CN106130066B - A kind of Multi-objective Robust control method for frequency for independent micro-grid system - Google Patents
A kind of Multi-objective Robust control method for frequency for independent micro-grid system Download PDFInfo
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Abstract
The present invention discloses a kind of Multi-objective Robust fractional order control method for frequency of independent micro-capacitance sensor, the present invention establishes the small signal frequency response model of each component of independent micro-grid system by Approach for Modeling of Small-Signal, independent micro-grid system robust circuit molding fractional order frequency control model is established on this basis, independent micro-grid system frequency departure is multiplied with the time cumulative and minimum, system power deviation is multiplied cumulative and minimum with the time, the Infinite Norm of robust circuit formation system matrix function is minimum, optimization object function of the robust controller output signal value minimum as assessment robust frequency controller performance, by robust stability and jamming performance index is inhibited to be respectively less than 1 as constraints, and it designs a kind of adaptive multi-objective constrained optimization solver and efficiently realizes that the optimization of robust circuit molding frequency control parameters is adjusted.Using the robust FREQUENCY CONTROL of the achievable independent micro-grid system multi-performance index trade-off optimization of the present invention.
Description
Technical field
It is the present invention relates to the allotment of new energy microgrid energy and administrative skill field intelligent control technology, more particularly to a kind of
Multi-objective Robust control method for frequency for independent micro-grid system.
Background technology
Independent micro-capacitance sensor provides a kind of feasible side to solve the Special sections such as remote mountain areas and coastal island power supply problem
Case, therefore the extensive research and extension application of domestic and international new energy and field of power is received in recent years.But photovoltaic generation
With wind-power electricity generation as the variation of Weather Of Area shows stronger randomness and intermittence, in addition the diversity of demand load and
The features such as complexity will likely result in the unbalanced supply-demand of independent micro-grid system active power so that wave occurs in system frequency
It is dynamic.Therefore, how to be realized in the case of the not true property of independent micro-grid system structural parameters and external interference steady, quick and accurate
True FREQUENCY CONTROL is the allotment of independent micro-grid system energy and one of the important technology problem that management domain must solve.Mesh
Before, the mainstream technology of independent micro-capacitance sensor frequency control includes mainly：(1) tradition based on genetic algorithm or Fuzzy particle swarm optimization
Integer rank PID or PI control technology, but there are oscillation amplitudes larger, response speed is relatively slow, anti-interference ability is insufficient, optimization algorithm
Inherent parameters adjust the defects of complicated, computational efficiency is relatively low；(2) optimizations such as genetic algorithm and Kriging agent models are based on to calculate
The Fractional Order PID control technology of method, but genetic algorithm includes the complicated evolutionary computation operation such as to select, intersect and make a variation, and algorithm is certainly
Body adjustable parameter is more, and computational efficiency is relatively low, and higher to the dependence of initial number of samples based on Kriging agent models, also together
There are algorithm inherent parameters to adjust the defects of complicated, computational efficiency is relatively low for sample；(3) control based on standard H infinity and μ analysis principles
Method processed, but there is also the evaluation performance indicator of robust controller is excessively single, it is difficult to complex optimum independent micro-grid system
FREQUENCY CONTROL performance.
In order to make up the deficiency of the above technology, in state natural sciences fund (No.51207112), Zhejiang Province's public welfare science and technology
Plan (Nos.2014C31074,2014C31093), Zhejiang Province's Natural Science Fund In The Light (Nos.LY16F030011,
LZ16E050002, LQ14F030006, LQ14F030007) etc. under the support of projects, the present invention discloses a kind of for independent micro- electricity
The Multi-objective Robust control method for frequency of net system.The present invention establishes independent micro-grid system each group by Approach for Modeling of Small-Signal
The small signal frequency response model of part establishes independent micro-grid system robust circuit molding fractional order FREQUENCY CONTROL mould on this basis
Cumulative and minimum, the system power deviation that independent micro-grid system frequency departure and time are multiplied is multiplied tired by type with the time
Adduction is minimum, robust circuit formation system matrix function Infinite Norm is minimum, robust controller output signal value minimum conduct
The optimization object function for assessing robust frequency controller performance by robust stability and inhibits jamming performance index to be respectively less than 1
As constraints, and designs a kind of adaptive multi-objective constrained optimization solver and efficiently realize that robust circuit is molded frequency control
The optimization of parameter processed is adjusted.
Invention content
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of multiple target for independent micro-grid system
Robust control method for frequency.
The purpose of the present invention is achieved through the following technical solutions：A kind of multiple target for independent micro-grid system
Robust control method for frequency, this approach includes the following steps：
(1) each component of independent micro-grid system (including wind-driven generator, photovoltaic battle array are established by Approach for Modeling of Small-Signal
Row, diesel-driven generator, fuel cell, lead-acid accumulator, flywheel energy storage system and converters) response of small signal frequency
Model establishes the control system model that fractional order frequency controller is molded based on robust circuit, independent micro-capacitance sensor on this basis
System monitoring computer reads system and reads independent micro grid control system model and load data；Wherein robust circuit molding point
Number order frequency controller CRTransfer function model it is as follows：
CR=W1C∞W2, wherein
Wherein, W1And W2Indicate weighting function, KrIndicate fractional order control device C∞Proportionality coefficient, Tr1With Tr2It indicates respectively
Two fractional order inertial element inertia time coefficients, λr1With λr2The fractional order order of two inertial elements is indicated respectively.
(2) parameter values of multi-objective constrained optimization solver, including external archival maximum number A are setmax, maximum changes
Generation optimization number Imax。
(3) the individual S of a real coding is randomly generatedI=(U-L) * R+L, wherein SI=[Kr,Tr1,Tr2,λr1,λr2], U
Indicate that robust circuit is molded fractional order frequency controller optimized variable upper and lower bound with L, R indicates one group and produced in 0 to 1 range
Raw uniform random number, and it is sky to enable external archival A.
(4) to current individual SIOptimized variable into row variation and keeps other group members constant one by one, generates 5 offspring individuals
{Sj, j=1,2 ..., 5 }, shown in specific mutation operation such as formula (2)~(4)：
Sj(xi)=SI(xi)+α.βmax(xi), i=1,2 ..., 5 (2)
Wherein
βmax(xi)=max (SI(xi)-L(xi),U(xi)-SI(xi)), i=1,2 ..., 5 (4)
Wherein, xiIndicate i-th of optimized variable, Sj(xi) and Sj(xi) individual S is indicated respectivelyjAnd SIIn i-th optimization
Variable, L (xi) and U (xi) lower limiting value and upper limit value of i-th of optimized variable, I are indicated respectivelycIndicate current iteration number, r1It is
The uniform random number generated in 0 and 1 range.
(5) { S is calculated according to formula (5)~(6)j, j=1,2 ..., 5 } the constraint violation amount g (S of all individualsj)；
Wherein p is the quantity of constraints.
(6) m fitness value { F of each individual is calculatedk(Sj), j=1,2 ..., 5, k=1,2 ..., m }, it is specific to calculate
Process is as follows：
(6.1) if SjFeasible solution, then Fk(Sj)=fk(Sj), j=1,2 ..., 5, k=1,2 ..., m, wherein fk(Sj) table
Show that k-th of fitness function of j-th of individual, specific calculate refer to right 2；
(6.2) if SjInfeasible solution, then Fk(Sj)=fk(Sj)+ηk.g(Sj), wherein ηkIndicate the punishment to violating constraint
The factor.
(7) using the Pareto fitness evaluations criterion based on non-dominated ranking to this 5 offspring individual { Sj, j=1,
2 ..., 5 } carry out Pareto sequences.
(8) if only existing a non-dominant individual, it is S to enable the individualn；If there is multiple non-dominant individuals, then
An individual is randomly choosed as Sn。
(9) using the external document A of update mechanism update based on crowding distance, specific implementation is as follows：
(9.1) if at least one body can dominate individual S in external archivaln, then individual SnIt is added without external archival A.
(9.2) if individual SnCertain individuals in external archival can be dominated, then are removed these individuals, and will be individual
SnExternal archival A is added.
(9.3) if all individuals in external archival and individual SnMutual not branch timing, if external archival number is not up to
Maximum number Amax, then by individual SnExternal archival A is added；If external archival number reaches maximum number AmaxAnd if individual SnPosition
In external archival most crowded places, then external archival A is added without；Otherwise individual SnIt will substitute most crowded positioned at external archival
The individual in place, to which external archival A be added.Crowding distance calculates specific as follows：Assuming that individual amount is in external document A
L, to the corresponding m fitness function { F of all individuals { A (i), i=1,2 .., l } in Ak(A (i)), i=1,2 .., l, k=
1,2 ..., m } according to ascending sort, so that Fk(A(O(1)))≤Fk(A(O(2)))≤…≤Fk(A (O (l))), wherein O
(1), (2) O ..., O (l) are ranking index number, Ak(O (i)) indicates that m-th of fitness function value is ordered as the corresponding outsides O (i)
Document individual；Ak(O (1)) and AkCrowding distance d (the A of (O (l))k(O (1))) and d (Ak(O (l))) be：d(Ak(O (1)))=d
(Ak(O (l)))=∞；For i=2 ..., (l-1), then AkCrowding distance d (the A of (O (i))k(O (i))) be：d(Ak(O
(i)))=[Ak(O (i+1))-Ak(O (i-1))]/[Fk(A (O (l)))-Fk(A(O(1)))]。
(10)SnUnconditionally substitute current individual SI。
(11) step (4) to (10) is repeated, reaches greatest iteration optimization number I until meetingmax。
(12) it is exported external archival as the Pareto disaggregation up to the present optimized, therefrom chooses Pareto disaggregation
In most intermediate individual the Optimal Parameters S of fractional order frequency controller is molded as robust circuitbest, transmit it to practical only
In vertical micro-grid system, independent micro-grid system monitor computer obtain the real-time running data of practical independent micro-grid system with
Waveform.
The Model for Multi-Objective Optimization of the robust fractional order FREQUENCY CONTROL of involved independent micro-grid system includes in step 6
Shown in multiple target fitness function and its constraints model such as formula (7)~(17)：
Minf (x)=min [f1(x),f2(x),f3(x),f4(x)], x=[Kr,Tr1,Tr2,λr1,λr2] (7)
f4(x)=| | [I C∞]T(1-PC∞)-1[I P]||∞, wherein P=W2P0W1 (11)
subject to||W1T||∞<1,||W2S||∞<1 (12)
S=(I+P0CR)-1 (13)
T=P0CR(I+P0CR)-1 (14)
L≤x≤U (17)
Wherein, t indicates system operation time, tminAnd tmaxWhen indicating initial time and the termination of system operation time respectively
Between, Δ f indicates system frequency deviation, Δ PgIndicate that system total power deviation, u indicate robust controller output signal amplitude, a1With
b1Weighting function W is indicated respectively1Zero and pole, KaIndicate W1Proportionality coefficient, P0Indicate controlled under system health
Object model, S and T indicate that sensitivity function and mending sensitivity function, Δ P indicate the disturbance mould under system uncertain factor respectively
Type, M and N indicate normal controlled device P respectively0Denominator and molecular model, Δ M and Δ N indicate controlled device not really respectively
The denominator and molecular model disturbed under qualitative factor, EVmax(X1Z1) indicate X1Z1Maximum characteristic root, X1And Z1It is equation respectively
(18) and the normal solution of (19)：
(A1-B1Sa -1D1 TC1)TX1+X1(A1-B1Sa -1D1 TC1)-X1B1Sa -1B1 T+C1 TRC1=0 (18)
(A1-B1Sa -1D1 TC1)TZ1+Z1(A1-B1Sa -1D1 TC1)-Z1B1Sa -1B1 T+C1 TRC1=0 (19)
Wherein, R=I+D1D1 T,Sa=I+D1 TD1, A1、B1、C1、D1For the coefficient square realized by the minimum space of empty object P
Battle array.
The invention has effective effect that：Using the achievable independent micro-grid system multi-performance index trade-off optimization of the present invention
Robust FREQUENCY CONTROL, with the following advantages not available for the prior art：In independent micro-grid system parameter uncertainty and do
The system run all right nargin higher under situations such as disturb, system frequency deviation and power deviation fluctuation are gentler, and regulating time is more
Short, control accuracy higher, controller output signal value is gentler, robust controller parameter optimization adjust it is more efficient, and optimize
Solver designs simpler with realization.
Description of the drawings
Fig. 1 is the topological structure and Multi-objective Robust fractional order FREQUENCY CONTROL principle schematic of independent micro-capacitance sensor；
Fig. 2 is the independent micro-capacitance sensor Multi-objective Robust fractional order FREQUENCY CONTROL functional-block diagram based on small-signal model；
Fig. 3 is the realization process schematic of independent micro-capacitance sensor Multi-objective Robust fractional order FREQUENCY CONTROL.
Specific implementation mode
The following further describes the present invention with reference to the drawings, and the objects and effects of the present invention will be apparent from.
Fig. 1 is the topological structure and Multi-objective Robust fractional order FREQUENCY CONTROL principle schematic of independent micro-capacitance sensor, independent micro-
Power grid primary clustering includes wind-driven generator, photovoltaic array, diesel-driven generator, fuel cell, lead-acid accumulator, flywheel energy storage system
System and converters, the method being combined according to Analysis on Mechanism and test data of experiment establish independent micro-capacitance sensor frequency control
System model processed, while establishing independent micro-capacitance sensor Multi-objective Robust score according to the multi-performance index of engineering demand and constraints
Order frequency controls Optimized model, and independent micro- electricity is realized by the score order frequency parameter that multi-objective constrained optimization solver optimizes
The Multi-objective Robust FREQUENCY CONTROL of net.
Fig. 2 is the independent micro-capacitance sensor Multi-objective Robust fractional order FREQUENCY CONTROL functional-block diagram based on small-signal model,
Middle TWTG、TPV、TDEG、TFC、TBESS、TFESSWind-driven generator, photovoltaic array, diesel-driven generator, fuel cell, plumbic acid are indicated respectively
The inertia time coefficient of accumulator, flywheel energy storage system, D and M1The constant and inertial system of electric system transmission function are indicated respectively
Number, PpWith PwPhotovoltaic array and wind-power electricity generation input power, P are indicated respectivelyWTG、PPV、PDEG、PFC、PBESS、PFESSWind is indicated respectively
The output power of power generator, photovoltaic array, diesel-driven generator, fuel cell, accumulator and flywheel energy storage system, PtIndicate wind
Power generates electricity and the sum of the power of photovoltaic generation, i.e. Pt=PWTG+PPV, PSIndicate the sum of the power that independent micro-grid system generates, i.e.,
PS=Pt+PDEG+PFC±PBESS±PFESS, PLIndicate load power, Δ PgIndicate system total power deviation, i.e. Δ Pg=PL-PS, Δ
F indicates that the frequency departure of independent micro-grid system, u indicate robust controller CROutput signal.
Fig. 3 is the realization process schematic of independent micro-capacitance sensor Multi-objective Robust fractional order FREQUENCY CONTROL.
By taking some 500kW independent micro-grid system of coastal area as an example, using the independent more mesh of micro-capacitance sensor proposed by the present invention
Mark robust fractional order FREQUENCY CONTROL is implemented.
(1) each component of independent micro-grid system (including wind-driven generator, photovoltaic battle array are established by Approach for Modeling of Small-Signal
Row, diesel-driven generator, fuel cell, lead-acid accumulator, flywheel energy storage system and converters) response of small signal frequency
Model is established the control system model for being molded fractional order frequency controller based on robust circuit, and establishes independence on this basis
The Model for Multi-Objective Optimization of micro-grid system robust fractional order FREQUENCY CONTROL, independent micro-grid system monitor computer and read system
Read independent micro grid control system model and load data.
In the present embodiment, condition of small signal spatial model meter of the independent micro-grid system near normal operating condition point
It calculates as follows：
Δ X=[Δ P in formulaWTG ΔPPV ΔPDEG ΔPFC ΔPBESS ΔPFESS Δf]TIndicate state vector, Δ
PWTG、ΔPPV、ΔPDEG、ΔPFC、ΔPBESS、ΔPFESSWind-driven generator, photovoltaic array, diesel-driven generator, fuel are indicated respectively
The changed power of battery, accumulator and flywheel energy storage system, Δ f indicate the frequency departure of independent micro-grid system,Indicate shape
The first derivative vector of state vector, Δ W=[Δ PwΔPpΔPl]TIndicate interference vector, Δ Pw、ΔPp、ΔPlWind is indicated respectively
The power swing of the power generation of power Generate, Generation, Generator volt and load interferes, and Δ U=u indicates system input vector, A1、B1、B2、C1、D1Indicate system
System coefficient matrix calculates as follows in the present embodiment：
Robust circuit is molded fractional order frequency controller CRTransfer function model it is as follows：
CR=W1C∞W2, wherein
Wherein, W1And W2Indicate weighting function, KrIndicate fractional order control device C∞Proportionality coefficient, Tr1With Tr2It indicates respectively
Two fractional order inertial element inertia time coefficients, λr1With λr2The fractional order order of two inertial elements is indicated respectively.
In the present embodiment, the Model for Multi-Objective Optimization of independent micro-grid system robust fractional order FREQUENCY CONTROL includes more mesh
It marks shown in fitness function and its constraints model such as following formula (3)~(13)：
Minf (x)=min [f1(x),f2(x),f3(x),f4(x)], x=[Kr,Tr1,Tr2,λr1,λr2] (3)
f4(x)=| | [I C∞]T(1-PC∞)-1[I P]||∞, wherein P=W2P0W1 (7)
subject to||W1T||∞<1,||W2S||∞<1 (8)
S=(I+P0CR)-1 (9)
T=P0CR(I+P0CR)-1 (10)
L≤x≤U (13)
Wherein, t indicates system operation time, tminAnd tmaxWhen indicating initial time and the termination of system operation time respectively
Between, Δ f indicates system frequency deviation, Δ PgIndicate that system total power deviation, u indicate robust controller output signal amplitude, a1With
b1Weighting function W is indicated respectively1Zero and pole, KaIndicate W1Proportionality coefficient, P0Indicate controlled under system health
Object model, S and T indicate that sensitivity function and mending sensitivity function, Δ P indicate the disturbance mould under system uncertain factor respectively
Type, M and N indicate normal controlled device P respectively0Denominator and molecular model, Δ M and Δ N indicate controlled device not really respectively
The denominator and molecular model disturbed under qualitative factor, the lower limit L and upper limit U of superior vector be respectively set to herein L=[0,
0.01,0.01,0,0] and U=[100,1,1,2,2], EVmax(X1Z1) indicate X1Z1Maximum characteristic root, X1And Z1The side of being respectively
The normal solution of journey (14) and (15)：
(A1-B1Sa -1D1 TC1)TX1+X1(A1-B1Sa -1D1 TC1)-X1B1Sa -1B1 T+C1 TRC1=0 (14)
(A1-B1Sa -1D1 TC1)TZ1+Z1(A1-B1Sa -1D1 TC1)-Z1B1Sa -1B1 T+C1 TRC1=0 (15)
Wherein R=I+D1D1 T,Sa=I+D1 TD1, A1、B1、C1、D1The coefficient square realized for the minimum space of controlled device P
Battle array.
(2) parameter values of multi-objective constrained optimization solver, including external archival maximum number A are setmax=50, most
Big iteration optimization number Imax=500.
(3) the individual S of a real coding is randomly generatedI=(U-L) * R+L, wherein SI=[Kr,Tr1,Tr2,λr1,λr2], U
Indicate that robust circuit is molded fractional order frequency controller optimized variable upper and lower bound with L, R indicates one group and produced in 0 to 1 range
Raw uniform random number, and it is sky to enable external archival A.
(4) to current individual SIOptimized variable into row variation and keeps other group members constant one by one, generates 5 offspring individuals
{Sj, j=1,2 ..., 5 }, shown in specific mutation operation such as formula (16)~(18)：
Sj(xi)=SI(xi)+α.βmax(xi), i=1,2 ..., 5 (16)
Wherein
βmax(xi)=max (SI(xi)-L(xi),U(xi)-SI(xi)), i=1,2 ..., 5 (18)
Wherein, xiIndicate i-th of optimized variable, Sj(xi) and Sj(xi) individual S is indicated respectivelyjAnd SIIn i-th optimization
Variable, L (xi) and U (xi) lower limiting value and upper limit value of i-th of optimized variable, I are indicated respectivelycIndicate current iteration number, r1It is
The uniform random number generated in 0 and 1 range.
(5) { S is calculated according to formula (19)~(20)j, j=1,2 ..., 5 } the constraint violation amount g (S of all individualsj)；
Wherein p is the quantity of constraints.
(6) m fitness value { F of each individual is calculatedk(Sj), j=1,2 ..., 5, k=1,2 ..., m }, it is specific to calculate
Process is as follows：
(6.1) if SjFeasible solution, then Fk(Sj)=fk(Sj), j=1,2 ..., 5, k=1,2 ..., m, wherein fk(Sj) table
Show that k-th of fitness function of j-th of individual, specific calculate refer to right 2；
(6.2) if SjInfeasible solution, then Fk(Sj)=fk(Sj)+ηk.g(Sj), wherein ηkIndicate the punishment to violating constraint
The factor.
(7) using the Pareto fitness evaluations criterion based on non-dominated ranking to this 5 offspring individual { Sj, j=1,
2 ..., 5 } carry out Pareto sequences.
(8) if only existing a non-dominant individual, it is S to enable the individualn；If there is multiple non-dominant individuals, then
An individual is randomly choosed as Sn。
(9) using the external document A of update mechanism update based on crowding distance, specific implementation is as follows：
(9.1) if at least one body can dominate individual S in external archivaln, then individual SnIt is added without external archival A.
(9.2) if individual SnCertain individuals in external archival can be dominated, then are removed these individuals, and will be individual
SnExternal archival A is added.
(9.3) if all individuals in external archival and individual SnMutual not branch timing, if external archival number is not up to
Maximum number Amax, then by individual SnExternal archival A is added；If external archival number reaches maximum number AmaxAnd if individual SnPosition
In external archival most crowded places, then external archival A is added without；Otherwise individual SnIt will substitute most crowded positioned at external archival
The individual in place, to which external archival A be added.Crowding distance calculates specific as follows：Assuming that individual amount is in external document A
L, to the corresponding m fitness function { F of all individuals { A (i), i=1,2 .., l } in Ak(A (i)), i=1,2 .., l, k=
1,2 ..., m } according to ascending sort, so that Fk(A(O(1)))≤Fk(A(O(2)))≤…≤Fk(A (O (l))), wherein O
(1), (2) O ..., O (l) are ranking index number, Ak(O (i)) indicates that m-th of fitness function value is ordered as the corresponding outsides O (i)
Document individual；Ak(O (1)) and AkCrowding distance d (the A of (O (l))k(O (1))) and d (Ak(O (l))) be：d(Ak(O (1)))=d
(Ak(O (l)))=∞；For i=2 ..., (l-1), then AkCrowding distance d (the A of (O (i))k(O (i))) be：d(Ak(O
(i)))=[Ak(O (i+1))-Ak(O (i-1))]/[Fk(A (O (l)))-Fk(A(O(1)))]。
(10)SnUnconditionally substitute current individual SI。
(11) step (4) to (10) is repeated, reaches greatest iteration optimization number I until meetingmax=500.
(12) it is exported external archival as the Pareto disaggregation up to the present optimized, therefrom chooses Pareto disaggregation
In most intermediate individual the Optimal Parameters S of fractional order frequency controller is molded as robust circuitbest, transmit it to practical only
In vertical micro-grid system, independent micro-grid system monitor computer obtain the real-time running data of practical independent micro-grid system with
Waveform.
It is analyzed by the independent micro-grid system running experiment Comparative result to use the technology of the present invention and the prior art,
We can be found that：Using the achievable independent micro-grid system frequency departure of the present invention, power deviation, stability margin, controller
The robust FREQUENCY CONTROL of multiple performance indicator trade-off optimizations such as output signal, with the following advantages not available for the prior art：
System run all right nargin higher under the situations such as independent micro-grid system parameter uncertainty and interference, system frequency deviation
Gentler with power deviation fluctuation, regulating time is shorter, and steady-state error smaller, controller output signal value is gentler, robust control
Device parameter optimization processed adjust it is more efficient, and optimization solver design with realization it is simpler.
Claims (2)
1. a kind of Multi-objective Robust fractional order control method for frequency of independent micro-capacitance sensor, which is characterized in that this method includes following
Step：
(1) it includes wind-driven generator, photovoltaic array, diesel oil to establish each component of independent micro-grid system by Approach for Modeling of Small-Signal
The small signal frequency response model of generator, fuel cell, lead-acid accumulator, flywheel energy storage system and converters,
The control system model that fractional order frequency controller is molded based on robust circuit, independent micro-grid system prison are established on this basis
It controls computer and reads the independent micro grid control system model of system reading and load data；Wherein robust circuit molding fractional order frequency
Rate controller CRTransfer function model it is as follows：
Wherein, W1And W2Indicate weighting function, KrIndicate fractional order control device C∞Proportionality coefficient, Tr1With Tr2Two are indicated respectively
Fractional order inertial element inertia time coefficient, λr1With λr2The fractional order order of two inertial elements is indicated respectively；
(2) parameter values of multi-objective constrained optimization solver, including external archival maximum number A are setmax, greatest iteration it is excellent
Change number Imax；
(3) the individual S of a real coding is randomly generatedI=(U-L) * R1+ L, wherein SI=[Kr,Tr1,Tr2,λr1,λr2], U and L
Indicate that robust circuit is molded fractional order frequency controller optimized variable upper and lower bound, R1Indicate that one group generates in 0 to 1 range
Uniform random number, and enable external archival A be sky；
(4) to current individual SIOptimized variable into row variation and keeps other group members constant one by one, generates 5 offspring individual { Sj,j
=1,2 ..., 5 }, shown in specific mutation operation such as formula (2)~(4)：
Sj(xi)=SI(xi)+α·βmax(xi), i=1,2 ..., 5
(2)
βmax(xi)=max (SI(xi)-L(xi),U(xi)-SI(xi)), i=1,2 ..., 5 (4)
Wherein, xiIndicate i-th of optimized variable, Sj(xi) and SI(xi) individual S is indicated respectivelyjAnd SIIn i-th of optimized variable, L
(xi) and U (xi) lower limiting value and upper limit value of i-th of optimized variable, I are indicated respectivelycIndicate current iteration number, r1It is in 0 and 1
The uniform random number generated in range；
(5) { S is calculated according to formula (5)~(6)j, j=1,2 ..., 5 } the constraint violation amount g (S of all individualsj)；
Wherein p is the quantity of constraints；
(6) m fitness value { F of each individual is calculatedk(Sj), j=1,2 ..., 5, k=1,2 ..., m }, specific calculating process
It is as follows：
(6.1) if SjFeasible solution, then Fk(Sj)=fk(Sj), j=1,2 ..., 5, k=1,2 ..., m, wherein fk(Sj) indicate jth
K-th of fitness function of individual；
(6.2) if SjInfeasible solution, then Fk(Sj)=fk(Sj)+ηk.g(Sj), wherein ηkIndicate to violate constraint punishment because
Son；
(7) using the Pareto fitness evaluations criterion based on non-dominated ranking to this 5 offspring individual { Sj, j=1,2 ..., 5 }
Carry out Pareto sequences；
(8) if only existing a non-dominant individual, it is S to enable the individualn, the wherein non-dominant (non-of subscript n expression
dominated)；If there is multiple non-dominant individuals, then an individual is randomly choosed as Sn；
(9) using the external document A of update mechanism update based on crowding distance, specific implementation is as follows：
(9.1) if at least one individual can dominate individual S in external archivaln, then individual SnIt is added without external archival A；
(9.2) if individual SnCertain individuals in external archival can be dominated, then are removed these individuals, and by individual SnAdd
Enter external archival A；
(9.3) if all individuals in external archival and individual SnMutual not branch timing, if external archival number is not up to maximum
Number Amax, then by individual SnExternal archival A is added；If external archival number reaches maximum number AmaxAnd if individual SnPositioned at outside
Most crowded places are achieved, then are added without external archival A；Otherwise individual SnIt will substitute positioned at external archival most crowded places
Individual, to which external archival A be added；Crowding distance calculates specific as follows：Assuming that individual amount is l in external document A, to A
In all individual { A (i), i=1,2 .., l } corresponding m fitness function { Fk(A (i)), i=1,2 .., l, k=1,
2 ..., m } according to ascending sort, so that Fk(A(O(1)))≤Fk(A(O(2)))≤…≤Fk(A (O (l))), wherein O
(1), (2) O ..., O (l) are ranking index number, Ak(O (i)) indicates that k-th of fitness function value is ordered as the corresponding outsides O (i)
Document individual；Ak(O (1)) and AkCrowding distance d (the A of (O (l))k(O (1))) and d (Ak(O (l))) be：d(Ak(O (1)))=d
(Ak(O (l)))=∞；For i=2 ..., (l-1), then AkCrowding distance d (the A of (O (i))k(O (i))) be：d(Ak(O
(i)))=[Ak(O (i+1))-Ak(O (i-1))]/[Fk(A (O (l)))-Fk(A(O(1)))]；
(10)SnUnconditionally substitute current individual SI；
(11) step (4) to (10) is repeated, reaches greatest iteration optimization number I until meetingmax；
(12) it is exported external archival as the Pareto disaggregation up to the present optimized, therefrom chooses Pareto solutions and concentrate most
Intermediate individual is molded the Optimal Parameters S of fractional order frequency controller as robust circuitbest, it is micro- to transmit it to practical independence
In network system, independent micro-grid system monitors the real-time running data and wave that computer obtains practical independent micro-grid system
Shape.
2. a kind of Multi-objective Robust fractional order control method for frequency of independent micro-capacitance sensor according to claim 1, feature
It is, the Model for Multi-Objective Optimization of the robust fractional order FREQUENCY CONTROL of involved independent micro-grid system includes more in step 6
Shown in target fitness function and its constraints model such as formula (7)~(17)：
Minf (x)=min [f1(x),f2(x),f3(x),f4(x)], x=[Kr,Tr1,Tr2,λr1,λr2]
(7)
f4(x)=| | [I C∞]T(1-PC∞)-1[I P]||∞, wherein P=W2P0W1 (11)
And | | W1TC||∞<1,||W2S||∞<1 (12)
S=(I+P0CR)-1 (13)
TC=P0CR(I+P0CR)-1 (14)
L≤x≤U (17)
Wherein, t indicates system operation time, tminAnd tmaxThe initial time of system operation time is indicated respectively and terminates the time,
Δ f indicates system frequency deviation, Δ PgIndicate that system total power deviation, u indicate robust controller output signal amplitude, a1And b1
Weighting function W is indicated respectively1Zero and pole, KaIndicate W1Proportionality coefficient, P0Indicate controlled pair under system health
As model, S and TCIndicate that sensitivity function and mending sensitivity function, Δ P indicate the disturbance mould under system uncertain factor respectively
Type, M and N indicate normal controlled device P respectively0Denominator and molecular model, Δ M and Δ N indicate controlled device not really respectively
The denominator and molecular model disturbed under qualitative factor, EVmax(X1Z1) indicate X1Z1Maximum characteristic root, X1And Z1It is equation respectively
(18) and the normal solution of (19)：
(A1-B1Sa -1D1 TC1)TX1+X1(A1-B1Sa -1D1 TC1)-X1B1Sa -1B1 T+C1 TRC1=0 (18)
(A1-B1Sa -1D1 TC1)TZ1+Z1(A1-B1Sa -1D1 TC1)-Z1B1Sa -1B1 T+C1 TRC1=0 (19)
Wherein, R=I+D1D1 T,Sa=I+D1 TD1, A1、B1、C1、D1The coefficient matrix realized for the minimum space of controlled device P.
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