CN106374765A - Inverter control system of sensor without back electromotive force and control method thereof - Google Patents

Abstract

The invention discloses an inverter control system of a sensor without back electromotive force and a control method thereof. The inverter control system of the sensor without back electromotive force is constructed by using a single-phase bridge-type inverter, a current sensor, a driver, an observer as well as electric wires and signal wires, the signal of the back electromotive force is taken as an unknown periodic function, a time-varying state-space model of the inverter is constructed, a time-varying Lebesgue observer is designed based on the time-varying state-space model, output current information is obtained in combination with the current sensor, the back electromotive force is reconstructed, the reconstructed back electromotive force is introduced into the current model predictive control algorithm of an inverter controller, so that accurate tracking of an output current signal when the inverter is free of the back electromotive force is realized.

Description

Inverter control system without back electromotive force sensor and control method thereof

Technical Field

The invention relates to an inverter control system without a back electromotive force sensor and a control method thereof.

Background

The inverter realizes that energy is changed from a direct current form to an alternating current form by controlling output current of an alternating current end, and is a core device for photovoltaic grid connection and alternating current motor control. The current control method of the inverter is a precondition for ensuring the normal work of the inverter. The conventional control method requires measuring the current and the back electromotive force of the output terminal through a sensor. The back emf can be the mains voltage or the induced emf of an ac motor, etc., depending on the application. High precision sensors increase the cost of the system; and failure of the sensor can result in system failure. Therefore, the controller meaning of few sensors is obvious.

Disclosure of Invention

The invention aims to provide an inverter control system without a back electromotive force sensor and a control method thereof, which can realize high-precision control of inverter current under the condition of not using a voltage sensor, reduce the use of the sensor, reduce the cost of an inverter controller and improve the reliability of the inverter controller.

The invention relates to an inverter control system without a reverse electromotive force sensor, which comprises an inverter, a current sensor, a reverse electromotive force, an observer, a controller and a driver, wherein one end of the inverter inputs direct current, the other end of the inverter outputs inverted alternating current, a current sensor is connected in series on an alternating current circuit, and the current sensor samples a current signal at a certain sampling frequency and sends the current signal to the observer; the observer reconstructs a voltage value of the back electromotive force by utilizing the sampling current signal based on a time-varying state space model; and the voltage value is sent to a controller, the controller generates a control signal based on a current model predictive control algorithm, and the control signal is sent to a driver to generate a corresponding high level and a corresponding low level and is sent to the inverter through a lead.

The control method of the inverter control system without the back electromotive force sensor comprises the following steps:

step 1, a current sensor samples a current signal at a certain sampling frequency, and sends the sampled current signal to an observer for observation;

step 2, the observer takes the sampled current signal and the back electromotive force to be reconstructed as a new state quantity, and an augmented state space model is established:

the sampled current signal is denoted as i_l(t) the back EMF signal to be reconstructed is denoted as U_s(t), the differential equation of the dynamics of the inverter control system is

$i_1{\left(t\right)}^{\′}=\frac{-R}{L}{i}_1\left(t\right)+(U_{dc}\×S-U_s(t\left)\right)---\left(1\right)$

Wherein i_l(t)' is the sampled current signal i_l(t) derivative with time, U_dcThe direct current power supply voltage is L, R, the inductor and the resistor are integrated in a system, S represents a control signal and has a value range of { -1,0,1}, S ═ 1 represents direct input of the direct current voltage, S ═ 0 represents no output of the direct current voltage, and S ═ 1 represents reverse output of the direct current voltage;

considering that the back electromotive force signal under the steady state working condition is a sine function, and the frequency of the back electromotive force signal is 50Hz and U of the power grid voltage_s(t) can be decomposed as the sum of the standard sine and cosine functions with amplitudes a and B, respectively:

U_s(t)＝Asin(ωt)+Bcos(ωt) (2)

where the angular frequency ω is 2 pi f, f is 50Hz, and a and B are constants, U can be calculated by observing the values of parameters a and B by an observer_s(t), namely, the counter electromotive force U can be realized_s(t) reconstructing, and substituting the parameters A and B into the formula (1), so as to obtain a new state space model in the form of an augmentation matrix of the inverter control system, wherein the state space model is a linear time-varying model, i.e. i_l(t) is defined as x₁A and B as new variables x₂、x₃The state space model expanding the formula (1) into the form of an augmented matrix is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\left[\begin{array}{ccc}\frac{-R}{L}& \frac{\cos \left(\mathrm{\ω}t\right)}{L}& \frac{\sin \left(\mathrm{\ω}t\right)}{L}\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]x+U_{dc}\×S\\ y=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]x\end{array}\right.---\left(3\right)$

wherein,represents the derivative of the vector x, y being the output current;

step 3, designing a time-varying Leeberg observer aiming at the formula (3), proving the effectiveness of the Leeberg observer, and realizing the online observation of the parameters A and B in the step 2 so as to reconstruct the back electromotive force U_s(t), the design of the Leiberg observer is based on the Lyapunov function, and the convergence of the Leiberg observer is ensured by adopting the Lassel invariant set principle;

step 4, the back electromotive force U obtained in the step 3 is used_s(t) to a controller, combining the sampled current signal i_l(t) substituting the formula (8) to solve the following optimal problem, generating a control signal S, sending the control signal S to a driver to generate corresponding high and low levels, and sending the control signal S to an inverter through a lead so as to enable a load current i_l(t) tracking the set sinusoidal desired current:

$\begin{array}{cc}\underset{S}{\min }& |i_1^{*}(k+1)-(1-\frac{{\mathrm{RT}}_s}{L})\×i_1(k+1)+U_s\left(k\right)-U_{dc}\×S|\end{array}$

s.t.S∈{-1,0,1} (8)。

the inverter control system without the back electromotive force sensor is constructed by utilizing the single-phase bridge inverter, the current sensor, the driver, the observer, the electric wire and the signal wire, the back electromotive force signal is used as an unknown periodic function, a time-varying state space model of the inverter is constructed, a time-varying Leeberg observer is designed based on the time-varying state space model, the output current information is obtained by combining the current sensor, the back electromotive force is reconstructed, the reconstructed back electromotive force is introduced into a current model prediction control algorithm of the inverter controller, and the accurate tracking of the output current signal of the inverter without the back electromotive force sensor is realized.

Drawings

FIG. 1 is a schematic diagram of an inverter control system without a back EMF sensor in accordance with the present invention;

FIG. 2 is a flow chart of the operation of the present invention;

FIG. 3 is an experimental result of reconstruction of the back EMF from the observed values of A and B of the present invention;

FIG. 4 is an experimental result of the reconstructed back EMF and true value error of the present invention;

FIG. 5 shows the current tracking experiment result based on the back electromotive force observation reconstruction.

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

Detailed Description

The inverter control system without the back electromotive force sensor is constructed by utilizing the single-phase bridge inverter, the current sensor, the driver, the observer, the electric wire and the signal wire, the current sensor is utilized to obtain output current information, the obtained current information is input into the Leeberg observer, the observed back electromotive force signal and the current signal measured by the current sensor are used for reconstructing a voltage value of the back electromotive force, the voltage value is applied to a current model prediction control algorithm of the controller to generate a control signal, the current actually output by the inverter can accurately and quickly track the expected current, and the accurate tracking of the inverter current when the inverter does not have the back electromotive force sensor is realized.

The invention relates to an inverter control system without a back electromotive force sensor, which comprises an inverter 3, a current sensor 4, a back electromotive force 5, an observer 7, a controller 8 and a driver 9, wherein one end of the inverter 3 is input into a direct current power supply 1, the other end of the inverter outputs inverted alternating current, a current sensor 4 is connected in series on an alternating current circuit, and the current sensor 4 samples a current signal at a certain sampling frequency and sends the current signal to the observer 7; the observer 7 reconstructs a voltage value of the back electromotive force 5 by using the sampling current signal based on a time-varying state space model; the voltage value is sent to a controller 8, the controller 8 generates a control signal based on a current model predictive control algorithm, the control signal is sent to a driver 9 to generate a corresponding high level and a corresponding low level, and the control signal is sent to the inverter 3 through a lead, so that the actual current can accurately and quickly track the expected current, and the accurate tracking of the current signal of the inverter without a back electromotive force sensor is realized.

As shown in fig. 2, the method for controlling an inverter control system without a back electromotive force sensor according to the present invention, especially focusing on the reconstruction of the back electromotive force, specifically includes the following steps:

step 1, constructing an inverter control system without a reverse electromotive force sensor, which comprises a single-phase bridge inverter 3, a current sensor 4, a reverse electromotive force 5, an observer 7, a controller 8 and a driver 9, wherein one end of the single-phase bridge inverter 3 inputs a direct current power supply, the other end outputs inverted alternating current, the inverted alternating current is connected in series with the current sensor 4, the current sensor 4 samples a current signal at a certain sampling frequency, and the sampled current signal is sent to the observer 7 for observation after integral amplification and filtering processing;

step 2, the observer 7 takes the sampled current signal and the back electromotive force to be reconstructed as a new state quantity, and an augmented state space model is established:

the sampled current signal is denoted as i_l(t), the back EMF signal to be reconstructedNumber is U_s(t), the dynamic process of the inverter control system can be described as:

$i_1{\left(t\right)}^{\′}=\frac{-R}{L}{i}_1\left(t\right)+(U_{dc}\×S-U_s(s\left)\right)---\left(1\right)$

wherein i_l(t) is the sampled current signal, U_s(t) is a reverse electromotive force, U_dcFor DC supply voltage, L, R for system integrated inductance and resistance, i_l(t)' is i_l(t) a derivative with respect to time, wherein S represents a control signal having a value range of { -1,0,1}, wherein S ═ 1 represents direct input of the dc voltage, S ═ 0 represents no output of the dc voltage, and S ═ 1 represents reverse output of the dc voltage;

considering that the back electromotive force signal under the steady state working condition is a sine function, and the frequency of the back electromotive force signal is 50Hz and U of the power grid voltage_s(t) can be decomposed as the sum of the standard sine and cosine functions with amplitudes a and B, respectively:

U_s(t)＝Asin(ωt)+Bcos(ωt) (2)

where the angular frequency ω 2 π f, f 50Hz, A andb is a constant, and U can be calculated by observing the values of the parameters A and B through an observer 7_s(t), namely, the counter electromotive force U can be realized_s(t) reconstructing, and substituting the parameters A and B into the formula (1), so as to obtain a new state space model in the form of an augmentation matrix of the inverter control system, wherein the state space model is a linear time-varying model, i.e. i_l(t) is defined as x₁A and B as new variables x₂、x₃The state space model developed from the original state space model (i.e., equation (1)) into the form of the augmented matrix is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\left[\begin{array}{ccc}\frac{-R}{L}& \frac{\cos \left(\mathrm{\ω}t\right)}{L}& \frac{\sin \left(\mathrm{\ω}t\right)}{L}\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]x+U_{dc}\×S\\ y=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]x\end{array}\right.---\left(3\right)$

wherein,represents the derivative of the vector x, y being the output current;

step 3, designing a time-varying Leiberg observer 7 according to the formula (3), proving the effectiveness of the Leiberg observer 7, and realizing online observation of the parameters A and B in the step 2, thereby reconstructing the back electromotive force, wherein the specific method comprises the following steps:

step 31 is to construct an observer model based on the inverter model, as shown in equation (4), initialize each state quantity, and when k is equal to 0, the state quantitySetting a parameter l₀The calculation period is Ts, and the state estimation value isCan be measured directly, this artificially constructed system is a state observer, by outputting the errorTo correct the estimation model of the state to make the state estimation valueThe system true state is approached:

$\left\{\begin{array}{c}\stackrel{\·}{\hat{x}}=\left[\begin{array}{ccc}\frac{-R}{L}& \frac{\cos \left(\mathrm{\ω}t\right)}{L}& \frac{\sin \left(\mathrm{\ω}t\right)}{L}\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]\hat{x}+U_{dc}\×S+\left[\begin{array}{c}-l_0\\ \frac{-\cos \left(\mathrm{\ω}t\right)}{L}\\ \frac{-\sin \left(\mathrm{\ω}t\right)}{L}\end{array}\right]\×\tilde{y}\\ \hat{y}=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\hat{x}\end{array}\right.---\left(4\right)$

wherein an error signal is definedThe dynamic system of the error signal is then:

$\stackrel{\·}{\tilde{x}}=\left[\begin{array}{ccc}\frac{-R}{L}-l_0& \frac{\cos \left(\mathrm{\ω}t\right)}{L}& \frac{\sin \left(\mathrm{\ω}t\right)}{L}\\ \frac{-\cos \left(\mathrm{\ω}t\right)}{L}& 0& 0\\ \frac{-\sin \left(\mathrm{\ω}t\right)}{L}& 0& 0\end{array}\right]\stackrel{\·}{\tilde{x}}---\left(5\right)$

if it is confirmed that when t → ∞ the state quantityWill converge on x, i.eApproaching to 0, the Lenberg observer 7 can be proved to observe the parameters A and B, namely the back electromotive force reconstruction method provided by the invention is proved to be effective, and the invention utilizes the design of the Lyapunov function and the Lassel invariant set principle to prove the effectiveness of the Leapunov function;

proposition 1 (design lyapunov function): definition ofI is a diagonal matrix, then V is a lyapunov function;

prove 1. since D is a positive definite diagonal matrix, at the same time

$\begin{array}{cc}\frac{dV}{dt}=-\frac{1}{2}(l_0+\frac{R}{L})& {\tilde{x}}_1^2\≤0\end{array}---\left(6\right)$

Wherein V is continuously differentiable and satisfies:

(1) v (0) ═ 0, for all

(2) At R²⁽ⁿ⁺¹⁾In (1),

therefore, V is a Lyapunov function, and proposition 1 is obtained;

proposition 2 (observer convergence analysis): state quantity of observerConverge to the state quantity x;

proof 2: because the error system is a time-varying system, the effectiveness of the observer 7 is proved by adopting a Lassel invariant set principle as follows:

definition setIt is known to be a consistent positive invariant set of the error system;

definition ofIs the largest invariant set in set S (R);

as is clear from the Lassel invariant set principle, when t → ∞ is reached, each starting point in S (R) converges to E, that is, for any arbitrary pointAll satisfy

At the same time, for Satisfy the requirement of

Since the set { cos (ω t) sin (ω t) } is linearly independent, the above equation solution exists and is unique,i.e. maximum invariant setIs a single element set, the elements of which are the original points, and the proposition 2 is determined;

step 4, discrete implementation of observer 7

From the observer equation:

$\{\begin{array}{c}\stackrel{\·}{\hat{x}}={\hat{a}}_0+\hat{A}cos\left(\mathrm{\ω}t\right)+\hat{B}sin\left(\mathrm{\ω}t\right)-1_0(\hat{y}-y)\\ \hat{A}=-\cos \left(\mathrm{\ω}t\right)(\hat{y}-y)\\ \hat{B}=-\sin \left(\mathrm{\ω}t\right)(\hat{y}-y)\\ y=x_1\\ \hat{y}={\hat{x}}_1\end{array}---\left(7\right)$

at the moment k, the collected current signal is integrated to obtain x₁(k) Writing a continuous observer into a discrete form, wherein the estimated value of each state at the k +1 moment is as follows:

$\left\{\begin{array}{c}{\hat{x}}_1(k+1)=Ts\[\hat{A}\left(k\right)\cos \left(\mathrm{\θ}\right(k)+\hat{B}(k\left)\sin \right(\mathrm{\θ}\left(k\right)-(l_0+\frac{R}{L})\left({\hat{x}}_1\right(k)-x_1(k\left)\right)\]+{\hat{x}}_1\left(k\right)\\ \hat{A}(k+1)=-Ts\cos \left(\mathrm{\θ}\right(k)\left({\hat{x}}_1\right(k)-x_1(k\left)\right)+\hat{A}\left(k\right)\\ \hat{B}(k+1)=-Ts\sin \left(\mathrm{\θ}\right(k\left)\right)\left({\hat{x}}_1\right(k)-x_1(k\left)\right)+\hat{B}\left(k\right)\end{array}\right.$

calculating errorWhen the relative error approaches 5%, the error is considered to be converged, the requirement is met, and the state estimation value is obtainedThe real state of the system is approached to obtain parametersSo that the frequency components at the moment k can be calculated, and the amplitude and the phase of the fundamental wave and each harmonic wave are further calculated; if the relative error does not meet the requirement, the observer 7 enters the next iteration and utilizes the output current i_l(t) correcting parameters a and B by the error of the measured value from the observed value; substituting the obtained parameter A, B into equation (2) to obtain the back electromotive force U_s(t)；

Noting the expected current as i_lT, the value at the k-th sampling instant is denoted i_lX (k) of U_s(k) And the actually measured output current i_l(k) Solving the following optimal problem:

$\begin{array}{cc}\underset{S}{\min }& |i_1^{*}(k+1)-(1-\frac{{\mathrm{RT}}_s}{L})\×i_1(k+1)+U_s\left(k\right)-U_{dc}\×S|\end{array}$

s.t.S∈{-1,0,1} (8)

namely, high-precision tracking of the current is realized, as shown in fig. 5;

step 5, the back electromotive force U is processed_sAnd (t) is sent to the controller 8, the controller 8 generates a control signal S based on the formula (8) (i.e. a current model predictive control algorithm), and the control signal S is sent to the driver 9 to generate a corresponding high level and a corresponding low level, and is sent to the inverter 3 through a lead, so that the actual current accurately and quickly tracks the expected current.

In order to verify the control effectiveness of the non-back electromotive force sensor, an experiment platform without the back electromotive force sensor is built. Fig. 3 and 4 reflect the process of identifying the back electromotive force, the back electromotive force is changed from 3V to 1.6V, and the observer identifies a new value in five cycles, as shown in fig. 3. And under the two different back electromotive forces, the error between the identification value and the true value is kept within 0:2V, as shown in FIG. 4. Fig. 5 illustrates that the tracking current is substantially unaffected by the jump to accurately track the desired current. Therefore, the control of the non-back electromotive force sensor of the invention does not reduce the reliability of the system; meanwhile, the use of sensors can be reduced, and the cost of the inverter controller is reduced.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the technical scope of the present invention, so that any minor modifications, equivalent changes and modifications made to the above embodiment according to the technical spirit of the present invention are within the technical scope of the present invention.

Claims (2)

1. An inverter control system without a reverse electromotive force sensor is characterized by comprising an inverter, a current sensor, a reverse electromotive force sensor, an observer, a controller and a driver, wherein one end of the inverter inputs direct current, the other end of the inverter outputs inverted alternating current, a current sensor is connected in series on an alternating current circuit, and the current sensor samples a current signal at a certain sampling frequency and sends the current signal to the observer; the observer reconstructs a voltage value of the back electromotive force by utilizing the sampling current signal based on a time-varying state space model; and the voltage value is sent to a controller, the controller generates a control signal based on a current model predictive control algorithm, and the control signal is sent to a driver to generate a corresponding high level and a corresponding low level and is sent to the inverter through a lead.

2. The control method of the inverter control system without the back electromotive force sensor according to claim 1, comprising the steps of:

step 1, a current sensor samples a current signal at a certain sampling frequency, and sends the sampled current signal to an observer for observation;

step 2, the observer takes the sampled current signal and the back electromotive force to be reconstructed as a new state quantity, and an augmented state space model is established:

the sampled current signal is denoted as i_l(t) the back EMF signal to be reconstructed is denoted as U_s(t), the differential equation of the dynamics of the inverter control system is

$i_l{\left(t\right)}^{\′}=\frac{-R}{L}{i}_l\left(t\right)+(U_{dc}\×S-U_s(t\left)\right)---\left(1\right)$

Wherein i_l(t)' is the sampled current signal i_l(t) timeDerivative of, U_dcThe direct current power supply voltage is L, R, the inductor and the resistor are integrated in a system, S represents a control signal and has a value range of { -1,0,1}, S ═ 1 represents direct input of the direct current voltage, S ═ 0 represents no output of the direct current voltage, and S ═ 1 represents reverse output of the direct current voltage;

considering that the back electromotive force signal under the steady state working condition is a sine function, and the frequency of the back electromotive force signal is 50Hz and U of the power grid voltage_s(t) can be decomposed as the sum of the standard sine and cosine functions with amplitudes a and B, respectively:

U_s(t)＝Asin(ωt)+Bcos(ωt) (2)

where the angular frequency ω is 2 pi f, f is 50Hz, and a and B are constants, U can be calculated by observing the values of parameters a and B by an observer_s(t), namely, the counter electromotive force U can be realized_s(t) reconstructing, and substituting the parameters A and B into the formula (1), so as to obtain a new state space model in the form of an augmentation matrix of the inverter control system, wherein the state space model is a linear time-varying model, i.e. i_l(t) is defined as x₁A and B as new variables x₂、x₃The state space model expanding the formula (1) into the form of an augmented matrix is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\left[\begin{array}{ccc}\frac{-R}{L}& \frac{cos\left(\mathrm{\ω}t\right)}{L}& \frac{sin\left(\mathrm{\ω}t\right)}{L}\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]x+U_{dc}\×S\\ y=\[\begin{array}{ccc}1& 0& 0\end{array}\]x\end{array}\right.---\left(3\right)$

wherein,represents the derivative of the vector x, y being the output current;

step 3, designing a time-varying Leeberg observer aiming at the formula (3), proving the effectiveness of the Leeberg observer, and realizing the online observation of the parameters A and B in the step 2 so as to reconstruct the back electromotive force U_s(t), the design of the Leiberg observer is based on the Lyapunov function, and the convergence of the Leiberg observer is ensured by adopting the Lassel invariant set principle;

step 4, the back electromotive force U obtained in the step 3 is used_s(t) to a controller, combining the sampled current signal i_l(t) substituting the formula (8) to solve the following optimal problem, generating a control signal S, sending the control signal S to a driver to generate corresponding high and low levels, and sending the control signal S to an inverter through a lead so as to enable a load current i_l(t) tracking the set sinusoidal desired current:

$\begin{array}{cc}\underset{S}{\min }& |i_l^{*}(k+1)-(1-\frac{{\mathrm{RT}}_s}{L})\×i_l(k+1)+U_s\left(k\right)-U_{dc}\×S|\\ s.t.& S\∈\{-1,0,1\}\end{array}---\left(8\right).$