CN110262223A - A kind of comprehensive model modelling approach of hydraulic turbine based on Fractional Order PID speed-regulating system - Google Patents
A kind of comprehensive model modelling approach of hydraulic turbine based on Fractional Order PID speed-regulating system Download PDFInfo
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Abstract
The present invention provides a kind of comprehensive model modelling approach of the hydraulic turbine of adaptive fractional rank PID speed-regulating system, the following steps are included: step 1: establishing the hydrogovernor simulation analysis mathematical model based on Fractional Order PID speed-regulating system, and optimize the objective function based on Fractional Order PID speed-regulating system using hybrid algorithm；Step 2: establishing the machinery hydraulic system and diversion system mathematical model of Turbine Governor System；Step 3: establishing hydraulic turbine generator model；The present invention utilizes MATLAB simulation modeling, classical PID speed-regulating system is improved on the basis of forefathers' research, according to instance analysis, it establishes and is able to reflect Turbine Governor System and the comprehensive model of generator system parameters, in practical applications to the operating condition of practical water turbine set, the variation of hydraulic turbine parameters has good reaction when in face of load fluctuation, provides safeguard for accident forecast with system safety operation.
Description
Technical field:
The present invention relates to power station mechanics, Turbine Governor System principles, and in particular to one kind is adjusted the speed based on Fractional Order PID
The comprehensive model modelling approach of the hydraulic turbine of system.
Background technique
Traditional Turbine Governor System control structure generally uses classical Turbine Governor System, i.e. parallel connection PID speed regulation
System control, has the advantages such as simple to operation, with the development of electric system, to the stability requirement of Hydropower Unit also not
Disconnected to improve, still, the hydraulic turbine system of PID governor system control in parallel has the following problems:
1. stablizing when starting slow；
2. occurring that stability is poor when system loading fluctuation, in face of the emergency event capacity of self-regulation deficiency etc. of electric system
Problem.
The shortcomings that in face of classical Turbine Governor System, a large amount of scholars propose advanced intelligentized control method mode, such as mould
PID control, BP neural network control, chaotic particle group control etc. are pasted, these researchs advanced optimize Turbine Governor System,
There is the speed adjusting performance of the hydraulic turbine to be obviously improved.
In view of the control mode of the domestic hydraulic turbine mostly uses the adjusting based on PID governor system control in parallel control
Mode brings smaller impact, the speed regulation system of the hydraulic turbine to electric system as far as possible in order to quick response system requirement
The optimization of system just seems most important.
There is remarkable progress to the Nonlinear Mechanism Modeling Research of the hydraulic turbine in terms of simulation modeling, but has not divided deeply
Analyse influence of the load fluctuation to Turbine Governor System；Load and generator model are generally equivalent to the transmitting letter of single order at present
Number, the practical problem limitation of reflection is bigger, for hydraulic turbine generator spy on the basis of reflecting water turbine governing performance
When property, dynamic load model and electric power system fault in the influence of Turbine Governor System up for further analyzing.
Summary of the invention
The hydraulic turbine is each when the present invention is to solve not reflecting dynamic load in the Nonlinear Mechanism modeling of the hydraulic turbine
The problem of item important parameter variation, propose a kind of comprehensive model modelling approach of the hydraulic turbine based on Fractional Order PID speed-regulating system.
In order to achieve the above object, the invention adopts the following technical scheme:
A kind of comprehensive model modelling approach of the hydraulic turbine of adaptive fractional rank PID speed-regulating system, comprising the following steps:
Step 1: establishing the hydrogovernor simulation analysis mathematical model based on Fractional Order PID speed-regulating system, and utilize
The hybrid algorithm optimization objective function based on Fractional Order PID speed-regulating system；
Step 2: establishing the machinery hydraulic system and diversion system mathematical model of Turbine Governor System；
Step 3: hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank water wheels
Machine model, and thus introduce exciter model and dynamic load model；
The step 1 specifically includes the following steps:
Step 1.1: Fractional Order PID speed-regulating system is obtained by classical PID speed-regulating system, method particularly includes:
The differential expressions of classical PID speed-regulating system are as follows:
U (t)=kpe(t)+kiDe(t)+kdDe(t)；
Wherein, kp indicates scale parameter, and setting range is 0.5~20；Ki indicates integral parameter, setting range 0.05s-
1~10s-1, kd indicate differential parameter, and setting range is 0~5s；
Tri- adjustment parameters of kp, ki, kd are replaced with into transient state slip coefficient bt, damping time constant Td, acceleration respectively
Time constant Tn, specific:
The transmission function of classical PID speed-regulating system are as follows:
Wherein, bt is transient state slip coefficient, takes 0~1.0；Td is damping time constant, and setting range is 2s~20s, Tn
For G-time constant, setting range is that 0~2s, pc and P are respectively that the power of the assembling unit is given and the power of the assembling unit, ycDistinguish with y
For guide vane opening is given and guide vane degree, fc and f are respectively that frequency is given and unit frequency, Δ f are frequency difference, and Δ f' is through overfrequency
Dead zone efFrequency departure afterwards；
The differential expressions of above-mentioned classical PID speed-regulating system are transformed to Fractional Order PID speed-regulating system by Laplace
Differential expressions:
U (t)=kpe(t)+kiDαe(t)+kdDμe(t)； (4)
Wherein α, μ > 0, α are integral order, and μ is differential order；
The transmission function of Fractional Order PID speed-regulating system are as follows:
Step 1.2: the objective function of Fractional Order PID speed-regulating system is defined, method particularly includes:
It is allocated as using double fault difference-product as the objective function of the Fractional Order PID speed-regulating system described in step 1.1:
Wherein, e (t) indicates the deviation of reality output and desired output, and t is time, ISEIndicate square deviation integral；
Step 1.3: using the objective function based on Fractional Order PID speed-regulating system described in hybrid algorithm Optimization Steps 1.2,
Method particularly includes:
By kp、ki、kd, five parameters of α, μ form initial drosophila positions, so that drosophila is carried out optimizing by flavor concentration, utilize BP
The deep search characteristic of neural network is to kp、ki、kd, five parameter optimizations of α, μ solve, specifically includes the following steps:
Step 1.3.1: initialization drosophila population scale groupsize (400) and maximum number of iterations maxnum (400),
Drosophila population position (X is randomly generatedaxis, Yaxis), iteration step value R is defined as (0.85-1)；
Step 1.3.2: randomization drosophila population position and direction, according to drosophila population position and initial point distance DDistDetermine
Drosophila population flavor concentration value Si；
Step 1.3.3: the flavor concentration of drosophila individual is calculated, by drosophila population flavor concentration value SiFlavor concentration is substituted into sentence
Determine function FfunctionIn, and flavor concentration optimum individual is found from each drosophila group；
Retain optimal flavor concentration bbestsmellWith corresponding (Xi, Yi) position, drosophila group SsmellThe coordinate is flown to,
bbest indesIndicate optimal drosophila position；
Step 1.3.4: the drosophila position coordinates (X that step 1.3.3 is obtainedi, Yi) input BP neural network hidden layer
nnet (2)(k), input and output are defined；
Wherein, i=1,2 ..., Q define n, Q value, Z according to controlled device complexityj (2)For drosophila population after optimization
(Xi, Yi) position, wij (2)For hidden layer weighting coefficient, Zi(k)(2)Take activation functions Sigmoid function；
Step 1.3.5: BP neural network output layer n is definednet (3)(k), drosophila individual is updated, chooses E (k) as performance mistake
Poor index, while retaining the position coordinates (X of the most dense drosophila individual of tastei, Yi)；
Step 1.3.6: the performance indicator calculated by judging previous step exports optimal ginseng when reaching maximum number of iterations
Number kp,ki,kd, α, μ, otherwise the process of end is transferred to step 1.3.2, until while reaching maximum number of iterations exports optimized parameter
kp,ki,kd, α, μ terminate process.
The step 2 specifically includes the following steps:
Step 2.1: the mathematical model of the machinery hydraulic system of Turbine Governor System is established, following methods are specifically used:
The effect of machinery hydraulic system is transform electric and to zoom into the mechanical displacement letter with certain operating force
Number；Due to second level servomotor responsive time constant Ty1Much smaller than main servomotor responsive time constant Ty, usually by it in modeling
It is reduced to an inertial element, wherein y is machinery hydraulic system output signal, may also indicate that guide vane opening relative size, according to
Water-Turbine Engine Adaption characteristic joined frequency dead band and saturation limiting element, main control valve and servomotor linear segment transmission function
Are as follows:
Step 2.2: the mathematical model of the diversion system of Turbine Governor System is established, following methods are specifically used:
According to the difference of diversion penstock length, on simulation modeling, rigidity testing machine model is used in 700m or less, is greater than
Elastic water hammer is used when 700m, water flow waterpower change procedure is described by following equation in diversion system:
The equation of motion:
Wherein H is head, and Q is water flow, and S is waterpipe cross-sectional area, and t is the time, and g is acceleration of gravity；
Flow equation:
Wherein a is water flow acceleration；
N=0 and n=1 is taken to obtain rigidity testing machine G through Taylor series expansion water attack equation in pressure diversion pipelineA1With
Elastic water hammer GA2Transmission function:
Wherein TWFor rigid water attack time constant, Tr=2L/V is elastic water attack time constant, and L is pressure diversion conduit deferent
Road length, V are water flow velocity of wave, H0For head, Q0For flow, V0For water flow base speed.
The step 3 specifically includes the following steps:
Hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank hydraulic turbine models,
And thus introduce exciter model and dynamic load model；Method particularly includes:
Step 3.1: the first order modeling that traditional hydraulic turbine generator model uses are as follows:
Wherein, f is unit frequency, and p is unit input power difference, and Tn is unit set inertia time constant, general TnFor 3s
~12s, enFor unit static frequency self-regulation coefficient, enTake 0.5~2.0s；
Above-mentioned first order modeling can not reflect actual Parameters of Hydro-generator and parameters of excitation system, herein by
The Synchronous Machine Models that MATLAB/Simulink emulation platform establishes five rank state-space equations are equivalent to hydrogenerator mould
Type defines the basic parameter characteristic of the hydraulic turbine, it is contemplated that the dynamic characteristic in stator and rotor magnetic field and Damper Winding, model etc.
Imitating circuit indicates in rotor reference system (dq frame).
Wherein, stator voltage equation are as follows:
Wherein UdFor stator d shaft voltage, UqFor stator q shaft voltage, φdAnd φqIndicate dp axis magnetic linkage, idAnd iqFor equivalent dq
Electric current under coordinate system, raFor equivalent resistance, dq axis time transient internal voltage is E "dWith E "q, X "dAnd X "qFor dq subtranient reactance；
Rotor f winding, dq winding voltage equation and equation of rotor motion are as follows:
Wherein d axis and q axis time constant (all as unit of s), d axis transient state is opened a way (Tdo') or short-circuit (Td') time
Constant, d axis subtransient is opened a way (Tdo ") or short-circuit (Td ") time constant, and q axis transient state is opened a way (Tqo') or short-circuit (Tq') time
Constant (only limits round rotor), and q axis subtransient is opened a way (Tqo ") or short-circuit (Tq ") time constant.E'qFor transient internal voltage, EeFor
Dq winding electromotive force, X 'dFor d axis transient state reactance, XdAnd XqFor dq axis reactance, W is rotor machinery angular speed, TjFor generating set
Inertia time constant, TmFor prime mover machine torque,To act on the uneven torque on armature spindle.
The invention has the benefit that
Hydrogovernor simulation analysis mathematical model of the foundation based on Fractional Order PID speed-regulating system of the present invention,
Using MATLAB simulation modeling, classical PID speed-regulating system is improved on the basis of forefathers' research, according to example point
Analysis, it is established that Turbine Governor System and the comprehensive model of generator system parameters are able to reflect, for hydraulic turbine machine
Pool-size, frequency, rotor windings, stator winding, excitation winding, number of magnetic pole pairs, output voltage current conditions, excitation voltage feelings
Condition, load variations situation can be made a concrete analysis of, and temporary stable state when all kinds of power station actual motions can be largely emulated
Variation compensates for the defect of traditional hydraulic turbine modeling；In practical applications to the operating condition of practical water turbine set, load is faced
The variation of hydraulic turbine parameters has good reaction when fluctuation, provides safeguard for accident forecast with system safety operation.
Detailed description of the invention:
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is hydrogovernor simulation analysis mathematics of the foundation based on Fractional Order PID speed-regulating system of the present invention
Model, and utilize the method flow diagram of the hybrid algorithm optimization objective function based on Fractional Order PID speed-regulating system；
Fig. 3 is the target letter based on Fractional Order PID speed-regulating system described using hybrid algorithm optimization of the present invention
Several method flow diagrams；
Classical PID speed-regulating system and Fractional Order PID governor system control Comparative result schematic diagram when Fig. 4 is load disturbance；
FOA-PID speed-regulating system and BP-PID governor system control Comparative result schematic diagram when Fig. 5 is load disturbance；
BP-PID speed-regulating system and BPFOA-FOPID governor system control Comparative result schematic diagram when Fig. 6 is load disturbance；
Hydraulic turbine excitation voltage, active, rotation speed change when Fig. 7 loads switching；
Three-phase current changes when Fig. 8 is load investment；
Fig. 9 is that three-phase current changes when loading section is cut off；
Figure 10 is BPFOA-PID double objective optimal control Comparative result schematic diagram；
Figure 11 is the schematic diagram of the adaptive optimizing result of BPFOA-FOPID.
Specific embodiment:
A kind of comprehensive model of the hydraulic turbine of adaptive fractional rank PID speed-regulating system of the present invention is built as shown in Figure 1:
Mould method, which comprises the following steps:
Step 1: establishing the hydrogovernor simulation analysis mathematical model based on Fractional Order PID speed-regulating system, and utilize
The hybrid algorithm optimization objective function based on Fractional Order PID speed-regulating system；
Step 2: establishing the machinery hydraulic system and diversion system mathematical model of Turbine Governor System；
Step 3: hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank water wheels
Machine model, and thus introduce exciter model and dynamic load model；
It is as shown in Figure 2: the step 1 specifically includes the following steps:
Step 1.1: Fractional Order PID speed-regulating system is obtained by classical PID speed-regulating system, method particularly includes:
The differential expressions of classical PID speed-regulating system are as follows:
U (t)=kpe(t)+kiDe(t)+kdDe(t)； (1)
Wherein, kp indicates scale parameter, and setting range is 0.5~20；Ki indicates integral parameter, setting range 0.05s-
1~10s-1；Kd indicates differential parameter, and setting range is 0~5s；
Then by kp、ki、kdThree adjustment parameters replace with transient state slip coefficient b respectivelyt, damping time constant Td, accelerate
Spend time constant Tn, it is specific:
The transmission function of classical PID speed-regulating system are as follows:
Wherein, bt is transient state slip coefficient, takes 0~1.0；Td is damping time constant, and setting range is 2s~20s；Tn
For G-time constant, setting range is 0~2s；Pc and P is respectively that the power of the assembling unit is given and the power of the assembling unit is (for power tune
Section mode)；ycIt is respectively that guide vane opening gives and guide vane degree with y；Frequency modulation mode and aperture regulation mode；Fc and f difference
It is given and unit (or power grid) frequency for frequency；Δ f is frequency difference；Δ f' is by frequency dead band efFrequency departure afterwards；
It is that Fractional Order PID adjusts the speed after Laplace is converted by the differential expressions (formula (1)) of classical PID speed-regulating system
The differential expressions of system are as follows:
U (t)=kpe(t)+kiDαe(t)+kdDμe(t)； (4)
Wherein α, μ > 0, α are integral order, and μ is differential order, and when the value of α and μ is all 1, then formula (4) becomes classical
PID speed-regulating system (formula (1)), the introducing of fractional calculus make traditional PID adjust more application and flexibility；
The transmission function of Fractional Order PID speed-regulating system are as follows:
Step 1.2: the objective function of Fractional Order PID speed-regulating system is defined, method particularly includes:
In order to optimize the speed adjusting performance of controlled hydraulic turbine system, it is allocated as using double fault difference-product as the score described in step 1.1
The objective function of rank PID speed-regulating system:
Wherein, e (t) indicates the deviation of reality output and desired output, and t is time, ISEIndicate square deviation integral, value
It is smaller, illustrate that the response speed of system is faster；ITAEIt is that time and square deviation integrate, value is smaller, and reflection system stability is got over
It is good；
It is as shown in Figure 3: step 1.3: using described in hybrid algorithm Optimization Steps 1.2 based on Fractional Order PID speed-regulating system
Objective function, method particularly includes:
By kp、ki、kd, five parameters of α, μ form initial drosophila positions, so that drosophila is carried out optimizing by flavor concentration, utilize BP
The deep search characteristic of neural network is to kp、ki、kd, five parameter optimizations of α, μ solve, specifically includes the following steps:
Step 1.3.1: initialization drosophila population scale groupsize (400) and maximum number of iterations maxnum (400),
Drosophila population position (X is randomly generatedaxis, Yaxis), iteration step value R is defined as (0.85-1)；
Step 1.3.2: randomization drosophila population position and direction, according to drosophila population position and initial point distance DDistDetermine
Drosophila population flavor concentration value Si；
Step 1.3.3: the flavor concentration of drosophila individual is calculated, by drosophila population flavor concentration value SiFlavor concentration is substituted into sentence
Determine function FfunctionIn, and flavor concentration optimum individual is found from each drosophila group；
Retain optimal flavor concentration bbestsmellWith corresponding (Xi, Yi) position, drosophila group SsmellThe coordinate is flown to,
bbest indesIndicate optimal drosophila position；
Step 1.3.4: the drosophila position coordinates (X that step 1.3.3 is obtainedi, Yi) input BP neural network hidden layer
nnet (2)(k), input and output are defined；
Wherein, i=1,2 ..., Q define n, Q value, Z according to controlled device complexityj (2)For drosophila population after optimization
(Xi, Yi) position, wij (2)For hidden layer weighting coefficient, Zi(k)(2)Take activation functions Sigmoid function；
Step 1.3.5: BP neural network output layer n is definednet (3)(k), drosophila individual is updated, chooses E (k) as performance mistake
Poor index, while retaining the position coordinates (X of the most dense drosophila individual of tastei, Yi)；
Step 1.3.6: the performance indicator calculated by judging previous step exports optimal ginseng when reaching maximum number of iterations
Number kp,ki,kd, α, μ, otherwise the process of end is transferred to step 1.3.2, until while reaching maximum number of iterations exports optimized parameter
kp,ki,kd, α, μ terminate process.
The step 2 specifically includes the following steps:
Step 2.1: the mathematical model of the machinery hydraulic system of Turbine Governor System is established, following methods are specifically used:
The effect of machinery hydraulic system is transform electric and to zoom into the mechanical displacement letter with certain operating force
Number；Due to second level servomotor responsive time constant Ty1Much smaller than main servomotor responsive time constant Ty, usually by it in modeling
It is reduced to an inertial element, wherein y is machinery hydraulic system output signal, may also indicate that guide vane opening relative size, according to
Water-Turbine Engine Adaption characteristic joined frequency dead band and saturation limiting element, main control valve and servomotor linear segment transmission function
Are as follows:
Step 2.2: the mathematical model of the diversion system of Turbine Governor System is established, following methods are specifically used:
The mathematical model of the diversion system of Turbine Governor System is established, and according to the difference of diversion penstock length, is imitated
Rigidity testing machine model generally is used in 700m or less in true modeling, when greater than 700m for precision the considerations of generally uses elastic water
Hammer, water flow waterpower change procedure is described by following equation in diversion system:
The equation of motion:
Wherein H is head, and Q is water flow, and S is waterpipe cross-sectional area, and t is the time, and g is acceleration of gravity；
Flow equation:
Wherein a is water flow acceleration；
N=0 and n=1 is taken to obtain rigidity testing machine G through Taylor series expansion water attack equation in pressure diversion pipelineA1With
Elastic water hammer GA2Transmission function:
Wherein TWFor rigid water attack time constant, Tr=2L/V is elastic water attack time constant, and L is pressure diversion conduit deferent
Road length, V are water flow velocity of wave, H0For head, Q0For flow, V0For water flow base speed.
The step 3 specifically includes the following steps:
Hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank hydraulic turbine models,
And thus introduce exciter model and dynamic load model；
Method particularly includes: traditional hydraulic turbine generator model is usually using first order modeling:
F is unit frequency；P is unit input power difference；Tn is that (dynamic frequency is special for unit (load) inertia time constant
Property time constant), general Tn be 3s~12s；En is unit (load) static frequency self-regulation (characteristic) coefficient, with load characteristic
Different and different, generally taking en is 0.5~2.0s；
Above-mentioned first order modeling can not reflect actual Parameters of Hydro-generator and parameters of excitation system, herein by
The Synchronous Machine Models that MATLAB/Simulink emulation platform establishes five rank state-space equations are equivalent to hydrogenerator mould
Type defines the basic parameter characteristic of the hydraulic turbine, it is contemplated that the dynamic characteristic in stator and rotor magnetic field and Damper Winding, model etc.
Imitating circuit indicates in rotor reference system (dq frame).
Wherein, stator voltage equation are as follows:
Wherein UdFor stator d shaft voltage, UqFor stator q shaft voltage, φdAnd φqIndicate dp axis magnetic linkage, idAnd iqFor equivalent dq
Electric current under coordinate system, raFor equivalent resistance, dq axis time transient internal voltage is E "dWith E "q, X "dWith X "qFor dq subtranient reactance；
Rotor f winding, dq winding voltage equation and equation of rotor motion are as follows:
Wherein d axis and q axis time constant (all as unit of s), d axis transient state is opened a way (Tdo') or short-circuit (Td') time
Constant, d axis subtransient is opened a way (Tdo ") or short-circuit (Td ") time constant, and q axis transient state is opened a way (Tqo') or short-circuit (Tq') time
Constant (only limits round rotor), and q axis subtransient is opened a way (Tqo ") or short-circuit (Tq ") time constant.E'qFor transient internal voltage, EeFor
Dq winding electromotive force, X 'dFor d axis transient state reactance, XdAnd XqFor dq axis reactance, W is rotor machinery angular speed, TjFor generating set
Inertia time constant, TmFor prime mover machine torque,To act on the uneven torque on armature spindle；
Excitation system is using IEEE typical DC exciter；When power system load increases suddenly, subtracts, to generator
It carries out automatic field forcing, subtract magnetic, to improve the stability of electric system.
The comprehensive model modelling approach of a kind of hydraulic turbine based on Fractional Order PID speed-regulating system proposed by the present invention, according to
Instance analysis is tested using MATLAB platform emulation, and Turbine Governor System Transfer Parameters (being shown in Table 1) is taken to be used as simulation example,
Due to the rotary speed property of water turbine set, the dead zone of revolving speed ± 0.001 (pu) is provided with to speed-regulating system, wherein hydraulic turbine generator
Partial parameters are shown in Table 2.
1 Turbine Governor System parameter of table
Wherein EqyIt is flow deviation relative value to the carry-over factor of servomotor deviation of stroke relative value, EqhFor flow deviation
Carry-over factor of the relative value to head deviation relative value, EyIt is opposite to servomotor deviation of stroke for hydraulic turbine torque deviation relative value
The carry-over factor of value, EhCarry-over factor of the hydraulic turbine torque deviation relative value to head deviation relative value.
2 hydraulic turbine generator parameter of table
Wherein PnFor rated power, VnFor rated line voltage, FnFor rated frequency, P is number of magnetic pole pairs, and H is inertia coeffeicent, d
Axis synchronous reactance xd, transient reactance Xd' and subtransient reactance Xd ", q axis synchronous reactance Xq, transient reactance Xq'(are only when circle turns
Son) and subtransient reactance Xq ", it is finally leakage reactance X1, WrefFor rated speed, VrefRated excitation voltage.
Compared from Tables 1 and 2: the present invention carries out Turbine Governor System on the basis of current research state
It improves, it is as shown in Figure 4-Figure 6 to compare current mainstream speed-regulating system speed regulation result；Loaded portion according to hydraulic turbine operation characteristic according to
With 40% and 75% two kind of load operating condition under investment, excision situation carry out simulation analysis, every simulation result of the hydraulic turbine is such as
Shown in Fig. 7-Fig. 9.
Compared to classical Turbine Governor System, a kind of water wheels based on Fractional Order PID speed-regulating system proposed by the present invention
The comprehensive model modelling approach of machine, based on Fractional Order PID speed-regulating system increasing due to controllable parameter, in regulating time and overshoot
It measures two aspects and is superior to classical Turbine Governor System；Using the Adaptive PID Control of FOA algorithm and BP neural network algorithm
Governing time, the overshoot of comparison PID and FOPID control significantly reduce, but above four kinds of control all there is system to shake number
More defects；Traditional mode of speed regulation at least shakes 4 system above and just starts to tend towards stability, using mixing drosophila algorithm (BP-
FOA) the Bi-objective FOPID optimal controller controlled further reduces regulating time and overshoot while drastically reducing shake
Swing number, it is thus only necessary to which just steadily, specific speed regulation optimization is as shown in Figure 10 for 2 subsystems.
It is as shown in figure 11: by FOA algorithm, BP neural network algorithm and herein the BP-FOA algorithm that designs carry out from
Optimizing Parameter analysis is adapted to, due to the high iteration step value of setting, the global optimizing ability of drosophila algorithm enhances, but the number of iterations
More, optimal time is long；The optimizing ability of BP neural network algorithm is strong, fast convergence rate, but easily falls into local optimum, in face of negative
There is wild effect when lotus fluctuation operation；BP-FOA algorithm utilizes BP neural network on the basis of global optimizing ability is strong
Fast convergence further reduces adaptive adjustment time, improves 24.58%, shows in face of load fluctuation stronger suitable
Ying Xingyu stability.
It is adjusted it can be seen that controlling FOPID adjuster by mixing drosophila algorithm Bi-objective in optimization by table 3, the comparison of table 4
There is obvious advantage in terms of fast time and control overshoot, is reduced on the basis of current mainstream BP neural network control algolithm
46.86% overshoot δ, shortens 36.59% regulating time Ts, wherein TrFor rise time, TpFor time to peak.
Different controller index simulation result comparisons under 3 load disturbance of table
Different controller optimization parameter comparisons under 4 load disturbance of table
It tests hydraulic turbine model initial strip 40% through BPFOA-FOPID biobjective scheduling to load, in 30s investment again 35%
Load, 35% load of 60s excision.It is stable when in the switching load of 30s and 60s, the fluctuation of speed is in ± 2%, 3.9s, it mentions significantly
High system stabilizing power；Due to the DC exciter of use, generator is used to encourage and subtract by force in load increase and decrease and is encouraged, substantially
It is able to reflect exciter operating condition；Generator exports power output and the output basic held stationary of current conditions in load fluctuation,
Embody good output performance.
This modeling analysis compared on the basis of establishing comprehensive hydraulic turbine model PID, FOPID, FOA algorithm with
And BP neural network controls four kinds of mainstream single goal control methods, proposes hybrid algorithm BPFOA-FOPID two-objective programming control
Mode processed tests it when in face of load fluctuation, to the quick-action and stability of Turbine Governor System control.Simulation result
Show that hydraulic turbine regulating time and overshoot significantly reduce under BPFOA-FOPID Bi-objective control mode, compare conventional control
Mode embodies stronger robustness and adaptability.
This patent utilizes MATLAB simulation modeling, is changed on the basis of forefathers' research to Turbine Governor System
Into according to instance analysis, it is established that it is able to reflect Turbine Governor System and the comprehensive model of generator system parameters,
For water turbine units capacity, frequency, rotor windings, stator winding, excitation winding, number of magnetic pole pairs, output voltage current conditions,
Excitation voltage situation, load variations situation can be made a concrete analysis of, and all kinds of power station actual motions can be largely emulated
When the variation of temporary stable state, compensate for the defect of traditional hydraulic turbine modeling.In practical applications to the operation feelings of practical water turbine set
Condition, the variation of hydraulic turbine parameters has good reaction when in face of load fluctuation, mentions for accident forecast with system safety operation
For ensureing.
Claims (4)
1. a kind of comprehensive model modelling approach of the hydraulic turbine of adaptive fractional rank PID speed-regulating system, which is characterized in that including with
Lower step:
Step 1: establishing the hydrogovernor simulation analysis mathematical model based on Fractional Order PID speed-regulating system, and utilize mixing
Objective function based on Fractional Order PID speed-regulating system described in algorithm optimization；
Step 2: establishing the machinery hydraulic system and diversion system mathematical model of Turbine Governor System；
Step 3: hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank hydraulic turbine moulds
Type, and thus introduce exciter model and dynamic load model.
2. a kind of comprehensive model modeling side of the hydraulic turbine of adaptive fractional rank PID speed-regulating system according to claim 1
Method, which is characterized in that the step 1 specifically includes the following steps:
Step 1.1: Fractional Order PID speed-regulating system is obtained by classical PID speed-regulating system, method particularly includes:
The differential expressions of classical PID speed-regulating system are as follows:
U (t)=kpe(t)+kiDe(t)+kdDe(t)；
Wherein, kp indicates scale parameter, and setting range is 0.5~20；Ki indicate integral parameter, setting range be 0.05s-1~
10s-1, kd indicate differential parameter, and setting range is 0~5s；
By kp、ki、kdThree adjustment parameters replace with transient state slip coefficient b respectivelyt, damping time constant Td, the acceleration time it is normal
Number Tn, it is specific:
The transmission function of classical PID speed-regulating system are as follows:
Wherein, bt is transient state slip coefficient, takes 0~1.0；Td is damping time constant, and setting range is 2s~20s, and Tn is to add
Velocity Time constant, setting range are that 0~2s, pc and P are respectively that the power of the assembling unit is given and the power of the assembling unit, ycIt is respectively to lead with y
Leaf aperture gives and guide vane degree, and fc and f are respectively that frequency is given and unit frequency, Δ f are frequency difference, and Δ f' is by frequency dead band
efFrequency departure afterwards；
The differential expressions of above-mentioned classical PID speed-regulating system are transformed to the differential of Fractional Order PID speed-regulating system by Laplace
Expression formula:
U (t)=kpe(t)+kiDαe(t)+kdDμe(t)； (4)
Wherein α, μ > 0, α are integral order, and μ is differential order；
The transmission function of Fractional Order PID speed-regulating system are as follows:
Step 1.2: the objective function of Fractional Order PID speed-regulating system is defined, method particularly includes:
It is allocated as using double fault difference-product as the objective function of the Fractional Order PID speed-regulating system described in step 1.1:
Wherein, e (t) indicates the deviation of reality output and desired output, and t is time, ISEIndicate square deviation integral；
Step 1.3: using the objective function based on Fractional Order PID speed-regulating system described in hybrid algorithm Optimization Steps 1.2, specifically
Method are as follows:
By kp、ki、kd, five parameters of α, μ form initial drosophila positions, so that drosophila is carried out optimizing by flavor concentration, utilize BP nerve
The deep search characteristic of network is to kp、ki、kd, five parameter optimizations of α, μ solve, specifically includes the following steps:
Step 1.3.1: initialization drosophila population scale groupsize (400) and maximum number of iterations maxnum (400), at random
Generate drosophila population position (Xaxis, Yaxis), iteration step value R is defined as (0.85-1)；
Step 1.3.2: randomization drosophila population position and direction, according to drosophila population position and initial point distance DDistDetermine drosophila
Population flavor concentration value Si；
Step 1.3.3: the flavor concentration of drosophila individual is calculated, by drosophila population flavor concentration value SiIt substitutes into flavor concentration and determines letter
Number FfunctionIn, and flavor concentration optimum individual is found from each drosophila group；
Retain optimal flavor concentration bbestsmellWith corresponding (Xi, Yi) position, drosophila group SsmellThe coordinate is flown to,
bbestindesIndicate optimal drosophila position；
Step 1.3.4: the drosophila position coordinates (X that step 1.3.3 is obtainedi, Yi) input BP neural network hidden layer nnet (2)
(k), input and output are defined；
Wherein, i=1,2 ..., Q define n, Q value, Z according to controlled device complexityj (2)For drosophila population (X after optimizationi, Yi)
Position, wij (2)For hidden layer weighting coefficient, Zi(k)(2)Take activation functions Sigmoid function；
Step 1.3.5: BP neural network output layer n is definednet (3)(k), drosophila individual is updated, E (k) is chosen and refers to for performance error
Mark, while retaining the position coordinates (X of the most dense drosophila individual of tastei, Yi)；
Step 1.3.6: the performance indicator calculated by judging previous step exports optimized parameter k when reaching maximum number of iterationsp,
ki,kd, α, μ, otherwise the process of end is transferred to step 1.3.2, until exporting optimized parameter k when reaching maximum number of iterationsp,ki,
kd, α, μ terminate process.
3. a kind of comprehensive model modeling side of the hydraulic turbine of adaptive fractional rank PID speed-regulating system according to claim 1
Method, which is characterized in that the step 2 specifically includes the following steps:
Step 2.1: the mathematical model of the machinery hydraulic system of Turbine Governor System is established, following methods are specifically used:
The effect of machinery hydraulic system is transform electric and to zoom into the mechanical displacement signal with certain operating force；By
In second level servomotor responsive time constant Ty1Much smaller than main servomotor responsive time constant Ty, usually it is reduced in modeling
One inertial element, wherein y is machinery hydraulic system output signal, may also indicate that guide vane opening relative size, according to the hydraulic turbine
Control characteristic joined frequency dead band and saturation limiting element, main control valve and servomotor linear segment transmission function are as follows:
Step 2.2: the mathematical model of the diversion system of Turbine Governor System is established, following methods are specifically used:
According to the difference of diversion penstock length, on simulation modeling, rigidity testing machine model is used in 700m or less, is greater than 700m
Shi Caiyong elastic water hammer, water flow waterpower change procedure is described by following equation in diversion system:
The equation of motion:
Wherein H is head, and Q is water flow, and S is waterpipe cross-sectional area, and t is the time, and g is acceleration of gravity；
Flow equation:
Wherein a is water flow acceleration；
N=0 and n=1 is taken to obtain rigidity testing machine G through Taylor series expansion water attack equation in pressure diversion pipelineA1And elasticity
Water hammer GA2Transmission function:
Wherein TWFor rigid water attack time constant, Tr=2L/V is elastic water attack time constant, and L is pressure diversion conduit deferent road length
Degree, V are water flow velocity of wave, H0For head, Q0For flow, V0For water flow base speed.
4. a kind of comprehensive model modeling side of the hydraulic turbine of adaptive fractional rank PID speed-regulating system according to claim 1
Method, which is characterized in that the step 3 specifically includes the following steps:
Hydraulic turbine generator model is established, by traditional single order hydraulic turbine generator model extension to 5 rank hydraulic turbine models, and by
This introduces exciter model and dynamic load model；Method particularly includes:
Step 3.1: the first order modeling that traditional hydraulic turbine generator model uses are as follows:
Wherein, f is unit frequency, and p is unit input power difference, and Tn is unit set inertia time constant, general TnFor 3s~12s,
enFor unit static frequency self-regulation coefficient, enTake 0.5~2.0s；
Above-mentioned first order modeling can not reflect actual Parameters of Hydro-generator and parameters of excitation system, herein by
The Synchronous Machine Models that MATLAB/Simulink emulation platform establishes five rank state-space equations are equivalent to hydrogenerator mould
Type defines the basic parameter characteristic of the hydraulic turbine, it is contemplated that the dynamic characteristic in stator and rotor magnetic field and Damper Winding, model etc.
Imitating circuit indicates in rotor reference system (dq frame).
Wherein, stator voltage equation are as follows:
Wherein UdFor stator d shaft voltage, UqFor stator q shaft voltage, φdAnd φqIndicate dp axis magnetic linkage, idAnd iqFor equivalent dq coordinate
It is lower electric current, raFor equivalent resistance, dq axis time transient internal voltage is E "dWith E "q, X "dAnd X "qFor dq subtranient reactance；
Rotor f winding, dq winding voltage equation and equation of rotor motion are as follows:
Wherein d axis and q axis time constant (all as unit of s), d axis transient state is opened a way (Tdo') or short-circuit (Td') time constant,
D axis subtransient is opened a way (Tdo ") or short-circuit (Td ") time constant, and q axis transient state is opened a way (Tqo') or short-circuit (Tq') time constant
(only limiting round rotor), q axis subtransient is opened a way (Tqo ") or short-circuit (Tq ") time constant.E'qFor transient internal voltage, EeFor dq around
Group electromotive force, X'dFor d axis transient state reactance, XdAnd XqFor dq axis reactance, W is rotor machinery angular speed, TjFor the used of generating set
Property time constant, TmFor prime mover machine torque,To act on the uneven torque on armature spindle.
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