CN106130077A - Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm - Google Patents

Abstract

Present invention electric automobile based on virtual synchronous electromotor algorithm compensation of power network voltage method, comprises the following steps: 1) electric automobile network interface use virtual synchronous electromotor algorithm, based on P f, Q V droop control；2) obtained and network interface output frequency w, phase angle theta by the mechanical equation of simulation synchronous generator；3) electrically equation part uses voltage and current double-loop control strategy based on dq coordinate system；4) increasing virtual impedance in electric equation part to control, virtual impedance includes constant virtual impedance and transient state virtual resistance, obtains virtual pressure drop, by step 1) the voltage instruction E that obtains instructs e as Voltage loop d axle_d, e_qEqual to 0, e_d、e_qRespectively with virtual pressure drop v_vd、v_vqMake difference and obtain the instruction of Voltage loop output voltage5) by step 3) output of electric current loop obtains and the dq axle modulated signal of network interface obtains the switch controlling signal of converter switches network again after PWM through coordinate transform, and then be used for driving switching network.

Description

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm

Technical field:

The invention belongs to the friendly grid-connected field of electric automobile based on virtual synchronous generator techniques, be specifically related to a kind of base Electric automobile compensation of power network voltage method in virtual synchronous electromotor algorithm.

Background technology:

New-energy electric vehicle can effectively reduce greenhouse gas emission, alleviates environmental pollution, is present stage traffic low-carbon (LC) Change one of important realization means of development.Development for reply electric automobile is universal with extensive, and research electric automobile close friend is also Net, utilizes the safe and stable operation that the electric automobile charge/discharge capacity of high permeability is electrical network to provide a supporting role and has great meaning Justice.

New-energy electric vehicle is as the distributed energy-storage system of a kind of movable type, and general employing power electronic equipment is made For and network interface, its potential assistant service must fully be excavated, and New-energy electric vehicle must provide necessary auxiliary to electrical network Help service.The electric automobile charge/discharge control method of application virtual synchronous generator techniques is the electronic vapour of the one proposed in recent years The good grid-connected solution of automobile friend.Virtual synchronous electromotor algorithm, by simulating the external characteristics of conventional synchronization electromotor, controls electricity Electrical automobile network interface provide inertia and damping to electrical network as conventional synchronization electromotor, reduce electric automobile network interface pair The impact of electrical network, promotes the adaptability that extensive electric automobile is accessed by electrical network.Virtual synchronous electromotor is to pass through droop control Realize electric automobile active power and the control of reactive power, when points of common connection line voltage is sent out with charge-discharge electric power instruction When raw symmetry is fallen, electric automobile network interface can produce a temporary impact electric current, threaten electric automobile charge and discharge device Safe and reliable operation, the biggest impact causing electric automobile charge and discharge device of grid voltage sags more serious impact electric current is more Seriously.Mostly the electric automobile charge/discharge control method of existing application virtual synchronous generator techniques is normal for line voltage Operating mode, rarely have document mention application virtual synchronous generator techniques electric automobile discharge and recharge at grid voltage sags or low electricity The operation problem of pressure.

Summary of the invention:

It is an object of the invention to deposit for existing electric automobile close friend's connect-in strategy based on virtual synchronous generator techniques The adaptive defect that voltage compensation is provided for electrical network of charge-discharge electric power can not changed according to the Voltage Drop situation of electrical network, carry Supply a kind of electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm.

For reaching above-mentioned purpose, the present invention adopts the following technical scheme that and realizes:

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm, comprises the following steps:

1) Three-Phase PWM Converter of the also network interface LC filtering of electric automobile charge and discharge device uses virtual synchronous electromotor Algorithm, this algorithm droop control based on P-f, Q-V forms power outer shroud, the active power of discharge and recharge instruct P_ref, idle merit Rate instruction Q_refObtain and mechanical output P of network interface with also network interface output frequency w, output reactive power q feedback_m, Voltage loop Instruction E；

2) model rotor mechanical equation part, according to the output mechanical power P of virtual synchronous generator power outer shroud_mWith reality Border active power of output P_eDifference through being calculated the output frequency w of virtual synchronous electromotor, and acquisition of being quadratured And the output phase angle theta of network interface；

3) electric equation part, uses voltage and current double-loop control strategy based on dq coordinate system, obtains through over-sampling Actual three-phase to virtual synchronous electromotor exports electric current, grid-connected interface side inductive current and output voltage, is carried out coordinate Conversion obtains exporting the dq component i of electric current_d、i_qDq component i with inductive current_ld、i_lqAnd the dq component v of output voltage_od、 v_oq；

4) in step 1) and step 3) on the basis of increase the virtual impedance under dq coordinate system and control, through step 3) sample The output electric current i arrived_d、i_qFlow through virtual impedance R_v、X_vProduce virtual pressure drop v_vd、v_vq, by step 1) and the Voltage loop that obtains instruction E E is instructed as the Voltage loop d axle under dq coordinate system_d, the Voltage loop q axle under dq coordinate system instructs e_qEqual to 0, e_d、e_qRespectively with void Intend pressure drop v_vd、v_vqMake difference and obtain the instruction of Voltage loop output voltage

5) by step 3) output of electric current loop obtains and the dq axle modulated signal of network interface obtains three-phase through coordinate transform Modulated signal under rest frame, the phase angle of coordinate transform is by step 2) obtain and network interface output phase angle theta, then pass through Obtain the switch controlling signal of converter switches network after PWM, and then be used for driving switching network.

The present invention is further improved by, step 1) in, introduce a COEFFICIENT K_delta, the active power instruction of discharge and recharge P_refWith the COEFFICIENT K introduced_deltaIt is multiplied and obtains new P_ref1,P_ref1Meritorious instruction as P-f droop control.

The present invention is further improved by, step 2) in, the computing formula of output frequency w and output phase angle theta is as follows:

$\frac{2H}{w_b}\frac{d\mathrm{\δ}w}{dt}=\frac{P_m-P_e}{S_b}-\frac{k_{damper}}{w_b}\mathrm{\δ}w$

δ w=w-w_grid

In formula, H is mechanical time constant H, k_damperFor damped coefficient, w_gridFor mains frequency, w_bOn the basis of frequency and, S_b It is rated power.

The present invention is further improved by, step 3) in, the output electric current i that sampled and coordinate transform obtains_d、i_qIncrease Add a passage, allow i_d、i_qFiltered i is obtained through high pass filter_{d_H}、i_{q_H}, concrete formula is as follows:

$\left\{\begin{array}{c}{i}_{d\_H}=i_d*\frac{s}{s+w_{c\_h}}\\ i_{q\_H}=i_q*\frac{s}{s+w_{c\_h}}\end{array}\right.$

In formula: w_{c_h}For High Pass Filter Cutoff Frequency, s is integral operator.

The present invention is further improved by, step 3) in, utilize the output electric current i that sampling and coordinate transform obtain_d、i_q With output voltage v_od、v_oq, calculate the active-power P of electric automobile output_e, reactive power q_o, then respectively through low-pass filtering Device obtains the filtered idle q of meritorious p, utilizes p and q to carry out calculating and judgement obtains step 1) in the COEFFICIENT K that introduces_delta, tool Body formula is as follows:

$\left\{\begin{array}{c}{P}_e=1.5(v_{od}*i_d+v_{oq}*i_q)\\ q_o=1.5(-v_{od}*i_q+v_{oq}*i_d)\end{array}\right.$

$\left\{\begin{array}{c}p=P_e*\frac{w_{c\_1}}{w_{c\_1}+s}\\ q=q_o*\frac{w_{c\_1}}{w_{c\_1}+s}\end{array}\right.$

In formula: w_{c_l}For low pass filter cutoff frequency.

The present invention is further improved by, step 4) in, it is constant that virtual impedance controls that virtual impedance is divided into two parts Virtual impedance R_cv、X_cvWith transient state virtual resistance Δ R_v, virtual pressure drop is divided into the constant virtual pressure drop v of two parts_cvd、v_cvqEmpty with transient state Intend pressure drop Δ v_vd、Δv_vq, concrete formula is as follows:

$\left\{\begin{array}{c}{v}_{cvd}=R_{cv}*i_d-X_{cv}*i_q\\ v_{cvq}=R_{cv}*i_q+X_{cv}*i_d\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\Δv}}_{vd}={\mathrm{\ΔR}}_v*i_{d\_H}\\ {\mathrm{\Δv}}_{vq}={\mathrm{\ΔR}}_v*i_{q\_H}\end{array}\right.$

$\left\{\begin{array}{c}{v}_{vd}=v_{cvd}+{\mathrm{\Δv}}_{vd}\\ v_{vq}=v_{cvq}+{\mathrm{\Δv}}_{vq}\end{array}\right..$

Compared with prior art, present invention electric automobile based on virtual synchronous electromotor algorithm compensation of power network voltage method Advantage be embodied in: when line voltage falls, electric automobile network interface output active reactive have one long-time Overshoot vibration, when causing electric automobile network interface exceed capacity and reach stable state system output have also exceeded capacity.

Further, before the meritorious instruction of P-f droop control, a COEFFICIENT K is introduced_delta, when grid voltage sags, Meritorious instruction so can maximally utilize electric automobile charge and discharge electric capacity according to grid voltage sags amplitude self-adaptative adjustment Amount compensation network voltage symmetry is fallen, and improves grid voltage quality, reduces meritorious output and avoids system to exceed capacity.

Further, the output electric current i that sampled and coordinate transform obtains_d、i_qIncrease a passage, allow i_d、i_qThrough too high Bandpass filter obtains filtered i_{d_H}、i_{q_H}, so can obtain electric automobile during electrical network generation Voltage Drop network interface The aperiodic component i.e. oscillating current of output electric current, provides passage and information for system suppression dash current.

Further, voltage x current sampled signal is utilized to calculate the active-power P of electric automobile output_e, reactive power q_o, Then obtaining the filtered idle q of meritorious p respectively through low pass filter, do so can obtain electrical network normal voltage and voltage When falling and network interface output active reactive steady-state value, according to the steady-state value design factor K of active reactive_delta, calculate in real time The steady-state value of active reactive can monitor the duty of system, it is to avoid system exceedes when electrical network normal voltage and Voltage Drop Capacity.

Further, transient state virtual resistance Δ R is increased_v, it is possible to during suppression grid voltage sags, the cycle of dash current divides Amount and aperiodic component, reduce the time constant of aperiodic component, and grid-connected interface hardware circuitry is rushed by suppression dash current Hit its working life of raising.

Accompanying drawing illustrates:

Fig. 1 is virtual synchronous electromotor P-f droop control and rotor mechanical equation simulation control block diagram；

Fig. 2 is Q-V droop control block diagram；

Fig. 3 is virtual impedance control block diagram；

Fig. 4 is COEFFICIENT K_deltaComputing block diagram and flow chart, Fig. 4 (a) is p, q computing block diagram, and Fig. 4 (b) is COEFFICIENT K_delta Calculation flow chart；

Fig. 5 Double closed-loop of voltage and current block diagram；

Fig. 6 is embodiment line voltage symmetry meritorious, reactive power waveform when falling；Wherein, Fig. 6 (a) is for applying this Bright institute extracting method is meritorious, reactive power waveform, and Fig. 6 (b) is rung by meritorious, the reactive power that do not add the carried decoupling method of the present invention Answer waveform；

Fig. 7 is embodiment COEFFICIENT K_deltaResult of calculation；

Fig. 8 is the virtual pressure drop of the transient state produced by transient state virtual resistance in embodiment.

Detailed description of the invention:

With specific embodiment, the present invention is described in further details below in conjunction with the accompanying drawings.

Present invention electric automobile based on virtual synchronous electromotor algorithm compensation of power network voltage method, comprises the following steps:

1) meritorious droop control and model rotor mechanical equation part, according to the reference of the active power of output of electric automobile Instruction P_refWith COEFFICIENT K_deltaIt is multiplied and obtains the reference instruction P of actual active power of output_ref1, export according to actual electric automobile Frequency w and instruction frequency w_refDifference, with sagging Coefficient m_pIt is multiplied and obtains Δ p, P_ref1Deduct Δ p and obtain mechanical output P_m, this Being P-f droop control, simulate the primary frequency function of conventional synchronization electromotor, as shown in fig. 1 on the left-hand side, concrete formula is as follows:

P_m=P_ref*K_delta-m_p(w-w_ref) (1)

Model rotor mechanical equation part, as shown on the right side of Fig. 1, simulates conventional synchronization electromotor by mechanical time constant H Rotary inertia, damped coefficient k_damperSimulation Damper Winding, obtains the output frequency w of electric automobile network interface, after integration To output phase theta, concrete formula is as follows:

$\frac{2H}{w_b}\frac{d\mathrm{\δ}w}{dt}=\frac{P_m-P_e}{S_b}-\frac{k_{damper}}{w_b}\mathrm{\δ}w---\left(2\right)$

δ w=w-w_grid (3)

W in formula_gridFor mains frequency, w_bOn the basis of frequency and, S_bIt is rated power；

2) idle droop control, as in figure 2 it is shown, the sagging simulation of Q-V is the automatic voltage regulator of conventional synchronization electromotor AVR, idle feedback q is actual output reactive power value after low-pass filtering, and concrete formula is as follows:

E=V_ref+n_q(Q_ref-q) (4)

3) virtual impedance control as it is shown on figure 3, virtual impedance effect under dq coordinate system be a virtual electric automobile also The internal resistance of network interface voltage source, the virtual impedance of the present invention includes two parts, and first output electric current flows through constant virtual impedance R_cv、 X_cvProduce constant virtual pressure drop v_cvd、v_cvq, this partial virtual pressure drop system transient state and stable state all have value, utilize this part empty Intend impedance and can improve system impedance ratio promotion decoupled active and reactive, but be easily caused if wherein virtual resistance is the least System damping not pedal system is unstable, so the present invention adds transient state virtual resistance Δ R_v, first electric automobile output electric current warp Flow through transient state virtual resistance after crossing high-pass filtering and produce transient state virtual pressure drop Δ v_vd、Δv_vq, this part pressure drop has value when transient state Being 0 during stable state, transient state virtual resistance can suppress the dash current produced because of grid voltage sags；Two parts virtual pressure drop sum For v_vd、v_vq, e_d、e_qRespectively with virtual pressure drop v_vd、v_vqMake difference and obtain the instruction of Voltage loop output voltageConcrete formula As follows:

$\left\{\begin{array}{c}{v}_{o,d}^{*}=e_d-v_{vd}\\ v_{o,q}^{*}=e_q-v_{vq}\end{array}\right.---\left(5\right)$

4) COEFFICIENT K_deltaCalculating, obtain output voltage v through over-sampling_od、v_oqWith output electric current i_d、i_q, through calculating To COEFFICIENT K_delta, concrete calculation flow chart as shown in Figure 4, exports meritorious P first with output voltage and Current calculation are actual_eWith Reactive power q_o, it is then passed through low pass filter and obtains filtered meritorious p and idle q, then carry out the stream as shown in Fig. 4 (b) Cheng Jinhang is calculated COEFFICIENT K_delta；Then step 1 is carried out) P-f droop control；

5) dq coordinate system Double closed-loop of voltage and current, as it is shown in figure 5, by step 3) the Voltage loop output order that obtainsAs the input of Voltage loop, the feedback quantity of Voltage loop is in electric automobile output voltage i.e. LC filter capacity Output voltage, the output of Voltage loop is as the instruction of internal ring electric current loop, and the feedback quantity of electric current loop is the inductance electricity on LC wave filter Stream, is obtained by the output of electric current loop and the dq axle modulated signal of network interface is under coordinate transform obtains three-phase static coordinate system Modulated signal, the phase angle of coordinate transform is by step 1) obtain and network interface output phase angle theta, then obtain after PWM The switch controlling signal of converter switches network, and then be used for driving switching network.

Embodiment:

When 1s, line voltage symmetry falls 32.14%, returns to normal voltage after 2s, and contrast adds the put forward void of the present invention Intend impedance design and power instruction self-adaptation control method and the electric automobile charge and discharge electric work being not added with the put forward control method of the present invention Rate controls effect.

1s moment line voltage symmetry falls 32.14%, returns to normal voltage after 2s, and under this operating mode, electric automobile is grid-connected The change of interface active power of output, reactive power waveform are as shown in Figure 6.Add the design of the present invention proposed virtual impedance and power refers to Making shown in electric automobile active reactive waveform such as Fig. 6 (a) of self-adaptation control method, during 0～1s, line voltage is normal Value, electric automobile is operated under electrical network orderly discharge and recharge dispatch command pattern the meritorious idle 0Var of 5000w of output, at 1s moment electricity Net voltage symmetry falls 32.14%, and now active reactive has an instantaneous impact, is then passed through the meritorious stable state that arrives and exports Arrival stable state that 3500w is idle output 9350Var, returns to again normal value at 2s moment line voltage, and now active reactive has One instantaneous impact, then the meritorious stable state output 5000w idle arrival stable state that arrives exports 0Var, and electric automobile returns to electricity Pressure symmetry falls the instruction output of front dispatching of power netwoks；Fig. 6 (b) show meritorious, the idle sound being added without institute of the present invention extracting method Answering waveform, as can be seen from Figure when there is grid voltage sags, active reactive has a long overshoot vibration, leads Send a telegraph electrical automobile and system output have also exceeded capacity time network interface exceedes capacity and reaches stable state.Therefore the carried electricity of the present invention Net voltage compensation strategy, it is possible to effective compensation grid voltage sags and substantially reduce dash current to and network interface Impact.

Fig. 7 show COEFFICIENT K_deltaOutput valve, as can be seen from the figure K before line voltage symmetry is fallen_deltaIt is equal to 1, K after line voltage recovers_deltaIt is also equal to 1, only falls 2～3s period K in line voltage symmetry_deltaIt is not equal to 1, according to The capacity K of electric automobile discharge and recharge_deltaValue reach steady-state value 0.7 through the fluctuation of 0.376s；Therefore the carried power of the present invention Adaptive approach have no effect on line voltage normal time electric automobile duty, only there is symmetry at line voltage in this strategy Working when falling, make the charge-discharge electric power instruction adaptive change of electric automobile, when grid voltage sags, system is to support Line voltage is main, and residual capacity active power of output instructs.

Fig. 8 show the virtual pressure drop under the dq coordinate system produced by transient state virtual resistance, v as can be seen from Figure_vd、 v_vqOnly having value in the transient process that voltage ripple of power network occurs, when stable state and when line voltage is normal, its value is 0；By This can be seen that the present invention carried virtual impedance method for designing does not produce void when systematic steady state and when line voltage is normal Intend pressure drop and affect power distribution and power decoupled, only suppress when transient state dash current to electric automobile the infringement of network interface.

To sum up, this example demonstrates the present invention and carried electric automobile compensation network based on virtual synchronous electromotor algorithm The effectiveness of voltage control strategy.The design parameter of embodiment arranges and sees table 1:

Table 1 embodiment parameter

Claims (6)

1. electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm, it is characterised in that include following step Rapid:

1) Three-Phase PWM Converter of the also network interface LC filtering of electric automobile charge and discharge device uses virtual synchronous electromotor to calculate Method, this algorithm droop control based on P-f, Q-V forms power outer shroud, the active power of discharge and recharge instruct P_ref, reactive power Instruction Q_refObtain and mechanical output P of network interface with also network interface output frequency w, output reactive power q feedback_m, voltage fourth finger Make E；

2) model rotor mechanical equation part, according to the output mechanical power P of virtual synchronous generator power outer shroud_mDefeated with reality Go out active-power P_eDifference through being calculated the output frequency w of virtual synchronous electromotor, and acquisition of being quadratured is grid-connected The output phase angle theta of interface；

3) electric equation part, uses voltage and current double-loop control strategy based on dq coordinate system, obtains void through over-sampling Intend the actual three-phase output electric current of synchronous generator, grid-connected interface side inductive current and output voltage, carried out coordinate transform Obtain exporting the dq component i of electric current_d、i_qDq component i with inductive current_ld、i_lqAnd the dq component v of output voltage_od、v_oq；

4) in step 1) and step 3) on the basis of increase the virtual impedance under dq coordinate system and control, through step 3) sampling obtains Output electric current i_d、i_qFlow through virtual impedance R_v、X_vProduce virtual pressure drop v_vd、v_vq, by step 1) and the instruction E conduct of the Voltage loop that obtains Voltage loop d axle instruction e under dq coordinate system_d, the Voltage loop q axle under dq coordinate system instructs e_qEqual to 0, e_d、e_qRespectively with virtual pressure Fall v_vd、v_vqMake difference and obtain the instruction of Voltage loop output voltage

5) by step 3) output of electric current loop obtains and the dq axle modulated signal of network interface obtains three phase static through coordinate transform Modulated signal under coordinate system, the phase angle of coordinate transform is by step 2) obtain and network interface output phase angle theta, then through PWM Obtain the switch controlling signal of converter switches network after modulation, and then be used for driving switching network.

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm the most according to claim 1, its It is characterised by, step 1) in, introduce a COEFFICIENT K_delta, the active power instruction P of discharge and recharge_refWith the COEFFICIENT K introduced_deltaPhase Multiplied to new P_ref1,P_ref1Meritorious instruction as P-f droop control.

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm the most according to claim 1, its It is characterised by, step 2) in, the computing formula of output frequency w and output phase angle theta is as follows:

$\frac{2H}{w_b}\frac{d\mathrm{\δ}w}{dt}=\frac{P_m-P_e}{S_b}-\frac{k_{damper}}{w_b}\mathrm{\δ}w$

δ w=w-w_grid

In formula, H is mechanical time constant H, k_damperFor damped coefficient, w_gridFor mains frequency, w_bOn the basis of frequency and, S_bIt it is volume Determine power.

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm the most according to claim 1, its It is characterised by, step 3) in, the output electric current i that sampled and coordinate transform obtains_d、i_qIncrease a passage, allow i_d、i_qPass through High pass filter obtains filtered i_{d_H}、i_{q_H}, concrete formula is as follows:

$\left\{\begin{array}{c}{i}_{d\_H}=i_d*\frac{s}{s+w_{c\_h}}\\ i_{q\_H}=i_q*\frac{s}{s+w_{c\_h}}\end{array}\right.$

In formula: w_{c_h}For High Pass Filter Cutoff Frequency, s is integral operator.

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm the most according to claim 2, its It is characterised by, step 3) in, utilize the output electric current i that sampling and coordinate transform obtain_d、i_qWith output voltage v_od、v_oq, calculate electricity The active-power P of electrical automobile output_e, reactive power q_o, then obtain filtered meritorious p respectively through low pass filter idle Q, utilizes p and q to carry out calculating and judgement obtains step 1) in the COEFFICIENT K that introduces_delta, concrete formula is as follows:

$\left\{\begin{array}{c}{P}_e=1.5(v_{od}*i_d+v_{oq}*i_q)\\ q_o=1.5(-v_{od}*i_q+v_{oq}*i_d)\end{array}\right.$

$\left\{\begin{array}{c}p=P_e*\frac{w_{c\_1}}{w_{c\_1}+s}\\ q=q_o*\frac{w_{c\_1}}{w_{c\_1}+s}\end{array}\right.$

In formula: w_{c_l}For low pass filter cutoff frequency.

Electric automobile compensation of power network voltage method based on virtual synchronous electromotor algorithm the most according to claim 1, its It is characterised by, step 4) in, virtual impedance controls to be divided into virtual impedance two parts constant virtual impedance R_cv、X_cvEmpty with transient state Intend resistance Δ R_v, virtual pressure drop is divided into the constant virtual pressure drop v of two parts_cvd、v_cvqPressure drop Δ v virtual with transient state_vd、Δv_vq, specifically Formula is as follows:

$\left\{\begin{array}{c}{v}_{cvd}=R_{cv}*i_d-X_{cv}*i_q\\ v_{cvq}=R_{cv}*i_q+X_{cv}*i_d\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\Δv}}_{vd}={\mathrm{\ΔR}}_v*i_{d\_H}\\ {\mathrm{\Δv}}_{vq}={\mathrm{\ΔR}}_v*i_{q\_H}\end{array}\right.$

$\left\{\begin{array}{c}{v}_{vd}=v_{cvd}+{\mathrm{\Δv}}_{vd}\\ v_{vq}=v_{cvq}+{\mathrm{\Δv}}_{vq}\end{array}\right..$