CN106372296B - A kind of hydraulic turbine multimachine differential equation calculation method with common conduit - Google Patents
A kind of hydraulic turbine multimachine differential equation calculation method with common conduit Download PDFInfo
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Abstract
The hydraulic turbine multimachine differential equation calculation method with common conduit that the present invention relates to a kind of, belongs to the hydraulic turbine and Hydraulic Power Unit stability analysis and control technology field.This method calculates the Seepage-stress coupling of share pipe with bifurcated pipe dynamic parameter, it establishes using bifurcated pipe as the single machine single tube elasticity water attack Differential Equation Model of core, the method calculated simultaneously using multimachine, calculate the temporal variations of pipe end hydraulic turbine head and flow, this method calculates the Seepage-stress coupling of share pipe using bifurcated pipe dynamic parameter, and the complete Seepage-stress coupling transient state Differential Equation Model of mode construction is calculated by multimachine, solve consistency problem of the Seepage-stress coupling in differential equation iterative calculation；Simulation calculation shows this method computational accuracy with higher.
Description
Technical field
The hydraulic turbine multimachine differential equation calculation method with common conduit that the present invention relates to a kind of, belongs to the hydraulic turbine and water
The analysis of power set steady and control technology field.
Background technique
Commonplace diversion and power mode is in run-of-river power station: being drawn by sharing main steel pipe (abbreviation share pipe)
Before water to Power Plant, then using multitube fork diversion to each Hydraulic Power Unit, referred to as with the multi-computer system of share pipe.
The variation of any fork pipe end hydraulic turbine discharge can all cause the hydraulic disturbance in share pipe, thus to the machine of other bifurcated pipes
Group generates disturbance, i.e. hydraulic coupling action.
Hydraulic Power System has an impact the effect of the hydraulic turbine mainly with the head and flow of hydraulic turbine inlet end face.It is various
Type, differing complexity Hydraulic Power System dynamic is converted into the variation of hydraulic turbine entrance head and flow, realizes
With the connection of the hydraulic turbine.Therefore, the Seepage-stress coupling system of share pipe is also handled using identical thinking.
Currently, the description to Hydraulic Power System mainly uses transmission function form.When studying Hydraulic Power Unit control strategy, pass
Delivery function form tool there is limitations that application is also inconvenient.For single machine single-main distribution, Hydraulic Power System differential side has been developed
The diversified forms such as journey model, generalized Hamiltonian model.Also there is research for the decoupling problem of share pipe system Seepage-stress coupling, including
Seepage-stress coupling matrix form based on pipeline transmission function form, being reduced to single machine single tube, to add Seepage-stress coupling item etc. a variety of
Form.Under the conditions of rigid water attack, waterpower dynamic simplification is first-order system, it is convenient to be converted into differential equation computation model.
And under elastic water attack, Seepage-stress coupling part still retains transmission function form, in the hydraulic turbine and Hydraulic Power Unit nonlinear analysis
It is inconvenient with being applied in control design case.
Since the hydraulic turbine is approximately stiffener, the algebraical sum differential equation of hydraulic turbine Calculating Torque during Rotary is in description water wheels machine power
When square transient state be it is of equal value, dynamic is actually to be determined by Hydraulic Power System dynamic.Therefore, in share pipe multi-computer system, water
The computational problem of power coupled system is most critical in the research for be involved in the problems, such as hydraulic turbine power.
Document " share pipeline section waterpower decoupling and non-linear hydraulic turbine model, Proceedings of the CSEE, 2012,32
(14): in pp103-108 ", the hydraulic coupling action in common conduit still uses transmission function form to describe, it is existing not
Foot mainly has two o'clock: first is that transmission function is not directly applicable the iterative calculation of the differential equation, this form is only from theory
On disclose the mechanism of action of Seepage-stress coupling；Second is that in Seepage-stress coupling Decoupling Analysis, using equivalent parameters approximation and to friction
Loss has carried out simplified processing, it is possible to cause big error.
In view of the above-mentioned problems, the present invention calculates the Seepage-stress coupling of share pipe using bifurcated pipe dynamic parameter, and based on multimachine
The complete Seepage-stress coupling transient state Differential Equation Model of mode construction is calculated, solves Seepage-stress coupling in differential equation iterative calculation
Consistency problem.Simulation calculation shows this method computational accuracy with higher.
Summary of the invention
For the above-mentioned problems of the prior art and deficiency, it is more that the present invention provides a kind of hydraulic turbine with common conduit
Machine differential equation calculation method.This method calculates the Seepage-stress coupling of share pipe using bifurcated pipe dynamic parameter, and calculates by multimachine
The complete Seepage-stress coupling transient state Differential Equation Model of mode construction solves one of Seepage-stress coupling in differential equation iterative calculation
Cause property problem；Simulation calculation shows that this method computational accuracy with higher, this method are achieved through the following technical solutions.
The hydraulic turbine multimachine differential equation calculation method with common conduit calculates share pipe with bifurcated pipe dynamic parameter
Seepage-stress coupling, establish using bifurcated pipe as the single machine single tube elasticity water attack Differential Equation Model of core, calculated simultaneously using multimachine
Method, calculate pipe end hydraulic turbine head and flow temporal variations, comprising the following steps:
Step 1: Hydraulic Power System characteristic parameter is calculated, is specifically calculated using following formula:
The known basic arrangement parameter of power station Hydraulic Power System: duct length L, round tube diameter D, coefficient of roughness N, gravity accelerate
Spend g, water-hammer wave speed α.Hydraulic turbine basic parameter: rated head Hr, metered flow Qr, no load discharge Qnl.It carries out as follows
It calculates:
Waterpower is surged the normalized value of impedance:
Pipeline flex time constant:
The friction loss factor of pipeline:
The conversion of hydraulic turbine characteristic parameter is relative value: hydraulic turbine head relative value hr=1, hydraulic turbine discharge relative value qr=
1, hydraulic turbine function relative value pr=1, hydraulic turbine no load discharge relative value qnl=Qnl/Qr。
Wherein: Zn(i)That the waterpower of the i-th segment pipe is surged impedance normalization value (dimensionless), g be acceleration of gravity (rice/
Second2), α(i)It is the water-hammer wave speed (meter per second) of the i-th segment pipe, A(i)It is the cross-sectional area (rice of the i-th segment pipe2), QrIt is the hydraulic turbine
Metered flow (rice3/ the second), HrIt is hydraulic turbine rated head (rice), Te(i)It is the flex time constant (second) of the i-th segment pipe, L(i)
It is the length (rice) of the i-th segment pipe, fp(i)It is the friction loss factor of the pipe of circular section of the i-th segment pipe, N(i)It is i-th section
The coefficient of roughness of pipeline, D(i)It is the round tube diameter (rice) of the i-th segment pipe.
In above-mentioned parameter definition, subscript " (i) " indicates the parameter of the i-th road fork pipelines, such as: Zn(i)It is the i-th segment pipe
Waterpower surge impedance normalization value.If subscript uses " T ", then it represents that be that share pipe corresponds to parameter, such as ZnTIndicate share pipe
The waterpower in road is surged impedance normalization value.
Step 2: the multimachine Differential Equation Model including Seepage-stress coupling is established:
Share pipe exit transient head hsRelative value:
hqT=-ZnTΔqT tanh(TeTs) (6)
I-th section of fork hydraulic turbine transient head:
hq(i)=-Zn(i)Δq(i)tanh(Te(i)s) (8)
Share pipe flow is equal to the sum of each bifurcated pipe flow:
Wherein, ZnTIt is that the waterpower of share pipe is surged the normalized value of impedance, Zn(i)It is that the waterpower of i-th section of bifurcated pipe is surged impedance
Normalized value, the n in summation sign ∑ indicates n sections of bifurcated pipes, TeTIt is the flex time constant (second) of share pipe, Te(i)It is
The flex time constant (second) of i-th section of bifurcated pipe, hsIt is the head relative value in share pipe exit, ht(i)It is the water wheels of No. i-th bifurcated pipe
Machine head relative value, hq(i)It is dynamic head relative value caused by No. i-th bifurcated pipe changes in flow rate, hqTIt is that share pipe changes in flow rate is drawn
The dynamic head relative value risen；qTIt is share pipe flow relative value, Δ qT=qT-qT0It is share pipe changes in flow rate relative value, qTIt is
Share pipe flow instantaneous value relative value, qT0It is share pipe flow initial value relative value, q(i)It is i-th section of bifurcated pipe flow relative value, Δ
q(i)=q(i)-q(i0)It is i-th section of bifurcated pipe changes in flow rate relative value, q(i)It is i-th section of bifurcated pipe flow instantaneous value relative value, q(i0)
It is i-th section of bifurcated pipe flow initial value relative value, fpTIt is share pipe friction loss factor, fp(i)It is i-th section of bifurcated pipe friction loss
Coefficient, s are Laplace transform operator notations.
Using flow continuity equation (9), the dynamic head of formula (6) can be analyzed to the Dynamic Water that each bifurcated pipe changes in flow rate generates
The sum of head, it may be assumed that
Wherein hq(i)TWhen being defined as changes in flow rate in i-th section of bifurcated pipe, the caused dynamic head variation in sharing pipeline section
Relative value.
Then the hydraulic turbine transient head formula (7) of i-th section of bifurcated pipe can further be write as:
According to orifice outflow principle, hydraulic turbine discharge are as follows:
(12) are substituted into equation (11), arrangement obtains:
By the tanh (T in equation (8)e(i)S) it is unfolded, omits high-order term, then (8) formula becomes:
It enables:
Then have:
R (s) is the Laplace transformation function of intermediate function r (t).According to Laplace transformation initial-value theorem:The 1-3 rank initial value for knowing r (t) is 0.Laplace inverse transformation is taken to (15), (16):
Wherein, q(i)0It is i-th section of bifurcated pipe flow q(i)Initial value relative value.
It enables: x1(i)=r (t)；x2(i)=r'(t)；x3(i)=r " (t), then (18) formula can be write as state equation form:
From (18), formula can also be written as follow form:
Above-mentioned equation is converted to from transmission function, variable x1(i)、x2(i)、x3(i)It is deviation relative value form.According to
Equalization point condition analysis, each initial guess are 0, therefore, form having the same when being indicated using relative value form.In subsequent portion
Part, each variable is all made of the expression of relative value form.
Formula (17) is rewritten into:
To (21) derivation, and (20) are utilized, obtained:
The corresponding guide vanes of water turbine governing equation of i-th section of bifurcated pipe are as follows:
(13) formula of utilization substitutes into above-mentioned (19) and (22), eliminates variable hq(i)。
Take x4(i)=q(i), x5(i)=y(i), then the differential side of No. i-th hydraulic turbine is constituted by equation (19), (22), (23)
Journey model is as follows:
Wherein, share pipe Seepage-stress coupling item is calculated using following formula:
U in above formula(i)It is the input control of i-th hydraulic turbine；x1(i)、x2(i)、x3(i)、x4(i)、x5(i)Indicate i-th water wheels
The state variable of machine, waterpower are surged the normalized value Z of impedancen(i), pipeline flex time constant Te(i)With the friction loss system of pipeline
Number fp(i)It is obtained according to step 1；x4(i)=q(i), q(i)It is i-th hydraulic turbine discharge relative value, i.e. q(i)=Q(i)/Qr, Q(i)It is
I-th hydraulic turbine discharge, rice3/ second, QrIt is rated discharge of hydraulic turbine, rice3/ the second；x5(i)=y(i), y(i)It is i-th water wheels owner
Servomotor is displaced relative value, i.e. y(i)=Y(i)/Ymax, Y(i)It is i-th owner's servomotor displacement, millimeter, YmaxIt is main servomotor position
Maximum value is moved, centimetre；y0(i)It is i-th owner's servomotor displacement initial value relative value, i.e. y0(i)=Y0(i)/Ymax, Y0(i)It is i-th
Owner's servomotor is displaced initial value, millimeter, yr(i)It is that main servomotor is displaced relative value, i.e. y under i-th machine declared working conditionr(i)=
Yr(i)/Ymax, Yr(i)It is the guide vane opening under i-th machine declared working condition, millimeter；Ty(i)It is that i-th unit main servomotor time is normal
Number, second；h0=H0/HrIt is power station hydrostatic head relative value, H0It is power station hydrostatic head, rice, HrIt is hydraulic turbine rated head, rice；
qT=QT/QrIt is the flow relative value of share pipe, QTIt is share pipe flow, rice3/ the second；fpTIt is the friction loss factor of share pipe；
hq(i)TIt is the i-th road bifurcated pipe changes in flow rate caused change of water level relative value in share pipe, n is bifurcated pipe under a share pipe
Quantity；
Step 3: the hydraulic turbine multimachine differential equation with common conduit calculates
Formula (24) is the multi-computer system differential equation, and multimachine refers to the hydraulic turbine system of shared aqueduct, such as a Guan Sanji
System, multimachine numerical value calculate three turbine-generator units that need to be calculated simultaneously under share pipe.Various convenient values can be used to calculate
Method is calculated, such as runge kutta method.Given input u(i), variable x is calculated using differential equation group4(i)(flow),
x5(i)The variation of (main servomotor displacement).Iterative calculation time step Δ t should be less than most short bifurcated pipe surge wave time of return, Δ
t≤2L(i)/α(i)。
After the temporal variations for obtaining state variable, q(i)=x4(i), y(i)=x5(i), calculated i-th in transient process using following formula
Platform hydraulic turbine head ht(i)Variation:
Obtaining hydraulic turbine head ht(i)With flow x4(i)Afterwards, the variation that algebraic equation calculates hydraulic turbine power can be used:
pm=Atht(q-qnl)
Wherein: qnlFor hydraulic turbine no load discharge relative value, i.e. qnl=Qnl/Qr；pmIt is that hydraulic turbine output mechanical power is opposite
Value, i.e. pm=Pm/Pr, PmIt is hydraulic turbine power (kilowatt)；AtFor coefficient, the A under declared working conditiont=1/ (1-qnl)；htPass through public affairs
Formula (26) is calculated；Q is that flow is equal to x4(i)。
The beneficial effects of the present invention are:
1, it is the dynamic of waterpower caused by each bifurcated pipe changes in flow rate by share pipe dynamic Decomposition, reflects share pipe waterpower coupling
The substantive characteristics of conjunction provides theoretical basis for the calculating of multimachine Seepage-stress coupling.
2, the dynamic variable of Hydraulic Power System indicates that composition is non-linear differential equations model using relative value form, fits
For the analysis of large disturbances and microvariations, versatility is enhanced.
3, waterpower dynamic conversion be relative value form the differential equation after, convenient for excitation controller, speed setting controller,
Generator and network system Differential Equation Model are directly connected to, and study the non-linear control strategy design of controller, and analysis
The stability of Hydraulic Power Unit, unit and power grid.Using convenient.
Detailed description of the invention
Fig. 1 is 1 transient process of the embodiment of the present invention, two hydraulic turbine change of water level figures；
Fig. 2 is 1 transient process of the embodiment of the present invention, two water turbine units changed power figures.
Specific embodiment
With reference to the accompanying drawings and detailed description, the invention will be further described.
Embodiment 1
The hydraulic turbine multimachine differential equation calculation method with common conduit calculates share pipe with bifurcated pipe dynamic parameter
Seepage-stress coupling, establish using bifurcated pipe as the single machine single tube elasticity water attack Differential Equation Model of core, calculated simultaneously using multimachine
Method, calculate pipe end hydraulic turbine head and flow temporal variations, comprising the following steps:
Step 1: calculating Hydraulic Power System characteristic parameter, calculates waterpower and surges the normalized value Z of impedancen(i), pipeline elasticity when
Between constant Te(i)With the friction loss factor f of pipelinep(i), wherein Zn(i)It is that the waterpower of the i-th segment pipe is surged impedance normalization value,
Dimensionless；Te(i)It is the flex time constant of the i-th segment pipe, second；fp(i)It is the friction damage of the pipe of circular section of the i-th segment pipe
Lose coefficient；
Step 2: the multimachine Differential Equation Model including Seepage-stress coupling is established:
Differential Equation Model are as follows:Wherein
U in above formula(i)It is the input control of i-th hydraulic turbine；x2(i)、x3(i)、x4(i)、x5(i)Indicate i-th hydraulic turbine
State variable, waterpower are surged the normalized value Z of impedancen(i), pipeline flex time constant Te(i)With the friction loss factor of pipeline
fp(i)It is obtained according to step 1；x4(i)=q(i), q(i)It is i-th hydraulic turbine discharge relative value, i.e. q(i)=Q(i)/Qr, Q(i)It is i-th
Platform hydraulic turbine discharge, rice3/ second, QrIt is rated discharge of hydraulic turbine, rice3/ the second；x5(i)=y(i), y(i)It is i-th water wheels owner's relay
Device is displaced relative value, i.e. y(i)=Y(i)/Ymax, Y(i)It is i-th owner's servomotor displacement, millimeter, YmaxIt is that main servomotor is displaced most
Big value, centimetre；y0(i)It is i-th owner's servomotor displacement initial value relative value, i.e. y0(i)=Y0(i)/Ymax, Y0(i)It is i-th owner
Servomotor is displaced initial value, millimeter, yr(i)It is that main servomotor is displaced relative value, i.e. y under i-th machine declared working conditionr(i)=Yr(i)/
Ymax, Yr(i)It is the guide vane opening under i-th machine declared working condition, millimeter；Ty(i)It is i-th unit main servomotor time constant, second；
h0=H0/HrIt is power station hydrostatic head relative value, H0It is power station hydrostatic head, rice, HrIt is hydraulic turbine rated head, rice；qT=QT/
QrIt is the flow relative value of share pipe, QTIt is share pipe flow, rice3/ the second；fpTIt is the friction loss factor of share pipe；hq(i)TIt is
I-th road bifurcated pipe changes in flow rate caused change of water level relative value in share pipe, n are the numbers of bifurcated pipe under a share pipe
Amount；
Step 3: it calculates:
Given input u(i), iterative calculation time step Δ t should be less than most short bifurcated pipe surge wave time of return, i.e. and Δ t≤
2L(i)/α(i), wherein L(i)For the length of the i-th segment pipe, rice, α(i)For the water-hammer wave speed of the i-th segment pipe, meter per second, using multimachine
Variable x is calculated in Differential Equation Model4(i)And x5(i)；
After the temporal variations for obtaining state variable, q(i)=x4(i), y(i)=x5(i), calculated i-th in transient process using following formula
Platform hydraulic turbine head ht(i)Variation:
This example is the emulation carried out with the data of some hydropower station, it is therefore an objective to which that examines this patent proposition has common conduit
Hydraulic turbine multimachine differential equation calculation method it is whether effective.For this purpose, calculating Hydraulic Power System parameter in the case where controlling u Stepped Impedance Resonators
Variation.
Diversion Hydraulic Power System in power station is two Bifurcation System of share pipe, and fork pipe end configures 2 identical Hydraulic Power Units
With identical Excitation and governor control device.
2 Hydraulic Power Units characteristic having the same and parameter are as follows:
Hr=312 (rice), Qr=53.5 (rice3/ the second), Pr=156 (megawatts), Qnl=6.42 (rice3/ the second), H0=313.9
(rice).
Take the water-hammer wave speed of each steel pipe identical, i.e. α(i)=1000 (meter per seconds), the coefficient of roughness of each steel pipe is identical, i.e. N(i)
=0.014.
Conversion is relative value: hr=1, qr=1, pr=1, qnl=0.12, h0=1.0061, main servomotor parameter: yr=
1.0, Ty=0.5 (second).
Governor is using typical parallel connection PID structure, control parameter KP=5.0, KD=2.5, KI=1.5, bp=
0.04。
Excitation controller is controlled using idle PI, KP1=1, KI1=1.5.
Step 1: Hydraulic Power System characteristic parameter is calculated
Hydraulic Power System characteristic parameter is calculated according to formula (1), (2), (3), it may be assumed that
Waterpower is surged the normalized value of impedance:
Pipeline flex time constant:
The friction loss factor of pipeline:
Take gravity acceleration g=9.81 (rice2/ the second), round steel pipe cross-sectional area A(i)=π D2 (i)/4。
Calculated result is listed in Table 1 below.
1 Hydraulic Power System characteristic parameter of table
| L(i)(m) | D(i)(m) | Zn(i) | Te(i)(s) | fp(i) | |
| Share pipe | 517 | 4.6 | 1.0518 | 0.5170 | 0.003471 |
| Bifurcated pipe 1 | 50 | 2.98 | 2.5062 | 0.0500 | 0.004554 |
| Bifurcated pipe 2 | 50 | 2.98 | 2.5062 | 0.0500 | 0.004554 |
Step 2: the multimachine Differential Equation Model including Seepage-stress coupling is established
Shown in the Seepage-stress coupling differential equation such as formula (24) established.
This example is a Guan Erji system, n=2.
Step 3: the hydraulic turbine multimachine differential equation with common conduit calculates
Two initial operating conditions of unit: No. 1 power of the assembling unit pt(1)=1.0, No. 2 power of the assembling unit pt(2)=1.0.
No. 1 machine power is constant, and No. 2 machine adjustment power are pt(2)=0.5.
The most short fork length of tube L of this example(1)=50m, α(1)=1000m/s takes iterative calculation time step Δ t=
0.001s meets condition Δ t≤2L(i)/α(i)。
Using second order runge kutta method, hydraulic turbine discharge and main relay is can be obtained in the Differential Equation Model of calculating formula (24)
The variation of device displacement.
Wherein, share pipe Seepage-stress coupling item is calculated using formula (25), it may be assumed that
After the temporal variations for obtaining state variable, q(i)=x4(i), y(i)=x5(i), hydraulic turbine water is calculated using formula (26)
The variation of head:
After obtaining hydraulic turbine head and flow, the variation that algebraic equation calculates hydraulic turbine power can be used:
pm=Atht(q-qnl)
Wherein: qnlFor hydraulic turbine no load discharge relative value, i.e. qnl=Qnl/Qr；pmIt is that hydraulic turbine output mechanical power is opposite
Value, i.e. pm=Pm/Pr, PmIt is hydraulic turbine power (kilowatt).
The actual calculation gives the variation such as attached drawing 1, the power of the assembling unit of two hydraulic turbine heads in power adjustment procedure
Variation such as attached drawing 2.Measured result under attached drawing calculated result operating condition identical as power station, hydraulic turbine head and power of the assembling unit variation
Trend be consistent, transient process data error is small.Illustrate that algorithm proposed by the present invention is effectively, to be able to satisfy engineering calculation
It is required that.
In conjunction with attached drawing, the embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
Put that various changes can be made.
Claims (1)
1. a kind of hydraulic turbine multimachine differential equation calculation method with common conduit, it is characterised in that: joined with bifurcated pipe dynamic
Number calculates the Seepage-stress coupling of share pipe, establishes using bifurcated pipe as the single machine single tube elasticity water attack Differential Equation Model of core, uses
The method that multimachine calculates simultaneously calculates the temporal variations of pipe end hydraulic turbine head and flow, comprising the following steps:
Step 1: calculating Hydraulic Power System characteristic parameter, calculates waterpower and surges the normalized value Z of impedancen(i), pipeline flex time it is normal
Number Te(i)With the friction loss factor f of pipelinep(i), wherein Zn(i)It is that the waterpower of the i-th segment pipe is surged impedance normalization value, it is immeasurable
Guiding principle；Te(i)It is the flex time constant of the i-th segment pipe, second；fp(i)It is the friction loss system of the pipe of circular section of the i-th segment pipe
Number；
Step 2: the multimachine Differential Equation Model including Seepage-stress coupling is established:
Differential Equation Model are as follows:Wherein
U in above formula(i)It is the input control of i-th hydraulic turbine；x2(i)、x3(i)、x4(i)、x5(i)Indicate that the state of i-th hydraulic turbine becomes
Amount, waterpower are surged the normalized value Z of impedancen(i), pipeline flex time constant Te(i)With the friction loss factor f of pipelinep(i)According to
Step 1 obtains；x4(i)=q(i), q(i)It is i-th hydraulic turbine discharge relative value, i.e. q(i)=Q(i)/Qr, Q(i)It is i-th hydraulic turbine
Flow, rice3/ second, QrIt is rated discharge of hydraulic turbine, rice3/ the second；x5(i)=y(i), y(i)It is i-th hydraulic turbine main servomotor displacement phase
To value, i.e. y(i)=Y(i)/Ymax, Y(i)It is i-th owner's servomotor displacement, millimeter, YmaxIt is main servomotor displacement maximum value, li
Rice；y0(i)It is i-th owner's servomotor displacement initial value relative value, i.e. y0(i)=Y0(i)/Ymax, Y0(i)It is i-th owner's servomotor
It is displaced initial value, millimeter, yr(i)It is that main servomotor is displaced relative value, i.e. y under i-th machine declared working conditionr(i)=Yr(i)/Ymax, Yr(i)
It is the guide vane opening under i-th machine declared working condition, millimeter；Ty(i)It is i-th unit main servomotor time constant, second；h0=H0/
HrIt is power station hydrostatic head relative value, H0It is power station hydrostatic head, rice, HrIt is hydraulic turbine rated head, rice；qT=QT/QrIt is altogether
With the flow relative value of pipe, QTIt is share pipe flow, rice3/ the second；fpTIt is the friction loss factor of share pipe；hq(i)TIt is the i-th road point
Bifurcated pipe changes in flow rate caused change of water level relative value in share pipe, n are the quantity of bifurcated pipe under a share pipe；
Step 3: it calculates:
Given input u(i), iterative calculation time step Δ t should be less than most short bifurcated pipe surge wave time of return, i.e. and Δ t≤
2L(i)/α(i), wherein L(i)For the length of the i-th segment pipe, rice, α(i)For the water-hammer wave speed of the i-th segment pipe, meter per second, using multimachine
Variable x is calculated in Differential Equation Model4(i)And x5(i)；
After the temporal variations for obtaining state variable, q(i)=x4(i), y(i)=x5(i), i-th water in transient process is calculated using following formula
Turbine head ht(i)Variation:
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| CN112651180B (en) * | 2020-12-31 | 2022-06-14 | 昆明理工大学 | Differential equation calculation method for one-pipe multi-machine hydroelectric generating set adjusting system |
| CN112947076B (en) * | 2021-01-31 | 2024-02-02 | 昆明理工大学 | Design method of cooperative controller of one-pipe multi-machine hydroelectric generating set |
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