CN106786715B - A kind of sagging control coefrficient of multi-end VSC-HVDC system determines method - Google Patents
A kind of sagging control coefrficient of multi-end VSC-HVDC system determines method Download PDFInfo
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Abstract
The present invention discloses a kind of sagging control coefrficient of multi-end VSC-HVDC system and determines method, and the mean value model for being primarily based on VSC establishes the direct current system state-space model containing sagging control, and the mechanism of action of sagging control is analyzed with this；Sagging coefficient is determined that problem is converted to using system Mixed Sensitivity Frobenius-Hankel Norm minimum as the optimization problem of target based on system model again, the constraint of closed-loop system characteristic value and steady-state error constraint are considered simultaneously, are optimal the stability of system and robustness.Method of the invention can utmostly guarantee stability of the system under disturbance, and system is made to have certain fault ride-through capacity；It can also be determined in conjunction with method with other sagging coefficients, increase constraint condition or change optimization aim, design the droop control device for meeting different requirements or realization different function.
Description
Technical field
The present invention relates to Coordinated Control fields between converter station in power grid construction, specially a kind of multiterminal VSC-HVDC system
Sagging control coefrficient of uniting determines method.
Background technique
Multiterminal voltage source converter based HVDC system (voltage source converter based
High voltage direct current, VSC-HVDC) it is increasingly becoming power grid construction new trend.It is more preferably to play
Hold the regulating power of VSC-HVDC system, wherein voltage sagging control essential between the research of coordinated control mode converter station
Comprehensive performance processed is preferable, is to apply coordinated control mode between more station at present, and the sagging control coefrficient of voltage determines the change of current
The power and voltage that station undertakes adjust task specific gravity, and then determine the stability of system, therefore the determination of sagging coefficient is most
It is important.
At present research in sagging coefficient mainly according to converter station capacity and power margin be configured with dynamic regulation,
Such as have research on the basis of considering converter station capacity count and converter station power margin come determine sagging coefficient (Zhu Rui can, Lee
Xing Yuan, Wu Feng consider that the VSC-MTDC system of power margin improves sagging control strategy [J] Sichuan University journal (engineering science
Version), 2015,47 (3): 137-143.), there is research to consider the influence of real-time working condition on this basis again, run work in system
Condition automatically adjusts sagging coefficient when changing, make in system imbalance power obtain an equitable breakdown (Zhu Rui can, Wang Yuhong, Li Xingyuan,
Equal .VSC-MTDC system dc voltage adaptive slop control strategy [J] Automation of Electric Systems, 2015,39 (4): 63-
68.).But the rare research to sagging control mathematical model at present, and also have ignored when determining sagging coefficient based on number
Learn the stability analysis of model.To measure influence of the controller to system stability, usually propose that different parameters refer to as evaluation
Mark, wherein S/T Mixed Sensitivity has proven to a kind of determination of stability index of maturation, can be used for evaluating droop control device
System stability is influenced.
Summary of the invention
In view of the above-mentioned problems, the purpose of the present invention is to provide one kind, and system can be made still to keep stability under disturbance
Determine that method, technical solution are as follows with the sagging control coefrficient of multi-end VSC-HVDC system of robustness:
A kind of sagging control coefrficient of multi-end VSC-HVDC system determines method, which comprises the following steps:
Step 1: ac and dc systems being decoupled according to the mean value model of VSC, Converter DC-side is equivalent to direct current
Stream source, DC line carry out π type equivalence, obtain multi-end VSC-HVDC system equivalent model；
Step 2: its state-space model is established according to multi-end VSC-HVDC system equivalent model:
In formula, x is state variable；ω is disturbance variable, and u is control variable, and ω and u are input variable；Y and z are
Output variable；A,Bω、Bu、CyAnd CzFor state matrix；And
X=[U1,...Ui,...,Un,iL1,...,iLk,...,iLm]T (2)
Wherein, n is inverter quantity, UiFor i-th of inverter DC voltage, m is DC line quantity, iLkTo flow through line
Road LkElectric current；ikFor i-th of inverter DC current, ncFor the quantity at DC voltage control end, nncFor the control of non-dc voltage
The quantity at end；
Its steady-state operation equation is obtained according to the specific topology of system, formula (1)-(4) arrangement is substituted into and obtains the transmitting of system
Jacobian matrix are as follows:
And
Step 3: the closed-loop system state-space model containing droop control device is established, by there is constrained optimization theory to seek
Sagging coefficient optimal value, method particularly includes:
1) closed-loop system characteristic value constrains: by droop control device u=K (y-Udcmin) formula (1) is substituted into, it obtains that sagging control is added
Closed-loop system state matrix after device processed is Ac=A+BuKCy；
Wherein, the matrix expression of droop control device isK in formula1For using the inverter 1 of sagging control
Sagging coefficient, k2For using the sagging coefficient of the inverter 2 of sagging control；AcFor the closed-loop system after droop control device is added
State matrix；UdcminThe voltage minimum allowed for direct current system；
To make closed-loop system keep stablizing, then the characteristic value real part of closed-loop system all takes negative value, corresponding constraint condition
Are as follows:
real(λi(Ac)) < 0 (i=1 ..., neig) (7)
In formula: λi(Ac) it is AcCharacteristic value；neigIt is characterized value quantity；
2) steady-state error constrains: the degree of each end DC voltage offset voltage minimum value being made to be maintained at certain restriction range
Interior, then the channel y steady-state error constrains and the channel z steady-state error constraint expression formula are as follows:
E (s)=y (s)-Udcmin(s)=[S (s) Gyω(s) -S(s)]v(s) (8)
ez(s)=[Gzω(s)+Gzu(s)KS(s)Gyω(s)-Gzu(s)KS(s)-I]v(s) (9)
In formula, v (s)=[ω (s) Udcmin(s)]TFor input variable, including disturbance variable and control variable minimum value；
S (s)=(I-KGyu(s))-1For narrow sense controlled device GyuSensitivity function；
Influence of the input variable to output variable and control variable is assessed with the ratio between two norms of variable, by steady-state error
Analysis is converted to the odd value analysis of transfer function matrix, and steady-state error constraint is then converted into the singular value of transmission function about
Beam；
3) the sensitivity function S of controlled device G and mending sensitivity function T are defined as
H is feedback controller in formula；
Make the FH Norm minimum of system sensitivity function and mending sensitivity function, it may be assumed that
In formula, JoptFor the optimal value of S/T Mixed Sensitivity performance indicator, KstabTo meet the constraint of S/T Mixed Sensitivity
PID controller parameter domain；
The optimization problem is solved, the sagging control coefrficient for being optimal system stability is obtained.
The beneficial effects of the present invention are: the present invention determines problem for the sagging control coefrficient of multi-end VSC-HVDC system, mention
A kind of sagging coefficient for considering system stability determines method out, and the mean value model for being primarily based on VSC is established containing sagging control
The direct current system state-space model of system, the mechanism of action of sagging control is analyzed with this；Then, system model is based on by sagging system
Number determines that problem is converted to using system Mixed Sensitivity Frobenius-Hankel Norm minimum as the optimization problem of target, together
When consider closed-loop system characteristic value constraint and steady-state error constraint, be optimal the stability of system and robustness；This method
It can utmostly guarantee stability of the system under disturbance, and make system that there is certain fault ride-through capacity；It can also be with it
His sagging coefficient determines that method combines, and increases constraint condition or changes optimization aim, designs and meet different requirements or realization not
The droop control device of congenerous.
Detailed description of the invention
Fig. 1 is the closed-loop system schematic diagram being added after droop control device.
Fig. 2 is four end VSC-HVDC system topology schematics.
Fig. 3 is four end VSC-HVDC system equivalent model schematic diagrames.
Fig. 4 a respectively holds DC voltage dynamic response figure when being marine wind electric field power output variation.
Fig. 4 b respectively holds active power dynamic response figure (VSC1, VSC2) when being marine wind electric field power output variation.
Fig. 4 c respectively holds active power dynamic response figure (VSC3, VSC4) when being marine wind electric field power output variation.
Fig. 4 d respectively holds DC current dynamic response figure (VSC1, VSC2) when being marine wind electric field power output variation.
Fig. 4 e respectively holds DC current dynamic response figure (VSC3, VSC4) when being marine wind electric field power output variation.
Fig. 5 a respectively holds DC voltage dynamic response figure when being ac bus three-phase shortcircuit ground fault.
Fig. 5 b respectively holds active power dynamic response figure (VSC1, VSC2) when being ac bus three-phase shortcircuit ground fault.
Fig. 5 c respectively holds active power dynamic response figure (VSC3, VSC4) when being ac bus three-phase shortcircuit ground fault.
Fig. 5 d respectively holds DC voltage dynamic response figure (VSC3) when being ac bus three-phase shortcircuit ground fault.
Fig. 5 e respectively holds DC voltage dynamic response figure (VSC4) when being ac bus three-phase shortcircuit ground fault.
Specific embodiment
Technical solution of the present invention and technical effect are described in further details in the following with reference to the drawings and specific embodiments.
A kind of sagging control coefrficient of multi-end VSC-HVDC system determines method, comprising the following steps:
Step 1: the mean value model based on VSC decouples ac and dc systems, and Converter DC-side is equivalent to direct current
Stream source, DC line carry out π type equivalence, obtain the equivalent model of VSC-HVDC system.
Step 2: its state-space model is established based on multi-end VSC-HVDC system equivalent model.Specifically:
The state-space model for enabling multi-end VSC-HVDC system is
In formula: x is state variable；ω is disturbance variable；U is control variable；Y and z is output variable；A, Bω, Bu, Cy, Cz
For state matrix.
1) state variable, value are as follows:
X=[U1,...Ui,...,Un,iL1,...,iLk,...,iLm]T (2)
In formula: n is inverter quantity, UiFor i-th of inverter DC voltage, m is DC line quantity, iLkTo flow through line
Road LkElectric current.
2) disturbance variable and control variable, they are all input variable, value are as follows:
In formula: ikFor i-th of inverter DC current, ncFor the quantity at DC voltage control end, nncFor non-dc voltage
The quantity of control terminal
3) output variable, value are as follows:
In formula: UiFor i-th of inverter DC voltage, ncFor the quantity at DC voltage control end, nncFor non-dc voltage
The quantity of control terminal.
Its steady-state operation equation is obtained according to the specific topology of system, formula (1)-(4) arrangement is substituted into and obtains the transmitting of system
Jacobian matrix are as follows:
Wherein
Transfer function matrix is divided into four parts, respectively represents the transitive relation between two inputs and two outputs,
Middle GyuFor the transfer matrix between control variable u and output variable y, namely controlled device in the narrow sense.Enable droop control device
Matrix expression is K, then the closed-loop system after droop control device is added is as shown in Figure 1, so far obtain closing containing droop control device
Loop system state-space model.
Step 3: optimal by there is constrained optimization theory to seek sagging coefficient according to closed-loop system state-space model
Value, wherein constraint condition is the constraint of closed-loop system characteristic value and steady-state error constraint, and optimization aim is to keep the S/T of closed-loop system mixed
Close the Frobeniu-Hankel Norm minimum of sensitivity.Specifically:
1) closed-loop system characteristic value constrains:
By droop control device u=K (y-Udcmin) formula (1) is substituted into, it obtains that the closed-loop system state after droop control device is added
Matrix is Ac=A+BuKCy.Wherein, the matrix expression of droop control device isK in formula1To use sagging control
Inverter 1 sagging coefficient, k2For using the sagging coefficient of the inverter 2 of sagging control；AcAfter droop control device is added
Closed-loop system state matrix；UdcminThe voltage minimum allowed for direct current system.
Closed-loop system is set to keep stablizing, then the characteristic value real part of closed-loop system must be all negative value namely closed-loop system
Pole needs to be entirely located in Left half-plane, a corresponding constraint condition are as follows:
real(λi(Ac)) < 0 (i=1 ..., neig) (7)
In formula: λi(Ac) it is AcCharacteristic value；neigIt is characterized value quantity.
2) steady-state error constrains:
Refer to that the degree of each end DC voltage offset voltage minimum value is maintained in certain restriction range, since closed-loop system is deposited
In output variable y and z, sagging control terminal DC voltage and non-sagging control terminal DC voltage, therefore steady-state error are respectively corresponded
Constraint can be divided into the constraint of the channel y steady-state error and the constraint of the channel z steady-state error.Each error variance expression formula can be obtained by Fig. 1:
E (s)=y (s)-Udcmin(s)=[S (s) Gyω(s) -S(s)]v(s) (8)
ez(s)=[Gzω(s)+Gzu(s)KS(s)Gyω(s)-Gzu(s)KS(s)-I]v(s) (9)
V (s)=[ω (s) U in formuladcmin(s)]TFor input variable, including disturbance variable and control variable minimum value；S
(s)=(I-KGyu(s))-1For narrow sense controlled device GyuSensitivity function.The Concept Evaluation energy of norm is introduced between variable
The gain of transmission assesses influence of the input variable to output variable and control variable with the ratio between two norms of variable, by stable state
Error analysis is converted to the odd value analysis of transfer function matrix, and steady-state error constrains the singular value for being then converted into transmission function
Constraint.
3) optimization aim based on S/T Mixed Sensitivity function:
The sensitivity function S and mending sensitivity function T of controlled device G is defined as:
H is feedback controller in formula.
S/T mixed sensitivity problem overall thought is to make the FH norm of system sensitivity function and mending sensitivity function most
It is small, it may be assumed that
J in formulaoptFor the optimal value of S/T Mixed Sensitivity performance indicator, KstabExpression meets the constraint of S/T Mixed Sensitivity
PID controller parameter domain.
It solves the above optimization problem, the sagging control coefrficient for being optimal system stability can be obtained, also to obtain the final product
To desired droop control device.
For the beneficial effect for detecting the method for the present invention, verified using realistic model emulation.
Four end VSC-HVDC systems are chosen as simulation example, structure is as shown in Figure 2.In Fig. 2, VSC1 and VSC2 connect
Marine wind electric field is connect, double-fed blower is all made of, VSC3 connects land AC network with VSC4, it is assumed that all AC networks are all hard
Forceful electric power net.VSC1 and VSC2, which is used, to be determined alternating voltage and determines frequency control, and VSC3 and VSC4 use the sagging control of voltage.
1) according to system topological and parameter, the equivalent model for obtaining four end VSC-HVDC systems is as shown in Figure 3.
2) according to the equivalent model of four end VSC-HVDC systems, its steady-state operation equation is obtained based on Kirchhoff's law
Are as follows:
Wherein:
State variable, disturbance variable, control variable and two output variables of system are respectively as follows:
Formula (14) are substituted into formula (12), arrangement obtains system state space model.
3) the sagging coefficient select permeability based on Optimum Theory, objective function are proposed for four end VSC-HVDC systems
As shown in formula (11), characteristic value is constrained as shown in formula (7), the constraint of y channel error are as follows:
The constraint of its z channel error are as follows:
Above-mentioned optimization problem is solved, sagging coefficient optimal solution is obtained are as follows:
The y channel error variable steady-state error of system is that 38.6621, z channel error variable steady-state error is at this time
39.9869 S/T Mixed Sensitivity is 0.3920.
After obtaining optimal sagging coefficient, apply different disturbance and failure in systems, verifies system in droop control device
Stability under effect.The perturbation scheme of Digital Simulation are as follows:
(1) WF1 contributes and is reduced to 75MW by 100MW when 5s；WF2 power output increases to 125MW by 100MW when 6s；WF1 when 7s
Power output restores rated value；WF2 power output restores rated value when 9s.The response feelings of each electrical quantity of system when marine wind electric field power output variation
Condition is as shown in Fig. 4 a- Fig. 4 e.
(2) three-phase shortcircuit ground fault occurs when 5s at VSC4 converter station ac bus, is cut off after 0.1s.Ac bus three
The response condition of each electrical quantity of system is as shown in Fig. 5 a- Fig. 5 e when phase short circuit grounding failure.
Simulation result shows utmostly guarantee system under disturbance based on droop control device designed by this method
Stability, and make system have certain fault ride-through capacity.In addition, this method can also determine method with other sagging coefficients
In conjunction with increase constraint condition or change optimization aim design the droop control devices for meeting different requirements or realization different function.
Claims (1)
1. a kind of sagging control coefrficient of multi-end VSC-HVDC system determines method, which comprises the following steps:
Step 1: ac and dc systems are decoupled according to the mean value model of VSC, Converter DC-side is equivalent to DC current source,
DC line carries out π type equivalence, obtains multi-end VSC-HVDC system equivalent model；
Step 2: its state-space model is established according to multi-end VSC-HVDC system equivalent model:
In formula, x is state variable；ω is disturbance variable, and u is control variable, and ω and u are input variable；Y and z is output
Variable；A,Bω、Bu、CyAnd CzFor state matrix；And
X=[U1,...Ui,...,Un,iL1,...,iLk,...,iLm]T (2)
Wherein, n is inverter quantity, UiFor i-th of inverter DC voltage, m is DC line quantity, iLkTo flow through route Lk
Electric current；ikFor i-th of inverter DC current, ncFor the quantity at DC voltage control end, nncFor non-dc voltage controling end
Quantity；
Its steady-state operation equation is obtained according to the specific topology of system, formula (1)-(4) arrangement is substituted into and obtains system transter
Matrix are as follows:
And
I is unit matrix in formula；
Step 3: the closed-loop system state-space model containing droop control device is established, it is sagging by there is constrained optimization theory to seek
Coefficient optimal value, method particularly includes:
1) closed-loop system characteristic value constrains: by droop control device u=K (y-Udcmin) formula (1) is substituted into, it obtains that droop control device is added
Closed-loop system state matrix afterwards is Ac=A+BuKCy；
Wherein, when there is 2 DC voltage control ends in system, namely when using the inverter quantity of sagging control as 2, sagging control
The matrix expression of device processed isK in formula1For the sagging coefficient of the 1st inverter using sagging control, k2For
The sagging coefficient of 2nd inverter using sagging control；AcFor the closed-loop system state matrix after droop control device is added；
UdcminThe voltage minimum allowed for direct current system；
To make closed-loop system keep stablizing, then the characteristic value real part of closed-loop system all takes negative value, corresponding constraint condition are as follows:
real(λi(Ac)) < 0 (i=1 ..., neig) (7)
In formula: λi(Ac) it is AcCharacteristic value；neigIt is characterized value quantity；
2) steady-state error constrains: being maintained at the degree of each end DC voltage offset voltage minimum value in certain restriction range, then y
The constraint of channel steady-state error and the channel z steady-state error constraint expression formula are as follows:
E (s)=y (s)-Udcmin(s)=[S (s) Gyω(s)-S(s)]v(s) (8)
ez(s)=[Gzω(s)+Gzu(s)KS(s)Gyω(s)-Gzu(s)KS(s)-I]v(s) (9)
In formula, v (s)=[ω (s) Udcmin(s)]TFor input variable, including disturbance variable and control variable minimum value；
S (s)=(I-KGyu(s))-1For narrow sense controlled device GyuSensitivity function；
Influence of the input variable to output variable and control variable is assessed with the ratio between two norms of variable, by analysis of steady-state error
The odd value analysis of transfer function matrix is converted to, steady-state error constraint is then converted into the singular value constraint of transmission function；
3) the sensitivity function S of controlled device G and mending sensitivity function T are defined as
H is feedback controller in formula；
Make the FH Norm minimum of system sensitivity function and mending sensitivity function, it may be assumed that
In formula, JoptFor the optimal value of S/T Mixed Sensitivity performance indicator, KstabFor the PID control for meeting the constraint of S/T Mixed Sensitivity
Device parameter field processed；
The optimization problem is solved, the sagging control coefrficient for being optimal system stability is obtained.
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| CN108182317B (en) * | 2017-12-27 | 2021-08-10 | 南京工程学院 | VSC-based flexible direct current transmission system modeling method |
| CN108321798B (en) * | 2018-02-05 | 2021-02-09 | 华北电力大学 | Open-loop mode analysis method suitable for multi-input multi-output system |
| CN109936146B (en) * | 2019-03-05 | 2022-08-19 | 国网湖南省电力有限公司电力科学研究院 | Wind power plant coordinated optimization control method based on improved sensitivity algorithm |
| CN110620495B (en) * | 2019-08-22 | 2022-05-10 | 中国电力科学研究院有限公司 | Method and device for restraining VSC short-circuit current |
| CN112366742A (en) * | 2020-10-30 | 2021-02-12 | 中国石油大学(华东) | MTDC damping controller based on H-infinity mixed sensitivity theory |
| CN112711846A (en) * | 2020-12-27 | 2021-04-27 | 中国电建集团河南省电力勘测设计院有限公司 | VSC-based HVDC system state space model establishing method |
| CN113162116B (en) * | 2021-05-07 | 2023-01-20 | 广东电网有限责任公司电力调度控制中心 | Method and system for optimizing control parameters of doubly-fed wind turbine through flexible direct grid-connected system |
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