CN110112940B - PWM rectifier self-adaptive sliding mode QPIR control method based on αβ coordinate system - Google Patents
PWM rectifier self-adaptive sliding mode QPIR control method based on αβ coordinate system Download PDFInfo
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Abstract
The invention discloses a QPIR (pulse-width modulation) control method for a PWM (pulse-width modulation) rectifier based on an αβ coordinate system, belonging to the technical field of power electronics and control thereofdref(ii) a II, obtaining idrefAs a given value of the active current of the inner ring, a given value of reactive iqrefSet to zero and output via a two-phase stationary αβ coordinate system
Thirdly, the mixture is prepared
And i of the grid sideα、iβComparing, and obtaining the current error through QPIR controller
And
fourthly, the obtained
And controlling the VSR to operate through SVPWM. According to the invention, self-adaptive sliding mode control is adopted, and compared with the traditional sliding mode controller which cannot track the change of sudden load change, the response characteristic of the system is improved; the inner ring adopts a quasi-proportional-integral resonance regulator, and the problems that the traditional PI controller is slow in tracking and regulating speed of a current inner ring reference instruction, has static errors, and is weak in inhibiting capacity of distortion disturbance of power grid voltage and the like are solved.
Description
Technical Field
The invention belongs to the technical field of power electronics and control thereof, and particularly relates to a PWM (pulse-width modulation) rectifier self-adaptive sliding mode QPIR (quadrature phase-locked loop) control method based on an αβ coordinate system.
Background
The control algorithm is the core of the PWM rectifier, and the quality of the control algorithm directly determines the operation effect of the rectifier. The primary purpose of the PWM rectifier is to maintain dc voltage stabilization and net side input current sinusoid. The traditional control strategies mainly comprise a current closed-loop vector control strategy (VOC) and a direct power control strategy (DPC). The vector control strategy based on the current closed loop has slow dynamic response and poor anti-interference performance on the disturbance such as power grid harmonic wave, load change and the like. The power inner loop of the DPC control strategy has the advantages of fast dynamic response and simple algorithm, but the adoption of the hysteresis comparator causes the system to have the defects of unfixed switching frequency, difficult filter design and the like. In addition, according to the imbalance of three-phase voltages and the difference of filtering modes, a control method when the three-phase voltages are unbalanced, a control method adopting an LCL filter and an LC filter and the like are provided in the prior art. In order to obtain a higher performance PWM rectifier, the following methods have been proposed by the scholars:
(1) based on Lyapunov stability theory control
The Lyapunov exponent describes the convergence characteristics of adjacent trajectories in system space. Because the three-phase PWM rectifier has the characteristics of strong coupling and multivariable, the traditional analysis method is difficult to meet the requirement of the rectifier on the stability in a large range. The HasanKomurugil establishes the Lyapunov equation of the PWM rectifier by taking the filter inductance of the rectifier and the energy storage capacitor on the direct current side as variables, and can intuitively judge the stability of the system according to the Lyapunov index. If the Lyapunov exponent is larger than zero, the system is unstable, otherwise, the system is stable. The Lyapull Ruff theory can effectively solve the control problem of VSR stability in a large range. The control method is based on a specific mathematical model which is constructed, the higher the accuracy of the model is, the better the performance of the system is, but since the construction method of the energy function is not unique, how to construct the most appropriate energy function is a key point of the control method, and the dynamic performance of the control method is deviated.
(2) Sliding mode variable structure control (SMC)
SMC is a nonlinear control characterized by "structural" uncertainty, which is made to follow a preset "sliding mode" trajectory as the current state of the system changes. The PWM rectifier is controlled by the sliding mode variable structure, so that the interference of power grid harmonic waves and load fluctuation can be effectively inhibited, and the method has the advantages of strong robustness, quick dynamic response and simple control structure. However, due to factors such as limited system inertia and system control energy, buffeting is generated when the state point passes through the switching surface, and system stability is affected. Buffeting is inherent and can only be attenuated but not eliminated.
(3) PWM rectifier control under grid imbalance condition
The main causes of grid imbalance are: three-phase load unbalance, asymmetric faults of a power grid (faults such as single-phase grounding short circuit, two-phase interphase short circuit and the like), operation of high-power single-phase load, non-full-phase transposition of a power transmission line and the like. Under the condition of unbalanced power grid, the performance requirements of the PWM rectifier are difficult to meet by the conventional method, and the negative sequence voltage of the PWM rectifier can generate low-order harmonic (mainly secondary harmonic), so that the normal operation of the rectifier is influenced, and even equipment is damaged. The negative sequence current of the rectifier is eliminated by adopting positive and negative sequence decomposition or adopting a method of a resonance regulator, so that low-order current harmonic waves are eliminated, and the performance of the rectifier is improved. However, the method needs to extract the positive and negative sequence components and the harmonic component of the voltage and the current of the power grid, needs a large number of filters and calculation links, is complex to implement, and is difficult to ensure the control effect due to the delay of a control system.
Disclosure of Invention
1. Technical problem to be solved by the invention
The invention aims to overcome the defects that the traditional PI controller is low in tracking and adjusting speed of a current inner loop reference instruction, has static errors, weak in inhibiting capacity of distortion disturbance of power grid voltage, poor in anti-interference performance of disturbance on load change and the like, and meanwhile, the traditional sliding mode controller cannot track the change when load sudden change occurs, so that the response characteristic of a system is influenced, and provides a PWM rectifier self-adaptive sliding mode QPIR control method based on an αβ coordinate system.
2. Technical scheme
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
the invention discloses a PWM (pulse-width modulation) rectifier self-adaptive sliding mode QPIR (quadrature-phase quadrature) control method based on an αβ coordinate system, which comprises the following steps of:
step one, taking the direct current bus voltage at the rectifying side as an outer ring, and obtaining a given value i of active current through a self-adaptive sliding mode controllerdref；
Step two, obtaining a given value idrefAnd given iqrefObtaining a current instruction value through a coordinate transformation module
Step three, obtaining the current instruction value
And i of the grid sideα、iβComparing, and obtaining the current error through QPIR controller
And
step four, finally obtaining
And controlling the VSR to operate through SVPWM.
Furthermore, in the step one, an adaptive sliding mode controller is adopted to form a voltage outer loop, and the error between the reference value and the actual value is taken as the state variable of the control system, namely the error e of the state variable is selectedv＝vdcref-vdcThe sliding mode surface switching function is selected as follows:
in the formula, vdcrefFor a given reference voltage, vdcβ feedback system for variable structure control of DC side output voltageNumber is equal to the DC side output voltage vdcA time constant associated with the first order response;
by detecting load current i in real timeLTo reconstruct the load resistance RLThe formula is:
will be provided with
Substituting the formula to obtain:
when the three-phase PWM rectifier operates at the unit power factor iq＝0，eq＝0，diqIf/dt is 0, then sq＝-ωLid/vdc(ii) a Under steady state conditions, idLet Ldi be DCd(dt is 0, available as s)d＝-(ed-Rid)/vdc(ii) a Under the condition of coordinate transformation with equal power,
Urmsthe effective value of the input phase voltage at the network side is given by the given reference voltage vdcrefIs constant, then dvdcref(dt is 0) and s isd、sqThe substitution formula is simplified and obtained
The outer loop voltage regulation equation is thus obtained, the output of which is taken as the given reference value of the current inner loop:
in the formula iLFor load current, C represents DC side capacitance, R represents inductance and impurities on lineThe dispersion impedance.
Further, the given value i to be obtained in step twodrefAnd given iqrefThe values on the stationary coordinate system of the two phases αβ are obtained by the synchronous rotating coordinate inverse transformation, i.e. 2r/2s transformation
And
the transformation formula is as follows:
wherein θ is the angle between d axis and α axis in the transformed coordinate system.
Furthermore, the current instruction value obtained in step three
And i of the grid sideα、iβComparing, specifically:
the current error is obtained by QPIR controller
And
in particular to
In the above formula, the resonant frequency ω0＝2πf≈314rad/s，KPAnd KIAre respectively the ratio and the integral coefficient, KRIs the resonant gain coefficient, ωcIs the cut-off frequency.
Further, step four is obtained by
Judging the sector where the space vector is located and calculating the action time of the space vector:
wherein T is the PWM period, T1Time of action, T, of the space vector V12Is the action time of the space vector V2;
similarly, the action time of the space vector of other sectors can be obtained; then, space vector switching points Tcm1, Tcm2 and Tcm3 are determined according to the located sectors, and finally, the IGBT is turned on according to the space vector switching points to generate PWM waveforms, so that the VSR is controlled to operate.
3. Advantageous effects
Compared with the prior art, the technical scheme provided by the invention has the following remarkable effects:
(1) according to the PWM rectifier self-adaptive sliding mode QPIR control method based on the αβ coordinate system, a QPIR controller is expanded into rectifier closed-loop control, error-free tracking adjustment of alternating current signals is achieved, and current disturbance can be effectively suppressed when the voltage of a power grid is distorted;
(2) according to the PWM rectifier self-adaptive sliding mode QPIR control method based on the αβ coordinate system, parameter selection basis of a QPIR controller is provided by controlling a variable method and defining harmonic impedance, and meanwhile, the self-adaptive sliding mode variable structure is introduced to control and improve the dynamic performance of a system and enhance the load disturbance resistance;
(3) the PWM rectifier self-adaptive sliding mode QPIR control method based on the αβ coordinate system overcomes the problems that a traditional PI controller is low in tracking and adjusting speed of a current inner loop reference instruction, has static errors, is weak in suppression capability of distortion disturbance of power grid voltage, and is poor in anti-interference performance of disturbance such as load change, and meanwhile, the response characteristic of a system is affected by the fact that the traditional sliding mode controller cannot track the change when load mutation occurs.
Drawings
FIG. 1 is a main circuit structure diagram of a three-phase PWM rectifier according to the present invention;
FIG. 2 is a root trace diagram of a PIR controller according to the present invention;
FIG. 3 is a bode diagram of PIR and quasi-PIR controllers in the present invention, in which FIG. 3(a) is an ideal bode diagram of the PIR controller, and FIG. 3(b) is a comparison diagram of frequency characteristics of the PIR and quasi-PIR controllers;
FIG. 4 is a schematic block diagram of a quasi-PIR controller according to the present invention;
FIG. 5 is a diagram showing the effect of the parameter change on the amplitude-frequency characteristic of the PIR controller in the present invention, wherein K is shown in FIG. 5(a)PAmplitude-frequency characteristic diagram of controller in variation, where K is shown in FIG. 5(b)IThe amplitude-frequency characteristic diagram of the controller in variation, where K is shown in FIG. 5(c)RThe amplitude-frequency characteristic diagram of the controller at the time of change, W in FIG. 5(d)CThe amplitude-frequency characteristic diagram of the controller during variation;
FIG. 6 is a schematic block diagram of an adaptive sliding mode variable architecture controller according to the present invention;
FIG. 7 is a block diagram of a three-phase PWM rectifier control system according to the present invention;
FIG. 8(a) of FIG. 8 is a block diagram of a harmonic compensation quasi-PIR controller; FIG. 8(b) of FIG. 8 is a harmonic compensation bode diagram;
FIG. 9 is a simulated waveform diagram of the DC side output voltage and the grid side input current at the time of system startup and sudden load change under normal grid voltage; fig. 9(a) is a simulated waveform diagram of the output voltage at the dc side and the input current at the grid side when the system is started under the control of the conventional sliding mode QPR; fig. 9(b) is a simulation waveform diagram of the output voltage at the dc side and the input current at the grid side when the load suddenly changes under the control of the conventional sliding mode QPR; FIG. 9(c) is a simulated waveform diagram of the output voltage at the DC side and the input current at the grid side when the system is started under the control of the adaptive sliding mode QPIR; fig. 9(d) is a simulation waveform diagram of the dc side output voltage and the grid side input current when the load suddenly changes under the adaptive sliding mode QPIR control.
FIG. 10 is a simulated waveform diagram of the DC side output voltage and the grid side input current when the grid side voltage and current waveforms and the load suddenly change under the grid voltage distortion in the present invention; fig. 10(a) is a simulated waveform diagram of the output voltage at the dc side and the input current at the grid side when the load suddenly changes under the control of the conventional sliding mode QPR; fig. 10(b) is a power grid side voltage and current waveform diagram under the control of the conventional sliding mode QPR; FIG. 10(c) is a simulated waveform diagram of the DC-side output voltage and the grid-side input current when the load suddenly changes under the control of the adaptive sliding-mode QPIR; fig. 10(d) is a power grid side voltage and current waveform diagram under adaptive sliding mode QPIR control.
FIG. 11 shows the grid side input voltage and current THD under the grid voltage distortion of the present invention; wherein, fig. 11(a) is the grid side voltage; fig. 11(b) shows the grid-side current under the control of the conventional sliding mode QPIR; fig. 11(c) shows the grid-side current under adaptive sliding-mode QPIR control.
Fig. 12 is a schematic diagram of a three-phase PWM rectifier control system according to the present invention.
The reference numerals in the schematic drawings illustrate:
i, a self-adaptive sliding mode controller; II, a coordinate transformation module; III, a quasi-PIR controller; IV, a space vector modulation module (SVPWM); v, a rectifier bridge.
Detailed Description
For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1
Referring to the drawings, the structure of a control system of the QPIR control method based on the adaptive sliding mode of the PWM rectifier under the αβ coordinate system in the normal power grid condition is shown in fig. 12, and the QPIR control method includes an adaptive sliding mode controller i, a coordinate transformation module (2r/2s) ii, and a quasi-PIR controller iiiThe system comprises a space vector modulation module (SVPWM) IV and a rectifier bridge V. In this embodiment, the dc bus voltage at the rectifying side is used as the outer loop, and the output i is controlled by the adaptive sliding modedref(ii) a Will obtain idrefAs a given value of the active current of the inner ring, a given value of reactive iqrefSet to zero and output via a two-phase stationary αβ coordinate system
Then will be
And i of the grid sideα、iβComparing, and obtaining the current error through QPIR controller
And
finally will obtain
And controlling the VSR to operate through SVPWM.
The control method of the embodiment is a new method invented by the inventor in the research and improvement process of the traditional dual PI and traditional sliding mode QPR control. The inventor indicates that the novel control method needs to use three modules of an adaptive sliding mode controller, a coordinate transformation (2r/2s) and a quasi-PIR controller in series during use, and the cooperation of parameters needs to be noticed, otherwise, the control failure can be caused.
The following describes the adaptive sliding mode QPIR control method and principle of the present embodiment in detail.
PWM rectifier topological structure and mathematical model
The main circuit topology of the three-phase voltage type two-level PWM rectifier is shown in figure 1. In fig. 1, the main circuit is formed by an IGBT, and the network side input voltage ea、ebAnd ecA three-phase symmetrical neutral-line-free connection mode is adopted; i.e. ia、ibAnd icThree-phase input current; l is filter inductanceThe inductance and the stray impedance on the line are represented by a resistor R; c represents a direct current side capacitor; v. ofdcOutputting voltage for the direct current side; rLIs a DC-side equivalent load, i.e. the load of a rectifierLIs the load current. In order to simplify the system structure, all power switches are assumed to be ideal elements, and the switching frequency is far greater than the network side fundamental frequency.
The mathematical model of the three-phase voltage type PWM rectifier under the three-phase static coordinate system is as follows:
Sa，Sb，Scfor the unipolar binary logic state of each phase bridge arm switch tube, the expression is as follows:
Skwhen the voltage is equal to 1, the upper bridge arm of the VSR is switched on, and the lower bridge arm is switched off;
Skwhen the value is-1, the lower arm of the VSR is turned on, and the upper arm is turned off, (k ∈ { a, b, c }).
The general mathematical model of the VSR based on the stationary coordinate system has the advantages of intuition and clear physical concept, but the function expression of the general mathematical model is nonlinear and time-varying parameters, so that the analysis difficulty of the VSR control strategy is increased, and the three-phase power supply is taken as an ideal balanced power supply to convert the PWM rectifier from the three-phase stationary coordinate system to the two-phase stationary coordinate system αβ, and the mathematical model is as follows:
in the formula, eα、eβIs the grid side voltage, i, in αβ coordinate systemα、iβIs the net side current in αβ coordinate system vα、vβIs the voltage across the switching tube under the αβ coordinate system, wherein vα、vβThe relationship to the switch state can be expressed as:
the mathematical model transformed by Park from the two-phase stationary coordinate system αβ to the rotating coordinate system dq is:
in the formula, ed、eqPhase voltages, respectively; i.e. id、iqPhase currents are respectively; sd、sqRespectively, the variables of the switching function in the coordinate system dq.
Self-adaptive sliding mode QPIR control method
The PWM rectifier is mainly controlled to realize unit power factor operation and network side current sine, and the stable output of direct current side voltage is ensured. The method aims at the problems that a traditional controller is difficult to track alternating current instructions without static errors, is slow in dynamic response and poor in anti-interference performance, has poor capability of inhibiting power grid voltage distortion disturbance in a current inner loop, and cannot track changes when load sudden changes occur, so that the response characteristics of a system are influenced and the like. The embodiment provides a novel control strategy combining QPIR control and adaptive sliding mode control, namely, a voltage outer ring adopts an adaptive sliding mode variable structure to control and stabilize output voltage at a direct current side, the load disturbance resistance of a system is improved, and a reference current command i is useddrefProviding the current to the inner loop; the current inner loop adopts quasi-PIR control, coordinate rotation transformation is not needed, cross coupling terms and feedforward compensation terms do not exist, static error-free tracking adjustment of alternating current signals can be achieved under a static coordinate system, and therefore good control over the network side current of the rectifier is achieved.
Current inner loop quasi-PIR controller design
PIR control is provided on the basis of traditional PI control, and aims to realize net side current sine and unit power factor operation without a static error tracking control alternating current instruction.
The conventional PI controller transfer function is:
gain at the fundamental frequency of the grid is
In the formula, KPIs a proportionality coefficient; kIIs an integral coefficient; omega0Is the cut-off frequency.
According to the internal model principle, in order to realize the quiet error-free control of the signal, a model of the signal must be included in the controller, and as can be seen from equation (6), the gain of the traditional PI controller at the fundamental frequency of the power grid is a finite value, so that the traditional PI controller has a steady-state error when tracking a sinusoidal current signal, and the quiet error-free tracking of the current is difficult to realize.
Unlike the PI controller, the PIR controller has a transfer function of:
gain at the fundamental frequency of the grid is
In the formula, the resonant frequency omega0＝2πf≈314rad/s，KPAnd KIAre respectively the ratio and the integral coefficient, KRIs the resonant gain factor. A root trace map of the transfer function is obtained as shown in fig. 2.
Therefore, it can be seen that the gain of the PIR control based on αβ two-phase stationary coordinate system at the fundamental frequency is infinite due to the addition of two open-loop poles with fixed frequency to the j ω axis of the transfer function of the controller, so that the system realizes zero steady-state error tracking at the frequency and can directly control the alternating current amount.
Fig. 3(a) is an amplitude-frequency characteristic curve of an ideal PIR controller, and its transfer function is shown in equation (7), but in practical application, the gain of the PIR controller at a non-fundamental frequency is small, and a power grid harmonic cannot be effectively suppressed once a power grid frequency shifts, so an easy-to-implement quasi-PIR controller is proposed on the basis of PIR control, and its transfer function is:
wherein ω iscThe frequency cut-off is mainly used for increasing the bandwidth of the R regulator so as to reduce the sensitivity of the R regulator to the grid frequency fluctuation.
As can be seen from fig. 3(b), compared with the PIR control, the quasi-PIR control has a larger gain at the non-fundamental frequency, and this characteristic satisfies the problem of small gain at the non-resonant point when the grid frequency fluctuates, and can effectively suppress the grid harmonics. In the following discussion, a quasi-PIR controller is used in place of a PIR controller.
Fig. 4 is a schematic block diagram of a quasi-PIR controller tracking a net-side sinusoidal current signal. In FIG. 4, iαIs the net side current under the two-phase stationary frame αβ,
is the inner loop reference current. In the parameter design process of the quasi-PIR controller, K is shown to influence the control performance of the quasi-PIR controller according to the formula (9)P、KI、KRAnd ωcThe four parameters are analyzed sequentially through a control variable method to influence the four control parameters on the performance of the rectifier system, and the influence of the parameter change on the amplitude-frequency characteristic of the PIR controller is shown in figure 5.
As can be seen from FIG. 5(a), the proportionality coefficient KPFor system harmonic impedance ZPIRGreater influence with KPIncreased by increasing, ZPIRThe larger the system is, the better the anti-interference performance of the system is; but if KPToo large, it will cause oscillations, resulting in system instability. K different in FIG. 5(b) and FIG. 5(c)I、KRHas an effect on the controller gain with no or little effect on the bandwidth, and the controller gain and KI、KRProportional relation, the larger the gain, the smaller the steady state error, but the harmonic component will follow the KI、KRIncreases in voltage, and adversely affects the net-side current waveform. Therefore, K is selectedIAnd KRThe steady-state error and harmonic component are considered simultaneously, so that the system is ensured to have enough gain near the fundamental frequency and has certain attenuation effect at the non-fundamental frequency. In FIG. 5(d) with ωcIncreasing, the gain and bandwidth at the non-fundamental frequency of the controller also increases. Since the network voltage frequency allows a fluctuation of + -0.5 Hz, i.e. omega, at the fundamental frequencyc1.0Hz,/pi, then ωc≈3.14rad/s。
From the above, when designing the PIR controller parameters, we should first determine ω according to the frequency fluctuation range allowed by the gridc(ii) a Secondly, K is selected according to gain requirements near fundamental frequency and network side harmonic sizeIAnd KR(ii) a And finally, determining K according to the harmonic impedance and considering the steady-state performance and the anti-interference performance of the systemP. In addition, K is also taken into accountP、KIAnd KRThe mutual influence between the two parts can ensure that the control system achieves the optimal working performance.
Voltage outer loop adaptive sliding mode controller design
The voltage outer ring mainly controls the output voltage v at the direct current sidedcEnsuring that it follows a given reference voltage vdcrefThe system has two control degrees, namely ① s, through analyzing a dq mathematical model formula (4) of the three-phase PWM rectifierdControlling the DC side voltage vdc；②sqControlling the operating state (unity power factor) of the system, i.e. controlling the reactive current iq. Selection of vdcAnd iqAs the output of the control system, the system control equation can be deduced according to the state model formula of the PWM rectifier as follows:
taking the error between the reference value and the actual value as the state variable of the control system, namely selecting the error e of the state variablev＝vdcref－vdc，
Then the sliding mode face switching function is selected as follows:
where k is the amplification gain for the purpose of obtaining the desired dynamic response while ensuring system stability, and β is the feedback coefficient of the variable structure control with the output voltage vdcThe time constant associated with the first order response.
It is well known that the sliding mode coefficients directly determine the performance characteristics of a sliding mode controller. In a conventional sliding mode controller, the sliding mode coefficient is about
The value of which is determined by the load resistance, and when a sudden load change occurs, the system cannot track the change, thereby affecting the response characteristic of the system. The embodiment detects the load current iLTo reconstruct the load resistance RLThe value of (c). Which has the formula of
Will be provided with
Is substituted by formula (11)
Substituting formula (12) into formula (13) to obtain
When the three-phase PWM rectifier operates at the unit power factor iq＝0，eq＝0，diqIf/dt is 0, then sq＝-ωLid/vdc(ii) a Under steady state conditions, idLet Ldi be DCd(dt is 0, available)sd＝-(ed-Rid)/vdc(ii) a Under the condition of coordinate transformation with equal power,
Urmsthe effective value of the input phase voltage at the network side is the DC reference voltage vdcrefIs constant, then dvdcref(dt is 0) and s isd、sqSubstituted formula (14) can be simplified
This results in an outer loop voltage regulation equation, the output of which is used as a given reference value for the current inner loop, i.e.
The schematic block diagram of the outer loop sliding mode voltage controller obtained by the method is shown in fig. 6. Combination of formula (16) and iqrefAnd when the output voltage is equal to 0, obtaining the voltage outer ring output which meets the output voltage of the direct current side and the input unit power factor of the network side.
Adaptive sliding mode QPIR controller design
From the above analysis, a schematic block diagram of the dual closed-loop control of the three-phase PWM rectifier based on the adaptive sliding-mode QPIR control can be obtained, as shown in fig. 7.
According to the detected power supply voltage and current, the component of the grid-side current in the αβ coordinate system is obtained by using the formula (2) in the static coordinate system, and the outer ring sliding mode control outputs idrefAs a given value of the active current of the inner ring, a given value of reactive iqrefSet to zero, and the value on the stationary coordinate system of the two phases αβ is obtained by 2r/2s transformation which is the inverse synchronous rotational coordinate transformation
And
the transformation formula is as follows:
wherein theta is the included angle between the d axis and the α axis in the transformation coordinate system, and the obtained current instruction value
And i of the grid sideα、iβComparing, specifically:
the current error is obtained by QPIR controller
And
in particular to
By obtaining
Judging the sector where the space vector is located and calculating the action time of the space vector:
wherein T is the PWM period, T1Time of action, T, of the space vector V12Is the action time of the space vector V2;
similarly, the action time of the space vector of other sectors can be obtained; then, space vector switching points Tcm1, Tcm2 and Tcm3 are determined according to the located sectors, and finally, the IGBT is turned on according to the space vector switching points to generate PWM waveforms, so that the VSR is controlled to operate.
Harmonic compensation
The incomplete sine wave signal has harmonic wave, and the harmonic wave compensation is to compensate the sine AC signal with harmonic wave into complete sine AC signal. The current inner loop adopts quasi-PIR control, and can compensate specific low-order harmonic waves while the calculation amount is small. Fig. 8(a) is a functional block diagram of a harmonic compensation quasi-PIR controller. The harmonic compensator controlled by the quasi-PIR only needs to superpose corresponding harmonic compensation on the original basis. As shown in fig. 8(b), resonance occurs at the fundamental wave, the 5 th harmonic, and the 7 th harmonic, respectively, and the phase angles are all 0 °, and the influence on the harmonic at other frequencies is small. The transfer function of the harmonic compensation in FIG. 8(a) is
According to the adaptive sliding mode QPIR control method of the PWM rectifier based on the αβ coordinate system, a three-phase PWM rectifier model is built in MATLAB/Simulink to verify the feasibility of the adaptive sliding mode variable structure QPIR control method under the condition of power grid voltage distortion.
The system simulation parameters are as follows: an ideal three-phase symmetrical power supply 220V/50Hz (5 th harmonic and 7 th harmonic are added) outputs a direct current voltage reference given value 720V, an input inductance L at an alternating current side is 4mH (an equivalent resistance R is 0.1 omega), a filter capacitor C at a direct current side is 3000 mu F, and a load resistance R L100 Ω, switching frequency 10 kHz.
Fig. 9 is a response waveform diagram of the direct-current side output voltage and the grid side input current when the system is started and the load suddenly changes under the normal grid voltage by the two control methods. As can be seen from fig. 9(a) and 9(b), when the conventional sliding-mode QPR control method is adopted, the time required for the voltage to reach the stable value is about 0.025s, and there is no overshoot before stabilization, and the ripple is small after stabilization; however, when the load suddenly changes, the traditional sliding mode controller cannot track the change, and the response characteristic of the system is influenced. When the adaptive sliding mode QPIR control method provided by this embodiment is adopted, as can be seen from fig. 9(c) and 9(d), the time required for the voltage to reach the stable value is about 0.025s, and there is no overshoot before stabilization, and when the load suddenly changes, the change can be quickly tracked to reach the steady state, which verifies that the outer-loop adaptive sliding mode control method can effectively improve the response speed of the system, and effectively track the sudden change process of the load, so that the system quickly reaches the steady state.
Fig. 10 is a response waveform diagram of the direct-current side output voltage and the grid side input current when the system starts and the load suddenly changes under the power grid voltage distortion by the two control methods. When the power grid voltage is distorted, as shown in fig. 11(a), the power grid-side voltage THD is 13.64%, as can be seen from fig. 10(a) and 10(b), when the conventional sliding mode QPR control method is adopted, the power grid-side current is not guaranteed to be sinusoidal, meanwhile, 6 frequency-doubled ripple exists in the output voltage at the direct current side, the ripple is large after stabilization, and the power grid-side current THD content is large and reaches 7.9%, as shown in fig. 11 (b); when the adaptive sliding mode QPIR control method proposed in this embodiment is adopted, when the grid voltage is distorted, the grid-side current is sinusoidal, as shown in fig. 10(c) and 10 (d); due to the addition of the harmonic compensator, 6-frequency ripple of the output voltage at the direct current side is eliminated, and the content of the current THD at the power grid side is very small, only 2.01%, as shown in fig. 11 (c).
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.
Claims (4)
1. A PWM rectifier adaptive sliding mode QPIR control method based on an αβ coordinate system is characterized by comprising the following steps:
step one, taking the direct current bus voltage at the rectifying side as an outer ring, and obtaining an active current given value i through a self-adaptive sliding mode controllerdref(ii) a Wherein, a voltage outer ring is formed by adopting a self-adaptive sliding mode controller, the error between a reference value and an actual value is taken as a state variable of a control system, namely, the error e of the state variable is selectedv＝vdcref-vdcThe sliding mode surface switching function is selected as follows:
in the formula, vdcrefFor a given reference voltage, vdcβ is a feedback coefficient of the variable structure control for the DC side output voltage, and is equal to the DC side output voltage vdcA time constant associated with the first order response;
by detecting load current i in real timeLTo reconstruct the load resistance RLThe formula is:
will be provided with
Substituting the formula to obtain:
when the three-phase PWM rectifier operates at the unit power factor, the reactive current iqGrid-side voltage q-axis component e ═ 0q＝0，diqIf/dt is 0, then sq＝-ωLid/vdc(ii) a Under steady state conditions, idFor active current, let Ldid(dt is 0, available as s)d＝-(ed-Rid)/vdc(ii) a L is a power grid side filter inductor; c is a direct current side capacitor; omega is the frequency of the power grid; under the condition of equal power coordinate transformation, the d-axis component of the voltage on the power grid side
UrmsThe effective value of the input phase voltage at the network side is given by the given reference voltage vdcrefIs constant, then dvdcrefThe number of switching functions in dq coordinate system is set to be sd、sqThe substitution formula is simplified and obtained
The outer loop voltage regulation equation is thus obtained, the output of which is taken as the given reference value of the current inner loop:
in the formula iLC represents a direct current side capacitor, and R represents an inductor and stray impedance on a line;
step two, setting the obtained active current value idrefAnd given value of reactive current iqrefObtaining a current instruction value through a coordinate transformation module
Step three, obtaining the current instruction value
Two components i obtained by 3/2 transformation of grid current on grid sideα、iβComparing, and obtaining the output value of QPIR controller by the quasi-proportional-integral resonance QPIR controller
And
step four, finally obtaining
And controlling the VSR of the three-phase voltage source type PWM rectifier to operate through SVPWM.
2. The adaptive sliding-mode QPIR control method for the PWM rectifier based on the αβ coordinate system according to claim 1, wherein the given value of active current i obtained in the second stepdrefAnd given value of reactive current iqrefThe values on the stationary coordinate system of the two phases αβ are obtained by the synchronous rotating coordinate inverse transformation, i.e. 2r/2s transformation
And
the transformation formula is as follows:
wherein θ is the angle between d axis and α axis in the transformed coordinate system.
3. The QPIR control method according to claim 2, wherein the current command values obtained in step three are used to control the PWM rectifier based on αβ coordinate system
And i of the grid sideα、iβComparing, specifically:
the current error is obtained by QPIR controller
And
in particular to
In the above formula, the resonant frequency ω0＝2πf≈314rad/s，KPAnd KIAre respectively the ratio and the integral coefficient, KRIs the resonant gain coefficient, ωcIs the cut-off frequency.
4. The QPIR control method for the PWM rectifier under the αβ coordinate system according to claim 3, wherein the step four is obtained by
Judging the sector where the space vector is located and calculating the action time of the space vector:
wherein T is the PWM period, T1Time of action, T, of the space vector V12Is a spaceThe action time of vector V2;
similarly, the action time of the space vector of other sectors can be obtained; then, space vector switching points Tcm1, Tcm2 and Tcm3 are determined according to the located sectors, and finally, the IGBT is turned on according to the space vector switching points to generate PWM waveforms, so that the VSR is controlled to operate.
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