CN106998074A - A kind of control method and system for modular multi-level flexible direct current current conversion station - Google Patents

Abstract

The invention provides a kind of control method and system for modular multi-level flexible direct current current conversion station, its control method includes step：The three-phase alternating current information obtained of sampling after virtual synchronous electric machine controller and circulation controller, obtains induced electromotive force and pressure regulation voltage respectively；According to induced electromotive force and pressure regulation voltage, three-phase voltage reference value is obtained；By PWM three-phase voltage reference value, output switching signal realizes the control to modular multilevel current conversion station.Control method proposed by the present invention can be according to the frequency and voltage variety of AC system, adjust automatically active power of output and reactive power, so as to effectively reduce frequency and the voltage pulsation of AC system.

Description

A kind of control method and system for modular multi-level flexible direct current current conversion station

Technical field

The present invention relates to Technology of HVDC based Voltage Source Converter field, and in particular to one kind is changed for modular multi-level flexible direct current Flow the virtual synchronous motor control method and system at station.

Background technology

Threatened in face of worldwide fossil energy crisis, Global climate change and environmental degradation etc., countries in the world are Through being fully recognized that, the development and utilization of the energy must be from traditional fossil energy to green renewable and clean energy resource transition.Wind Electricity and photovoltaic generation etc. have become the principal mode of energy resource supply as important regenerative resource.Distributed energy permeates Rate increase, conventional synchronization generator installation ratio declines, and the spinning reserve capacity and rotary inertia of power system are relatively reduced, this Outside, due to distributed energy fluctuation and intermittent collective effect, system occurs in that the influence power grid security such as net source coordination is steady Surely the problem of running.

HVDC Transmission Technology is in reactive requirement, the stability of a system, extensive access clean energy resource and Large Copacity remote conveying There is obvious advantage, the today particularly reached its maturity in Technology of HVDC based Voltage Source Converter, it is mended in dynamic reactive in terms of electricity Repay, there is remarkable advantage in terms of trend reversion and system control, become one of best means of regenerative resource access, Also the structure for following power transmission network provides a brand-new technical scheme.

However, the control mode of conventional flex direct current transportation is based on vector control technology, on the basis of the control strategy Upper flexible direct current power transmission system can realize that dynamic electric voltage is supported, active and idle independent decoupling, and be the conveying of active power There is provided reliable and stable approach.In conventional flex DC transmission system, the decoupling of spatial orientation vector is easily by system control Parameters variation processed and mismatch etc. influence.In addition, the grid-connected transverter under conventional vector control strategy is difficult to provide in low-frequency range Suitable damping, easily causes the extensive off-grid of sub-synchronous resonance of alternating-current system and grid-connected current conversion station, it seriously threatens electricity The stability of Force system voltage and frequency, particularly during electrical power system transient failure, grid-connected current conversion station can not be provided enough Big inertia, easily causes system frequency unstability.

Send outside accordingly, it would be desirable to which one kind can improve regenerative resource and Operation of Electric Systems security, stability can be improved With the control technology of reliability.

The content of the invention

In order to overcome the above-mentioned deficiencies of the prior art, changed the invention provides one kind for modular multi-level flexible direct current The control method and system at station are flowed, its control method includes step：The three-phase alternating current information obtained sample respectively through virtual synchronous After electric machine controller and circulation controller, induced electromotive force and pressure regulation voltage are obtained；According to induced electromotive force and pressure regulation voltage, obtain Obtain three-phase voltage reference value；By PWM three-phase voltage reference value, output switching signal, realization is changed modular multilevel Flow the control at station.

The three-phase alternating current information obtained of sampling after virtual synchronous electric machine controller and circulation controller, is sensed respectively Electromotive force and pressure regulation voltage, including：The equation of motion of mechanical motion unit rotor is as follows in virtual synchronous electric machine controller：

In formula：J is rotor moment of inertia, T_mFor machine torque, T_eFor electromagnetic torque, D_pIt is specified for damped coefficient, ω * Frequency, ω are power network actual frequency；

The electric equation of electromagnetic unit stator winding is as follows in virtual synchronous electric machine controller：

In formula：u_abcFor the output end voltage of stator winding, i_abcIt is induction electric for the output end current of stator winding, e Gesture, R_sFor winding loss, L_sFor synchronous reactance.

The calculation formula of induced electromotive force is as follows：

In formula：E is that induced electromotive force, θ are electrical angle, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current, For rated frequency ω * and power network actual frequency ω difference；

WithFor the phase relation of three-phase, it is defined as follows shown：

Damped coefficient is the relation that active power and frequency change, and its definition is as follows：

Wherein, Δ P is active power setting value P_setWith the difference of active-power P, Δ θ changes for electrical angle.

The expression formula of active power of output is as follows：

Wherein,For i_abcWithBoth inner products,For rated frequency^ω* with power network actual frequency ω's Difference, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current.

Its control system includes：Control module, the three-phase alternating current information obtained of sampling is respectively through virtual synchronous motor control After device and circulation controller, induced electromotive force and pressure regulation voltage are obtained；Voltage synthesizer, for receiving induced electromotive force and pressure regulation After instruction, three-phase voltage reference value is exported；Modulation module, by PWM three-phase voltage reference value, output switching signal is real Now to the control of modular multilevel current conversion station.

Virtual synchronous electric machine controller includes mechanical motion unit and electromagnetic motion unit；

The equation of motion of rotor is as follows in mechanical motion unit：

In formula：J is rotor moment of inertia, T_mFor machine torque, T_eFor electromagnetic torque, D_pIt is specified for damped coefficient, ω * Frequency, ω are power network actual frequency；

The electric equation of stator winding is as follows in electromagnetic unit：

In formula：u_abcFor the output end voltage of stator winding, i_abcIt is induction electric for the output end current of stator winding, e Gesture, R_sFor winding loss, L_sFor synchronous reactance.

The calculation formula of induced electromotive force is as follows：

In formula：E is that induced electromotive force, θ are electrical angle, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current, For rated frequency ω * and power network actual frequency ω difference；

WithFor the phase relation of three-phase, it is defined as follows shown：

Damped coefficient is the relation that active power and frequency change, and its definition is as follows：

Wherein, Δ P is active power setting value P_setWith the difference of active-power P, Δ θ changes for electrical angle.

The expression formula of active power of output is as follows：

Wherein,For i_abcWithBoth inner products,For rated frequency ω * and power network actual frequency ω Difference, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current.

Compared with immediate prior art, the technical scheme that the present invention is provided has the advantages that：

1st, conventional synchronization generator is waved equation and electromagnetic equation introducing controller by control method proposed by the present invention In, current conversion station simulates conventional synchronization generator in external characteristics and operation mechanism, and then causes current conversion station to possess voltage regulation and frequency modulation Function, provides certain voltage and frequency support for AC system, improves the stability and reliability of system.

2nd, control method proposed by the present invention can be according to the frequency and voltage variety of AC system, adjust automatically output Active power and reactive power, so as to effectively reduce frequency and the voltage pulsation of AC system.

3rd, the present invention provides inertia and damping for system, and making the controlling of whole flexible direct current system has more preferable Shandong Rod, the large-scale grid connection of distributed energy is realized while system stable operation ability is improved.

Brief description of the drawings

Fig. 1 is overall control method block diagram of the invention；

Fig. 2 is the control strategy block diagram of virtual synchronous electric machine controller of the present invention.

Embodiment

Technical scheme is described in further details with reference to Figure of description.

The purpose of the present invention is to design a kind of control method of modular multilevel current conversion station, the control of flexible direct current converter station System processed is made up of sampling module, control module, voltage synthesizer and the part of modulation module five.

Sampling module provides three-phase voltage and electricity for the control module including virtual synchronous machine controller and circulation controller Stream input information, the output voltage of control module synthesized in voltage synthesizer after as modulation module input, so as to reach To the purpose of modular multilevel current conversion station output voltage control.

Control method proposed by the present invention by conventional synchronization generator wave equation and electromagnetic equation is introduced into controller, Current conversion station simulates conventional synchronization generator in external characteristics and operation mechanism so that current conversion station possesses the function of voltage regulation and frequency modulation, is The certain voltage of AC system offer and frequency support, improve the stability and reliability of system.

Modularization multi-level converter virtual synchronous motor control method proposed by the present invention：By flexible direct current converter station External characteristics and the mathematical modeling of synchronous motor, the equation of motion, electromagnetic equation (transient state or stable state) and working characteristics equivalent.

, it is necessary to use for reference the control method of flexible direct current transverter and conventional synchronization motor on control strategy.Virtual synchronous The control algolithm of motor needs to use the variables such as voltage and power, so to ensure the stability and accuracy of current conversion station output, The voltage x current double -loop control of current conversion station is used on the control structure.For conventional synchronization motor, prime mover and speed regulator It is responsible for providing mechanical output and regulation output frequency, exciter control system is responsible for adjusting excitation voltage.

In virtual synchronous motor, replaced by some intimate units, wherein, the synchronous electricity of field regulator simulation What the control function of exciter control system in machine, power and frequency regulator were simulated is the control function of speed regulator.Control system The output voltage and electric current of converter valve are gathered, the mechanical output for obtaining virtual synchronous motor by power and frequency regulator is instructed, The excitation voltage instruction of virtual synchronous motor is obtained by field regulator, after being calculated by virtual synchronous motor control algorithms, System frequency and the reference value of voltage are obtained, then is controlled out by producing drive signal after Double Loop Control System and modulating system Turning on and off for pipe is closed, so as to complete whole closed-loop system.

The core of control method proposed by the present invention is the design of virtual synchronous electric machine controller, and circulation controller and PWM and the vector controlled of conventional flex DC converter do not have essential distinction, and non-invention core does not do detailed opinion State.

Virtual synchronous electric machine controller will realize what is exported according to the frequency and voltage variety adjust automatically of AC system Active power and reactive power, the functional task of frequency and voltage support are provided for AC system, therefore can be sent out with conventional synchronization The control method of motor sets about processing.

As shown in Fig. 2 using PI controllers, and convolution (3) and (6), it can then obtain proposed by the present invention virtual Synchronous motor control strategy block diagram, including：Active frequency modulation function module and idle voltage regulation function module, can realize transverter Power output is adjusted according to the demand of AC system, and frequency and voltage support are provided for system.

Based on classical second order sync generator model, to make transverter preferably simulate and realize the property of synchronous motor Can, it should while considering mechanical movement and the electromagnetic motion relation of synchronous motor.

The mechanical movement of synchronous generator enables to current conversion station in power due to the presence of rotary inertia and damped coefficient With there is inertia, and power oscillation damping in the dynamic relationship of frequency, equation of rotor motion is as follows：

J is rotor moment of inertia in formula；T_mAnd T_eRespectively generator mechanical torque and electromagnetic torque；D_pFor damped coefficient； Respectively specified (reference) angular frequencies of ω * and ω and power network actual angular frequency.

Obtained mains frequency is solved in above formula, the active regulating power of transverter is realized, in the control of virtual synchronous machine Middle simulation is speed regulator.

The electromagnet portion of synchronous generator is modeled using the electric equation of stator winding as prototype, i.e.,

U in formula_abcAnd i_abcRespectively stator three-phase output end voltage and current；E is three-phase induction electromotive force；R_sAnd L_sPoint Wei not stator armature winding loss and synchronous reactance.The modeling only considers emphatically the voltage-current relationship characteristic of stator, more Simply, and do not consider in it electromagnetic property.

To make Controlling model algorithm preferably simulate synchronous generator from mechanism, meter and the magnetic linkage between rotor and stator are closed System, can derive

θ is that angular frequency * integrates obtained electrical angle in formula；M_fFor mutual inductance between stator and rotor；i_fFor rotor windings electricity Stream；

WithFor the phase relation of ABC three-phases, it is defined as follows shown：

Make the expression formula that inner product derives power respectively simultaneously for the active power of output P and reactive power Q of transverter, It is as follows：

Wherein,For i_abcWithBoth inner products,For i_abcWithBoth is interior Product.

(1) in formula damped coefficient substantially characterize be active power and frequency change relation, the following institute of its definition Show：

Wherein, Δ P is active power setting value P_setWith calculated value P difference, Δ θ changes for electrical angle.Damped coefficient is set Surely it can be set according to system, such as changed power 100%, frequency fluctuation 0.5%.

Note under steady state conditions, the selected of damped coefficient setting value should not typically cause frequency to change more than 0.5Hz.Separately Outside because the FREQUENCY CONTROL of proposition does not have time delay process, so smaller, the general foundation equation J that the value of rotary inertia should be set =D_pt_cTo determine, wherein t_cFor time constant, relevant with system, general value is several milliseconds to a few tens of milliseconds.

The idle Regulation Control function of control method is also needed sagging by reactive voltage in addition to using formula (7) is based on Control obtains idle input parameter, allows it to track ac grid voltage well.Similar, idle sagging coefficient reflection Be reactive power and voltage variation relation, its definition is as follows：

Wherein, Δ V represents alternating voltage setting value V_setWith measured value V_gDifference, that is, represent alternating voltage to reference value Offset, Δ Q represents reactive power setting value Q_setWith the variable quantity of calculated value Q difference, i.e. reactive power.

Idle sagging coefficient can be calculated according to formula (7) and obtained according to the setting of system desired value, and reactive power, and be made It is that negative-feedback and idle setting value, the reactive power value one of droop control work, forms idle pressure regulation part, encouraged so as to simulate Magnestat function.

Equation (3) is the relational expression of control inverter output voltage, and generally Exciting Windings for Transverse Differential Protection electric current is DC current, Have almost no change, one can be ignored behind equation.

It is worth noting that：Inverter Station and converting plant can be controlled, it is necessary to note tide simultaneously using the design method The change in stream direction can cause the change of formal notation, and when carrying out converting plant virtual synchronous machine control using the method, build Additional constant DC voltage control is discussed, to provide reliable dc source for Inverter Station.

Based on same inventive concept, what it is present invention also offers a kind of reduction layer-specific access direct-current commutation failure risk is System, is illustrated below.

The system that the present invention is provided can include：

Control module, for receiving after three-phase sample information, output induced electromotive force and pressure regulation voltage；Voltage synthesizer, For receiving after induced electromotive force and pressure regulation instruction, three-phase voltage reference value is exported；Modulation module, three-phase voltage reference value warp After PWM module, output switching signal realizes the control to modular multilevel current conversion station.

Control module includes：Virtual synchronous machine controller and circulation controller；Virtual synchronous machine controller and circulation control Device is received after three-phase sample information, and induced electromotive force and the pressure regulation voltage are exported respectively.Virtual synchronous electric machine controller includes Mechanical motion unit and electromagnetic motion unit.

The equation of motion of rotor is as follows in mechanical motion unit：

In formula：J is rotor moment of inertia, T_mFor machine torque, T_eFor electromagnetic torque, D_pIt is specified for damped coefficient, ω * Frequency, ω are power network actual frequency.

The electric equation of stator winding is as follows in electromagnetic unit：

In formula：u_abcFor the output end voltage of stator winding, i_abcIt is induction electric for the output end current of stator winding, e Gesture, R_sFor winding loss, L_sFor synchronous reactance.

Magnetic linkage relation between rotor and stator winding is as follows：

In formula：E is that induced electromotive force, θ are electrical angle, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current, For the rated frequency ω * and power network actual frequency ω difference；

WithFor the phase relation of three-phase, it is defined as follows shown：

Damped coefficient is the relation that active power and frequency change, and its definition is as follows：

Wherein, Δ P is active power setting value P_setWith the difference of active-power P, Δ θ changes for electrical angle.

The expression formula of active power of output is as follows：

Wherein,For i_abcWithBoth inner products,For rated frequency ω * and power network actual frequency ω Difference, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current.

It should be understood by those skilled in the art that, embodiments herein can be provided as method, system or computer program Product.Therefore, the application can be using the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware Apply the form of example.Moreover, the application can be used in one or more computers for wherein including computer usable program code The computer program production that usable storage medium is implemented on (including but is not limited to magnetic disk storage, CD-ROM, optical memory etc.) The form of product.

The application is the flow with reference to method, equipment (system) and computer program product according to the embodiment of the present application Figure and/or block diagram are described.It should be understood that can be by every first-class in computer program instructions implementation process figure and/or block diagram Journey and/or the flow in square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided The processor of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce A raw machine so that produced by the instruction of computer or the computing device of other programmable data processing devices for real The device for the function of being specified in present one flow of flow chart or one square frame of multiple flows and/or block diagram or multiple square frames.

These computer program instructions, which may be alternatively stored in, can guide computer or other programmable data processing devices with spy Determine in the computer-readable memory that mode works so that the instruction being stored in the computer-readable memory, which is produced, to be included referring to Make the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one square frame of block diagram or The function of being specified in multiple square frames.

These computer program instructions can be also loaded into computer or other programmable data processing devices so that in meter Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented processing, thus in computer or The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one The step of function of being specified in individual square frame or multiple square frames.

Finally it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, institute The those of ordinary skill in category field with reference to above-described embodiment still can to the present invention embodiment modify or Equivalent substitution, these any modifications or equivalent substitution without departing from spirit and scope of the invention are applying for this pending hair Within bright claims.

Claims (8)

1. a kind of control method for modular multi-level flexible direct current current conversion station, it is characterised in that the control method bag Include step：

The three-phase alternating current information obtained of sampling after virtual synchronous electric machine controller and circulation controller, obtains induction electric respectively Gesture and pressure regulation voltage；

According to the induced electromotive force and the pressure regulation voltage, three-phase voltage reference value is obtained；

By three-phase voltage reference value described in PWM, output switching signal is realized to the modular multilevel current conversion station Control.

2. control method as claimed in claim 1, it is characterised in that the three-phase alternating current information that the sampling is obtained is respectively through void Intend after synchronous motor controller and circulation controller, obtain induced electromotive force and pressure regulation voltage, including：

The equation of motion of mechanical motion unit rotor is as follows in the virtual synchronous electric machine controller：

$J\frac{d\mathrm{\ω}*}{dt}=T_m-T_e-D_p(\mathrm{\ω}*-\mathrm{\ω})$

In formula：J is rotor moment of inertia, T_mFor machine torque, T_eFor electromagnetic torque, D_pFor damped coefficient, ω * be rated frequency, ω is power network actual frequency；

The electric equation of electromagnetic unit stator winding is as follows in the virtual synchronous electric machine controller：

$u_{abc}=-R_s{i}_{abc}-L_s\frac{{\mathrm{di}}_{abc}}{dt}+e$

In formula：u_abcFor the output end voltage of the stator winding, i_abcIt is sensing for the output end current of the stator winding, e Electromotive force, R_sFor winding loss, L_sFor synchronous reactance；

The calculation formula of the induced electromotive force is as follows：

$e=\stackrel{\·}{\mathrm{\θ}}{M}_f{i}_f\stackrel{\‾}{sin\mathrm{\θ}}-M_f\frac{{\mathrm{di}}_f}{dt}\stackrel{\‾}{cos\mathrm{\θ}}$

In formula：E is that induced electromotive force, θ are electrical angle, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current,To be described Rated frequency ω * and power network actual frequency ω difference；

WithFor the phase relation of three-phase, it is defined as follows shown：

$\begin{array}{c}\stackrel{\‾}{sin\mathrm{\θ}}=\left(\begin{array}{ccc}sin\mathrm{\θ}& sin(\mathrm{\θ}-\frac{2\mathrm{\π}}{3})& sin(\mathrm{\θ}+\frac{2\mathrm{\π}}{3})\end{array}\right)\\ \stackrel{\‾}{cos\mathrm{\θ}}=\left(\begin{array}{ccc}cos\mathrm{\θ}& cos(\mathrm{\θ}-\frac{2\mathrm{\π}}{3})& cos(\mathrm{\θ}+\frac{2\mathrm{\π}}{3})\end{array}\right)\end{array}.$

3. control method as claimed in claim 2, it is characterised in that the damped coefficient is that active power and frequency change Relation, its definition is as follows：

$D_p=\frac{\mathrm{\Δ}P}{\mathrm{\Δ}\mathrm{\θ}}$

Wherein, Δ P is active power setting value P_setWith the difference of active-power P, Δ θ changes for electrical angle.

4. control method as claimed in claim 3, it is characterised in that the expression formula of the active power of output is as follows：

$P=\stackrel{\&CenterDot;}{\mathrm{\&theta;}}{M}_f{i}_f<i_{abc},\stackrel{\&OverBar;}{sin\mathrm{\&theta;}}>$

Wherein, P be active power, θ be electrical angle,For the output end current i of the stator winding_abcAnd phase RelationBoth inner products,For the rated frequency ω * and power network actual frequency ω difference, M_fFor stator and turn Mutual inductance, i between son_fFor rotor winding current.

5. a kind of control system for modular multi-level flexible direct current current conversion station, it is characterised in that the control system bag Include：

Control module, the three-phase alternating current information obtained of sampling after virtual synchronous electric machine controller and circulation controller, is obtained respectively To induced electromotive force and pressure regulation voltage；

Voltage synthesizer, for receiving after the induced electromotive force and pressure regulation instruction, exports three-phase voltage reference value；

Modulation module, by three-phase voltage reference value described in PWM, output switching signal is realized how electric to the modularization The control of flat current conversion station.

6. control system as claimed in claim 5, it is characterised in that the virtual synchronous electric machine controller includes mechanical movement Unit and electromagnetic motion unit；

The equation of motion of rotor is as follows in the mechanical motion unit：

$J\frac{d\mathrm{\&omega;}*}{dt}=T_m-T_e-D_p(\mathrm{\&omega;}*-\mathrm{\&omega;})$

In formula：J is rotor moment of inertia, T_mFor machine torque, T_eFor electromagnetic torque, D_pFor damped coefficient, ω * be rated frequency, ω is power network actual frequency；

The electric equation of stator winding is as follows in the electromagnetic unit：

$u_{abc}=-R_s{i}_{abc}-L_s\frac{{\mathrm{di}}_{abc}}{dt}+e$

In formula：u_abcFor the output end voltage of the stator winding, i_abcIt is sensing for the output end current of the stator winding, e Electromotive force, R_sFor winding loss, L_sFor synchronous reactance；

The calculation formula of the induced electromotive force is as follows：

$e=\stackrel{\&CenterDot;}{\mathrm{\&theta;}}{M}_f{i}_f\stackrel{\&OverBar;}{sin\mathrm{\&theta;}}-M_f\frac{{\mathrm{di}}_f}{dt}\stackrel{\&OverBar;}{cos\mathrm{\&theta;}}$

In formula：E is that induced electromotive force, θ are electrical angle, M_fFor mutual inductance, i between stator and rotor_fFor rotor winding current,To be described Rated frequency ω * and power network actual frequency ω difference；

WithFor the phase relation of three-phase, it is defined as follows shown：

$\begin{array}{c}\stackrel{\&OverBar;}{sin\mathrm{\&theta;}}=\left(\begin{array}{ccc}sin\mathrm{\&theta;}& sin(\mathrm{\&theta;}-\frac{2\mathrm{\&pi;}}{3})& sin(\mathrm{\&theta;}+\frac{2\mathrm{\&pi;}}{3})\end{array}\right)\\ \stackrel{\&OverBar;}{cos\mathrm{\&theta;}}=\left(\begin{array}{ccc}cos\mathrm{\&theta;}& cos(\mathrm{\&theta;}-\frac{2\mathrm{\&pi;}}{3})& cos(\mathrm{\&theta;}+\frac{2\mathrm{\&pi;}}{3})\end{array}\right)\end{array}.$

7. control system as claimed in claim 6, it is characterised in that the damped coefficient is that active power and frequency change Relation, its definition is as follows：

$D_p=\frac{\mathrm{\&Delta;}P}{\mathrm{\&Delta;}\mathrm{\&theta;}}$

Wherein, Δ P is active power setting value P_setWith the difference of active-power P, Δ θ changes for electrical angle.

8. control system as claimed in claim 7, it is characterised in that the expression formula of the active power of output is as follows：

$P=\stackrel{\&CenterDot;}{\mathrm{\&theta;}}{M}_f{i}_f<i_{abc},\stackrel{\&OverBar;}{\sin \mathrm{\&theta;}}>$

Wherein, P be active power, θ be electrical angle,For the output end current i for the stator winding_abcAnd phase Position relationBoth inner products,For the rated frequency ω * and power network actual frequency ω difference, M_fFor stator and Mutual inductance, i between rotor_fFor rotor winding current.