The content of the invention
For the deficiency of current Hydropower Unit model closed-loop identification method, the present invention proposes a kind of Hydropower Unit model refinement
Type subspace closed-loop identification method, it is based on the brief subspace state space system identification of the prediction form (PARSIM-K) of PSO parameter optimizations
Hydropower Unit model is recognized, the method makes full use of the Toplitz structures and SVD depression of orders of Markov matrix parameter,
Extension Observable matrix, estimating system matrix are obtained, and parameter p, f is optimized with PSO, such that it is able to greatly improve water power
The reliability and degree of accuracy of unit model closed-loop identification.
For achieving the above object, it is proposed, according to the invention, a kind of Hydropower Unit model refinement type subspace closed-loop identification side is provided
Method, comprises the steps:
S1 sets up the water turbine governing closed-loop model with output frequency noise;
S2 determines pumping signal and unit frequency noise signal, and gathers guide vane opening and unit frequency number;
Parameter p, f in S3 optimization PARSIM-K algorithms, parameter p, f after being optimized, wherein f and p are represented respectively not
Come time domain parameter and in the past time domain parameter;
S4 realizes being improved PARSIM-K algorithms with parameter p, f after optimizing, and using the PARSIM-K after improving
Algorithm identification closed loop Hydropower Unit zero load model, you can realize the closed-loop identification to Hydropower Unit zero load model.
As present invention further optimization, wherein, the tool of parameter p, f optimized with PSO in PARSIM-K algorithms
Body process is:
S31 arranges primary position, velocity interval and Studying factors;
S32 evaluates particle, and according to fitness function the individual extreme value and colony's extreme value of current particle are calculated;
S33 more new particles;
S34 estimates [(ΓfLz),HK f,GK f] item, realize weighting SVD and estimating system matrix, and more new individual extreme value and group
Body extreme value;
S35 detects whether to meet termination condition, if current iteration number of times reaches maximum times, terminates, and exports optimal solution
Particle be parameter p, f, and obtain best estimate model, otherwise go to step S32.
Used as present invention further optimization, the fitness function isIts
In, L represents sampled data number, and k represents kth time iteration, and j represents j-th sampled data, and y (j) is actual measurement output number
According to ykJ () represents input to estimate the output data of model during actual measurement input.
As present invention further optimization, unit output frequency noise for average be 0, variance be definite value white noise.
Noise is the factor that can not ignore in closed-loop identification, and is more tallied with the actual situation with noisy system model.
In this programme, the water turbine governing closed-loop model set up considers impact of the frequency noise to closed-loop identification, establishes
Turbine Governor System model with output frequency noise, unit output frequency noise is that 0, variance is the white of definite value for average
Noise.
As present invention further optimization, wherein it is determined that the given step signal of frequency is pumping signal, so that stator
Opening amount signal meets persistent excitation condition rank (UL)≥f+p。
In general, by the contemplated above technical scheme of the present invention compared with prior art, with following beneficial effect
Really:
1) method of the present invention is proposed and is directly applied for Hydropower Unit model closed-loop identification method, it is not necessary to using conventional
Open-loop Identification or closed loop turn on ring discrimination method, and consider unit frequency noise closed-loop identification affected;
2) method of the present invention improves the brief subspace state space system identification of prediction form, and PSO algorithms are carried out to parameter p, f
Optimization, improves the degree of accuracy and reliability of algorithm;
3) method of the present invention algorithm complex is low, it is easy to programming and engineer applied.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention become more apparent, below in conjunction with accompanying drawing and exemplary reality
Example is applied, the present invention will be described in further detail.It should be appreciated that exemplary embodiment described herein is only to explain this
Invention, the scope of application being not intended to limit the present invention.
A kind of Hydropower Unit model refinement type subspace closed-loop identification method of the embodiment of the present invention, it is in the analysis hydraulic turbine
On the basis of speed governing closed loop system and unit output frequency noise are to the impact of closed-loop identification, using PSO algorithms to predicting form
Parameter p, f of brief subspace state space system identification is iterated optimization, and by the brief Subspace Identification side of prediction form after optimization
Method is applied to the closed-loop identification of Hydropower Unit zero load model.
Specifically, the Hydropower Unit model refinement type subspace closed-loop identification method of the present embodiment specifically includes following step
Suddenly:
Step 1 sets up the water turbine governing closed-loop model with frequency noise, and arranges model parameter.
The system model block diagram set up in the present embodiment is as shown in Figure 1.Fig. 2 is PID controller model and electro-hydraulic servo system
System model.Fig. 3 is hydrogenerator and load model.Parametric variable definition such as table 1:
Adaptive System of Water-Turbine Engine model parameter variable-definition of the table 1 with noise
In Fig. 1, x is machine class frequency;xrIt is unit given frequency;yPIDIt is PID controller output signal;Y is that servomotor is led
Leaf aperture.
Step 2 selectes Persistent Excitation signal and unit output frequency noise signal.
In the present embodiment, Hydropower Unit zero load model is selected according to the definition of Persistent Excitation signal and engineering requirements
Simulation excitation signal.
Persistent Excitation signal definition is:Input signal u is the definitiveness sequence that length is L, meets u ∈ RmIf, formula (1)
Set up, then u is hm rank Persistent Excitations.
PARSIM-K algorithms require that list entries u is f+p rank Persistent Excitations, and selected pumping signal can either ensure be
System is stable, and the requirement of excitation order is met again.In the present embodiment, the given step signal of selected frequency is pumping signal, in emulation
(whether guide vane opening signal u) meets persistent excitation condition rank (U for detection model inputL)≥f+p。
In addition, in the present embodiment, according to the selected Hydropower Unit zero load model emulation frequency noise signal such as signal to noise ratio.Closing
Noise is the factor that can not ignore in ring identification, and is more tallied with the actual situation with noisy system model.Therefore, the present embodiment
In establish the Turbine Governor System model with output noise, wherein unit output frequency noise is set to average for 0, side
Differ from as definite value (for example) band-limited white noise.Specifically, formula (2) is output signal-to-noise ratio definition, after collection output data,
Can determine that the noise variance of machine class frequency.
SNR=10*lg (var (y)/var (o))=20*lg (V (y)/V (o)) (2)
Wherein, var represents variance;V represents signal amplitude;Y is output;O is output noise, it is assumed that for average be 0, variance
For the white noise of definite value.
Parameter p, f of the step 3 in PSO algorithm optimization PARSIM-K algorithms, parameter p, f after being optimized.
In this programme, it is contemplated that impact of parameter p, f to recognizing in PARSIM-K algorithms.Specifically, first, the present embodiment
In, the linear time invariant system of predictor form is:
xk+1=AKxk+BKuk+Kyk (3a)
yk=Cxk+Duk+ek (3b)
Wherein, x ∈ RnExpression state;u∈RmRepresent input;y∈RlRepresent output;e∈RlRepresent new breath;K represents karr
Graceful filtering gain matrix;AK=A-KC;BK=B-KD.And model meets hypothesis below:
A) matrix (A, B) is controllable, and matrix (A, C) is observable, matrix AK=A-KC is that strict Hull is tieed up hereby
(Hurwitz) matrix (in discrete sense).
B) new breath { ekIt is fixed, zero-mean, white-noise process, its auto-variance is:As i ≠ j, ε (eje'j)=Re,
ε(eie'j)=0.Wherein, RePositive definite.
C) data are collected by L sampling time.In open cycle system, following condition is set up:For all of i and j, ε
(uie'j)=0.In closed loop system, if D=0, as i < j, ε (uie'j)=0, you can by feeding back yiTo estimate
ui;If D=0, as i≤j, ε (uie'j)=0, you can by feeding back yi-1(or output earlier) is estimating ui。
D) it is input into { ukIt is quasi-steady and f+p rank Persistent Excitations.Wherein, f and p represent respectively future horizon parameter and past
Time domain parameter.
The basic thought of Subspace Identification algorithm is that the input that will measure, output data are divided in the past and following two parts.
To known a length of L (L>>Max (f, p)) output sequence y and status switch x is defined as below:
yfi=[yp+i-1 yp+i ... yL-f+i-1], ypi=[yi-1 yi ... yL-f-p+i-1]
Yf=[yT f1 yT f2 ... yT ff]T, Yp=[yT p1 yT p2 ... yT pf]T
Xk-p=[xk-p xk-p+1 ... xk-p+L-1], Xk=[xk xk+1 ... xk+L-1]
Wherein, i=1 ..., L.The definition similar with new breath e of input data u, is obtained block Hankel matrix Uf∈Rmf×N、Up
∈Rmp×N、Ef∈Rlf×N、Ep∈Rlp×N、Yf∈Rlf×N、Yp∈Rlp×N(N=L-f-p+1).
If making xf=AK pxp+LzZp, derived by formula (3) iteration and known:
Yf=ΓK fxf+HK fUf+GK fYf+Ef
=ΓK f(AK pxp+LzZp)+HK fUf+GK fYf+Ef
(4)
Wherein, xf=xf1∈Rn×N,LzIt is against extension controllable matrix, ΓK fTo extend Observable square
Battle array, HK fAnd GK fIt is down triangular Toeplitz matrix.Matrix concrete structure is as follows:
Wherein,
In the present embodiment, PARSIM-K algorithms are especially by step 3.1) and step 3.2) realize.
3.1) [(Γ is estimatedfLz),HK f,GK f] item.
Matrix HK fAnd GK fIt is strict piecemeal lower triangular structure, is known by formula (4):
yf1=ΓK f1(AK pxp+LzZp)+HK f1uf1+ef1 (5a)
Work as i=2 ..., during f, yfi=ΓK fi(AK pxp+LzZp)+HK fiuf1+GK fiyf1+yfi+efi
(5b)
Wherein, yf2=HK f1uf2;Work as i=3 ..., during f,
Due to AKIt is strict Hull dimension hereby matrix, it is assumed that parameter p of selection is sufficiently large so thatThen by formula (5)
Estimate [(ΓfiLz),HK fi,GK fi] item.
3.2) weighting SVD and estimating system matrix are realized.
To matrixRealize weighting SVD:
Wherein, (Un, Sn, Vn) it is the SVD items being associated with n maximum singular value, RnRepresent SVD individual with remaining (fl-n)
The associated error of item, weight matrix W1=I,
Finally, it is rightWithCarry out method of least square and be calculated system estimation matrix.
It is above-mentioned that PARSIM-K Algorithm Analysis are understood, after setting parameter p, f, can be entered with the input, output data that measure
Row matrix computing, obtains identification result.To different closed loop systems, it is adaptable to which parameter p, f of the system is also different.Parameter setting
It is too small, identification result error may be caused larger;Parameter setting is excessive, then can increase unnecessary calculating.Therefore, will
When PARSIM-K algorithms are applied to different closed loop systems, it is necessary to select suitable algorithm parameter p, f.PSO algorithms in this programme
Parametric variable definition such as table 2.
The PSO algorithm parameter variable-definitions of table 2
Hydropower Unit zero load model is emulated, in one embodiment, the PARSIM-K algorithm parameters after PSO optimizations are
P=f=29.Innovatory algorithm flow chart is as shown in Figure 4.
To different closed loop systems, it is adaptable to which parameter p, f of the system is also different.PSO optimizes PARSIM-K algorithm parameters
The step of p, f, is as follows:
Step (3.3.1) is initialized.Primary position, velocity interval, Studying factors etc. are set.
Step (3.3.2) evaluates particle.Individual extreme value and the colony pole of current particle are calculated according to fitness function
Value.Fitness function isWherein, L represents sampled data number;K represents kth
Secondary iteration;J represents j-th sampled data;Y (j) is actual measurement output data;ykJ () represents input for actual measurement input
When estimate model output data.
The renewal of step (3.3.3) particle.Speed renewal equation and location updating equation are respectively Wherein, v is
Speed;X is position;I represents ith sample data c1、c2It is Studying factors;rand1,2It is the random number between [0,1];
Pbest, gbest represent respectively individual extreme value and colony's extreme value.
Step (3.3.4) estimates [(ΓfLz),HK f,GK f] item, realize weighting SVD and estimating system matrix.More new individual pole
Value and colony's extreme value.
Step (3.3.5) detects whether to meet termination condition.If current iteration number of times reaches maximum times, terminate, it is defeated
Go out the particle (i.e. parameter p, f) of optimal solution, and obtain best estimate model, otherwise go to step (3.3.2).
Step 4 substitutes into parameter p, f after PSO algorithm optimizations in PARSIM-K algorithms, repeat step 3.1 and 3.2, application
In closed loop Hydropower Unit zero load model identification in so as to realize Hydropower Unit zero load model closed-loop identification.
To verify the effectiveness of the inventive method, (parameter 1 is p=28, f=14, parameter can to randomly select two groups of parameters
2 is p=25, f=48) contrasted with the parameter after PSO optimizations.Hydropower Unit zero load model adopts discrete modela0、a1、b0And b1It is parameter to be identified, and defines the following two kinds model accuracy evaluation index.
Root-mean-square error (root mean square error, RMSE):
Mean absolute percentage error (mean absolute percentage error, MAPE):
Table 3 is actual parameter and the contrast for estimating model parameter.
As shown in Table 3, most connect with actual parameter value using the estimation model parameter of the PARSIM-K algorithms of PSO parameters optimization
Closely, and frequency curve is higher with the actual curve goodness of fit;The estimation model parameter value and actual parameter of parameter 1 and the algorithm of parameter 2
Value has larger error, particularly, parameter b0And b1Substantial deviation actual value, the estimation model output frequency curve of parameter 2 is steady
State value has deviateed actual frequency curve steady-state value.
The true model of table 3 and estimation model parameter
Table 4 is the contrast of model accuracy index.As shown in Table 4, its model accuracy of the estimation model of algorithm after PSO parameters optimization
Index RMSE and MAPE are respectively less than the model accuracy of parameter 1 and parameter 2, show that the PARSIM-K algorithms of PSO parameters optimization are effective
Improve algorithm identification precision.
The model accuracy index of table 4 is contrasted
The unloaded estimation mould of Hydropower Unit gone out based on the PARSIM-K method closed-loop identifications of PSO parameters optimization in the present embodiment
Type is identical with true model, and the superiority of the inventive method is illustrated compared with the PARSIM-K methods for being not optimised parameter.
As it will be easily appreciated by one skilled in the art that the foregoing is only presently preferred embodiments of the present invention, not to
The present invention, all any modification, equivalent and improvement made within the spirit and principles in the present invention etc. are limited, all should be included
Within protection scope of the present invention.