CN102545227B - Phase-sequence-identification-based adaptive control method for active power filter - Google Patents

Abstract

The invention discloses a phase-sequence-identification-based adaptive control method for an active power filter. The method comprises the following steps of: (1) performing phase sequence identification on the voltage of a power grid; (2) extracting the phase of the voltage of the power grid; (3) acquiring load current, direct current bus voltage and compensating current; (4) constructing a modulation signal; and (5) generating a pulse width modulation (PWM) switching signal for controlling a switching tube of the active power filter. By the method, the adaptive control and normal running of the active power filter can be realized under positive and negative sequence power grid voltage conditions, the process of detecting the phase sequence of the power grid by additional detection equipment is eliminated, and the active power filter can be adaptively controlled and runs regardless of positive and negative sequence connection; and the method can be easily implemented on a digital signal processor (DSP) chip by adopting C programming.

Description

A kind of self-adaptation control method of the Active Power Filter-APF based on phase sequence identification

Technical field

The invention belongs to the control technology field of electric-power filter, be specifically related to a kind of self-adaptation control method of the Active Power Filter-APF based on phase sequence identification.

Background technology

In recent years along with the develop rapidly of industrial technology, society's electrifing degree improves constantly, in electrical network, the reactive loads such as various large capacity induction motors, specific type of electric machine are widely used, the powerful load access of these large capacity operation of power networks uses not only consumption idle in a large number, and produce a large amount of harmonic waves, the severe contamination electrical network, reduce the electrical network service efficiency, affects power supply quality.In order to alleviate these harmful effects, can have access to active power filter (APF) by the points of common connection at load and electrical network (PPC) and stablize PCC voltage, improve the electrical network quality of power supply; Therefore Active Power Filter-APF can realize dynamically following the tracks of the idle and harmonic wave of compensating load.

Generally, the control strategy of Active Power Filter-APF all is based under line voltage positive sequence condition and designs, therefore these equipment must carry out wiring with the three-phase electricity of positive sequence when application.

But under a lot of actual conditions of industry spot, do not have corresponding sign about phase sequence on threephase cable, before Active Power Filter-APF will being accessed electrical network, must first by checkout gear, to threephase cable, carry out phase sequence and detect identification, after determining that ABC mutually, again threephase cable is pressed positive sequence wiring corresponding to Active Power Filter-APF, the normal operation of guarantee electric-power filter.Whole process is relatively complicated, needs corresponding checkout equipment, needs operating personnel to detect discriminatory analysis, wastes time and energy, and also expends corresponding device resource.

But therefore how to develop the control strategy of a cover self adaptation electrical network phase sequence, make Active Power Filter-APF no matter with electrical network positive sequence or negative phase-sequence wiring situation under can work, be a problem that is worth research.

Summary of the invention

The invention provides a kind of self-adaptation control method of the Active Power Filter-APF based on phase sequence identification, can realize adaptive control and the normal operation of Active Power Filter-APF under positive and negative order line voltage condition.

A kind of self-adaptation control method of the Active Power Filter-APF based on phase sequence identification, comprise the steps:

(1) gather line voltage, line voltage is carried out phase sequence identification, obtain the phase sequence of line voltage;

(2) extract the phase place of line voltage according to described phase sequence;

(3) gather DC bus-bar voltage and the offset current of load current and Active Power Filter-APF;

(4) structure modulation signal;

A. make load current obtain harmonic current d q component through Clarke conversion, Park conversion and filtering successively according to described phase sequence and phase place;

B. according to described phase sequence and phase place respectively to offset current with line voltage carries out the Clarke conversion successively and the Park conversion is compensated electric current d q component and line voltage d q component;

C. make DC bus-bar voltage regulate through voltage control the output variable and the addition of harmonic current q axle component that obtain and obtain current-order q axle component;

D. make offset current d q component, current-order q axle component and harmonic current d axle component regulate through Current Control the output variable and the addition of line voltage d q component that obtain and obtain voltage instruction d q component;

E. make voltage instruction d q component obtain modulation signal through Park inverse transformation and Clarke inverse transformation successively according to described phase sequence and phase place;

(5) utilize PWM (pulse width modulation) modulator that described modulation signal and given triangular carrier signal are compared, generate pwm switching signal, with the switching tube in Active Power Filter-APF, control.

In described step (1), the method for line voltage being carried out phase sequence identification is:

1) line voltage is carried out the Clarke conversion, obtain α axle component and the beta-axis component of line voltage; 2) adopt the Park transformation matrix $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)$ α axle component and beta-axis component to line voltage carry out the Park conversion, obtain d axle component and the q axle component of line voltage; Wherein: θ is the phase place of line voltage;

3) d axle component and the q axle component of line voltage are judged detection:

If $\left(\begin{array}{c}{u}_d\\ u_q\end{array}\right)=V_m\·\left(\begin{array}{c}0\\ -1\end{array}\right),$ The phase sequence of line voltage is positive sequence;

If $\left(\begin{array}{c}{u}_d\\ u_q\end{array}\right)=V_m\·\left(\begin{array}{c}\sin \left(2\mathrm{\θ}\right)\\ \cos \left(2\mathrm{\θ}\right)\end{array}\right),$ The phase sequence of line voltage is negative phase-sequence;

Wherein: u _dAnd u _qBe respectively d axle component and the q axle component of line voltage, V _mAmplitude for line voltage.

In described step (2), the process of line voltage being carried out phase extraction is: make line voltage as input signal, after Clarke conversion, Park conversion, arc tangent conversion, PI regulate, superpose feedforward angular frequency and integral transformation, export the phase place of line voltage successively;

Described arc tangent conversion is based on following formula:

$\mathrm{\Δ\θ}=\arctan \frac{\mathrm{seq}\·u_d}{-u_q}$

Wherein: u _dAnd u _qBe respectively d axle component and the q axle component of line voltage, Δ θ is phase error signal; If the line voltage phase sequence is positive sequence, seq=1; If the line voltage phase sequence is negative phase-sequence, seq=-1.

Described Park conversion based on the Park transformation matrix be:

If the line voltage phase sequence is positive sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right);$

If the line voltage phase sequence is negative phase-sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}-\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right);$

Described Park inverse transformation based on Park inverse transformation matrix be:

If the line voltage phase sequence is positive sequence, $T{\left(\mathrm{\θ}\right)}^{-1}=\left(\begin{array}{cc}\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right);$

If the line voltage phase sequence is negative phase-sequence, $T{\left(\mathrm{\θ}\right)}^{-1}=\left(\begin{array}{cc}-\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right);$

Wherein: T (θ) is the Park transformation matrix, T (θ) ^-1For Park inverse transformation matrix, θ is the phase place of line voltage.

Described load current is to flow into the electric current of load from electrical network, and described DC bus-bar voltage is the input voltage of Active Power Filter-APF DC side, and described offset current is the electric current that Active Power Filter-APF injects to electrical network; Described d q component comprises d axle component and q axle component.

The inventive method can realize adaptive control and the normal operation of Active Power Filter-APF under positive and negative order line voltage condition, saved and adopted the testing process of additional detections equipment to the electrical network phase sequence, no matter positive and negative order wiring, can make the adaptive control of active electric power filter and operation; And the inventive method can adopt the C Programming with Pascal Language, realizes on DSP (digital signal processor) chip, implements simple and easy.

Description of drawings

Fig. 1 is the steps flow chart schematic diagram of the inventive method.

Fig. 2 is the execution schematic flow sheet of phase-locked loop.

Fig. 3 is the schematic diagram of active power filter system.

Fig. 4 is the schematic flow sheet that the present invention constructs modulation signal.

When Fig. 5 is line voltage positive sequence, adopt the inventive method line voltage synchronous oscillogram.

When Fig. 6 is the line voltage negative phase-sequence, do not adopt the inventive method line voltage synchronous oscillogram.

When Fig. 7 is the line voltage negative phase-sequence, adopt the inventive method line voltage synchronous oscillogram.

When Fig. 8 is line voltage positive sequence, adopt the offset current oscillogram of the inventive method Active Power Filter-APF.

When Fig. 9 is the line voltage negative phase-sequence, adopt the offset current oscillogram of the inventive method Active Power Filter-APF.

Embodiment

, in order more specifically to describe the present invention, below in conjunction with the drawings and the specific embodiments, self-adaptation control method of the present invention is elaborated.

As illustrated in fig. 1 and 2, a kind of self-adaptation control method of the Active Power Filter-APF based on phase sequence identification, comprise the steps:

(1) gather line voltage u _s, to line voltage u _sCarry out phase sequence identification, obtain line voltage u _sPhase sequence.

1) according to following formula, line voltage is carried out the Clarke conversion, obtain α axle component and the beta-axis component of line voltage;

$\left(\begin{array}{c}{u}_{\mathrm{\α}}\\ u_{\mathrm{\β}}\end{array}\right){=T}_{\mathrm{\α\β}}\·\left(\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right)$ $T_{\mathrm{\α\β}}=\frac{2}{3}\·\left(\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right)$

Wherein: u _αAnd u _βBe respectively α axle component and the beta-axis component of line voltage, T _{α β}For Clarke transformation matrix, u _a, u _bAnd u _cBe respectively line voltage u _sPhase voltage on the abc-coordinate system.

2) adopt the Park transformation matrix $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)$ According to following formula, α axle component and the beta-axis component of line voltage carried out the Park conversion, obtain d axle component and the q axle component of line voltage;

$\left(\begin{array}{c}{u}_d\\ u_q\end{array}\right)=T\left(\mathrm{\θ}\right)\·\left(\begin{array}{c}{u}_{\mathrm{\α}}\\ u_{\mathrm{\β}}\end{array}\right)$

Wherein: θ is the phase place of line voltage, and T (θ) is the Park transformation matrix, u _dAnd u _qBe respectively d axle component and the q axle component of line voltage.

3) d axle component and the q axle component of line voltage are judged detection:

If $\left(\begin{array}{c}{u}_d\\ u_q\end{array}\right)=V_m\·\left(\begin{array}{c}0\\ -1\end{array}\right),$ The phase sequence of line voltage is positive sequence;

If $\left(\begin{array}{c}{u}_d\\ u_q\end{array}\right)=V_m\·\left(\begin{array}{c}\sin \left(2\mathrm{\θ}\right)\\ \cos \left(2\mathrm{\θ}\right)\end{array}\right),$ The phase sequence of line voltage is negative phase-sequence;

Wherein: V _mAmplitude for line voltage.

(2) utilize phase-locked loop to extract line voltage u according to phase sequence _sPhase theta.

As shown in Figure 3, make line voltage u _sAs input signal, successively through Clarke conversion (T _{α β}), Park conversion (T (θ)), arc tangent conversion, PI regulate (PI (z)), stack feedforward angular frequency _iAnd integral transformation (V _co(z)) after, output line voltage u _sPhase theta; Wherein:

The Park conversion based on the Park transformation matrix be:

If line voltage u _sPhase sequence is positive sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right);$

If line voltage u _sPhase sequence is negative phase-sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}-\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right);$

The arc tangent conversion is based on following formula:

$\mathrm{\Δ\θ}=\arctan \frac{\mathrm{seq}\·u_d}{-u_q}$

Wherein: θ is the phase place (for the Park conversion, θ is the phase place of a upper control cycle line voltage, and the initial value of θ is 0) of line voltage, and Δ θ is phase error signal; If line voltage u _sPhase sequence is positive sequence, seq=1; If line voltage u _sPhase sequence is negative phase-sequence, seq=-1.

PI (proportional integral) regulate based on transfer function as follows:

$\mathrm{PI}\left(z\right)=K_P(1+\frac{K_{I}z}{z-1})$

Wherein: K _PAnd K _IBe respectively proportionality coefficient and integral coefficient, in present embodiment, K _P=0.1282477, K _I=0.0088825.

Regulate the angular frequency corrected signal Δ ω of generation and given feedforward angular frequency through PI _iAfter superimposed, obtain angular frequency signal ω.

Integral transformation based on transfer function as follows:

$V_{\mathrm{co}}\left(z\right)=\frac{T_s}{z-1}$

Wherein: T _sFor the sampling period, in present embodiment, T _s=100 μ s.

(3) gather load current i _LAnd the DC bus-bar voltage u of Active Power Filter-APF APF _dcWith offset current i _C

Wherein, load current i _LFor flow into the electric current of load, DC bus-bar voltage u from electrical network _dcFor the input voltage of Active Power Filter-APF APF DC side (is the DC support capacitor C _dcThe voltage at two ends), offset current i _CFor the electric current of Active Power Filter-APF APF to the electrical network injection, in present embodiment, the power of Active Power Filter-APF APF is 264kVA, the primary power switch device of Active Power Filter-APF APF adopts the IGBT (Insulated Gate Bipolar Transistor, insulated gate bipolar transistor) of the 4th generation EconoDUALTM3 of Infineon company.

(4) structure modulation signal u _m, as shown in Figure 4;

A. make load current i according to phase sequence and phase theta _LObtain harmonic current d q component through Clarke conversion, Park conversion and filtering successively;

Wherein, make load current i _LAs input signal, the output signal that obtains through the fertile hereby low pass filter LPF of second order Bart deducts input signal, obtains harmonic current d q component through the load current d q component of Clarke conversion, Park conversion output.

The transfer function of the fertile hereby low pass filter of second order Bart is as follows:

$F\left(z\right)=\frac{{\mathrm{az}}^2+\mathrm{bz}+c}{z^2+\mathrm{dz}+e}$

In present embodiment, the fertile hereby low-pass filter coefficients a=0.000119037 of second order Bart, b=0.000238075, c=0.000119037, d=-1.968908074, e=0.9693842236.

B. according to phase sequence and phase theta respectively to offset current i _CWith line voltage u _sCarry out successively Clarke conversion and Park conversion and be compensated electric current d q component and line voltage d q component;

C. make DC bus-bar voltage u _dcRegulate through voltage control the output variable and the addition of harmonic current q axle component that obtain and obtain current-order q axle component;

Wherein, to DC bus-bar voltage u _dcThe process of carrying out the voltage control adjusting is: make DC bus-bar voltage u _dcWith given direct voltage instruction stack, output after the voltage signal that obtains is regulated by the PI controller; In present embodiment, the direct voltage instruction is 700V, and the transfer function of PI controller is as follows:

$\mathrm{PI}\left(z\right)=K_P(1+\frac{K_{I}z}{z-1})$

Wherein: K _P=3.49781, K _I=0.00125.

D. make offset current d q component, current-order q axle component and harmonic current d axle component regulate through Current Control the output variable and the addition of line voltage d q component that obtain and obtain voltage instruction d q component;

Wherein, the process of Current Control adjusting is: make harmonic current d axle component deduct offset current d axle component, obtain error current d axle component; Make current-order q axle component deduct offset current q axle component, obtain error current q axle component; Make d axle component and the output after two current controllers (be comprised of repetitive controller and PI controller, signal is successively through repetitive controller and PI controller) are regulated respectively of q axle component of error current.

In present embodiment, the transfer function of repetitive controller is as follows:

$C\left(z\right)=\frac{z^{k-N}}{1-Q\·z^{-N}}\·\frac{{\mathrm{az}}^2+\mathrm{bz}+c}{z^2+\mathrm{dz}+e}$

Wherein: N=200, k=4, Q=0.9, a=0.172906263, b=0.345812527, c=0.172906263, d=-0.53014084, e=0.221765890.

The transfer function of PI controller is as follows:

$\mathrm{PI}\left(z\right)=K_P(1+\frac{K_{I}z}{z-1})$

Wherein: K _P=0.4, K _I=0.005.

E. make voltage instruction d q component obtain modulation signal u through Park inverse transformation and Clarke inverse transformation successively according to phase sequence and phase theta _m

Wherein, to signal carry out the Park conversion based on the Park transformation matrix as follows:

If line voltage u _sPhase sequence is positive sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right);$

If line voltage u _sPhase sequence is negative phase-sequence, $T\left(\mathrm{\θ}\right)=\left(\begin{array}{cc}-\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right);$

To signal carry out the Park inverse transformation based on Park inverse transformation matrix the following is:

If the line voltage phase sequence is positive sequence, $T{\left(\mathrm{\θ}\right)}^{-1}=\left(\begin{array}{cc}\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right);$

If the line voltage phase sequence is negative phase-sequence, $T{\left(\mathrm{\θ}\right)}^{-1}=\left(\begin{array}{cc}-\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right).$

(5) utilize the PWM modulator to make modulation signal u _mCompare with given triangular carrier signal, generate some roads pwm switching signal, respectively the master power switch in Active Power Filter-APF APF is controlled.

In present embodiment, the PWM modulator carries out Digital Implementation by the task manager of DSP.

Below, by the series of experiments oscillogram, verify that present embodiment can all can realize adaptive control and the normal operation of Active Power Filter-APF under positive and negative order line voltage condition.

Fig. 5 is in line voltage positive sequence situation, the synchronized experimental waveform while adopting present embodiment, and line voltage d-axle component and q-axle component show as DC quantity, illustrate that phase sequence is identified as positive sequence, and phase-locked loop can synchronously be followed the tracks of line voltage.

Fig. 6 is in line voltage negative phase-sequence situation, the synchronized experimental waveform while not adopting present embodiment, and line voltage d-axle component and q-axle component show as of ac, illustrate when phase sequence is negative phase-sequence, and phase-locked loop can not normal synchronized be followed the tracks of line voltage.

Fig. 7 is in line voltage negative phase-sequence situation, synchronized experimental waveform while adopting present embodiment, line voltage d-axle component and q-axle component show as DC quantity, illustrate that phase sequence is identified as negative phase-sequence, and phase-locked loop can synchronously be followed the tracks of line voltage, guarantees the normal control of ensuing Active Power Filter-APF and operation.

Fig. 8 and Fig. 9 are respectively in line voltage positive sequence, negative phase-sequence situation, the offset current oscillogram of Active Power Filter-APF while adopting present embodiment; As seen no matter positive and negative order wiring, present embodiment can make the adaptive control of active electric power filter and operation.

Claims (5)

1. the self-adaptation control method based on the Active Power Filter-APF of phase sequence identification, comprise the steps:

(1) gather line voltage, line voltage is carried out phase sequence identification, obtain the phase sequence of line voltage;

(2) extract the phase place of line voltage according to described phase sequence;

(3) gather DC bus-bar voltage and the offset current of load current and Active Power Filter-APF;

(4) structure modulation signal;

A. make load current obtain harmonic current dq component through Clarke conversion, Park conversion and filtering successively according to described phase sequence and phase place;

B. according to described phase sequence and phase place respectively to offset current with line voltage carries out the Clarke conversion successively and the Park conversion is compensated electric current dq component and line voltage dq component;

C. make DC bus-bar voltage regulate through voltage control the output variable and the addition of harmonic current q axle component that obtain and obtain current-order q axle component;

Wherein, the process that DC bus-bar voltage is regulated through voltage control is: make DC bus-bar voltage and given direct voltage instruction stack, the voltage signal that obtains is exported after regulating by the PI controller; Wherein, the direct voltage instruction is 700V, and the transfer function of PI controller is as follows:

Wherein: K _P=3.49781, K _I=0.00125, z is the z transformation operator;

D. make offset current dq component, current-order q axle component and harmonic current d axle component regulate through Current Control the output variable and the addition of line voltage dq component that obtain and obtain voltage instruction dq component;

The process that described Current Control is regulated is: make harmonic current d axle component deduct offset current d axle component, obtain error current d axle component; Make current-order q axle component deduct offset current q axle component, obtain error current q axle component; Make d axle component and the q axle component of error current all by current controller, regulate rear output, described current controller is comprised of repetitive controller and PI controller, and signal is output after repetitive controller and the adjusting of PI controller successively; Wherein,

The transfer function of repetitive controller is as follows:

Wherein: N=200, k=4, Q=0.9, a=0.172906263, b=0.345812527, c=0.172906263, d=-0.53014084, e=0.221765890;

The transfer function of PI controller is as follows:

Wherein: K _P=0.4, K _I=0.005;

E. make voltage instruction dq component obtain modulation signal through Park inverse transformation and Clarke inverse transformation successively according to described phase sequence and phase place;

(5) utilize the PWM modulator that described modulation signal and given triangular carrier signal are compared, generate pwm switching signal, with the switching tube in Active Power Filter-APF, control.

2. the self-adaptation control method of the Active Power Filter-APF based on phase sequence identification according to claim 1, it is characterized in that: in described step (1), the method for line voltage being carried out phase sequence identification is:

1) line voltage is carried out the Clarke conversion, obtain α axle component and the beta-axis component of line voltage;

2) adopt the Park transformation matrix

α axle component and beta-axis component to line voltage carry out the Park conversion, obtain d axle component and the q axle component of line voltage; Wherein: θ is the phase place of line voltage;

3) d axle component and the q axle component of line voltage are judged detection:

If

The phase sequence of line voltage is positive sequence;

If

The phase sequence of line voltage is negative phase-sequence;

Wherein: u _dAnd u _qBe respectively d axle component and the q axle component of line voltage, V _mAmplitude for line voltage.

3. the self-adaptation control method of the Active Power Filter-APF based on phase sequence identification according to claim 1, it is characterized in that: in described step (2), the process of line voltage being carried out phase extraction is: make line voltage as input signal, after Clarke conversion, Park conversion, arc tangent conversion, PI regulate, superpose feedforward angular frequency and integral transformation, export the phase place of line voltage successively;

Described arc tangent conversion is based on following formula:

Wherein: u _dAnd u _qBe respectively d axle component and the q axle component of line voltage, Δ θ is phase error signal; If the line voltage phase sequence is positive sequence, seq=1; If the line voltage phase sequence is negative phase-sequence, seq=-1.

4. the self-adaptation control method of according to claim 1 or 3 described Active Power Filter-APFs based on phase sequence identification is characterized in that:

Described Park conversion based on the Park transformation matrix be:

If the line voltage phase sequence is positive sequence,

If the line voltage phase sequence is negative phase-sequence,

Wherein: T (θ) is the Park transformation matrix, and θ is the phase place of line voltage.

5. the self-adaptation control method of the Active Power Filter-APF based on phase sequence identification according to claim 1 is characterized in that: described Park inverse transformation based on Park inverse transformation matrix be:

If the line voltage phase sequence is positive sequence,

If the line voltage phase sequence is negative phase-sequence,

Wherein: T (θ) ^-1For Park inverse transformation matrix, θ is the phase place of line voltage.

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