CN106681133B - A kind of Hydropower Unit model refinement type subspace closed-loop identification method - Google Patents
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Abstract
The invention discloses a kind of Hydropower Unit model refinement type subspace closed-loop identification methods, belong to Hydropower Unit model modeling and identification technique field, the brief subspace state space system identification of prediction form based on PSO parameter optimization is applied to Hydropower Unit model closed-loop identification comprising the steps of: (1) establish the water turbine governing closed-loop system model for having output frequency noise；(2) influence of parameter p, f to identification in the brief subspace state space system identification of prediction form (PARSIM-K) is considered, and with PSO algorithm optimization parameter p, f；(3) closed loop Hydropower Unit zero load model is recognized using improved algorithm.This method has many advantages, such as that algorithm is quick, high reliablity, is easily programmed realization, can go out suitable algorithm parameter according to Hydropower Unit model optimizations different in practice, improved algorithm effectively increases identification precision.
Description
Technical field
The invention belongs to Hydropower Unit model modelings and identification technique field, and in particular to a kind of Hydropower Unit model refinement
Type subspace closed-loop identification method.
Background technique
With being growing for electric system scale, the accuracy of the safety and stability of system to Hydropower Unit model
More stringent requirements are proposed.Turbine Governor System has the characteristics that non-minimum phase, non-linear, complexity is exclusive, therefore, right
Hydropower Unit model carries out accurately identification and contains hydroelectric electric power to hydroelectric generation large-scale grid connection, timely adjustment
The scheduling strategy of system and realize that its safe and stable, economical operation has important practical significance.
Open-loop Identification can be carried out to load module, but when idle condition, frequency dead band 0, unit frequency-tracking power grid frequency
Rate, unloaded Model Distinguish belong to closed-loop identification.Previous Hydropower Unit Model Distinguish research lays particular emphasis on Open-loop Identification method, compares
Compared with for, closed-loop identification method is more deficient.Compared to Open-loop Identification, closed-loop identification easily and fast, and is applied wide in the industry
It is general.But the method currently used for Hydropower Unit zero load Model Distinguish is the discrimination method that ring is turned on based on closed loop.
Subspace state space system identification to realize is distinguished by SVD reduced order state spatial model and to the linear projection of data matrix
Know.The brief subspace state space system identification of prediction form (PARSIM-K) is a kind of subspace state space system identification of optimization.Prediction form
Brief subspace state space system identification (PARSIM-K) is a kind of subspace closed-loop identification method, such as bibliography (Pannocchia
G, Calosi M.A predictor form PARSIMonious algorithm for closed-loop subspace
Identification.Journal of Process Control, 2010,20:517-524) to PARSIM-K carried out compared with
Specifically to introduce, specifically, this method is broadly divided into two steps: 1) estimating [(ΓfLz),HK f,GK f] item；2) it realizes and adds
Weigh SVD and estimating system matrix.The algorithm makes full use of and develops HfAnd GfThe characteristics of being down triangular Toeplitz matrix, has
Effect solves the problems, such as the closed-loop identification of noise and input data correlation, improves computational efficiency, ensure that the consistency of algorithm,
To realize the Hydropower Unit zero load Model Distinguish to frequency noise is had.But since PARSIM-K algorithm parameter is few, algorithm
Identification result be affected by parameter p, f so that at present PARSIM-K algorithm in reliability and precision all there is also deficiency,
It is difficult to meet the requirement of current Hydropower Unit model closed-loop identification.
Summary 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, the brief subspace state space system identification of prediction form (PARSIM-K) based on PSO parameter optimization
Hydropower Unit model is recognized, this method makes full use of the Toplitz structure and SVD depression of order of Markov matrix parameter,
Extension Observable matrix, estimating system matrix are obtained, and parameter p, f is optimized with PSO, so as to greatly improve water power
The reliability and accuracy of unit model closed-loop identification.
To achieve 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 includes the following steps:
S1 establishes the water turbine governing closed-loop system model for having output frequency noise；
S2 determines pumping signal and unit frequency noise signal, and acquires guide vane opening and unit frequency number；
S3 optimizes parameter p, f in PARSIM-K algorithm, and parameter p, f after being optimized, wherein f and p are respectively indicated not
Come time domain parameter and in the past time domain parameter；
S4 improves PARSIM-K algorithm with parameter p, the f realization after optimizing, and uses improved PARSIM-K
Algorithm recognizes closed loop Hydropower Unit zero load model, and the closed-loop identification to Hydropower Unit zero load model can be realized.
As present invention further optimization, wherein the tool with parameter p, f in PSO optimization PARSIM-K algorithm
Body process are as follows:
Primary position, velocity interval and Studying factors are arranged in S31；
S32 evaluates particle, and the individual extreme value and group's extreme value of current particle are calculated according to fitness function；
S33 more new particle；
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 is detected whether to meet termination condition, if current iteration number reaches maximum times, be terminated, and exports optimal solution
Particle, that is, parameter p, f, and obtain best estimate model, otherwise go to step S32.
As present invention further optimization, the fitness function is
Wherein, L indicates sampled data number, and k indicates kth time iteration, and j indicates j-th of sampled data, and y (j) is that actual measurement exports number
According to yk(j) indicate that input is that the output data of model is estimated when actual measurement input.
As present invention further optimization, unit output frequency noise is the white noise that mean value is 0, variance is definite value.
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 the present solution, the influence that the water turbine governing closed-loop system model established considers frequency noise to closed-loop identification, establishes
Turbine Governor System model with output frequency noise, unit output frequency noise be mean value be 0, variance is the white of definite value
Noise.
As present invention further optimization, wherein determining that frequency gives step signal is pumping signal, to make guide vane
Opening amount signal meets persistent excitation condition rank (UL)≥f+p。
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect
Fruit:
1) method of the invention, which proposes, is directly applied for Hydropower Unit model closed-loop identification method, does not need using previous
Open-loop Identification or closed loop turn on ring discrimination method, and consider unit frequency noise on closed-loop identification influence；
2) method of the invention improves the brief subspace state space system identification of prediction form, and PSO algorithm carries out parameter p, f
Optimization, improves the accuracy and reliability of algorithm；
3) algorithm complexity of the invention is low, is easily programmed and engineer application.
Detailed description of the invention
There can be optimal understanding to the present invention in conjunction with attached drawing referring to following explanation.In the accompanying drawings, identical part
It can be indicated by identical label.
Fig. 1 is the hydraulic turbine system model framework chart with noise established；
Fig. 2 is controller and executing agency's structural block diagram；
Fig. 3 is hydraulic turbine generator and load model；
Fig. 4 is algorithm flow block diagram；
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached 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, in the analysis hydraulic turbine
On the basis of closed-loop system and unit output frequency noise are adjusted the speed to the influence of closed-loop identification, using PSO algorithm to prediction 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
It is rapid:
Step 1 establishes the water turbine governing closed-loop system model for having frequency noise, and model parameter is arranged.
The system model block diagram established 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 unit 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 are as follows: input signal u is the certainty sequence that length is L, meets u ∈ RmIf formula (1)
It sets up, then u is hm rank Persistent Excitation.
It is f+p rank Persistent Excitation that PARSIM-K algorithm, which requires list entries u, and selected pumping signal can either guarantee be
System is stablized, and meets the requirement of excitation order.In the present embodiment, selected frequency gives step signal for 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.It is 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 be set as mean value be 0, side
Difference be definite value (such as) band-limited white noise.Specifically, formula (2) is output signal-to-noise ratio definition, after acquiring output data,
It can determine the noise variance of unit frequency.
SNR=10*lg (var (y)/var (o))=20*lg (V (y)/V (o)) (2)
Wherein, var indicates variance；V indicates signal amplitude；Y is output；O is output noise, it is assumed that be mean value be 0, variance
For the white noise of definite value.
Parameter p, f in step 3 PSO algorithm optimization PARSIM-K algorithm, parameter p, f after being optimized.
In the present solution, considering influence of parameter p, f to identification in PARSIM-K algorithm.Specifically, firstly, the present embodiment
In, the linear time invariant system of fallout predictor form are as follows:
xk+1=AKxk+BKuk+Kyk (3a)
yk=Cxk+Duk+ek (3b)
Wherein, x ∈ RnExpression state；u∈RmIndicate input；y∈RlIndicate output；e∈RlIndicate new breath；K indicates karr
Graceful filtering gain matrix；AK=A-KC；BK=B-KD.And model meets following hypothesis:
A) matrix (A, B) is controllable, and matrix (A, C) is observable, matrix AK=A-KC is that stringent Hull is tieed up hereby
(Hurwitz) matrix (in discrete sense).
B) { e is newly ceasedkIt is fixed, zero-mean, white-noise process, auto-variance are as follows: and 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 i and j, ε
(uie'j)=0.In closed-loop system, if D=0, as i < j, ε (uie'j)=0, can be by feeding back yiTo estimate
ui；If D=0, as i≤j, ε (uie'j)=0, can be by feeding back yi-1(or output earlier) estimates ui。
D) { u is inputtedkIt is quasi-steady and f+p rank Persistent Excitation.Wherein, f and p respectively indicates future horizon parameter and past
Time domain parameter.
The basic thought of Subspace Identification algorithm is the input that will be measured, output data is divided into passing by and following two parts.
Such as given a definition to known a length of L (L > > max (f, p)) output sequence y and status switch x:
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.Input data u definition similar with new breath e, can be 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 enabling xf=AK pxp+LzZp, known by the derivation of formula (3) iteration:
Yf=ΓK fxf+HK fUf+GK fYf+Ef
=ΓK f(AK pxp+LzZp)+HK fUf+GK fYf+Ef
(4)
Wherein, xf=xf1∈Rn×N,LzFor inverse extension controllable matrix, ΓK fTo extend Observable square
Battle array, HK fAnd GK fIt is down triangular Toeplitz matrix.Matrix specific structure is as follows:
Wherein,
In the present embodiment, PARSIM-K algorithm is realized especially by step 3.1) and step 3.2).
3.1) estimate [(ΓfLz),HK f,GK f] item.
Matrix HK fAnd GK fIt is stringent piecemeal lower triangular structure, is known by formula (4):
yf1=ΓK f1(AK pxp+LzZp)+HK f1uf1+ef1 (5a)
Work as i=2 ..., when f, yfi=ΓK fi(AK pxp+LzZp)+HK fiuf1+GK fiyf1+yfi+efi
(5b)
Wherein, yf2=HK f1uf2；Work as i=3 ..., when f,
Due to AKIt is stringent Hull dimension hereby matrix, it is assumed that the 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 SVD associated with n maximum singular value, RnIt indicates and residue (fl-n) a SVD
The associated error of item, weight matrix W1=I,
Finally, rightWithIt carries out least square method and system estimation matrix is calculated.
It is above-mentioned PARSIM-K algorithm is analyzed it is found that setting parameter p, f after, can be into the input that measures, output data
Row matrix operation, obtains identification result.To different closed-loop systems, parameter p, f suitable for the system is also different.Parameter setting
It is too small, it is larger to may cause identification result error；Parameter setting is excessive, then will increase unnecessary calculating.Therefore, will
When PARSIM-K algorithm is applied to different closed-loop systems, it is necessary to select suitable algorithm parameter p, f.PSO algorithm in this programme
Parametric variable definition such as table 2.
2 PSO algorithm parameter variable-definition of table
Hydropower Unit zero load model is emulated, in one embodiment, the PARSIM-K algorithm parameter after PSO optimization is
P=f=29.Innovatory algorithm flow chart is as shown in Figure 4.
To different closed-loop systems, parameter p, f suitable for the system is also different.PSO optimizes PARSIM-K algorithm parameter
P, the step of f is as follows:
Step (3.3.1) initialization.Primary position, velocity interval, Studying factors etc. are set.
Step (3.3.2) evaluates particle.Individual extreme value and the group pole of current particle are calculated according to fitness function
Value.Fitness function isWherein, L indicates sampled data number；K indicates kth
Secondary iteration；J indicates j-th of sampled data；Y (j) is actual measurement output data；yk(j) indicate that input is that actual measurement inputs
When estimate model output data.
The update of step (3.3.3) particle.Speed renewal equation and location updating equation are respectively Wherein, v is
Speed；X is position；I indicates ith sample data c1、c2It is Studying factors；rand1,2It is the random number between [0,1]；
Pbest, gbest respectively indicate individual extreme value and group'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 group's extreme value.
Step (3.3.5) detects whether to meet termination condition.If current iteration number reaches maximum times, terminate, it is defeated
The particle (i.e. parameter p, f) of optimal solution out, and best estimate model is obtained, otherwise go to step (3.3.2).
Step 4 substitutes into parameter p, f after PSO algorithm optimization in PARSIM-K algorithm, repeats step 3.1 and 3.2, application
The closed-loop identification of Hydropower Unit zero load model is realized in the identification of closed loop Hydropower Unit zero load model.
For the validity for verifying the method for the present invention, can randomly selecting two groups of parameters, (parameter 1 is p=28, f=14, parameter
2 be p=25, f=48) it is compared with the parameter after PSO optimization.Hydropower Unit zero load model uses 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 the comparison of actual parameter and estimation model parameter.
As shown in Table 3, it is most connect using the estimation model parameter and actual parameter value of the PARSIM-K algorithm of PSO Optimal Parameters
Closely, and frequency curve and the actual curve goodness of fit are higher；The estimation model parameter value and actual parameter of 2 algorithm of parameter 1 and parameter
Value has large error, in particular, parameter b0And b1The estimation model output frequency curve of substantial deviation true value, parameter 2 is steady
State value has deviateed actual frequency curve steady-state value.
3 true model of table and estimation model parameter
Table 4 is the comparison of model accuracy index.As shown in Table 4, its model accuracy of the estimation model of algorithm after PSO Optimal Parameters
Index RMSE and MAPE are respectively less than the model accuracy of parameter 1 and parameter 2, show that the PARSIM-K algorithm of PSO Optimal Parameters is effective
Improve algorithm identification precision.
The comparison of 4 model accuracy index of table
Mould is estimated in the Hydropower Unit zero load that PARSIM-K method closed-loop identification in the present embodiment based on PSO Optimal Parameters goes out
Type is identical with true model, and the superiority of the method for the present invention is illustrated compared with the PARSIM-K method for being not optimised parameter.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (4)
1. a kind of Hydropower Unit model refinement type subspace closed-loop identification method, includes the following steps:
S1 establishes the water turbine governing closed-loop system model for having output frequency noise；
S2 determines pumping signal and unit frequency noise signal, and acquires guide vane opening and unit frequency number；
S3 optimizes parameter p, f in PARSIM-K algorithm, and parameter p, f after being optimized, and wherein f and p respectively indicate future
Time domain parameter and in the past time domain parameter；
S4 improves PARSIM-K algorithm with parameter p, the f realization after optimizing, and uses improved PARSIM-K algorithm
Closed loop Hydropower Unit zero load model is recognized, the closed-loop identification to Hydropower Unit zero load model can be realized；
Wherein, parameter p, f in the optimization PARSIM-K algorithm in step S3 is realized by PSO algorithm, detailed process are as follows:
Primary position, velocity interval and Studying factors are arranged in S31；
S32 evaluates particle, and the individual extreme value and group's extreme value of current particle are calculated according to fitness function；
S33 more new particle；
S34 estimates [(ΓfLz),HK f,GK f] item, realize weighting SVD and estimating system matrix, and more new individual extreme value and group pole
Value；Wherein, Γf KTo extend Observable matrix, HK fAnd GK fFor down triangular Toeplitz matrix；The weighting SVD is to utilize weight
Matrix realizes singular value decomposition；The sytem matrix is systematic observation matrix A, B, C, D, K；
S35 is detected whether to meet termination condition, if current iteration number reaches maximum times, be terminated, and exports the grain of optimal solution
Son is parameter p, f, and obtains best estimate model, otherwise goes to step S32.
2. a kind of Hydropower Unit model refinement type subspace closed-loop identification method according to claim 1, wherein described suitable
Response evaluation function isWherein, L indicates sampled data number, and k indicates kth time repeatedly
Generation, j indicate j-th of sampled data, and y (j) is actual measurement output data,It indicates to estimate when input is actual measurement input
Count the output data of model.
3. a kind of Hydropower Unit model refinement type subspace closed-loop identification method according to claim 1 or 2, wherein machine
Group output frequency noise is the white noise that mean value is 0, variance is definite value.
4. a kind of Hydropower Unit model refinement type subspace closed-loop identification method according to claim 1 or 2, wherein really
Determine frequency to give step signal to be the pumping signal, so that guide vane opening signal be made to meet persistent excitation condition rank (UL)≥
f+p。
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