CN110460058A - A kind of control method of non-linear THE UPFC - Google Patents
A kind of control method of non-linear THE UPFC Download PDFInfo
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- CN110460058A CN110460058A CN201810424722.8A CN201810424722A CN110460058A CN 110460058 A CN110460058 A CN 110460058A CN 201810424722 A CN201810424722 A CN 201810424722A CN 110460058 A CN110460058 A CN 110460058A
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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
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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Abstract
The invention discloses a kind of control methods of non-linear THE UPFC, comprising: establishes mathematical model of the THE UPFC under dq coordinate system, voltage source converter uses pulse width modulation controlled mode, establishes the mathematical model of affine nonlinear system；Output function, nonlinear coordinate transformation and state back analysis equations are selected, the fifth-order nonlinearity of THE UPFC is system converting for Bu Lunuofu disjunction mark quasi-linear system；For the Bu Lunuofuji linear system of foundation, using flow controller inside linear pole-assignment design THE UPFC.The defect that the present invention may deteriorate for the performance of conventional linear controller by operating point wide variation, consider the nonlinear characteristic of THE UPFC, a kind of NONLINEAR OPTIMAL CONTROL method based on Differential Geometry State Variable Feedback Linearization Method theory is proposed, it is expansible to be applied to all exchange flexible transmission system and devices based on voltage source converter.
Description
Technical field
The invention belongs to electric power system and its automation field, in particular to a kind of control of non-linear THE UPFC
Method processed.
Background technique
Modern power industry System Development is rapid, on the one hand meets the needs of whole society is to electric energy as far as possible, guarantees society's warp
On the other hand the high speed development of Ji also brings series of challenges, such as systems organization and optimizing resource allocation problem, the peace of bulk power grid
Full stable operation problem, power flowcontrol and Economic Dispatch Problem etc., wherein how improving power grid transmission capacity to the maximum extent, mentioning
High system stability and reliability, effectively limitation these problems of system short-circuit levels of current are more and more prominent and by pass
Note.Existing AC transmission system is difficult to meet power flowcontrol under tradition machinery formula control method and improves the need of transmission line capability
It wants.After the 1970s, the Development of Power Electronic Technology based on high power device is swift and violent, and and computer information technology
It is combined with control theory, provides a new direction in order to solve the above problem.
Flexible AC transmitting system technology can carry out power grid quick, frequent, continuous, flexible and be accurately controlled, from
And match with the various quick controls of generator, substantially increase the power flowcontrol ability and various dynamics of electric system
Can, so that traditional " hardness " AC transmission system dependent on mechanical switch is upgraded to fusion high-power electric and electronic skill
" flexibility " AC transmission system of art, computer information technology and Advanced Control Techniques.In flexible AC transmitting system device,
Parallel static synchronous compensator (STATCOM) can provide reactive compensation to system to maintain node voltage, but control route
Trend ability is weaker；And static synchronous series compensator (SSSC) can provide series voltage compensation to system to control route tide
Stream, but parallel reactive current compensation can not be provided；The two respectively has the advantage and disadvantage of oneself.THE UPFC (Unified
Power Flow Controller, UPFC) combine two kinds of devices of static synchronous compensator and static synchronous series compensator
Advantage, the ability of existing compensated line voltage, load disturbance, and the function of having compensating reactive power electric current, maintain node voltage, therefore
The research hotspot of academia is rapidly become.
A parallel static synchronous compensator and static synchronous series compensator is also been developed in THE UPFC
The key function not having, that is, the ability for active power of handling up.Independent static synchronous compensator and Static Synchronous Series are mended
Repay device can only absorb and issue reactive power but not be attached to energy storage device in the case where all can not be with systems exchange wattful power
Rate；Parallel connection side static synchronous compensator and series side static synchronous series compensator pass through direct current in THE UPFC
Hold connection back-to-back, this provides channel for the exchange of active power, so that series side and side in parallel are in individual absorption and sending
While reactive power, active power can also be absorbed and issue, but premise is to ensure that the flat of series-parallel two sides active power
Weighing apparatus, controller is uniformly processed in this way and is achieved that the four quadrant running on power diagram.
Since THE UPFC and electric system are inherently nonlinear systems, current THE UPFC
Approximate linearization method is mostly used in Optimal Control Design greatly or lacks the Intelligentized method of strict mathematical foundation, is not counted accurately
And the nonlinear characteristic of THE UPFC, it has been done not when carrying out exact linearization control design to THE UPFC
With the simplification of degree, linearization procedure is sufficiently complete, causes to be easy to cause controller performance to dislike in operating point wide variation
Change even loss of stability.
Summary of the invention
The purpose of the present invention is to provide a kind of control methods of non-linear THE UPFC, improve Unified Power Flow control
The nonlinear characteristic of device processed makes its stable operation in operating point wide variation.
Realize the technical solution of the object of the invention are as follows: a kind of control method of non-linear THE UPFC, including with
Lower step:
Step 1, mathematical model of the THE UPFC under dq coordinate system is established, voltage source converter uses pulsewidth
Modulation control mode establishes the mathematical model of the affine nonlinear system of THE UPFC；
Step 2, according to the mathematical model for the affine nonlinear system established in step 1, output function, non-linear seat are selected
Mark transformation and state back analysis equations, the fifth-order nonlinearity of THE UPFC is system converting for Bu Lunuofu disjunction mark almost linear
System；
Step 3, for the Bu Lunuofuji linear system of foundation, Unified Power Flow control is designed using linear pole-assignment
Flow control method inside device processed.
Further, it in step 1, according to the equivalent circuit of THE UPFC, is represented with the differential equation and is sat in dq
Mathematical model under mark system is gone out to unite according to the pulse width modulation controlled mode of voltage source by the Derivation of Mathematical Model under dq coordinate system
The mathematical model of 4 input, the 45 rank affine nonlinear systems of output of one flow controller.
Further, it in step 2, according to the mathematical model for the affine nonlinear system that step 1 is established, selects affine non-thread
Property system state variables obtain the complete Liapunov output function of system as Systematic selection output function；To affine non-
Linear system carries out the coordinate transform in the space from x to z, establishes state back analysis equations, and five ranks of THE UPFC are non-thread
Property it is system converting be Bu Lunuofu disjunction mark quasi-linear system.
Further, in step 3, for the Bu Lunuofuji linear system of foundation, using linear pole-assignment meter
The optimum gain and Linear Control of calculation system are restrained, and are instructed computing system state balance point by Line Flow, are obtained optimal control law
Parameter, obtain the optimal control law of former nonlinear system finally by control law inverting.
Compared with prior art, the present invention its remarkable advantage is: (1) with the electric current and direct current of two sides AC side of converter
Capacitance voltage is as quantity of state, the mathematical model and the mathematical modulo under synchronous rotary dq coordinate of establishing THE UPFC
Type has specific physical significance；(2) mould of 4 input, the 45 rank affine nonlinear systems of output of THE UPFC is established
Type, and the model meets linearization condition, it can further progress exact linearization method；(3) linearization procedure is fed back using state
It realizes, keeps linearization procedure more accurate, trend control inside THE UPFC is finally designed using Method of Pole Placement
Device processed, such feedback oscillator and Linear Control rule can be determined by freely configuring system features value；(4) exact linearization method is effective
The essential shortcoming for overcoming traditional approximate linearization method is adapted to the wide variation of control operating point, to solve control
The control problem of device and other non-linear power electronic equipments provides a new approach.
Detailed description of the invention
Fig. 1 is that the present invention is based on the control method flow charts of non-linear THE UPFC.
Fig. 2 is THE UPFC equivalent circuit structure of the present invention.
Fig. 3 is THE UPFC nonlinear Control schematic diagram of the present invention.
Specific embodiment
In conjunction with Fig. 1, a kind of control method of non-linear THE UPFC, comprising the following steps:
Step 1: establishing mathematical model of the THE UPFC under dq coordinate system, voltage source converter VSC is used
Pulse width modulation controlled mode, establish THE UPFC satisfaction can refine condition 4 input 4 output 5 ranks it is affine non-thread
The mathematical model of property system；Specifically: using THE UPFC two sides AC side of converter and DC capacitor voltage as shape
State amount establishes the mathematical model of THE UPFC, carries out Park transformation to the model, obtains THE UPFC same
Mathematical model under step rotation dq coordinate system, voltage source converter VSC use PWM control mode, and thus establishing satisfaction can essence
The mathematical model of 4 input, the 45 rank affine nonlinear systems of output of trueization condition.
Step 2: selecting liapunov function, non-linear seat according to the mathematical model of the affine nonlinear system of foundation
Mark transformation and state back analysis equations, the fifth-order nonlinearity of THE UPFC is system converting for Bu Lunuofu disjunction mark almost linear
System；Specifically: liapunov function is selected for the mathematical model for the affine nonlinear system established, system is carried out from x
State back analysis equations are established to the coordinate transform in the space z in space, are by the fifth-order nonlinearity of THE UPFC is system converting
Bu Lunuofu disjunction mark quasi-linear system.
Step 3: designing Unified Power Flow using linear pole-assignment for the Bu Lunuofuji linear system established
The inside flow controller of controller；Specifically: for the Bu Lunuofuji linear system of foundation, using linear POLE PLACEMENT USING side
Method calculates optimum gain, instructs computing system state balance point by Line Flow, obtains the parameter of optimal control law, finally by
Control law inverting obtains the optimal control law of former nonlinear system, obtains NONLINEAR OPTIMAL CONTROL schematic diagram.
The content of present invention is described in detail below with reference to embodiment.
Embodiment
A kind of control method of non-linear THE UPFC, comprising the following steps:
Step 1: establishing mathematical model of the THE UPFC under dq coordinate system, voltage source converter VSC is used
Pulse width modulation controlled mode establishes the mathematical model of 4 input, the 45 rank affine nonlinear systems of output of THE UPFC；
According to THE UPFC equivalent circuit diagram, THE UPFC nonlinear mathematical model is established, is indicated are as follows:
As shown in Fig. 2, UdcIndicate the voltage on capacitor C, e1,e2Indicate the voltage of two converters output, I1,I2It indicates
Converter flows to the electric current of power grid, L1,R1Indicate the equivalent inductance and equivalent resistance that VSC1 exchange is surveyed, L1, R2Indicate VSC2 exchange
The equivalent inductance and equivalent resistance of survey, UsThe voltage of bus, U are accessed for simultaneously translocationrFor 2 voltage of bus.
e1d,e1q,e2d,e2qThe respectively d of two converter VSC1 and VSC2 output voltages of THE UPFC, q axis point
Amount, i1d,i1qIndicate electric current i1D, q axis component, i2d,i2qIndicate electric current i2D, q axis component, ω indicate angular frequency, usd,usq
Indicate 1 voltage u of bussD, q axis component, urd,urqIndicate 1 voltage u of busrD, q axis component obtains it under dq coordinate
Mathematical model is indicated with the differential equation are as follows:
VSC uses PWM control mode, k1,k2And δ1,δ2For the PWM harmonic ratio and phase angle of VSC1 and VSC2, is defined as:
Formula (3) substitution formula (2) is obtained into 4 inputs 4 and exports 5 rank affine nonlinear deterministic mathematical models are as follows:
x∈R5For state variable, u ∈ R4To control variable, x=[x1,x2,x3,x4,x5]T=[i1d,i1q,i2d,i2q,Udc
]T, u=[u1,u2,u3,u4]T=[k1cosδ1,k1sinδ2,k2cosδ2,k2sinδ2]T,ursd=urd-usd, ursq=urq-usq。
The expression formula of affine nonlinear deterministic mathematical model can also indicate are as follows:
Step 2: according to the mathematical model of the affine nonlinear system of foundation, liapunov function, appropriate non-is selected
Linear coordinate transformation and state back analysis equations, the fifth-order nonlinearity of THE UPFC is system converting for Bu Lunuofu disjunction mark
Quasi-linear system；
It is defeated there are one group in above-mentioned THE UPFC nonlinear deterministic mathematical model according to exact linearization method theory
Function h (x)=[h out1(x),h2(x),h3(x),h4(x)]T, so that the sum of relationship degree of affine nonlinear system meets: r1+r2
+r3+r4The relationship degree collection of=n=5, i.e. nonlinear affine system are combined into r={ r1,r2,r3,r4, enable r={ 2,1,1,1 }.
The n rank nonlinear system of m input m output meets each output function hi(x) to the k of vector field f (x)iRank Lie is led
It is several to each vector field gj(x) Lie derivative is equal to zero, i.e.,
According to formula (5), h1(x) meet following partial differential equations:
There are the solutions that one is similar to liapunov function for formula (7):
Wherein d is arbitrary constant, and the first three items of (8) formula right side of the equal sign successively represent THE UPFC parallel connection side electricity
The energy stored in sense, side inductance in parallel and DC bus capacitor.
In view of the major function of THE UPFC is side in parallel compensating reactive power electric current, the active and nothing of series side control
Function trend selects three state variable i of system to simplify the calculation1q,i2d,i2qAs output function h2(x)~h4(x), unified tide
One group of complete output function of stream controller system are as follows:
Select the nonlinear coordinate transformation from the space x to the space z as follows for system (5) formula:
Formula (10) derivation can be obtained:
One group of new control variable is defined according to formula (11):
Enable v=[v1,v2,v3,v4]TFor new control variable, u=[u1,u2,u3,u4]TFor the control of former nonlinear system
Vector, a (x), b (x) are respectively 4 × 1 ranks and 4 × 4 level matrix numbers, wherein
Formula (12) can be written as follow form:
V=a (x)+b (x) u (13)
Formula (12) are substituted into formula (11) available Bu Lunuofu disjunction mark pseudotype linear system:
THE UPFC original nonlinear system turns to following linear system by exact linear:
Wherein,
Step 3: designing Unified Power Flow using linear pole-assignment for the Bu Lunuofuji linear system established
Flow controller inside controller.
To above-mentioned linear system formula (15), the order of matrix [B AB] is 5, therefore the linear system is controllable, Linear Control rule are as follows:
V=-Kz (16)
Feedback gain matrix K is calculated using Method of Pole Placement, and there is following form:
The characteristic equation of linear system is
Det (sI- (A-BK))=(s- λ1)(s-λ2)(s-λ3)(s-λ4)(s-λ5)=0 (18)
5 characteristic roots of system are λ1~λ5, feedback gain matrix K can be by freely configuring λ1~λ5Determine, into
And it can determine Linear Control and restrain.
The control target of control system is so that state variable is converged to equalization point, and equalization point vector makes by former nonlinear system
The equalization point vector x of system*Gained after being coordinately transformed according to relationship z=φ (x) shown in formula (10), therefore actually linear feedback
Control v is the function of state variable difference, therefore formula (16) should be following form:
Wherein z*It is x=x*When the corresponding space z value, it is flat that affine nonlinear system (5) formula shares 5 state variables
Weigh point, in practical application, the typical control model of THE UPFC are as follows: series circuit load disturbance P, Q, side control in parallel
Reactive current i1qWith DC voltage Udc, according to the Power Theory under dq coordinate, the tidal current table of route where THE UPFC
Up to formula are as follows:
If the no-load voltage ratio of THE UPFC series transformer is n, i.e. i2: 1=n:1, it can be by Line Flow according to above formula
Instruct P*,Q*Terminal voltage u is compensated with THE UPFCrd,urqSeries transformer output current-order is calculated, that is, is balanced
PointWith
WithIt is directly given by the instruction of upper one layer of system-level controller, remaining equalization pointBy being
The equilibrium state equation group of system is found out, and is enabled in formula (4)It can obtain:
It willIt substitutes into above-mentioned 5 rank equation group, can obtain:
Wherein
The pre- feedback relationship of dominant vector defined according to formula (13) can inverting obtain the optimum control of former nonlinear system
Restrain u:
U=b (x)-1(v-a(x))-b(x)-1[-K(φ(x)-φ(x*))-a(x)]
Wherein, the same formula of the definition of φ (x) (10), the same formula of the definition of matrix a (x), b (x) (13).Fig. 3 is that the present invention is unified
Flow controller nonlinear Control schematic diagram.
The defect that the present invention may deteriorate for the performance of conventional linear controller by operating point wide variation considers
The nonlinear characteristic of THE UPFC proposes a kind of based on the non-thread of Differential Geometry State Variable Feedback Linearization Method theory
Property method for optimally controlling, it is expansible be applied to all exchange flexible transmission system and devices based on voltage source converter.
Claims (4)
1. a kind of control method of non-linear THE UPFC, which comprises the following steps:
Step 1, mathematical model of the THE UPFC under dq coordinate system is established, voltage source converter uses pulsewidth modulation
Control mode establishes the mathematical model of the affine nonlinear system of THE UPFC；
Step 2, according to the mathematical model for the affine nonlinear system established in step 1, output function, non-linear scale is selected to become
Change with state back analysis equations, by the fifth-order nonlinearity of THE UPFC it is system converting be Bu Lunuofu disjunction mark almost linear system
System；
Step 3, for the Bu Lunuofuji linear system of foundation, THE UPFC is designed using linear pole-assignment
Internal flow control method.
2. the control method of non-linear THE UPFC according to claim 1, which is characterized in that in step 1, root
According to the equivalent circuit of THE UPFC, the mathematical model under dq coordinate system is represented with the differential equation, according to voltage source
Pulse width modulation controlled mode, by the Derivation of Mathematical Model under dq coordinate system go out THE UPFC 4 input 4 output 5 ranks
The mathematical model of affine nonlinear system.
3. the control method of non-linear THE UPFC according to claim 1, which is characterized in that in step 2, root
According to the mathematical model for the affine nonlinear system that step 1 is established, select affine nonlinear system state variable as Systematic selection
Output function obtains the complete Liapunov output function of system；The seat in the space from x to z is carried out to affine nonlinear system
Mark transformation, establishes state back analysis equations, and the fifth-order nonlinearity of THE UPFC is system converting for Bu Lunuofu disjunction mark standard
Linear system.
4. the control method of non-linear THE UPFC according to claim 1, which is characterized in that in step 3, needle
To the Bu Lunuofuji linear system of foundation, using the optimum gain and Linear Control of linear pole-assignment computing system
Rule instructs computing system state balance point by Line Flow, obtains the parameter of optimal control law, obtain finally by control law inverting
To the optimal control law of former nonlinear system.
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Cited By (4)
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| CN109038659A (en) * | 2018-07-26 | 2018-12-18 | 湖南工业大学 | DFIG grid side converter low voltage traversing control method based on state feedback linearization |
| CN112398139A (en) * | 2020-09-23 | 2021-02-23 | 国网浙江省电力有限公司湖州供电公司 | Impedance equivalent simulation method for static synchronous series compensator of power grid |
| CN114142782A (en) * | 2021-10-09 | 2022-03-04 | 华侨大学 | Fault estimation and compensation method for asynchronous motor actuator |
| CN114142537A (en) * | 2021-08-20 | 2022-03-04 | 华北电力大学（保定） | Active power and reactive power decoupling control method based on rotary current controller |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109038659A (en) * | 2018-07-26 | 2018-12-18 | 湖南工业大学 | DFIG grid side converter low voltage traversing control method based on state feedback linearization |
| CN112398139A (en) * | 2020-09-23 | 2021-02-23 | 国网浙江省电力有限公司湖州供电公司 | Impedance equivalent simulation method for static synchronous series compensator of power grid |
| CN112398139B (en) * | 2020-09-23 | 2022-09-02 | 国网浙江省电力有限公司湖州供电公司 | Impedance equivalent simulation method for static synchronous series compensator of power grid |
| CN114142537A (en) * | 2021-08-20 | 2022-03-04 | 华北电力大学（保定） | Active power and reactive power decoupling control method based on rotary current controller |
| CN114142537B (en) * | 2021-08-20 | 2023-08-25 | 华北电力大学（保定） | Active and reactive power decoupling control method based on rotary flow controller |
| CN114142782A (en) * | 2021-10-09 | 2022-03-04 | 华侨大学 | Fault estimation and compensation method for asynchronous motor actuator |
| CN114142782B (en) * | 2021-10-09 | 2023-08-29 | 华侨大学 | Estimation and compensation method for faults of asynchronous motor actuator |
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