CN105978003B - A kind of additional wide area damping control design method of power system for considering time lag - Google Patents
A kind of additional wide area damping control design method of power system for considering time lag Download PDFInfo
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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
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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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
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Abstract
The invention discloses a kind of additional wide area damping control design method of power system for considering time lag, including step (1)：Using power system damping most weak oscillation mode as target control pattern, the best position of AVR and FACTS equipment is determined, the electric power system model and WADC models comprising AVR and FACTS equipment for not considering time lag factor is further set up.Step (2)：On the basis of the electric power system model comprising AVR and FACTS equipment and WADC models of time lag factor is not considered, Time Delay is introduced, and then set up the model for the closed loop time-lag power system for considering time lag factor.Step (3)：According to the model of closed loop time-lag power system, the mathematical modeling of WADC parameter optimizations is built.Step (4)：Using PSO algorithms, WADC optimized parameter in solution procedure (3).In each iterative optimization procedure, it is considered to time lag factor, using the critical eigenvalue of the SOD Algorithm for Solving closed loop time-lag power systems rightmost side, this maximum target of damping to reach critical eigenvalue.
Description
Technical field
The present invention relates to a kind of additional wide area damping control design method of power system for considering time lag.
Background technology
The complicated mechanism of extensive interconnected network and severe service condition, the dynamic behaviour for making its overall be difficult to analysis and
Control.The low-frequency oscillation repeatedly occurred in interconnected electric power system, threatens the safe and stable operation of power network, restricts region
The ability to transmit electricity on interior and interval some major transmission line roads so that the initial target that trans-regional electric energy dispatches this Power System Interconnection is difficult
To complete.
With WAMS (Wide Area Measurement System, WAMS) technology continue to develop with into
It is ripe, WAMS is used for the formation closed-loop control of extensive interconnected electric power system, is one of direction of power system development.WAMS can
The information such as the transimission power of generator's power and angle, rotating speed and interregional interconnection are provided in real time, for design wide area damping control
With suppression system inter-area oscillations, there is provided new data platform.Wide area signal based on WAMS, fully reflection system local oscillation
With the modal information of inter-area oscillations, provide it to damping controller and constitute closed-loop control, result in superior control performance.
However, the problem of also bringing new to the control of system using Wide-area Measurement Information.Modern digital communication network is
WAMS information transfers provide strong physical support, although information interchange is convenient and swift, still, it is contemplated that transmission range compared with
Far, Wide-area Measurement Information is transmitted in a communication network has inevitable communication delay.When time lag is larger, damping may result in
Controller action effect is deteriorated, or even induces power system unstability.
At present, it is considered to which the wide area stability contorting of time-delay can be largely classified into wide area robust PSS controls and wide area damp
Control two major classes.Wide area robust PSS controls are primarily focused on is applied to power system by robust control theory, by means of robust control
Tool box processed can complete the design of single damping controller, sensitive based on loop shaping, gain scheduling and mixing at present
The Wide-area Time-delay damping controller design method of the technologies such as degree.But in the design process, because system and time lag are respectively provided with not
Certainty to system model and Time Delay, it is necessary to carry out depression of order and approximate processing.The error of model reduction and approximate link, directly
Connect the performance for affecting robust controller.
For wide area damping control (Wide Area Damping Controller, WADC) design, mainly pin
To power system stabilizer, PSS (Power System Stabilizer, PSS), the automatic voltage regulator in power network
(Automatic Voltage Regular, AVR) and typical flexible AC transmitting system (Flexible Alternative
Current Transmission Systems, FACTS) additional damping controller of equipment (SVC, TCSC etc.) optimizes and sets
Meter.Current research is mostly based on single, fixed time lag power system, there is multiple, stochastic Time-Delay situation to system and grinds
Study carefully also less.These researchs are all to use Method of Pole Placement design parameter mostly, and time lag factor is introduced into Optimized model, Huo Zheshe
The appropriate time lag compensation link of meter, to improve the robustness and damping of controller, and has no crucial special with power system
The achievement in research of WADC optimization designs based on value indicative calculating.In addition, existing calculated based on WAMS and Modified particle swarm optimization
The SVC additional damping controller Optimization Designs of method, the relevant information of oscillation mode is obtained by Prony analysis tools, should
With modified particle swarm optiziation optimal control parameter, but this method does not account for the delay of Wide-area Measurement Information to control effect
Influence.
The content of the invention
In order to solve the shortcoming of prior art, the present invention provides a kind of additional wide area damp control of power system for considering time lag
Device design method processed.This method calculate real system critical eigenvalue and judgement system stability when, take into full account communication
Influence of the time lag to system damping performance, can greatly improve the damping of inter-area oscillation mode, strengthen the stability of time lag system.
To achieve the above object, the present invention uses following technical scheme：
A kind of additional wide area damping control design method of power system for considering time lag, comprises the following steps：
Step (1)：Using power system damping most weak oscillation mode as target control pattern, determine that AVR and FACTS are set
Standby best position, further set up do not consider the electric power system model comprising AVR and FACTS equipment of time lag factor with
WADC models；
Step (2)：Do not considering the electric power system model and WADC models comprising AVR and FACTS equipment of time lag factor
On the basis of, Time Delay is introduced, and then set up the model for the closed loop time-lag power system for considering time lag factor；
Step (3)：According to the model of closed loop time-lag power system, the mathematical modeling of WADC parameter optimizations is built；
Step (4)：Using particle group optimizing (Particle Swarm Optimization, PSO) algorithm, solution procedure
(3) WADC optimized parameter in；
In each iterative optimization procedure, it is considered to time lag factor, using SOD Algorithm for Solving closed loops time-lag power system most
The critical eigenvalue on right side, this maximum target of damping to reach critical eigenvalue.
In the step (1), using the joint geometric measures method based on controllability and observability, AVR and FACTS equipment is determined
Best position.
In the step (1), using the joint geometric measures method based on controllability and observability, AVR and FACTS equipment is determined
Best position detailed process, including：
Step (1.1)：The parameter of given AVR and FACTS equipment, some nodes of power system are set as AVR and FACTS
Standby alternative installation site；
Step (1.2)：Calculate containing the initial of the system load flow equation and state variable for having installed AVR and FACTS equipment
Value, forms system linearity coefficient matrix；According to linearisation coefficient matrix, the critical eigenvalue of power system is calculated and its right
The left and right characteristic vector answered, and set the oscillation mode to be investigated of power system；
Step (1.3)：Under the oscillation mode of setting, using the reference value of AVR and FACTS equipment as input, with different
Feedback signal is output, calculates the joint geometric measures of the controllability and observability of AVR and FACTS equipment；
Step (1.4)：Compare the modulus value size of the joint geometric measures of controllability and observability, filter out joint geometric measures
The maximum node of modulus value is defined as the best position of AVR and FACTS equipment, using its corresponding control signal as additional
WADC feedback signal, input WADC constitutes closed-loop control, so as to increase the damping capacity of system.
The address installed in step (1.4) according to AVR the and FACTS equipment of selection and feedback signal, set up following system
System linearized state-space model：
In formula：X is the state vector of system, and u and y are respectively input vector and output vector；A, B, C, D are respectively system
State matrix, input matrix, output matrix and straight-through matrix.If the characteristic value of matrix A is λi(i=1 ..., n), accordingly
Left and right eigenvectors matrix is：U=[u1,u2,…,un], V=[v1,v2,…,vn].Wherein, uiAnd viRespectively ith feature
The left and right characteristic vector of value.After standardization processing, U and V meet UHV=VHU=In, InFor n rank unit matrix.
I-th of oscillation mode λ of systemiControllability geometric measures mciWith controllability geometric measures moiIt can be calculated by following formula：
In formula：bkArranged for input matrix B kth；clFor output matrix C l rows；α(ui,bk) it is input vector bkAnd a left side
Characteristic vector uiAngle；θ(cl T,vi) it is output vector clWith right characteristic vector viAngle；| | and | | | | represent respectively
Modulus of access and European norm.
For oscillation mode λi, can the joint geometric measures of control/controllability be：
mcoi(k, l)=mci(k)moi(l)
In step (1.4), calculated according to (1.3) the obtained joint geometric measures of energy control/controllability determine AVR and
The best position of FACTS equipment.If mcoi(k, l) ≠ 0, then illustrate that u can be passed throughkAnd ylControl model λi。mcoi(k, l) takes
U during maximumkAnd ylIt is maximally effective；Work as mcoiWhen (k, l) takes maximum, if ukAnd ylSignal be derived from the same area, shake
Swing pattern λiLocal damping control can be passed through；If conversely, ukAnd ylSignal be derived from different regions, then need with wide-area control come
Damp corresponding oscillation mode.
In the step (1), additional WADC structure is similar with tradition PSS.It is made up of lead-lag link, belongs to dynamic
Compensator.Closed-loop control is formed using it, the damping capacity of power system can be lifted.
In the step (2), time-lag power system model is as follows：
In formula：Δ x is the state variable of system.τ=[τ1,…,τi,…,τm]T, τi>0 is the transmission of i-th of wide area signal
Time lag, i=1,2 ..., m, maximum of which time lag is expressed as τmax。It is the state matrix of system, is dense matrix；It is the hangover state matrix of system, is sparse matrix.Δ x (t) is the increment of t system state variables,
Δx(t-τi) it is t- τiThe increment of moment system state variables,For the increment of t system state variables derivative.Δx
(0) it is the initial value (i.e. primary condition) of system state variables, and is abbreviated asThe feature for the time-lag power system that above formula is represented
Equation is：
In formula：λ is characterized value, and v is characterized the corresponding right characteristic vector of value.
In the step (3), additional WADC Parametric optimization problems mathematical modeling is expressed as：
Max J, J=min { ζi, the set of i ∈ electromechanic oscillation modes }
In formula：ζiFor the damping ratio of i-th of oscillation mode of system, cost function J is expressed as the whole electromechanical oscillations moulds of system
Minimum damping ratio, K in formuladFor the multiplication factor of the voltage control loop section of AVR and FACTS equipment, KaFor additional damping controller
Multiplication factor, T1~T4For the time constant of lead-lag link；WithRespectively multiplication factor KdHigher limit and
Lower limit；WithRespectively multiplication factor KaHigher limit and lower limit；WithWhen respectively
Between constant T1~T4Higher limit and lower limit.
In the step (4), using PSO algorithms, before the WADC optimized parameters in solution procedure (3), in addition to：Set
Population number and maximum iteration simultaneously initialize population.
In the step (4), according to spectral mapping theorem, the characteristic value positioned at left half complex plane of closed loop time-lag power system
Solution operator is mapped in the unit circle of z-plane, the characteristic value positioned at right half complex plane is mapped in outside unit circle.
In the step (4), Solution operator is entered using equidistant linear multistep method (Linear Multi-Step, LMS)
Row processing, according to the eigenvalue λ of time-lag power system and the characteristic value of Solution operator (spectrum) μ corresponding relations, tries to achieve time lag power train
The critical eigenvalue of system.
Solution operator T (h):X → X is defined as the primary condition (state) at the θ moment in space XBeing mapped to the h+ θ moment is
System state ψ linear operator.
In formula：H is transfer step-length, 0≤h≤τmax；xtThe part solution of etching system when=x (t+ θ) is t >=0.By spectrum mapping
Theorem understands there is following relation between Solution operator T (h) spectrum μ and the eigenvalue λ of time lag system：
In formula：σ () represent spectrum, represent exclude.
Theoretical by semigroup of operators, the Solution operator in Banach spaces is infinite dimensional.In order to calculate Solution operator
Characteristic value to T (h), it is necessary to carry out discretization.After discretization, corresponding with Solution operator, finite dimension a approximate matrix is obtained,
The critical eigenvalue of former time lag system is can be obtained by by calculating the characteristic value of approximate matrix.
It is based in the step (4) in SOD Algorithm for Solving time-lag power system critical eigenvalues, using equidistant LMS
Method carries out approximate processing to the related Solution operator of differential equations with delay (Delay Differential Equations, DDE), can
Former problem is converted into the eigenvalue problem for solving a canonical matrix.
Assuming that h≤τmax, Solution operator can be expressed as form：
The first row of right-hand side expression is initial-value problem in above formula, can be solved using LMS methods.
Using equidistant point θj=jh, j=-N ..., 0, discretization is carried out to Solution operator, N is more than or equal to τmax/h
Smallest positive integral, i.e.,
The expression formula of LMS methods is：
At mesh point, with ψjIt is approximate to replace ψ (θj), withIt is approximate to replaceThen ψjWithMathematical relationship expression
Formula：
In formula：TNFor Solution operator T (h) discretization matrix, i.e.,：
TNLast block row Γ be polynomial eigenvalue problem coefficient matrix, be specifically represented by：
Especially, when system only contains a time lag and N=τ/h is integer, Γ can be explicitly expressed as follows：
Γ=[Γ0,0n×n(N-k-1),Γ1]
In each iterative process of PSO algorithms of the step (4), the search information of more new particle according to the following formula：
In formula：K is the number of times that current iteration is calculated,Component is tieed up for the d of particle i search speeds, WithThe upper and lower bound of search speed is represented respectively,The d for projecting to search space for i-th of particle ties up component；
pbestdTo project to the d dimension components of search space to the optimum position of current i-th of particle；gbestdFor current all grains
The optimum position of son search projects to the d dimension components of search space；c1And c2For aceleration pulse；Rand () and Rand ()
It is the random number between two 0 to 1；ω is weight coefficient.
To improve convergence rate, the linear narrowing weight coefficient in each iterative process of PSO algorithms of step (4).
In formula：K is current iteration number of times；K is as ω=ωminWhen algorithm iterations；ωmaxAnd ωminRespectively just
The weight coefficient maximum and minimum value set during beginningization algorithm.
Beneficial effects of the present invention are：
(1) this method of the invention is used for the additional WADC for designing AVR and FACTS equipment, can greatly improve interval and shake
The damping of pattern is swung, strengthens the stability of time lag system；In the critical eigenvalue and the stabilization of judgement system for calculating real system
During property, influence of the communication delay to system damping performance has been taken into full account；
(2) method of the invention combines both algorithms of SOD and PSO, and designed additional wide area damping control is same
Original local PSS is mutually coordinated, each other in the absence of the reciprocation for being unfavorable for system damping performance；
(3) method of the invention is using critical eigenvalue as the additional wide area damping control of design, it is to avoid traditional
Wide area power system stabilizer and Robust Damping controller design method based on POLE PLACEMENT USING need to drop system model
Rank and the deficiency that approximate processing is carried out to time lag, purpose is strong, control device is direct, action effect is obvious, and not any
Conservative.
Brief description of the drawings
Fig. 1 is time-lag power system schematic diagram；
Fig. 2 is the SVC stability analysis models for considering additional wide-area damping control；
Fig. 3 is the TCSC stability analysis models for installing additional wide-area damping control；
Fig. 4 combines the calculation process of geometric measures for controllable/ornamental of target pattern；
Fig. 5 is the additional WADC design flow diagrams based on PSO algorithms；
Fig. 6 is the additional WADC design methods flow chart of the time-lag power system based on SOD algorithms of the invention.
Embodiment
The present invention will be further described with embodiment below in conjunction with the accompanying drawings：
As shown in Figure 1：Time Delay is introduced in the modeling process of actual large-scale electrical power system.Time-lag power system bag
Closed containing the connection exported without time-lag power system, wide area Feedback Delays, additional WADC and wide area between the part of time lag four, each several part
System is as shown in the figure.In Fig. 1, yfFor the output without time-lag power system, ydfTo consider the wide area feedback signal after Feedback Delays
And it is used as the input of damping controller, ycFor the output of wide area damping control, ydcTo consider wide area damp delayed during output
The output of controller, while also serving as the control input of no time-lag power system.
Time lag system is located at the characteristic value of left half complex plane and is mapped to Solution operator in the unit circle of z-plane, and time lag
The characteristic value that system is located at right half complex plane is mapped in outside unit circle.Therefore, the characteristic value of Solution operator is utilized, it is possible to solve
Corresponding time lag system critical eigenvalue.
As shown in Figures 2 and 3, additional WADC structure and PSS are similar, are made up of lead-lag link and belong to dynamic benefit
Repay device.Additional WADC state-space expression can be written as：
In formula：Δxc=[Δ V1 ΔV2 ΔV3 ΔVIS]T；
In formula：ΔV1、ΔV2、ΔV3For the intermediate variable of WADC links, Δ VISFor WADC output variable there is provided
Feedback control is constituted to FACTS equipment, K is multiplication factor, and T is time constant.
As shown in figure 4, using the joint geometric measures method based on controllability and observability, determining AVR and FACTS equipment most
The detailed process of good installation site, including：
Step (1.1)：The parameter of given AVR and FACTS equipment, some nodes of power system are set as AVR and FACTS
Standby alternative installation site；
Step (1.2)：Calculate containing the initial of the system load flow equation and state variable for having installed AVR and FACTS equipment
Value, forms system linearity coefficient matrix；According to linearisation coefficient matrix, the critical eigenvalue of power system is calculated and its right
The left and right characteristic vector answered, and set the oscillation mode to be investigated of power system；
Step (1.3)：Under the oscillation mode of setting, using the reference value of AVR and FACTS equipment as input, with different
Feedback signal is output, calculates the joint geometric measures of the controllability and observability of AVR and FACTS equipment；
Step (1.4)：Compare the modulus value size of the joint geometric measures of controllability and observability, filter out joint geometric measures
The maximum node of modulus value is defined as the best position of AVR and FACTS equipment, using its corresponding control signal as additional
WADC feedback signal, input WADC constitutes closed-loop control, so as to increase the damping capacity of system.
As Fig. 5 shows, the additional WADC designs based on PSO algorithms specifically include following steps：
Step (4.1)：Population number and maximum iteration are set, and initialize population
Step (4.2)：Run simulation model；
Step (4.3)：Consider time lag factor, the rightmost side critical eigenvalue of time-lag power system is calculated based on SOD algorithms
And its damping ratio, design controller parameter；
Step (4.4)：Population Regeneration, judges whether to reach the iterations upper limit or meets required precision, if it is not,
Then return to step (4.2) is recalculated, if it is, output Optimal Parameters.
In the step (4.4), additional WADC Parametric optimization problems mathematical modeling is expressed as：
Max J, J=min { ζi, the set of i ∈ electromechanic oscillation modes }
In formula：ζiFor the damping ratio of i-th of oscillation mode of system, cost function J is expressed as the whole electromechanical oscillations moulds of system
Minimum damping ratio, K in formuladFor the multiplication factor of the voltage control loop section of AVR and FACTS equipment, KaFor additional damping controller
Multiplication factor, T1~T4For the time constant of lead-lag link；WithRespectively multiplication factor KdHigher limit and
Lower limit；WithRespectively multiplication factor KaHigher limit and lower limit；WithWhen respectively
Between constant T1~T4Higher limit and lower limit.
In the step (4.4), in each iterative process of PSO algorithms, the search information of more new particle according to the following formula：
In formula：K is the number of times that current iteration is calculated,Component is tieed up for the d of particle i search speeds, WithThe upper and lower bound of search speed is represented respectively,The d for projecting to search space for i-th of particle ties up component；
pbestdTo project to the d dimension components of search space to the optimum position of current i-th of particle；gbestdFor current all grains
The optimum position of son search projects to the d dimension components of search space；c1And c2For aceleration pulse；Rand () and Rand ()
It is the random number between two 0 to 1；ω is weight coefficient.
To improve convergence rate, the linear narrowing weight coefficient in each iterative process of PSO algorithms of step (4).
In formula：K is current iteration number of times；K is as ω=ωminWhen algorithm iterations；ωmaxAnd ωminRespectively just
The weight coefficient maximum and minimum value set during beginningization algorithm.
As shown in fig. 6, a kind of additional wide area damping control design method of power system of consideration time lag of the present invention, bag
Include following steps：
Step (1)：Using power system damping most weak oscillation mode as target control pattern, determine that AVR and FACTS are set
Standby best position, further set up do not consider the electric power system model comprising AVR and FACTS equipment of time lag factor with
WADC models；
Step (2)：Do not considering the electric power system model and WADC models comprising AVR and FACTS equipment of time lag factor
On the basis of, Time Delay is introduced, and then set up the model for the closed loop time-lag power system for considering time lag factor；
Step (3)：According to the model of closed loop time-lag power system, the mathematical modeling of WADC parameter optimizations is built；
Step (4)：Using PSO algorithms, WADC optimized parameter in solution procedure (3).In each iterative optimization procedure
In, it is considered to time lag factor, using the critical eigenvalue of the SOD Algorithm for Solving closed loop time-lag power systems rightmost side, to reach key
This maximum target of the damping of characteristic value.
In specific implementation process, in step (1), using the joint geometric measures method of controllability and observability, determine AVR and
The best position of FACTS equipment.
The address installed according to AVR the and FACTS equipment of selection and feedback signal, set up following system linearization state empty
Between model：
In formula：X is the state vector of system, and u and y are respectively input vector and output vector；A, B, C, D are respectively system
State matrix, input matrix, output matrix and straight-through matrix.If the characteristic value of matrix A is λi(i=1 ..., n), accordingly
Left and right eigenvectors matrix is：U=[u1,u2,…,un], V=[v1,v2,…,vn].Wherein, uiAnd viRespectively ith feature
The left and right characteristic vector of value.After standardization processing, U and V meet UHV=VHU=In, InFor n rank unit matrix.
I-th of oscillation mode λ of systemiControllability geometric measures mciWith controllability geometric measures moiIt can be calculated by following formula：
In formula：bkArranged for input matrix B kth；clFor output matrix C l rows；α(ui,bk) it is input vector bkAnd a left side
Characteristic vector uiAngle；θ(cl T,vi) it is output vector clWith right characteristic vector viAngle；| | and | | | | represent respectively
Modulus of access and European norm.
For oscillation mode λi, can the joint geometric measures of control/controllability be：
mcoi(k, l)=mci(k)moi(l)
If mcoi(k, l) ≠ 0, then illustrate that u can be passed throughkAnd ylControl model λi。mcoi(k, l) takes u during maximumkAnd ylIt is
It is maximally effective；Work as mcoiWhen (k, l) takes maximum, if ukAnd ylSignal be derived from the same area, oscillation mode λiCan be by local
Damping control；If conversely, ukAnd ylSignal be derived from different regions, then need to damp corresponding oscillation mode with wide-area control.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, not to present invention protection model
The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not
Need to pay various modifications or deform still within protection scope of the present invention that creative work can make.
Claims (10)
1. a kind of additional wide area damping control design method of power system for considering time lag, it is characterised in that including following step
Suddenly：
Step (1)：Using power system damping most weak oscillation mode as target control pattern, AVR and FACTS equipment is determined
Best position, further sets up the electric power system model and WADC that include AVR and FACTS equipment for not considering time lag factor
Model；
Step (2)：Do not considering the electric power system model comprising AVR and FACTS equipment of time lag factor and the base of WADC models
On plinth, Time Delay is introduced, and then set up the model for the closed loop time-lag power system for considering time lag factor；
Step (3)：According to the model of closed loop time-lag power system, the mathematical modeling of WADC parameter optimizations is built；
Step (4)：Using PSO algorithms, WADC optimized parameter, in each iterative optimization procedure, is examined in solution procedure (3)
Time lag factor is considered, using the critical eigenvalue of the SOD Algorithm for Solving closed loop time-lag power systems rightmost side, to reach critical eigenvalue
This maximum target of damping.
2. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, in the step (1), using the joint geometric measures method of controllability and observability, determine AVR and FACTS equipment most
The Optimal Feedback signal of good installation site and additional wide area damping control.
3. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 2, it is special
Levy and be, in the step (1), determine the detailed process of the best position of AVR and FACTS equipment, including：
Step (1.1)：The parameter of given AVR and FACTS equipment, regard some nodes of power system as AVR and FACTS equipment
Alternative installation site；
Step (1.2)：Calculate containing the system load flow equation for having installed AVR and FACTS equipment and the initial value of state variable, shape
Into system linearity coefficient matrix；According to linearisation coefficient matrix, the critical eigenvalue of power system is calculated and its corresponding
Left and right characteristic vector, and set the oscillation mode to be investigated of power system；
Step (1.3)：Under the oscillation mode of setting, using the reference value of AVR and FACTS equipment as input, with different feedbacks
Signal is output, calculates the joint geometric measures of the controllability and observability of AVR and FACTS equipment；
Step (1.4)：Compare the modulus value size of the joint geometric measures of controllability and observability, filter out the modulus value of joint geometric measures
Maximum node is defined as the best position of AVR and FACTS equipment, regard its corresponding control signal as additional WADC's
Feedback signal, input WADC constitutes closed-loop control, so as to increase the damping capacity of system.
4. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, additional wide area damping control is made up of lead-lag link, belongs to dynamic compensator.
5. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, according to spectral mapping theorem, the characteristic value positioned at left half complex plane of closed loop time-lag power system is mapped to Solution operator position
In in the unit circle of z-plane, the characteristic value positioned at right half complex plane is mapped in outside unit circle.
6. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 5, it is special
Levy and be, using the characteristic value of Solution operator, solve corresponding closed loop time-lag power system critical eigenvalue.
7. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, in the step (4), using PSO intelligent algorithms, before the WADC optimized parameters in solution procedure (3), in addition to：
Population number and maximum iteration are set and population is initialized.
8. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 6, it is special
Levy and be, in the step (4), Solution operator is handled using equidistant LMS, according to the characteristic value of time-lag power system
With the characteristic value corresponding relation of Solution operator, the critical eigenvalue of time-lag power system is tried to achieve.
9. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, in each iterative process of PSO algorithms of the step (4), the search information of more new particle according to the following formula：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>d</mi>
</mrow>
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</mfenced>
In formula：K is the number of times that current iteration is calculated,Component is tieed up for the d of particle i search speeds, WithThe upper and lower bound of search speed is represented respectively；The d for projecting to search space for i-th of particle ties up component；pbestd
To project to the d dimension components of search space to the optimum position of current i-th of particle；gbestdFor current all particle search
Optimum position project to search space d dimension component；c1And c2For aceleration pulse；Rand () and Rand () difference tables
Show a random number being located between 0 to 1；ω is weight coefficient.
10. a kind of additional wide area damping control design method of power system for considering time lag as claimed in claim 1, it is special
Levy and be, to improve convergence rate, the linear narrowing weight coefficient in each iterative process of PSO algorithms of step (4).
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| CN107346892B (en) * | 2017-04-24 | 2021-01-15 | 国家电网公司 | PSS design method based on wide area multi-signal input hierarchical control |
| CN107910880B (en) * | 2017-11-29 | 2019-12-20 | 山东大学 | Wide-area damping controller optimal parameter setting method based on interval oscillation mode |
| CN108808705B (en) * | 2018-07-13 | 2020-05-22 | 山东大学 | Time-lag power system electromechanical oscillation mode calculation method based on low-order SOD-PS-II-R algorithm |
| CN109149601B (en) * | 2018-09-05 | 2020-10-16 | 北京建筑大学 | Parameter determination method and system for wide-area damping controller of power system |
| CN111181167A (en) * | 2018-11-09 | 2020-05-19 | 国网内蒙古东部电力有限公司经济技术研究院 | Method for improving stability of power grid at transmitting end by using static var compensator |
| CN110365009A (en) * | 2019-06-22 | 2019-10-22 | 东北电力大学 | A kind of wide area damp optimal control method suitable for interconnected electric power system |
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