CN107102204A - Suitable for line voltage distortion and unbalanced voltage-phase detection method - Google Patents

Suitable for line voltage distortion and unbalanced voltage-phase detection method Download PDF

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CN107102204A
CN107102204A CN201710288561.XA CN201710288561A CN107102204A CN 107102204 A CN107102204 A CN 107102204A CN 201710288561 A CN201710288561 A CN 201710288561A CN 107102204 A CN107102204 A CN 107102204A
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msubsup
msup
omega
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张晓滨
黄佳敏
伍文俊
苏战停
何瑞
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Xian University of Technology
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Xian University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R25/00—Arrangements for measuring phase angle between a voltage and a current or between voltages or currents
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
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Abstract

The invention discloses suitable for line voltage distortion and unbalanced voltage-phase detection method, specifically implement according to following steps：Step 1, by voltage resultant vector and project to rotating speed and turn on adjustable VSF, VSF steering is set as counterclockwise；Step 2, using LPF from exAnd eyThe middle low frequency component extracted less than 0.5Hz, and calculate positive sequence fundamental voltage phase；Step 3, VSF steering is set as that counterclockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, the phase of m voltage of positive sequence is calculated；Step 4, VSF steering is set as clockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, the phase of m voltage of negative phase-sequence is calculated.The present invention solves the problem of conventional phase detection method has error when line voltage distorts uneven, and the detection method need not adjust PI parameters in addition so that the adjustment process of phase-detection is simple；This method can detect any voltage-phase of the positive-negative sequence specified.

Description

Suitable for line voltage distortion and unbalanced voltage-phase detection method
Technical field
The invention belongs to electric and electronic technical field, it is related to a kind of line voltage that is applied to and distorts and unbalanced voltage phase Position detecting method.
Background technology
Micro-capacitance sensor is by some distributed power sources (Distributed Generation, DG), energy storage device and born on the spot The controllable system of lotus composition, with isolated island and grid-connected two kinds of operational modes, wherein DG is generally accessed via three-phase grid-connected inverter Power network.In order to realize off-grid grid-connected switching and the electric current of unity power factor be injected to power network, combining inverter needs to detect public The voltage-phase of common tie point (Point of Common Coupling, PCC).Due to accessing a large amount of parallel network reverses in micro-capacitance sensor Device, line impedance generally be can not ignore, therefore PCC voltages contain background harmonicses and negative phase-sequence and show as distortion and uneven.Three The voltage-phase detection of phase combining inverter generally uses the software phase-lock loop (Synchronous based on synchronous coordinate system Reference Frame Phase Locked Loop, SRF-PLL), when voltage distortion is uneven, negative sequence component meeting therein 2 double-frequency oscillations are produced in SRF-PLL Synchronous Reference Frame Transform result, even if vibration pair can not be completely eliminated in low pass filter The influence of accuracy of detection, so that phase detection result has error.
The content of the invention
It is applied to line voltage distortion and unbalanced voltage-phase detection method it is an object of the invention to provide one kind, should Method solves the problem of conventional phase detection method has error when line voltage distorts uneven, in voltage distortion and not Voltage-phase detection can be carried out during balance exactly.
The technical solution adopted in the present invention is, it is adaptable to which line voltage distorts and unbalanced voltage-phase detection side Method, specifically implements according to following steps：
Step 1, by voltage resultant vector and project to rotating speed and turn on adjustable VSF, VSF steering is set as inverse Clockwise, speed setting is ω ', and wherein ω ' is power frequency angular speed as defined in micro-capacitance sensor；
Step 2, using LPF from exAnd eyThe middle low frequency component extracted less than 0.5Hz, and calculate positive sequence fundamental voltage phase Position, wherein exFor coordinate of the voltage vector in VSF x-axis, eyFor coordinate of the voltage vector in VSF y-axis；
Step 3, VSF steering is set as that counterclockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, The phase of m voltage of positive sequence is calculated, wherein m is the number of times of harmonic wave；
Step 4, VSF steering is set as clockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected to VSF, calculates the phase of m voltage of negative phase-sequence.
The features of the present invention is also resided in,
Step 1 is specifically implemented according to following steps：
Step 1.1, if distortion and unbalance voltage be：
In formula：Em +For the amplitude of m positive sequence voltage；Em -For the amplitude of m negative sequence voltage；θm +For m positive sequence voltage just Beginning phase angle；θm -For the initial phase angle of m negative sequence voltage；M is overtone order；T is the time；Subscript ﹢ represents positive sequence, and subscript ﹣ is represented Negative phase-sequence；ω is the angular frequency of voltage fundamental；
Step 1.2, it will be distorted unbalanced voltage synthesized voltage vector e using formula (2), voltage vector e is：
In formula：eRFor coordinate of the voltage vector on complex plane real axis；eIFor seat of the voltage vector in the complex plane imaginary axis Mark；
Step 1.3, the angle that e bears semiaxis with the imaginary axis is θ, coordinate e of the voltage vector on complex plane real axis and the imaginary axisRWith eIFor：
In formula：| e | it is the amplitude of voltage vector；
Step 1.4, rotating speed is set up for ω ', is turned to as VSF counterclockwise；The angle of semiaxis is born with the imaginary axis by VSF x-axis The angle that semiaxis is born for ω ' t+ γ, e and the imaginary axis is θ, and the angle for obtaining e and x-axis is ω ' t+ γ-θ, so seats of the e on VSF It is designated as：
In formula：T represents the time；γ is the initial phase angle of xy coordinate systems, takes random value；
Step 1.5, by eRAnd eIValue substitute into formula (4) coordinates of the e on VSF be：
Step 2 is specifically implemented according to following steps：
Step 2.1, extracting coordinate of the positive sequence fundamental voltage on VSF using LPF is：
Step 2.2, in t, VSF x-axis and the imaginary axis bear the angle ω ' t+ γ of semiaxis for known quantity；According to positive sequence base Coordinate of the wave voltage vector on VSF obtains positive sequence fundamental voltage vector and the angle of x-axis isPositive sequence fundamental wave The phase ω t+ θ of voltage1 +Equal to the angle that positive sequence fundamental voltage vector and the imaginary axis bear semiaxis, in t positive sequence fundamental voltage phase Position calculation formula be：
Step 3 is specifically implemented according to following steps：
Step 3.1, according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining coordinates of the e on VSF is：
Step 3.2, extracting coordinate of the m voltage of positive sequence on VSF using LPF is：
Step 3.3, in t, VSF x-axis and the imaginary axis bear the angle m ω ' t+ γ of semiaxis for known quantity；According to positive sequence m Coordinate of the secondary voltage vector on VSF obtains m voltage vector of positive sequence and the angle of x-axis isPositive sequence m times The phase m ω t+ θ of voltagem +Equal to the angle that m voltage vector of positive sequence and the imaginary axis bear semiaxis, in m voltage-phase of t positive sequence Calculation formula be：
Step 4 is specifically implemented according to following steps：
Step 4.1, according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining coordinates of the e on VSF is：
Step 4.2, extracting coordinate of the m voltage of negative phase-sequence on VSF using LPF is：
Step 4.3, in t, VSF x-axis is known quantity with the angle m ω ' t+ γ of imaginary axis positive axis；According to negative phase-sequence m Coordinate of the secondary voltage vector on VSF obtains m voltage vector of negative phase-sequence and the angle of x-axis isNegative phase-sequence m times The phase m ω t+ θ of voltagem -Equal to m voltage vector of negative phase-sequence and the angle of imaginary axis positive axis, in m voltage phase of t negative phase-sequence Position calculation formula be：
The beneficial effects of the invention are as follows, it is adaptable to line voltage distorts and unbalanced voltage-phase detection method and SRF- PLL is compared, and the method for detecting phases by voltage distortion and unbalanced does not influence；Phase-detection need not adjust PI parameters, make The adjustment process for obtaining phase-detection is simple；The method for detecting phases can detect the harmonious wave voltage of the positive-negative sequence fundamental wave being arbitrarily designated Phase；The method for detecting phases complexity is also without obvious increase.
Brief description of the drawings
Fig. 1 is the present invention suitable for line voltage distortion and the theory diagram of unbalanced voltage-phase detection method；
Fig. 2 is virtual synchronous coordinate system schematic diagram；
Fig. 3 is the virtual synchronous coordinate system for detecting negative sequence voltage phase；
Fig. 4 is three-phase voltage oscillogram when line voltage distortion is uneven；
Fig. 5 is A phases line voltage, A phase positive sequence fundamental voltages and its phase-detection oscillogram；
Fig. 6 is A phases line voltage, the subharmonic voltage of A phases positive sequence 5 and its phase-detection oscillogram；
Fig. 7 is A phases line voltage, A phase negative phase-sequence fundamental voltages and its phase-detection oscillogram.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and detailed description.
The present invention is applied to line voltage distortion and unbalanced voltage-phase detection method, as shown in figure 1, it is specific according to Following steps are implemented：
Step 1, by voltage resultant vector and project to rotating speed and turn to adjustable virtual synchronous coordinate system (Virtual Synchronization Frame, VSF) on, VSF steering is set as counterclockwise, speed setting is ω ', wherein ω ' is power frequency angular speed as defined in micro-capacitance sensor；
Step 2, using low pass filter (Low pass filter, LPF) from exAnd eyThe middle low frequency extracted less than 0.5Hz Component, and calculate positive sequence fundamental voltage phase, wherein exFor coordinate of the voltage vector in VSF x-axis, eyFor voltage vector Coordinate in VSF y-axis；
Step 3, VSF steering is set as that counterclockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, The phase of m voltage of positive sequence is calculated, wherein m is the number of times of harmonic wave；
Step 4, VSF steering is set as clockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected to VSF, calculates the phase of m voltage of negative phase-sequence.
Step 1 is specifically implemented according to following steps：
Step 1.1, if distortion and unbalance voltage be：
In formula：Em +For the amplitude of m positive sequence voltage；Em -For the amplitude of m negative sequence voltage；θm +For m positive sequence voltage just Beginning phase angle；θm -For the initial phase angle of m negative sequence voltage；M is overtone order；T is the time；Subscript ﹢ represents positive sequence, and subscript ﹣ is represented Negative phase-sequence；ω is the angular frequency of voltage fundamental；
Step 1.2, it can be regarded as by positive and negative using will distort unbalanced voltage synthesized voltage vector e, e of formula (2) Sequence fundamental wave harmonic voltage vector is synthesized, and amplitude and phase angle are time-varying, and voltage vector e is：
In formula：eRFor coordinate of the voltage vector on complex plane real axis；eIFor seat of the voltage vector in the complex plane imaginary axis Mark；
Step 1.3, the angle that e bears semiaxis with the imaginary axis is θ, the space geometry relation according to Fig. 2, and voltage vector is multiple Coordinate e on plane real axis and the imaginary axisRAnd eIFor：
In formula：| e | it is the amplitude of voltage vector；
Step 1.4, rotating speed is set up for ω ', is turned to as VSF counterclockwise；The angle of semiaxis is born with the imaginary axis by VSF x-axis The angle that semiaxis is born for ω ' t+ γ, e and the imaginary axis is θ, and the angle for obtaining e and x-axis is ω ' t+ γ-θ, so seats of the e on VSF It is designated as：
In formula：T represents the time；γ is the initial phase angle of xy coordinate systems, takes random value；
Step 1.5, by eRAnd eIValue substitute into formula (4) coordinates of the e on VSF be：
Step 2 is specifically implemented according to following steps：
Step 2.1, coordinate of the positive sequence fundamental voltage on VSF is extracted for (national grid specified volume exists using LPF Less than 3000000 kilowatts of power network allows frequency departure to be ± 0.5Hz, therefore ω-ω ' are in 0~0.5Hz)：
Step 2.2, in t, VSF x-axis and the imaginary axis bear the angle ω ' t+ γ of semiaxis for known quantity；According to positive sequence base Coordinate of the wave voltage vector on VSF obtains positive sequence fundamental voltage vector and the angle of x-axis isSuch as Fig. 2 institutes Show space geometry relation, the phase ω t+ θ of positive sequence fundamental voltage1 +Equal to the folder that positive sequence fundamental voltage vector and the imaginary axis bear semiaxis Angle, be in the calculation formula of t positive sequence fundamental voltage phase：
Step 3 is specifically implemented according to following steps：
Step 3.1, as shown in Fig. 2 according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining e on VSF Coordinate be：
Step 3.2, extracting coordinate of the m voltage of positive sequence on VSF using LPF is：
Step 3.3, in t, VSF x-axis and the imaginary axis bear the angle m ω ' t+ γ of semiaxis for known quantity；According to positive sequence m Coordinate of the secondary voltage vector on VSF obtains m voltage vector of positive sequence and the angle of x-axis isShown in Fig. 2 Space geometry relation, the phase m ω t+ θ of m voltage of positive sequencem +Equal to the angle that m voltage vector of positive sequence and the imaginary axis bear semiaxis, It is in the calculation formula of m voltage-phase of t positive sequence：
Step 4 is specifically implemented according to following steps：
Step 4.1, as shown in figure 3, according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining e on VSF Coordinate be：
Step 4.2, extracting coordinate of the m voltage of negative phase-sequence on VSF using LPF is：
Step 4.3, in t, VSF x-axis is known quantity with the angle m ω ' t+ γ of imaginary axis positive axis；According to negative phase-sequence m Coordinate of the secondary voltage vector on VSF obtains m voltage vector of negative phase-sequence and the angle of x-axis isSuch as Fig. 3 institutes Show, the phase m ω t+ θ of m voltage of negative phase-sequencem -Equal to m voltage vector of negative phase-sequence and the angle of imaginary axis positive axis, in t negative phase-sequence The calculation formula of m voltage-phase is：
In order to verify the validity of this algorithm, emulated on MATLAB/Simulink, line voltage is by positive sequence fundamental wave Voltage superposition 0.2pu negative phase-sequence fundamental voltage and the 0.05pu subharmonic voltage of positive sequence 5 are constituted.
Fig. 4 is three-phase voltage oscillogram when line voltage distorts uneven；Fig. 5 is A phases line voltage, A phase positive sequence bases Wave voltage and its phase-detection oscillogram；Fig. 6 is A phases line voltage, the subharmonic voltage of A phases positive sequence 5 and its phase-detection waveform Figure；Fig. 7 is A phases line voltage, A phase negative phase-sequence fundamental voltages and its phase-detection oscillogram.It can be seen that the inspection of the application present invention The actual phase angle of voltage-phase and voltage that survey method is obtained is completely the same.Therefore the present invention is applied to line voltage distortion and uneven The voltage-phase detection method of weighing apparatus accurately can detect fundamental wave, harmonic wave and negative sequence voltage from distortion and unbalanced voltage Phase information.
The present invention be applied to line voltage distortion and unbalanced voltage-phase detection method have the following advantages：With SRF- PLL is compared, and the method for detecting phases by voltage distortion and unbalanced does not influence；Phase-detection need not adjust PI parameters, make The adjustment process for obtaining phase-detection is simple；The method for detecting phases can detect the harmonious wave voltage of the positive-negative sequence fundamental wave being arbitrarily designated Phase；The method for detecting phases complexity is also without obvious increase.

Claims (5)

1. suitable for line voltage distortion and unbalanced voltage-phase detection method, it is characterised in that specifically according to following step It is rapid to implement：
Step 1, by voltage resultant vector and project to rotating speed and turn on adjustable VSF, VSF steering is set as counterclockwise Direction, speed setting is ω ', and wherein ω ' is power frequency angular speed as defined in micro-capacitance sensor；
Step 2, using LPF from exAnd eyThe middle low frequency component extracted less than 0.5Hz, and positive sequence fundamental voltage phase is calculated, its Middle exFor coordinate of the voltage vector in VSF x-axis, eyFor coordinate of the voltage vector in VSF y-axis；
Step 3, VSF steering is set as that counterclockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, is calculated Go out the phase of m voltage of positive sequence, wherein m is the number of times of harmonic wave；
Step 4, VSF steering is set as, for clockwise, adjustment of rotational speed is m ω ', and voltage vector e is projected into VSF, counting Calculate the phase of m voltage of negative phase-sequence.
2. according to claim 1 be applied to line voltage distortion and unbalanced voltage-phase detection method, its feature It is, step 1 is specifically implemented according to following steps：
Step 1.1, if distortion and unbalance voltage be：
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In formula：Em +For the amplitude of m positive sequence voltage；Em -For the amplitude of m negative sequence voltage；θm +For the initial phase of m positive sequence voltage Angle；θm -For the initial phase angle of m negative sequence voltage；M is overtone order；T is the time；Subscript ﹢ represents positive sequence, and subscript ﹣ represents negative phase-sequence； ω is the angular frequency of voltage fundamental；
Step 1.2, it will be distorted unbalanced voltage synthesized voltage vector e using formula (2), voltage vector e is：
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In formula：eRFor coordinate of the voltage vector on complex plane real axis；eIFor coordinate of the voltage vector in the complex plane imaginary axis；
Step 1.3, the angle that e bears semiaxis with the imaginary axis is θ, coordinate e of the voltage vector on complex plane real axis and the imaginary axisRAnd eIFor：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>R</mi> </msub> <mo>=</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mi>sin</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>I</mi> </msub> <mo>=</mo> <mo>-</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mi>cos</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
In formula：| e | it is the amplitude of voltage vector；
Step 1.4, rotating speed is set up for ω ', is turned to as VSF counterclockwise；The angle for bearing semiaxis with the imaginary axis by VSF x-axis is ω ' The angle that t+ γ, e bear semiaxis with the imaginary axis is θ, and the angle for obtaining e and x-axis is ω ' t+ γ-θ, so coordinates of the e on VSF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>x</mi> </msub> <mo>=</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mo>&amp;lsqb;</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;theta;</mi> <mo>+</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;theta;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>e</mi> <mi>R</mi> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>e</mi> <mi>I</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>y</mi> </msub> <mo>=</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>|</mo> <mi>e</mi> <mo>|</mo> <mo>&amp;lsqb;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;theta;</mi> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;theta;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>e</mi> <mi>R</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>e</mi> <mi>I</mi> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
In formula：T represents the time；γ is the initial phase angle of xy coordinate systems, takes random value；
Step 1.5, by eRAnd eIValue substitute into formula (4) coordinates of the e on VSF be：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>x</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>y</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
3. according to claim 2 be applied to line voltage distortion and unbalanced voltage-phase detection method, its feature It is, step 2 is specifically implemented according to following steps：
Step 2.1, extracting coordinate of the positive sequence fundamental voltage on VSF using LPF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mn>1</mn> <mi>x</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mn>1</mn> <mo>+</mo> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mn>1</mn> <mo>+</mo> </msubsup> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mn>1</mn> <mo>+</mo> </msubsup> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mn>1</mn> <mo>+</mo> </msubsup> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Step 2.2, in t, VSF x-axis and the imaginary axis bear the angle ω ' t+ γ of semiaxis for known quantity；According to positive sequence fundamental wave electricity Coordinate of the pressure vector on VSF obtains positive sequence fundamental voltage vector and the angle of x-axis isPositive sequence fundamental voltage Phase ω t+ θ1 +Equal to the angle that positive sequence fundamental voltage vector and the imaginary axis bear semiaxis, in t positive sequence fundamental voltage phase Calculation formula is：
<mrow> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mn>1</mn> <mo>+</mo> </msubsup> <mo>=</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>-</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mfrac> <msubsup> <mi>e</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <msqrt> <mrow> <msup> <msubsup> <mi>e</mi> <mrow> <mn>1</mn> <mi>x</mi> </mrow> <mo>+</mo> </msubsup> <mn>2</mn> </msup> <mo>+</mo> <msup> <msubsup> <mi>e</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
4. according to claim 3 be applied to line voltage distortion and unbalanced voltage-phase detection method, its feature It is, step 3 is specifically implemented according to following steps：
Step 3.1, according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining coordinates of the e on VSF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>x</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>c</mi> <mi>s</mi> <mi>o</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>y</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Step 3.2, extracting coordinate of the m voltage of positive sequence on VSF using LPF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mi>m</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mi>m</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
Step 3.3, in t, VSF x-axis and the imaginary axis bear the angle m ω ' t+ γ of semiaxis for known quantity；According to m electricity of positive sequence Coordinate of the pressure vector on VSF obtains m voltage vector of positive sequence and the angle of x-axis isM voltage of positive sequence Phase m ω t+ θm +Equal to the angle that m voltage vector of positive sequence and the imaginary axis bear semiaxis, in the meter of m voltage-phase of t positive sequence Calculating formula is：
<mrow> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>=</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>-</mo> <mi>arcsin</mi> <mfrac> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <msqrt> <mrow> <msup> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> <mo>+</mo> </msubsup> <mn>2</mn> </msup> <mo>+</mo> <msup> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>+</mo> </msubsup> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
5. according to claim 4 be applied to line voltage distortion and unbalanced voltage-phase detection method, its feature It is, step 4 is specifically implemented according to following steps：
Step 4.1, according to the geometrical relationship that e and x-axis angle are m ω ' t+ γ-θ, obtaining coordinates of the e on VSF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>x</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>y</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>sin</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>+</mo> </msubsup> <mo>-</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Step 4.2, extracting coordinate of the m voltage of negative phase-sequence on VSF using LPF is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> <mo>-</mo> </msubsup> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mi>m</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>-</mo> </msubsup> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <msubsup> <mi>E</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mi>m</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msup> <mi>&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>-</mo> <mi>&amp;gamma;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Step 4.3, in t, VSF x-axis is known quantity with the angle m ω ' t+ γ of imaginary axis positive axis；According to m electricity of negative phase-sequence Coordinate of the pressure vector on VSF obtains m voltage vector of negative phase-sequence and the angle of x-axis isM voltage of negative phase-sequence Phase m ω t+ θm -Equal to m voltage vector of negative phase-sequence and the angle of imaginary axis positive axis, in m voltage-phase of t negative phase-sequence Calculation formula is：
<mrow> <mi>m</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&amp;theta;</mi> <mi>m</mi> <mo>-</mo> </msubsup> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mfrac> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>-</mo> </msubsup> <msqrt> <mrow> <msup> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> <mo>-</mo> </msubsup> <mn>2</mn> </msup> <mo>+</mo> <msup> <msubsup> <mi>e</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> <mo>-</mo> </msubsup> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mo>&amp;prime;</mo> </msup> <mi>t</mi> <mo>+</mo> <mi>&amp;gamma;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> 3
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