CN104734545A - PWM rectifier control method based on model prediction and voltage square control - Google Patents

Abstract

The invention discloses a PWM rectifier control method based on model prediction and voltage square control. The square of the output direct-current side voltage is controlled to serve as the given inner ring active current, the quick response of a controller is ensured through the linear relation between the square of the voltage and the active current, and the anti-disturbance capacity of a rectifier is further enhanced through the model prediction control of the inner ring current. The cost function of model prediction is quickly obtained through the finite set on-off state so that the control method can be easily achieved on a digital controller. The dynamic response and the anti-disturbance capacity of the whole controller can be enhanced through the selection of the weighting coefficient in the cost function and the coordination with the pre-charging soft start strategy. By means of the double-closed-loop control method, the quick response and the high anti-disturbance capacity for load disturbance are achieved while it is ensured that the alternating-current side of the rectifier reaches the unit power factor and the current total harmonic distortion rate reaches the national standard requirement. By means of the double-closed-loop control method combined with the voltage square model prediction control, the control over the unit power factor and the disturbance resistance of the three-phase voltage type PWM rectifier is achieved, and great reference value is provided for engineering.

Description

Based on the control method of the PWM rectifier that model prediction and voltage squared control

Technical field

The present invention relates to the research field such as Three-phase PWM Voltage Rectifier, flexible AC/DC converter, particularly the double-closed-loop control method of three-phase full-bridge controlled rectifier.

Background technology

Along with social progress and industrial development, the superior function that power electronic equipment has in electric power system transmission of electricity distribution and power transformation, is adopted in a large number by consumption industries such as industrial or agricultural.But power electronic equipment, as nonlinear load, can inject a large amount of reactive powers and harmonic wave to electrical network.First, reactive power can affect the stability of electric power system, can affect the power quality of other users of electric power system points of common connection.Secondly, harmonic wave can make the mechanical rotating device in electric power system as aging in generator, transformer life; The inductance in electrical network and electric capacity generation resonance can be made, endanger its safe operation; The protective relaying device misoperation of electric power system can be made; The communication apparatus of electric power system can be made to be interfered.In power electronic equipment, because direct current widely uses in industrial and agricultural production, rectifying installation has accounted for very large proportion.But, traditional rectification circuit, as diode uncontrollable rectifier or Thyristor Controlled rectification, because device self and the delayed of control method cause it inevitably to occur harmonic wave and reactive power problem, produce above-described harm, great threat is caused to the safe and stable operation of electric power system.

Unity Power Factor PWM Rectifier Based (PWM rectifier) based on full control device just obtains the strong interest of research and the engineer widely of scholar after proposing.PWM rectifier has plurality of advantages: AC can unity power factor runs, output dc voltage can boost smooth adjustment, extremely low input harmonics content, AC and DC side energy in bidirectional flow and dynamic response etc. fast.These advantages bring huge market prospects to the development and application of PWM rectifier.Present PWM rectifier has been applied to flexible direct current power transmission system and mesolow utility power quality control system, becomes and improves effective ways that are defeated, distribution system Stability and dependability.

Along with the development of PWM rectifier, tradition there will be following problem based on the two close cycles PI control strategy of voltage oriented control (VOC) in engineer applied: the interference rejection ability that its DC side exports is strong not, and dynamic responding speed is fast not.Especially when being applied to electric automobile charging pile, due to the load disturbance of the spontaneous charging of electric automobile random in a large number, the VD of charging pile is fallen, the efficiency of impact charging.Therefore, a kind of novel control strategy is needed to realize strengthening further the dynamic effects of PWM rectifier and interference rejection ability.

For PWM rectifier dynamic response and the strong not problem of DC side interference rejection ability, many research work and achievement are suggested.What have has researched and proposed a kind of control strategy based on Model Predictive Control, outer voltage and current inner loop are all realized by PREDICTIVE CONTROL, to reach the Delay control inaccessiable fast dynamic response of tradition based on PI (pi controller), but the method do not consider output dc voltage as inner ring active current give timing, the relation of its nonlinear change can cause inaccuracy and the poor efficiency of control action.Further, differentiate can expend huge computing time with the method for separating cost function.As further perfect, have again the control method of the cost function having researched and proposed a kind of fixed solving model of finite aggregate on off state frequently PREDICTIVE CONTROL, but this method can increase the harmonic content of ac-side current.Also have a class to propose to adopt the method for load feedforward for the problem that load disturbance response speed is slow, but its hardware adds measurement point, cost is uprised.For this reason, also need to carry out systematic research to the control strategy problem based on PWM rectifier DC side Ability of Resisting Disturbance.

Summary of the invention

In order to solve the problem, the object of the invention is to propose a kind of control method of the PWM rectifier controlled based on model prediction and voltage squared, be exactly specifically the outer voltage control object of Three-phase PWM Voltage Rectifier is adopted outlet side direct voltage square, current inner loop adopts Model Predictive Control, and adopt finite aggregate on off state to carry out the cost function of solving model PREDICTIVE CONTROL, coordinate the soft start policy of precharge to realize PWM rectifier for the strong interference rejection ability exporting DC side; In corresponding Model Predictive Control, the selection of the weight coefficient of cost function directly can determine THD (total harmonic distortion factor) content and the Immunity Performance of whole PWM rectifier.

Emphasis of the present invention is in the weight coefficient of Confirming model PREDICTIVE CONTROL and rapid solving cost function part.

In order to achieve the above object, the technical solution adopted in the present invention is:

A kind of double-closed-loop control method controlled based on model prediction and voltage squared, utilize the voltage squared linear with active current as outer shroud, take Model Predictive Control as core, adopt PREDICTIVE CONTROL and the output interference rejection ability of optimal control to PWM rectifier to improve, step is as follows:

Step 1, determines the discrete models of Three-phase PWM Voltage Rectifier

Step 1.1, according to Kirchhoff's second law and current law, calculate the rectifier Mathematical Modeling under abc coordinate system, its expression formula is as follows:

$\left\{\begin{array}{c}\mathrm{esa}=L\frac{{\mathrm{di}}_a}{\mathrm{dt}}+{\mathrm{Ri}}_a+V_{\mathrm{aN}}+V_{\mathrm{No}}\\ \mathrm{esb}=L\frac{d{i}_b}{\mathrm{dt}}+R{i}_b+V_{\mathrm{bN}}+V_{\mathrm{No}}\\ \mathrm{esc}=L\frac{{\mathrm{di}}_c}{\mathrm{dt}}+{\mathrm{Ri}}_c+V_{\mathrm{cN}}+V_{\mathrm{No}}\end{array}\right.$

Wherein, esx (x=a, b, c) represents AC voltage, i _x(x=a, b, c) represents ac-side current, and L represents AC filter inductance value, R represent adding of the equivalent resistance of line resistance, inductance and the equiva lent impedance of switching device and.N point represents the reference point position of DC side, and O point represents the neutral point of AC three-phase voltage; V _xN(x=a, b, c) represents the voltage of rectifier AC three inputs to DC side reference point respectively; V _nOrepresent the voltage of DC side reference point to AC neutral point;

Step 1.2, for ease of controlling, utilizing phase-locked loop pll to obtain the current phase theta=ω t of line voltage, and obtaining based on the Mathematical Modeling under dq coordinate system by the Mathematical Modeling under abc coordinate system through synchronous rotating angle, as follows:

$\left\{\begin{array}{c}L\frac{{\mathrm{di}}_d}{\mathrm{dt}}=e_d+\mathrm{\ω}{\mathrm{Li}}_d-{\mathrm{Ri}}_d-v_{\mathrm{dc}}{s}_d\\ L\frac{{\mathrm{di}}_q}{\mathrm{dt}}=e_q+\mathrm{\ω}{\mathrm{Li}}_q-{\mathrm{Ri}}_q-v_{\mathrm{dc}}{s}_q\\ C\frac{{\mathrm{dv}}_{\mathrm{dc}}}{\mathrm{dt}}=i_q{s}_q+i_d{s}_d-i_L\end{array}\right.$

Wherein, d axle represents active power axle, and q axle represents reactive power axle, and 90 degree, the delayed q axle of d axle; In formula: e _d, e _qaC line voltage esa, esb, the esc component under dq coordinate system, in like manner: i _d, i _qrectifier AC line current i _a, i _b, i _ccomponent under dq coordinate system; S _d, S _qon off state S _a, S _b, S _ccomponent under dq coordinate system, ω represents the power frequency angular velocity of rotation of electrical network, v _dcrepresent DC voltage value.The transformation matrix that above-mentioned conversion uses is:

$T_{\mathrm{abc}-\mathrm{dq}}=\frac{2}{3}\left[\begin{array}{ccc}\sin \left(\mathrm{\ωt}\right)& \sin (\mathrm{\ωt}-2\mathrm{\π}/3)& \sin (\mathrm{\ωt}+2\mathrm{\π}/3)\\ \cos \left(\mathrm{\ωt}\right)& \cos (\mathrm{\ωt}-2\mathrm{\π}/3)& \cos (\mathrm{\ωt}+2\mathrm{\π}/3)\end{array}\right]$

In matrix: T _abc-dqexpression is by the conversion of abc coordinate system to dq coordinate system, and ω t is the phase place of the current electric grid voltage utilizing phase-locked loop pll to obtain in step 1.2;

Step 1.3, by front two current equations in the differential Mathematical Modeling under dq coordinate system by forward direction Euler's formula discretization, wherein, T represents the sampling period, and k represents sampling instant, s _d, s _qfor on off state S _kcomponent under dq coordinate system; The Mathematical Modeling that discretization obtains is the electric current discrete models of Three-phase PWM Voltage Rectifier, and its expression formula is as follows:

$\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right]=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\ωT}\\ -\mathrm{\ωT}& 1-\frac{\mathrm{RT}}{L}\end{array}\right]\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]+\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right]\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$

Order $i\left(k\right)=\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]$ For controlled variable, $v_r\left(k\right)=\left[\begin{array}{c}{v}_{\mathrm{rd}}\left(k\right)\\ v_{\mathrm{rq}}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$ For control variables, and make $A=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\ωT}\\ -\mathrm{\ωT}& 1-\frac{\mathrm{RT}}{L}\end{array}\right],B=\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right],$ Then above-mentioned electric current discrete models can be reduced to following formula:

i(k+1)＝Ai(k)+Bv _r(k)

Step 2, determines to take voltage squared as the outer voltage of control object

Step 2.1, for Three-phase PWM Voltage Rectifier, does square operation by output DC voltage, and exports with reference to also doing square operation by presetting given DC side, and two squared voltage are carried out doing difference and regulating through PI controller;

Step 2.2, the output after PI controller in step 2.1 regulates is as the reference set-point i of active current in current inner loop _d ^*;

By the set-point v of DC voltage _dc ^*with the current sample values v of DC voltage _dcdo after square operation obtains corresponding square value respectively, then by subtracter, by command value square to deduct current sample values square, difference is afterwards by outer voltage PI controller C _vs () controls to export the set-point obtaining active current;

Step 3, the finite aggregate on off state of inner ring current model prediction solves

Step 3.1, detects PWM rectifier AC three-phase voltage e _a, e _b, e _c, three-phase current i _a, i _b, i _cwith DC side output voltage v _dc, three-phase voltage and three-phase current are carried out the computing of three-phase static coordinate system to two-phase rotating coordinate system, after computing, obtain active voltage actual value e _d, active current actual value i _dwith reactive voltage actual value e _q, reactive current actual value i _q;

Step 3.2, for the discrete models that step 1.3 is determined, its control variables (namely corresponding on off state) S _konly have 8 kinds of states (7 kinds of different variablees), be expressed as follows:

$S=\{\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\},$ Wherein

For the on off state that each is determined, all bring determined discrete models in step 1.3 into, calculate a kind of predicted value, obtain 8 kinds of predicted values altogether:

${i(k+1)}_n=\left[\begin{array}{c}{i}_d{(k+1)}_n\\ i_q{(k+1)}_n\end{array}\right],(n=\mathrm{1,2}...8)$

Step 3.3, in order to realize unity power factor, makes referenced reactive current value i _q ^*=0, active current command value i _d ^*determined by step 2.2; Bring the predicted value of eight kinds obtained in active current command value, referenced reactive current value and step 3.2 into cost function in, calculate eight kinds of cost function value J _n(n=1,2 ... 8).Wherein, α represents the weight coefficient of active current, and β represents the weight coefficient of reactive current;

Step 3.4, according to the cost function value generated in step 3.3, carries out size sequence, and selects minimum value wherein, obtain least cost function value minJ ∈ { J ₁, J ₂j ₈; And predicted value during this least cost function value of record generation in the corresponding step 3.3 needed $i(k+1)=\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right];$

Step 3.5, bring the least cost function value generated in step 3.4 and corresponding predicted value into determine in step 1.3 discrete models, backwards calculation goes out required control variables v _ron off state S corresponding in (k) _k;

The main-process stream of whole step 3 algorithm is: the AC three-phase voltage of the current time rectifier of first sampling, three-phase current and DC voltage value; Then, calculate 8 kinds of predicted values by rectifier discrete models successively for 8 kinds of on off states, 8 kinds of predicted values substituted in cost function formula respectively successively, on off state corresponding when calculating least cost function value, then exports this on off state;

Step 4, the determination of voltage vector and the generation of pwm signal

Step 4.1, on off state S determined in step 3.5 _k(k=a, b, c), goes out corresponding to the voltage vector U under two-phase rest frame by following formulae discovery _α, U _b;

$\left\{\begin{array}{c}{u}_{\mathrm{\α}}=\frac{2}{3}{u}_{\mathrm{dc}}[s_a-\frac{1}{2}(s_b+s_c)]\\ u_{\mathrm{\β}}=\frac{\sqrt{3}}{3}{u}_{\mathrm{dc}}(s_b-s_c)\end{array}\right.$

Wherein, u _dcrepresent the DC voltage that present sample obtains;

Step 4.2, by step 4.1 gained voltage vector U _α, U _βmodulated by the method for Space Vector Modulation Strategy SVPWM, obtain the drive pulse signal of six groups of IGBT;

Step 5, the selection of weight coefficient and the cooperation of soft start policy

Step 5.1, first meritorious electric current weighting factor alpha is determined, according to the interference rejection ability of Three-phase PWM Voltage Rectifier DC side output voltage, can fall after DC voltage is disturbed again, suitable meritorious weight coefficient α is selected according to the size fallen, its value is less, and Voltage Drop can be less;

Step 5.2, determines the weight coefficient β of reactive current, determines idle weight coefficient β according to the total harmonic distortion factor THD of ac-side current, and the change of its value and the variation relation of THD follow following rule:

1), when active current weight coefficient is much larger than reactive current weight coefficient, namely during α > > β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is less;

2), when the weight coefficient of active current is less than reactive current weight coefficient, namely during α < β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is larger;

Step 5.3, determines the precharge voltage value of soft start policy.When active current weight coefficient α reduces, DC voltage falls and can therefore reduce, but the startup overshoot process of Three-phase PWM Voltage Rectifier meeting Shaoxing opera is strong.When active current weight coefficient α more hour, the pre-charge voltage of DC side output capacitance should be increased.

Voltage squared is as outer shroud control object, and inner ring active current is linear, and enable the change accurate response of voltage in active current, precise control is rapid.

Interior circular current adopts Model Predictive Control, solve the Delay control inaccessiable fast dynamic response problem of tradition based on PI, whole inner ring rate of current is fast, precise control, simultaneously, Model Predictive Control changes weight coefficient can make current transformer have stronger robustness to disturbance, has good effect to disturbance suppression.

The cost function of finite aggregate on off state solving model prediction, avoids the method that tradition solves derivative and can expend huge computing time and take a large amount of memory spaces, be easy to realize on digitial controller.

The soft start policy of precharge coordinate the weight coefficient of cost function to change can to make rectifier have to realize under the prerequisite compared with high inhibition load disturbance start-up course rapidly, overshoot reduces.

Compared to the prior art comparatively, the present invention possesses following advantage:

The present invention is characterised in that the control method of the voltage squared outer shroud linear with active current and the two close cycles that adopts the current inner loop of Model Predictive Control to combine, and adopts the soft start policy of finite aggregate on off state rapid solving cost function cooperation precharge to make PWM rectifier reach stronger Ability of Resisting Disturbance and dynamic response faster.Voltage squared can make the shock wave of the outer loop voltag of interior circular current accurate response as control object, makes controller effective fast.Inner ring current model PREDICTIVE CONTROL achieves the Delay control inaccessiable fast dynamic response of tradition based on PI, simultaneously, the change of model prediction weight coefficient can make current transformer play very strong robustness to disturbance, has stronger inhibitory action for load disturbance.Differentiate for tradition and separate cost function and can expend the huge time and take the deficiency of a large amount of memory spaces, present invention employs the method for finite aggregate on off state, quick and precisely, be easy to realize in digitial controller.

Accompanying drawing explanation

Fig. 1 is Three-phase PWM Voltage Rectifier main circuit topological structure.

Fig. 2 is the control method flow chart based on voltage squared.

Fig. 3 is the Model Predictive Control flow chart solving cost function based on finite aggregate on off state.

Fig. 4 is the total system control block diagram based on voltage squared and Model Predictive Control.

Fig. 5 is the graph of a relation that active current weight coefficient falls with output DC side maximum voltage.

Fig. 6-1 is the graph of a relation (as β < α) of reactive current weight coefficient and total harmonic distortion factor.

Fig. 6-2 is graphs of a relation (as β > α) of reactive current weight coefficient and total harmonic distortion factor.

Fig. 7-1 is the start-up course figure coordinating precharge time institute invention control method.

Fig. 7-2 is the start-up course figure without precharge time institute invention control method.

Fig. 8 be the DC side of invention control method when reaching stable state export and AC electric current and voltage figure.

Fig. 9 is DC voltage and active current, reactive current variation diagram when there is load disturbance.

Figure 10 is the comparison diagram that load disturbance time institute invention control method and conventional method occur.

Embodiment

Below in conjunction with example, the present invention will be described in more detail.

As shown in drawings, the present invention proposes a kind of double-closed-loop control method controlling the Three-phase PWM Voltage Rectifier combined based on Model Predictive Control and voltage squared.The outer voltage control object of Three-phase PWM Voltage Rectifier is adopted outlet side direct voltage square, current inner loop adopts Model Predictive Control, and adopt fixed finite aggregate on off state frequently to carry out the cost function of solving model PREDICTIVE CONTROL, coordinate the soft start policy of precharge to realize PWM rectifier for the strong interference rejection ability exporting DC side.Emphasis of the present invention is in the weight coefficient of Confirming model PREDICTIVE CONTROL and rapid solving cost function part, and its step is as follows:

Step 1, determines the discrete models of Three-phase PWM Voltage Rectifier

Step 1.1, three-phase voltage type rectifier main circuit topological structure as shown in Figure 1, according to Kirchhoff's second law and current law, calculate the rectifier Mathematical Modeling under abc coordinate system, its expression formula is as follows:

$\left\{\begin{array}{c}\mathrm{esa}=L\frac{{\mathrm{di}}_a}{\mathrm{dt}}+{\mathrm{Ri}}_a+V_{\mathrm{aN}}+V_{\mathrm{No}}\\ \mathrm{esb}=L\frac{d{i}_b}{\mathrm{dt}}+R{i}_b+V_{\mathrm{bN}}+V_{\mathrm{No}}\\ \mathrm{esc}=L\frac{{\mathrm{di}}_c}{\mathrm{dt}}+{\mathrm{Ri}}_c+V_{\mathrm{cN}}+V_{\mathrm{No}}\end{array}\right.$

Wherein, esx (x=a, b, c) represents AC voltage, i _x(x=a, b, c) represents ac-side current, and L represents AC filter inductance value, R represent adding of the equivalent resistance of line resistance, inductance and the equiva lent impedance of switching device and.N point represents the reference point position of DC side, and O point represents the neutral point of AC three-phase voltage.V _xN(x=a, b, c) represents the voltage of rectifier AC three inputs to DC side reference point respectively.V _nOrepresent the voltage of DC side reference point to AC neutral point.

Step 1.2, for ease of controlling, utilizing phase-locked loop pll to obtain the current phase theta=ω t of line voltage, and obtaining based on the Mathematical Modeling under dq coordinate system by the Mathematical Modeling under abc coordinate system through synchronous rotating angle, as follows:

$\left\{\begin{array}{c}L\frac{{\mathrm{di}}_d}{\mathrm{dt}}=e_d+\mathrm{\&omega;}{\mathrm{Li}}_d-{\mathrm{Ri}}_d-v_{\mathrm{dc}}{s}_d\\ L\frac{{\mathrm{di}}_q}{\mathrm{dt}}=e_q+\mathrm{\&omega;}{\mathrm{Li}}_q-{\mathrm{Ri}}_q-v_{\mathrm{dc}}{s}_q\\ C\frac{{\mathrm{dv}}_{\mathrm{dc}}}{\mathrm{dt}}=i_q{s}_q+i_d{s}_d-i_L\end{array}\right.$

Wherein, d axle represents active power axle, and q axle represents reactive power axle, and 90 degree, the delayed q axle of d axle.In formula: e _d, e _qaC line voltage esa, esb, the esc component under dq coordinate system, in like manner: i _d, i _qrectifier AC line current i _a, i _b, i _ccomponent under dq coordinate system; S _d, S _qon off state S _a, S _b, S _ccomponent under dq coordinate system, ω represents the power frequency angular velocity of rotation of electrical network, v _dcrepresent DC voltage value.The transformation matrix that above-mentioned conversion uses is:

$T_{\mathrm{abc}-\mathrm{dq}}=\frac{2}{3}\left[\begin{array}{ccc}\sin \left(\mathrm{\&omega;t}\right)& \sin (\mathrm{\&omega;t}-2\mathrm{\&pi;}/3)& \sin (\mathrm{\&omega;t}+2\mathrm{\&pi;}/3)\\ \cos \left(\mathrm{\&omega;t}\right)& \cos (\mathrm{\&omega;t}-2\mathrm{\&pi;}/3)& \cos (\mathrm{\&omega;t}+2\mathrm{\&pi;}/3)\end{array}\right]$

In matrix: T _abc-dqexpression is by the conversion of abc coordinate system to dq coordinate system, and ω t is the phase place of the current electric grid voltage utilizing phase-locked loop pll to obtain in step 1.2.

Step 1.3, by front two current equations in the differential Mathematical Modeling under dq coordinate system by forward direction Euler's formula discretization, wherein, T represents the sampling period, and k represents sampling instant, s _d, s _qfor on off state S _kcomponent under dq coordinate system.The Mathematical Modeling that discretization obtains is the electric current discrete models of Three-phase PWM Voltage Rectifier, and its expression formula is as follows:

$\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right]=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\&omega;T}\\ -\mathrm{\&omega;T}& 1-\frac{\mathrm{RT}}{L}\end{array}\right]\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]+\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right]\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$

Order $i\left(k\right)=\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]$ For controlled variable, $v_r\left(k\right)=\left[\begin{array}{c}{v}_{\mathrm{rd}}\left(k\right)\\ v_{\mathrm{rq}}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$ For control variables, and make $A=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\&omega;T}\\ -\mathrm{\&omega;T}& 1-\frac{\mathrm{RT}}{L}\end{array}\right],B=\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right],$ Then above-mentioned electric current discrete models can be reduced to following formula:

i(k+1)＝Ai(k)+Bv _r(k)

Step 2, determines to take voltage squared as the outer voltage of control object

Step 2.1, for Three-phase PWM Voltage Rectifier, does square operation by output DC voltage, and exports with reference to also doing square operation by presetting given DC side, and two squared voltage are carried out doing difference and regulating through PI controller.

Step 2.2, the output after PI controller in step 2.1 regulates is as the reference set-point i of active current in current inner loop _d ^*.

The control block diagram of whole step 2 is as shown in Figure 2: wherein, C _vs () is the PI controller of outer voltage, v _dc ^*represent the set-point of DC voltage, v _dcrepresent the current sample values of DC voltage, it does after square operation obtains corresponding square value respectively, then by subtracter, by command value square to deduct current sample values square, difference is afterwards by outer voltage PI controller C _vs () controls to export the set-point obtaining active current.

Step 3, the finite aggregate on off state of inner ring current model prediction solves

Step 3.1, detects PWM rectifier AC three-phase voltage e _a, e _b, e _c, three-phase current i _a, i _b, i _cwith DC side output voltage v _dc, three-phase voltage current is carried out the computing of three-phase static coordinate system to two-phase rotating coordinate system, after computing, obtains active voltage actual value e _d, active current actual value i _dwith reactive voltage actual value e _q, reactive current actual value i _q.

Step 3.2, for the discrete models that step 1.3 is determined, its control variables (namely corresponding on off state) S _konly have 8 kinds of states (7 kinds of different variablees), be expressed as follows:

$S=\{\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\},$ Wherein

For the on off state that each is determined, all bring determined discrete models in step 1.3 into, calculate a kind of predicted value, obtain 8 kinds of predicted values altogether:

${i(k+1)}_n=\left[\begin{array}{c}{i}_d{(k+1)}_n\\ i_q{(k+1)}_n\end{array}\right],(n=\mathrm{1,2}...8)$

Step 3.3, in order to realize unity power factor, makes referenced reactive current value i _q ^*=0, active current command value i _d ^*determined by step 2.2.Bring the predicted value of obtain in the command value of active current, reactive current and step 3.2 eight kinds into cost function in, calculate eight kinds of cost function value J _n(n=1,2 ... 8).Wherein, α represents the weight coefficient of active current, and β represents the weight coefficient of reactive current.

Step 3.4, according to the cost function value generated in step 3.3, carries out size sequence, and selects minimum value wherein, obtain least cost function value minJ ∈ { J ₁, J ₂j ₈.And predicted value during this least cost function value of record generation in the corresponding step 3.3 needed $i(k+1)=\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right].$

Step 3.5, bring the least cost function value generated in step 3.4 and corresponding predicted value into determine in step 1.3 discrete models, backwards calculation goes out required control variables v _ron off state S corresponding in (k) _k.

The general flow chart of whole step 3 algorithm as shown in Figure 3.That is, first to sample the AC three-phase voltage of current time rectifier, three-phase current and DC voltage value.Then, calculate 8 kinds of predicted values by rectifier discrete models successively for 8 kinds of on off states, 8 kinds of predicted values substituted in cost function formula respectively successively, on off state corresponding when calculating least cost function value, then exports this on off state.

Step 4, the determination of voltage vector and the generation of pwm signal

Step 4.1, on off state S determined in step 3.5 _k(k=a, b, c), goes out corresponding to the voltage vector U under two-phase rest frame by following formulae discovery _α, U _β.

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;}}=\frac{2}{3}{u}_{\mathrm{dc}}[s_a-\frac{1}{2}(s_b+s_c)]\\ u_{\mathrm{\&beta;}}=\frac{\sqrt{3}}{3}{u}_{\mathrm{dc}}(s_b-s_c)\end{array}\right.$

Wherein, u _dcrepresent the DC voltage that present sample obtains.

Step 4.2, by step 4.1 gained voltage vector U _α, U _βmodulated by the method for Space Vector Modulation Strategy SVPWM, obtain the drive pulse signal of six groups of IGBT.

Step 5, the selection of weight coefficient and the cooperation of soft start policy

Step 5.1, first meritorious electric current weighting factor alpha is determined, according to the interference rejection ability of Three-phase PWM Voltage Rectifier DC side output voltage, can fall after DC voltage is disturbed again, suitable meritorious weight coefficient α is selected according to the size fallen, its value is less, and Voltage Drop can be less.Its relation can with reference to shown in accompanying drawing 5:

Step 5.2, determines the weight coefficient β of reactive current, determines idle weight coefficient β according to the total harmonic distortion factor THD of ac-side current, and the change of its value and the variation relation of THD follow following rule:

1), when active current weight coefficient is much larger than reactive current weight coefficient, namely during α > > β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is less.As shown in accompanying drawing 6-1:

2), when the weight coefficient of active current is less than reactive current weight coefficient, namely during α < β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is larger.As shown in accompanying drawing 6-2:

Step 5.3, determines the precharge voltage value of soft start policy.When active current weight coefficient α reduces, DC voltage falls and can therefore reduce, but the Shaoxing opera that the startup overshoot process of Three-phase PWM Voltage Rectifier can become is strong.When active current weight coefficient α reduces, the pre-charge voltage of DC side output capacitance should be increased.As the result that Fig. 7-1 is when adopting precharge soft start policy, if Fig. 7-2 is results when not adopting precharge.

Verifying according to above-mentioned steps in simulation software with the two close cycles strategy of Model Predictive Control based on voltage squared control in the present invention, the control chart of whole system as shown in Figure 4, simulation results show is under the prerequisite realizing rectifier AC unity power factor and DC-side Voltage Stabilization (as illustrated in Figure 8 and 9 reference), and the design of voltage squared outer shroud effectively ensures it and inner ring active current is linear to make switch motion accurate and effective.Simultaneously the choosing of weight coefficient of Model Predictive Control has had further raising (as shown in Figure 10) for the dynamic responding speed of Three-phase PWM Voltage Rectifier and interference rejection ability than traditional control method.The method is correct, reliable, for engineer applied provides good reference value.

Claims (5)

1. the control method of the PWM rectifier controlled based on model prediction and voltage squared, it is characterized in that: utilize the voltage squared linear with active current as outer shroud, take Model Predictive Control as core, adopt PREDICTIVE CONTROL and the output interference rejection ability of optimal control to PWM rectifier to improve, step is as follows:

Step 1, determines the discrete models of Three-phase PWM Voltage Rectifier

Step 1.1, according to Kirchhoff's second law and current law, calculate the rectifier Mathematical Modeling under abc coordinate system, its expression formula is as follows:

$\left\{\begin{array}{c}\mathrm{esa}=L\frac{{\mathrm{di}}_a}{\mathrm{dt}}+{\mathrm{Ri}}_a+V_{\mathrm{aN}}+V_{\mathrm{No}}\\ \mathrm{esb}=L\frac{{\mathrm{di}}_b}{\mathrm{dt}}+{\mathrm{Ri}}_b+V_{\mathrm{bN}}+V_{\mathrm{No}}\\ \mathrm{esc}=L\frac{{\mathrm{di}}_c}{\mathrm{dt}}+{\mathrm{Ri}}_c+V_{\mathrm{cN}}+V_{\mathrm{No}}\end{array}\right.$

Wherein, esx (x=a, b, c) represents AC voltage, i _x(x=a, b, c) represents ac-side current, L represents AC filter inductance value, R represent adding of the equivalent resistance of line resistance, inductance and the equiva lent impedance of switching device and, N point represents the reference point position of DC side, O point represents the neutral point of AC three-phase voltage, V _xN(x=a, b, c) represents the voltage of rectifier AC three inputs to DC side reference point respectively, V _nOrepresent the voltage of DC side reference point to AC neutral point;

Step 1.2, for ease of controlling, utilizing phase-locked loop pll to obtain the current phase theta=ω t of line voltage, and obtaining based on the Mathematical Modeling under dq coordinate system by the Mathematical Modeling under abc coordinate system through synchronous rotating angle, as follows:

$\left\{\begin{array}{c}L\frac{{\mathrm{di}}_d}{\mathrm{dt}}=e_d+{\mathrm{\&omega;Li}}_d-{\mathrm{Ri}}_d-v_{\mathrm{dc}}{s}_d\\ L\frac{{\mathrm{di}}_q}{\mathrm{dt}}=e_q+{\mathrm{\&omega;Li}}_q-{\mathrm{Ri}}_q-v_{\mathrm{dc}}{s}_q\\ C\frac{{\mathrm{dv}}_{\mathrm{dc}}}{\mathrm{dt}}=i_q{s}_q+i_d{s}_d-i_L\end{array}\right.$

Wherein, d axle represents active power axle, and q axle represents reactive power axle, and 90 degree, the delayed q axle of d axle, in formula: e _d, e _qaC line voltage, esa, esb, the esc component under dq coordinate system, in like manner: i _d, i _qrectifier AC line current i _a, i _b, i _ccomponent under dq coordinate system; S _d, S _qon off state S _a, S _b, S _ccomponent under dq coordinate system, ω represents the power frequency angular velocity of rotation of electrical network, v _dcrepresent DC voltage value, the transformation matrix that above-mentioned conversion uses is:

$T_{\mathrm{abc}-\mathrm{dq}}=\frac{2}{3}\left[\begin{array}{ccc}\sin \left(\mathrm{\&omega;t}\right)& \sin (\mathrm{\&omega;t}-2\mathrm{\&pi;}/3)& \sin (\mathrm{\&omega;t}+2\mathrm{\&pi;}/3)\\ \cos \left(\mathrm{\&omega;t}\right)& \cos (\mathrm{\&omega;t}-2\mathrm{\&pi;}/3)& \cos (\mathrm{\&omega;t}+2\mathrm{\&pi;}/3)\end{array}\right]$

In matrix: T _abc-dqexpression is by the conversion of abc coordinate system to dq coordinate system, and ω t is the phase place of the current electric grid voltage utilizing phase-locked loop pll to obtain in step 1.2;

Step 1.3, will _dqfront two current equations in differential Mathematical Modeling under coordinate system are by forward direction Euler's formula discretization, wherein, T represents the sampling period, and k represents sampling instant, s _d, s _qfor on off state S _kcomponent under dq coordinate system, the Mathematical Modeling that discretization obtains is the electric current discrete models of Three-phase PWM Voltage Rectifier, and its expression formula is as follows:

$\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right]=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\&omega;T}\\ -\mathrm{\&omega;T}& 1-\frac{\mathrm{RT}}{L}\end{array}\right]\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right]\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$

Order $i\left(k\right)=\left[\begin{array}{c}{i}_d\left(k\right)\\ i_q\left(k\right)\end{array}\right]$ For controlled variable, $v_r\left(k\right)=\left[\begin{array}{c}{v}_{\mathrm{rd}}\left(k\right)\\ v_{\mathrm{rq}}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{e}_d\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_d\left(k\right)\\ e_q\left(k\right)-v_{\mathrm{dc}}\left(k\right)s_q\left(k\right)\end{array}\right]$ For control variables, and make $A=\left[\begin{array}{cc}1-\frac{\mathrm{RT}}{L}& \mathrm{\&omega;T}\\ -\mathrm{\&omega;T}& 1-\frac{\mathrm{RT}}{L}\end{array}\right],$ $B=\left[\begin{array}{cc}\frac{T}{L}& 0\\ 0& \frac{T}{L}\end{array}\right],$ Then above-mentioned electric current discrete models can be reduced to following formula:

i(k+1)＝Ai(k)+Bv _r(k)

Step 2, determines to take voltage squared as the outer voltage of control object

Step 2.1, for Three-phase PWM Voltage Rectifier, does square operation by output DC voltage, and exports with reference to also doing square operation by presetting given DC side, and two squared voltage are carried out doing difference and regulating through PI controller;

Step 2.2, the output after PI controller in step 2.1 regulates is as the reference set-point i of active current in current inner loop _d ^*;

The main-process stream of whole step 2 is by the set-point v of DC voltage _dc ^*with the current sample values v of DC voltage _dcdo after square operation obtains corresponding square value respectively, then by subtracter, by command value square to deduct current sample values square, difference is afterwards by outer voltage PI controller C _vs () controls to export the set-point obtaining active current;

Step 3, the finite aggregate on off state of inner ring current model prediction solves

Step 3.1, detects PWM rectifier AC three-phase voltage e _a, e _b, e _c, three-phase current i _a, i _b, i _cwith DC side output voltage v _dc, three-phase voltage and three-phase current are carried out the computing of three-phase static coordinate system to two-phase rotating coordinate system, after computing, obtain active voltage actual value e _d, active current actual value i _dwith reactive voltage actual value e _q, reactive current actual value i _q;

Step 3.2, for the discrete models that step 1.3 is determined, the on off state S that its control variables is namely corresponding _konly have 8 kinds of states, 7 kinds of different variablees, are expressed as follows:

$S=\{\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\},$ Wherein

For the on off state that each is determined, all bring determined discrete models in step 1.3 into, calculate a kind of predicted value, obtain 8 kinds of predicted values altogether:

$I{(k+1)}_n=\left[\begin{array}{c}{i}_d{(k+1)}_n\\ i_q{(k+1)}_n\end{array}\right],(n=\mathrm{1,2}...8)$

Step 3.3, in order to realize unity power factor, makes referenced reactive current value i _q ^*=0, active current command value i _d ^*determined by step 2.2, bring the predicted value of eight kinds obtained in active current command value, referenced reactive current value and step 3.2 into cost function in, calculate eight kinds of cost function value J _n(n=1,2 ... 8), wherein, α represents the weight coefficient of active current, and β represents the weight coefficient of reactive current;

Step 3.4, according to the cost function value generated in step 3.3, carries out size sequence, and selects minimum value wherein, obtain least cost function value minJ ∈ { J ₁, J ₂j ₈, and predicted value during this least cost function value of record generation in the corresponding step 3.2 needed $i(k+1)=\left[\begin{array}{c}{i}_d(k+1)\\ i_q(k+1)\end{array}\right];$

Step 3.5, bring the least cost function value generated in step 3.4 and corresponding predicted value into determine in step 1.3 discrete models, backwards calculation goes out required control variables v _ron off state S corresponding in (k) _k;

The main-process stream of whole step 3 algorithm is: the AC three-phase voltage of the current time rectifier of first sampling, three-phase current and DC voltage value.Then, calculate 8 kinds of predicted values by rectifier discrete models successively for 8 kinds of on off states, 8 kinds of predicted values substituted in cost function formula respectively successively, on off state corresponding when calculating least cost function value, then exports this on off state;

Step 4, the determination of voltage vector and the generation of pwm signal

Step 4.1, on off state S determined in step 3.5 _k(k=a, b, c), goes out corresponding to the voltage vector U under two-phase rest frame by following formulae discovery _a, U _b;

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;}}=\frac{2}{3}{u}_{\mathrm{dc}}[s_a-\frac{1}{2}(s_b+s_c)]\\ u_{\mathrm{\&beta;}}=\frac{\sqrt{3}}{3}{u}_{\mathrm{dc}}(s_b-s_c)\end{array}\right.$

Wherein, u _dcrepresent the DC voltage that present sample obtains;

Step 4.2, by step 4.1 gained voltage vector U _a, U _bmodulated by the method for Space Vector Modulation Strategy SVPWM, obtain the drive pulse signal of six groups of IGBT;

Step 5, the selection of weight coefficient and the cooperation of soft start policy

Step 5.1, first meritorious electric current weighting factor alpha is determined, according to the interference rejection ability of Three-phase PWM Voltage Rectifier DC side output voltage, can fall after DC voltage is disturbed again, suitable meritorious weight coefficient α is selected according to the size fallen, its value is less, and Voltage Drop can be less;

Step 5.2, determines the weight coefficient β of reactive current, determines idle weight coefficient β according to the total harmonic distortion factor THD of ac-side current, and the change of its value and the variation relation of THD follow following rule:

1), when active current weight coefficient is much larger than reactive current weight coefficient, namely during α >> β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is less;

2), when the weight coefficient of active current is less than reactive current weight coefficient, namely during α < β, when reactive current weight coefficient β is less, the total harmonic distortion factor THD of ac-side current is larger;

Step 5.3, determines the precharge voltage value of soft start policy, and when active current weight coefficient α reduces, DC voltage falls and can therefore reduce, but the startup overshoot process of Three-phase PWM Voltage Rectifier meeting Shaoxing opera is strong; When active current weight coefficient α more hour, the pre-charge voltage of DC side output capacitance should be increased.

2. the control method of a kind of PWM rectifier controlled based on model prediction and voltage squared according to claim 1, it is characterized in that: voltage squared is as outer shroud control object, linear with inner ring active current, enable the change accurate response of voltage in active current, precise control is rapid.

3. the control method of a kind of PWM rectifier controlled based on model prediction and voltage squared according to claim 1, it is characterized in that: interior circular current adopts Model Predictive Control, solve the Delay control inaccessiable fast dynamic response problem of tradition based on PI, whole inner ring rate of current is fast, precise control, meanwhile, Model Predictive Control changes weight coefficient can make current transformer have stronger robustness to disturbance, has good effect to disturbance suppression.

4. the control method of a kind of PWM rectifier controlled based on model prediction and voltage squared according to claim 1, it is characterized in that: the cost function of finite aggregate on off state solving model prediction, avoid the method that tradition solves derivative can expend huge computing time and take a large amount of memory spaces, be easy to realize at digitial controller.

5. the control method of a kind of PWM rectifier controlled based on model prediction and voltage squared according to claim 1, is characterized in that: the soft start policy of precharge coordinates the weight coefficient of cost function to change can to make system to realize compared with the prerequisite of high inhibition load disturbance that start-up course is rapid, overshoot is little having.