimal switching state to realize current control by comparing values of the cost function in different switching states.
2. The few-sensor model predictive control method of the three-phase voltage source type rectifier according to claim 1, characterized in that the B-phase voltage is developed into a Fourier series, specifically as follows:
wherein ebIs the phase of B phase voltage, theta is the phase, a0Represents ebA direct current component ofiAnd biRepresents ebN represents ebThe highest order of the harmonic orders contained.
3. The method of claim 1, wherein the cost function is as follows:
wherein
A, B, C, the optimal switching state is the switching combination that minimizes J.
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