CN105375527B - The control method and system of faulty grids combining inverter - Google Patents

The control method and system of faulty grids combining inverter Download PDF

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CN105375527B
CN105375527B CN201510935051.8A CN201510935051A CN105375527B CN 105375527 B CN105375527 B CN 105375527B CN 201510935051 A CN201510935051 A CN 201510935051A CN 105375527 B CN105375527 B CN 105375527B
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component
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sequence
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CN105375527A (en
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杜雄
王国宁
顾师达
杨友耕
邹小明
夏俊
吴越
时颖
孙鹏菊
周雒维
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Chongqing University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers

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Abstract

A kind of control method of power network combining inverter provided by the invention, comprises the following steps：S1. the voltage signal of faulty grids, the α component of voltages and β the component of voltages voltage signal being converted into rest frame are obtained, and determines positive sequence voltage component up=uαp+juβpWith negative sequence voltage components un=uαn+juβn；S2. the positive sequence voltage component of faulty grid voltage and the amplitude and phase of negative sequence voltage components are calculated according to the positive sequence voltage component and negative sequence voltage components of failure voltage signal；S3. according to the positive sequence voltage component amplitude of faulty grid voltage, phase and negative sequence voltage components amplitude, phase and the forward-order current component and negative-sequence current component that set power calculation control electric current；S4. pwm control signal is formed according to the forward-order current component and negative-sequence current component of control electric current and controls combining inverter action output grid-connected current；The accurate control to faulty grids combining inverter is realized, and greatly simplifies calculating process, improves corresponding speed.

Description

The control method and system of faulty grids combining inverter
Technical field
The present invention relates to a kind of control method and system, more particularly to a kind of control method of faulty grids combining inverter And system.
Background technology
With the extensive application of new energy power generation technology, combining inverter is connection power network as one of its hardcore With the interface of generation of electricity by new energy, because power network scale is more and more huger, operating mode also becomes complicated, and combining inverter will not only export Active power, will also be in electric network fault, it is necessary to which the reactive power compensation line voltage certain to power network output, therefore, grid-connected Inverter dispatches active power of output when can have active and idle fan-out capability and normal work in electric network fault Ability.
In order to realize the output of the quantitative power of combining inverter, it is necessary to enter to the positive and negative order components and amplitude of the voltage of power network Row detection, provides input signal, power calculation is to provide reference current for current control, and suppresses electric network fault for power calculation Influence.
In the prior art, the extraction for mains voltage signal is carried out in the following way：In rotating coordinate system and static Work completion under coordinate system, first transforms to three-phase power grid voltage and current signal under rotating coordinate system, voltage and current letter Number there is of ac to be changed into DC quantity, be easy to power calculation, while adoption rate integral controller, realize DC feedback amount track to Determine power, then DC quantity contravariant is changed under rest frame, so as to realize the synchronization signal detection of AC signal and electric current control System, and nonserviceable lower, it is necessary to realize the control of power using decoupling circuit, but rotation transformation and anti-in calculating process Conversion and decoupling processing calculating process are complicated, and response speed is slow, and control accuracy is low, and in rest frame, existing side Formula is unable to the positive and negative order components of output voltage and electric current, so as to be unfavorable for the control of the precision of combining inverter.
It is, therefore, desirable to provide a kind of control method of new combining inverter, can obtain positive sequence in rest frame Component of voltage and negative sequence voltage components and forward-order current component and negative-sequence current component, are realized to faulty grids combining inverter Accurate control, and greatly simplify calculating process, improve corresponding speed.
The content of the invention
In view of this, can be quiet it is an object of the invention to provide a kind of control method of faulty grids combining inverter Positive sequence voltage component and negative sequence voltage components and forward-order current component and negative-sequence current component, realization pair are only controlled in coordinate system The accurate control of faulty grids combining inverter, and calculating process is greatly simplified, improve corresponding speed.
A kind of control method of power network combining inverter provided by the invention, comprises the following steps：
S1. obtain the voltage signal of faulty grids, by the voltage signal be converted into α component of voltages in rest frame and β component of voltages, and determine positive sequence voltage component up=uαp+juβpWith negative sequence voltage components un=uαn+juβn；
S2. the positive sequence of faulty grid voltage is calculated according to the positive sequence voltage component and negative sequence voltage components of failure voltage signal The amplitude and phase of component of voltage and negative sequence voltage components；
S3. according to the positive sequence voltage component amplitude of faulty grid voltage, negative sequence voltage components amplitude, phase and setting work( Rate calculates the forward-order current component and negative-sequence current component of control electric current；
S4. modulated signal is exported according to the forward-order current component and negative-sequence current component of control electric current and forms PWM controls Signal simultaneously controls combining inverter action output grid-connected current.
Further, in step S2, positive sequence voltage component amplitude, the negative phase-sequence electricity of failure voltage signal are calculated according to equation below Press component amplitude and phase：
θp=arctan (uβp/uαp)；
θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive sequence The phase of component, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαn Represent the negative sequence component of α components, uβnRepresent the negative sequence component of β components.
Further, in step S3, the forward-order current component and negative-sequence current component of control electric current calculate according to equation below：
Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and idle work( Rate component.
Correspondingly, present invention also offers a kind of control system of faulty grids combining inverter, including：
Voltage signal extraction unit, complex variable is converted to for obtaining the voltage signal of faulty grids, and by voltage signal Positive sequence voltage component and negative sequence voltage components, and calculate positive sequence voltage component amplitude, negative sequence voltage components amplitude and phase Position；
Power calculation unit, positive sequence voltage component amplitude, negative sequence voltage for the output of receiving voltage signal extraction unit Component amplitude and phase, and combine the forward-order current component and negative-sequence current component of given power calculation control electric current；
Current control unit, for receive control electric current forward-order current component and negative-sequence current component and export PWM letter Number control combining inverter action.
Further, the voltage signal of faulty grids is converted into positive sequence voltage by voltage signal extraction unit according to following manner Component and negative sequence voltage components：
By the voltage conversion of faulty grids into the α component of voltages and β component of voltages in rest frame, and according to α electricity Press the positive sequence voltage component and the positive sequence voltage component and negative sequence voltage components meter of negative sequence voltage components and β component of voltages of component Calculate the amplitude and phase of positive sequence voltage component and negative sequence voltage components：
θp=arctan (uβp/uαp)；
θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive sequence The phase of component, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαn Represent the negative sequence component of α components, uβnRepresent the negative sequence component of β components.
Further, power calculation unit calculates the forward-order current component and negative-sequence current point of control electric current according to equation below Amount：
Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and idle work( Rate component.
Beneficial effects of the present invention：The control method of faulty grids combining inverter provided by the invention, without calculating During carry out rotating coordinate system conversion and its inverse transformation, it is not required that uneoupled control is carried out in control process, can Positive sequence voltage component and negative sequence voltage components and forward-order current component and negative-sequence current component are controlled in rest frame, it is real Now to the accurate control of faulty grids combining inverter, and calculating process is greatly simplified, improve corresponding speed.
Brief description of the drawings
The invention will be further described with reference to the accompanying drawings and examples：
Fig. 1 is the schematic diagram of the present invention.
Fig. 2 is the schematic diagram of the positive sequence Generalized Integrator of the present invention.
Fig. 3 is the schematic diagram of the negative phase-sequence Generalized Integrator of the present invention.
Fig. 4 is the schematic diagram of the voltage signal extraction unit of the present invention.
Fig. 5 is the schematic diagram of the frequency adaptive unit of the present invention.
Fig. 6 is the current control unit schematic diagram of the present invention.
Embodiment
Fig. 1 is the schematic diagram of the present invention, and Fig. 2 is the schematic diagram of the positive sequence Generalized Integrator of the present invention, and Fig. 3 is of the invention The schematic diagram of negative phase-sequence Generalized Integrator, Fig. 4 are the schematic diagram of the voltage signal extraction unit of the present invention, and Fig. 5 is the frequency of the present invention The schematic diagram of rate adaptive unit, Fig. 6 is the current control unit schematic diagram of the present invention, as illustrated, provided by the invention one The control method of kind power network combining inverter, comprises the following steps：
S1. obtain the voltage signal of faulty grids, by the voltage signal be converted into α component of voltages in rest frame and β component of voltages, and determine positive sequence voltage component up=uαp+juβpWith negative sequence voltage components un=uαn+juβn；Wherein, due to power network Voltage is three-phase system, and therefore, in calculating process, voltage signal is converted to by α voltages by three amount expressions of three-phase voltage Two amounts of component and β component of voltages are indicated, and α component of voltages and β component of voltages can be expressed as complex variable, so as to letter Change calculating process, positive sequence voltage component and negative phase-sequence can exported in rest frame by synchronizing signal extraction unit Component of voltage, so as to avoid the conversion of rotating coordinate system and decoupling computation in calculating process, calculating process is greatly simplified, Improve control accuracy；
S2. the positive sequence of faulty grid voltage is calculated according to the positive sequence voltage component and negative sequence voltage components of failure voltage signal The amplitude and phase of component of voltage and negative sequence voltage components；
S3. according to the positive sequence voltage component amplitude of faulty grid voltage, negative sequence voltage components amplitude, phase and setting work( Rate calculates the forward-order current component and negative-sequence current component of control electric current；
S4. modulated signal is exported according to the forward-order current component and negative-sequence current component of control electric current, and forms PWM controls Signal simultaneously controls combining inverter action output grid-connected current, wherein, pwm control signal is exported using existing according to modulated signal Technology, not in this to go forth；By the effect of this method, without carrying out the conversion of rotating coordinate system in calculating process And its inverse transformation, it is not required that uneoupled control is carried out in control process, positive sequence voltage can be controlled in rest frame Component and negative sequence voltage components and forward-order current component and negative-sequence current component, are realized to parallel network reverse under faulty grid conditions The accurate control of device, and calculating process is greatly simplified, improve corresponding speed.
In the present embodiment, in step S2, according to equation below calculate failure voltage signal positive sequence voltage component amplitude with Phase, negative sequence voltage components amplitude with phase：
θp=arctan (uβp/uαp)；
θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive sequence The phase of component, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαn Represent the negative sequence component of α components, uβnRepresent the negative sequence component of β components.
In the present embodiment, in step S3, the forward-order current component and negative-sequence current component of control electric current are according to equation below Calculate：
Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and idle work( Rate component.
Correspondingly, present invention also offers a kind of control system of faulty grids combining inverter, including：
Voltage signal extraction unit, complex variable is converted to for obtaining the voltage signal of faulty grids, and by voltage signal Positive sequence voltage component and negative sequence voltage components, and calculate positive sequence voltage component amplitude and phase, negative sequence voltage components amplitude With with phase；
Power calculation unit, positive sequence voltage component amplitude, negative sequence voltage for the output of receiving voltage signal extraction unit Component amplitude and phase, and combine the forward-order current component and negative-sequence current component of given power calculation control electric current；
Current control unit, for the forward-order current component of electric current and the control of negative-sequence current component, output modulation letter Number, and then the action of output pwm signal control combining inverter, current control unit is broad sense proportional integrator, such as Fig. 6 institutes Show, wherein, the parameter k in Fig. 6pAnd kiCalculated and obtained according to the Phase margin of the open-loop transfer function of current loop, belong to existing Technology.
Wherein, the synchronizing signal that voltage signal extraction unit is positive sequence Generalized Integrator, negative phase-sequence Generalized Integrator forms carries Unit and frequency adaptive unit is taken to form, as Figure 2-Figure 5, in Fig. 4 backfeed loop, positive sequence Generalized Integrator can To realize the positive sequence voltage component of the positive sequence voltage component track reference signal of output, negative phase-sequence Generalized Integrator can realize output Negative sequence voltage components track reference signal negative sequence voltage components, therefore positive sequence voltage component and negative phase-sequence can be extracted respectively Component of voltage, frequency adaptive unit are gained positive sequence voltage component and negative sequence voltage components and its conjugation component, utilize feedback The effect of the integrator in loop, realize to line voltage frequency-tracking.Exporting for frequency adaptive structure carries to Generalized Integrator For frequency information, the output of Generalized Integrator provides input for frequency adaptive structure, and the two forms a loop, real time correction The accuracy of the component of voltage of extraction, wherein, in negative phase-sequence Generalized Integrator in parameter K take 0.707, ensure the step of system Response performance is optimal.
In the present embodiment, the voltage signal of faulty grids is converted into positive sequence by voltage signal extraction unit according to following manner The amplitude and phase of component of voltage and negative sequence voltage components：
By the voltage conversion of faulty grids into the α component of voltages and β component of voltages in rest frame, and according to α electricity Press the positive sequence voltage component and the positive sequence voltage component and negative sequence voltage components meter of negative sequence voltage components and β component of voltages of component Calculate the amplitude and phase of positive sequence voltage component and negative sequence voltage components：
θp=arctan (uβp/uαp)；
θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive sequence The phase of component, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαn Represent the negative sequence component of α components, uβnRepresent the negative sequence component of β components.
In the present embodiment, power calculation unit calculates the forward-order current component and negative phase-sequence electricity of control electric current according to equation below Flow component：
Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and idle work( Rate component,
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with The present invention is described in detail good embodiment, it will be understood by those within the art that, can be to the skill of the present invention Art scheme is modified or equivalent substitution, and without departing from the objective and scope of technical solution of the present invention, it all should cover at this Among the right of invention.

Claims (2)

  1. A kind of 1. control method of faulty grids combining inverter, it is characterised in that：Comprise the following steps：
    S1. the voltage signal of faulty grids is obtained, the α component of voltages and β the electricity voltage signal being converted into rest frame Component is pressed, and determines positive sequence voltage component up=uαp+juβpWith negative sequence voltage components un=uαn+juβn；
    S2. the positive sequence voltage of faulty grid voltage is calculated according to the positive sequence voltage component and negative sequence voltage components of failure voltage signal The amplitude and phase of component and negative sequence voltage components；
    S3. according to the positive sequence voltage component amplitude of faulty grid voltage, negative sequence voltage components amplitude, phase and setting power meter Calculate the forward-order current component and negative-sequence current component of control electric current；
    S4. modulated signal is exported according to the forward-order current component and negative-sequence current component of control electric current and forms pwm control signal And control combining inverter action output grid-connected current；
    In step S2, positive sequence voltage component amplitude, the negative sequence voltage components amplitude of failure voltage signal are calculated according to equation below And phase：
    <mrow> <msub> <mi>U</mi> <mi>p</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>&amp;alpha;</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>&amp;beta;</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <msub> <mi>U</mi> <mi>n</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>&amp;alpha;</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>&amp;beta;</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>;</mo> </mrow>
    θp=arctan (uβp/uαp)；
    θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive-sequence component Phase, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαnRepresent The negative sequence component of α components, uβnRepresent the negative sequence component of β components；
    In step S3, the forward-order current component and negative-sequence current component of control electric current calculate according to equation below：
    <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>Pu</mi> <mi>p</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>jQu</mi> <mi>p</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>+</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>
    <mrow> <msub> <mi>I</mi> <mrow> <mi>n</mi> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>Pu</mi> <mi>n</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>jQu</mi> <mi>n</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>+</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>
    Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and reactive power point Amount.
  2. A kind of 2. control system of faulty grids combining inverter, it is characterised in that：Including：
    Voltage signal extraction unit, complex variable is being converted to just for obtaining the voltage signal of faulty grids, and by voltage signal Sequence voltage component and negative sequence voltage components, and calculate positive sequence voltage component amplitude, negative sequence voltage components amplitude and phase；
    Power calculation unit, positive sequence voltage component amplitude, negative sequence voltage components for the output of receiving voltage signal extraction unit Amplitude and phase, and combine the forward-order current component and negative-sequence current component of given power calculation control electric current；
    Current control unit, for receiving forward-order current component and negative-sequence current component and the output pwm signal control of control electric current The action of combining inverter processed；
    The voltage signal of faulty grids is converted into positive sequence voltage component and negative phase-sequence by voltage signal extraction unit according to following manner Component of voltage：
    By the voltage conversion of faulty grids into α component of voltages and β component of voltages in rest frame, α component of voltages are just The positive sequence voltage component and negative sequence voltage components of sequence voltage component and negative sequence voltage components and β component of voltages calculate positive sequence voltage The amplitude and phase of component and negative sequence voltage components：
    <mrow> <msub> <mi>U</mi> <mi>p</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>&amp;alpha;</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>&amp;beta;</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <msub> <mi>U</mi> <mi>n</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>&amp;alpha;</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>&amp;beta;</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>;</mo> </mrow>
    θp=arctan (uβp/uαp)；
    θn=arctan (uβn/uαn)；Wherein UpRepresent positive-sequence component amplitude, UnRepresent negative sequence component amplitude, θpRepresent positive-sequence component Phase, θnRepresent the phase of negative sequence component, uαpFor the positive-sequence component of α components, uβpRepresent the positive-sequence component of β components, uαnRepresent The negative sequence component of α components, uβnRepresent the negative sequence component of β components；
    Power calculation unit calculates the forward-order current component and negative-sequence current component of control electric current according to equation below：
    <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>Pu</mi> <mi>p</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>jQu</mi> <mi>p</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>+</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>
    <mrow> <msub> <mi>I</mi> <mrow> <mi>n</mi> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>Pu</mi> <mi>n</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>jQu</mi> <mi>n</mi> </msub> </mrow> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <msubsup> <mi>u</mi> <mi>p</mi> <mo>*</mo> </msubsup> <mo>+</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <msubsup> <mi>u</mi> <mi>n</mi> <mo>*</mo> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>
    Wherein, up *It is upConjugate complex number, un *It is unConjugate complex number, P and Q are respectively given active power and reactive power point Amount.
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