CN115929534B - Method for inhibiting pressure pulsation induced active oscillation based on Hamiltonian model - Google Patents
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Abstract
The invention relates to a method for inhibiting pressure pulsation induced active oscillation based on a Hamiltonian model, and belongs to the technical field of stability analysis and control of water turbines. Introducing the pressure pulsation characteristic into a Hamiltonian model of the hydroelectric generating set, adopting a Hamiltonian structure correction theory to design an equivalent control law, and inhibiting the active oscillation amplitude by controlling input damping; taking the power fluctuation of the water turbine induced by the draft tube pressure fluctuation head as additional excitation to obtain a Hamiltonian model containing the influence of the draft tube pressure fluctuation; and modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, deriving a control law, and controlling the output of the hydroelectric generating set by controlling injection damping. The Hamiltonian additional control unit is added on the basis of the traditional hydroelectric generating set control structure to form a new control structure with mechanical and electrical part coupling association, active oscillation is restrained by controlling injection damping, the output of the hydroelectric generating set is controlled accordingly, and the active oscillation amplitude of the hydroelectric generating set can be restrained effectively.
Description
Technical Field
The invention relates to a method for inhibiting pressure pulsation induced active oscillation based on a Hamiltonian model, and belongs to the technical field of stability analysis and control of water turbines.
Background
The problem of active oscillation of the unit is caused by pressure pulsation of a draft tube of the mixed-flow water turbine, and the problem is one of limiting factors that the unit cannot operate in a vibration area. However, in a dual-carbon background, in a power system with a high new energy source and a high duty ratio, the hydroelectric generating set is used as an adjusting power source, in order to increase the active adjusting range of the hydroelectric generating set, it may be unavoidable to expand the operating area to the vibration area, and the problem of suppressing active oscillation in the partial load area becomes one of key technologies to be solved urgently.
The problem that the active fluctuation of the unit, which occurs when the mixed-flow turbine runs under partial load, affects the running stability of the unit is reported in the literature at home and abroad. The early solution is mainly researched from the aspect of optimizing the design of the water turbine and the draft tube structure and reducing the pressure pulsation angle of the draft tube. Although some effective results are achieved in terms of structural design of the water turbine and draft tube, and engineering measures, this problem is not well solved. In recent years, according to the active oscillation characteristics of a partial load area, the problem of suppressing the active oscillation is researched from the aspect of control strategy design, so that the active oscillation amplitude can be reduced to a certain extent, and the running stability of the hydroelectric generating set in the partial load area is improved. The control strategy is used as an auxiliary means for expanding the running area of the water turbine, and attention is paid to all parties.
From the dynamics perspective, the active oscillation problem of the partial load region operation is solved, and the core problem to be solved is to promote the active oscillation damping of the unit system and inhibit the oscillation amplitude. In the current control theory, a control design theory which aims at improving the damping of a system is definitely a generalized Hamiltonian control theory with stronger systematicness.
CN101915203a discloses a damping injection control method for improving the power angle oscillation of a hydroelectric generating set, based on structural analysis of a damping matrix of a hamilton model of the hydroelectric generating set, self-correlation factors of the power angle of the set are increased, and a variable structure control strategy is provided to realize control of the set through applicability analysis of an equivalent control law. However, the internal parameter association mechanism provided by the hamiltonian model is not fully utilized in the research.
CN103779870a discloses a hydropower island frequency suppression method taking the water pressure pulsation condition of a draft tube into consideration, which simulates the actual pulsation condition of the draft tube through a resonance function, and establishes a water turbine model taking the water pressure pulsation of the draft tube into consideration and the elastic water column into consideration, thereby obtaining a high-voltage direct-current transmission end hydropower island frequency oscillation waveform caused by the water pressure pulsation of the draft tube, and suppressing island transmission end frequency oscillation caused by the water pressure pulsation of the draft tube through a newly designed direct-current frequency limiter.
Disclosure of Invention
The invention aims to provide a Hamiltonian model-based method for inhibiting pressure pulsation from inducing active oscillation, which solves the problem that the control effect is poor due to the fact that the internal parameter association is not considered in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme: a method for suppressing pressure pulsation induced active oscillation based on a Hamiltonian model is characterized by comprising the following steps of: introducing the pressure pulsation characteristic into a Hamiltonian model of the hydroelectric generating set, adopting a Hamiltonian structure correction theory to design an equivalent control law, and inhibiting the active oscillation amplitude by controlling input damping; the method specifically comprises the following steps:
step one: taking the power fluctuation of the water turbine induced by the draft tube pressure fluctuation head as additional excitation to obtain a Hamiltonian model containing the influence of the draft tube pressure fluctuation;
step two: and modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, deriving a control law, and controlling the output of the hydroelectric generating set by controlling injection damping.
The further technical proposal is that the specific steps of the step one are as follows
The induced turbine mechanical power fluctuation Δp of draft tube pressure pulsation is:
Δp＝A t h pre (q-q nl )sin(2πf pre t)
wherein A is t Is the coefficient, h pre Is the per-unit value of the amplitude of the pressure pulsation head of the draft tube, q and q nl The per unit value of the flow of the water turbine and the no-load flow is respectively;
taking the water turbine power fluctuation deltap induced by the draft tube pressure pulsation head as additional excitation, the Hamiltonian model containing the draft tube pressure pulsation influence is obtained as follows:
take x= [ x ] 1 x 2 x 3 x 4 x 5 ] T ＝[qyδω 1 E′ q ]The Hamiltonian of the unit is as follows:
wherein T is y Is the time constant of the servomotor, q nl Is no-load flow, omega is the angular speed of the unit; a is that t Is the gain coefficient of the water turbine; u (U) s Is the bus voltage, X d ′ ∑ Is the d-axis transient reactance, X q∑ Is q-axis synchronous reactance, X f Is the reactance of the exciting winding, X ad Is the d-axis armature reaction reactance;
the hamilton equation is:
wherein algebraic equations are:
f (x) is the input stimulus, which is generated by the draft tube pressure pulsation head; wherein, the up (x) dissipation realizes the formed control, and u (x) is the input control of the main servomotor; t (T) w Is the water flow inertia time constant(s); t (T) j Is a unit inertia time constant(s); t (T) y Is a servomotor time constant(s); q, q nl Is the flow and no-load flow (pu); f (f) p Is the pipeline loss coefficient; h is a 0 Is the hydrostatic head (pu) of the water turbine; y, y 0 Is the opening degree of the guide vane and the opening degree initial value (pu); omega B = 314.16 is the unit angular velocity base value (rad/s); omega 1 =ω -1, ω is unit angular velocity (pu); a is that t Is the gain coefficient of the water turbine; e (E) q ' is the q-axis transient electromotive force (pu); delta is the generator power angle (rad); d is the equivalent damping coefficient of the unit; t (T) d0 ' is d-axis open circuit transient time constant(s), U s Is the bus voltage (pu), X d ′ ∑ Is d-axis transient reactance (pu), X q∑ Is q-axis synchronous reactance (pu), X f Is the exciting winding reactance (pu), X ad Is the d-axis armature reaction reactance (pu); p is p m Is the turbine power (pu);
the further technical proposal is that the specific steps of the second step are as follows
The structure correction matrix is selected as follows: j (J) a (x)＝0，R a (x) Is that
The control law after the structure correction is obtained is as follows:
and controlling the output of the hydroelectric generating set according to the control law.
A further technical proposal is that r is as follows 25 The value of the (c) is as follows: actually measuring the active oscillation amplitude under the pressure pulsation of the draft tube under a given working condition, calculating a damping factor under the corresponding amplitude, fitting a curve with the abscissa as the damping factor and the ordinate as the active oscillation amplitude, and taking the damping factor corresponding to the lowest point of the curve as r 25 Is a value of (2).
The beneficial effects of the invention are as follows:
1. the Hamiltonian model containing the influence of the pressure pulsation of the draft tube is obtained by taking the power fluctuation of the water turbine induced by the pressure pulsation head of the draft tube as additional excitation; modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, deriving a control law, and utilizing control injection damping to obtain a control method of coupling association between mechanical and electrical parts, so as to control the output of the hydroelectric generating set, and effectively inhibit the active oscillation amplitude of the generating set.
2. The control algorithm provided by the discovery essentially increases the damping of the hydroelectric generating set, is applied to inhibiting the active oscillation of a partial load area of the hydroelectric generating set, and can play a role in inhibiting the active fluctuation of the hydroelectric generating set in response to the running regulation of the generating set such as the starting of the generating set to pass through the vibration area and the active regulation of the generating set.
Drawings
Fig. 1 is a hamilton control structure of a water motor unit according to embodiment 1 of the present invention.
Fig. 2 shows the hydraulic turbine head and mechanical power fluctuations of example 2 of the present invention.
Fig. 3 is a comparison of active power oscillations of the generator of example 2 of the present invention.
Fig. 4 is a graph showing the amplitude of the active oscillation as a function of the damping factor for example 2 of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and detailed description.
Example 1
And the Hamiltonian structure is utilized to correct a control design theory, and the effective oscillation amplitude of the unit, which is induced by the pressure pulsation of the operating draft tube in the partial load area of the hydroelectric generating set, is restrained by controlling the equivalent injection damping, so that the operating range of the unit is expanded. The method specifically comprises the following steps:
step one: and constructing a Hamiltonian model of the hydroelectric generating set containing the influence of the pressure pulsation by using the mechanical power fluctuation induced by the pressure pulsation as additional input excitation.
According to the periodic characteristics of the draft tube pressure pulsation during partial load operation, the water turbine head is modified into the following form in combination with the definition of the IEEEWorkinginggroup about the water turbine head:
h＝h t +h pre sin(2πf pre t)(1)
in the formula, h t Is the relative value of the water turbine head, h, defined by IEEEWorkinginggroup pre Is the relative value of the amplitude of the pressure pulsation head of the draft tube, h is the relative value of the water turbine head after the pressure pulsation head is counted, f pre Is the frequency of the pressure pulsations (Hz).
Under the definition above, the turbine power is:
p is the power of the turbineRelative value, A t Is a coefficient, q nl The relative values of the flow and the idle flow of the water turbine are respectively p t Is the relative value of the turbine power defined by IEEEWorkingGroup, Δp is the turbine power oscillation produced by the head of pressure pulsation, Δp=a t h pre (q-q nl )sin(2πf pre t)。
The power fluctuation deltap of the water turbine induced by the pressure pulsation head of the draft tube is used as additional excitation, and the power fluctuation deltap is used as an additional excitation input item to be kept unchanged in Hamiltonian transformation, so that the original form of Hamiltonian of the water turbine is unchanged, and only the excitation input item is added, so that a new Hamiltonian model is obtained as follows.
Take x= [ x ] 1 x 2 x 3 x 4 x 5 ] T ＝[qyδω 1 E′ q ]The Hamiltonian of the unit is as follows:
the hamilton equation is:
wherein,, u (x) is the main servomotor input control; Δf (x) is the input stimulus; t (T) w Is the water flow inertia time constant(s); t (T) j Is a unit inertia time constant(s); t (T) y Is a servomotor time constant(s); f (f) p Is the pipeline loss coefficient; h is a 0 Is the relative value of the static head of the water turbine; y, y 0 The relative value between the opening degree of the guide vane and the initial value of the opening degree; omega B 314.16 is the unit angular velocity base value (rad/s), ω 1 =ω -1, ω is the unit angular velocity relative value; e (E) q ' is the relative value of the q-axis transient electromotive force; delta is the generator power angle (rad); d is the equivalent damping coefficient of the unit; t (T) d0 ' is the d-axis open circuit transient time constant(s); u (U) s Is the relative value of bus voltage; x'. d∑ Is the d-axis transient reactance relative value; x is X q∑ Is the q-axis synchronous reactance relative value; x is X f Is the relative reactance value of the exciting winding; x is X ad Is the relative value of the d-axis armature reaction reactance.
Step two: modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, deriving a control law, and utilizing control injection damping;
let the Hamiltonian system form:
state variable x e R n Control u E R m ,m<n, H (x) is the energy function of the system, the structural matrix J (x) is antisymmetric, the damping matrix R (x) is a semi-positive symmetric matrix, and g (x) is an input channel matrix.
Constant structure correction J for a given system a And R is a The correction matrix is J d (x)＝J(x)+J a ，R d (x)＝R(x)+R a Satisfy J d (x)＝-J d (x) T ，R d (x)＝R d (x) T . If the input matrix g is full of rank, then (g T g) Reversible, hamiltonian equivalent control after structure correction is as follows:
u(x)＝v * +α(x) (6)
v * is at a given equilibrium point x * Is to satisfy:
alpha (x) is the additional control resulting from the structural modification, calculated using the following formula:
combining with a Hamiltonian model of the hydroelectric generating set, selecting a structural correction matrix as follows: j (J) a (x)＝0，R a (x) Is that
Substituting formula (8) gives additional control as follows:
unfolding the hamiltonian partial derivative and combining the hamiltonian partial derivative with the formula (6) to obtain:
in the above equation the generator state parameter crosses the turbine state parameter in the additional control part, i.e. a coupling between the mechanical and electrical parts is established.
The control law given by the formula (11) is followed to obtain the hamilton control structure of the hydroelectric generating set as shown in fig. 1.
Step three: the r is 25 The value of the (c) is as follows: actually measuring the active oscillation amplitude under the pressure pulsation of the draft tube under a given working condition, calculating a damping factor under the corresponding amplitude, fitting a curve with the abscissa as the damping factor and the ordinate as the active oscillation amplitude, and taking the damping factor corresponding to the lowest point of the curve as r 25 Is a value of (2).
Example 2
Calculation with data of a certain hydropower station.
Because the hydro-generator set object system is a single-unit single-pipe system, the complex water diversion system is converted into the single-unit single-pipe water diversion system by taking the change of the water head and the flow at the inlet of the water turbine as the core according to the arrangement form of the hydro-power system of the hydropower station.
The main parameters of the system are as follows: pipe length l=517 (meters), pipe diameter d=3.3 (meters), rated flow Q r =53.5 (cubic meters/second), nominal head H r 312 (meters), water hammer wave velocity α=1100 (meters/second), main servomotor time constant T y =0.5 (seconds).
Step one: the mechanical power fluctuation induced by the pressure pulsation is used as additional input excitation, and a Hamiltonian model of the hydroelectric generating set containing the influence of the pressure pulsation is constructed;
according to the derivation of the first invention, the induced mechanical power fluctuation of the water turbine, which is obtained by the draft tube pressure pulsation, is as follows:
Δp＝A t h pre (q-q nl )sin(2πf pre t)(12)
the additional excitation is taken as the power fluctuation deltap of the water turbine induced by the draft tube pressure pulsation head, and the Hamiltonian model containing the influence of the draft tube pressure pulsation is obtained as follows.
Take x= [ x ] 1 x 2 x 3 x 4 x 5 ] T ＝[qyδω 1 E′ q ]The Hamiltonian of the unit is as follows:
the hamilton equation is:
step two: modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, deriving a control law, and utilizing control injection damping;
according to the physical meaning represented by Hamiltonian damping matrix elements, and combining the purpose of damping injection, selecting a structural correction matrix as follows: j (J) a (x)＝0，R a (x) Is that
Substituting formula (8) gives additional control as follows:
unfolding the hamiltonian partial derivative, and combining the hamiltonian partial derivative with the control law (6) to obtain a control law after structure correction, wherein the control law is as follows:
the control law given by the formula (11) is followed to obtain the hamilton control structure of the hydroelectric generating set as shown in fig. 1.
Step three: and establishing a simulation calculation model by adopting actual parameters of the hydroelectric generating set, and determining the optimal value of the Hamiltonian damping matrix correction element r25 by adopting a simulation calculation method given that the actual measured draft tube pressure pulsation amplitude head and pulsation frequency are measured under a certain working condition.
Specifically, as shown in fig. 4, the active oscillation amplitude under the pressure pulsation of the draft tube is actually measured under a given working condition, and the damping factor under the corresponding amplitude is calculated, the damping factor is fitted into a curve with the abscissa as the damping factor and the ordinate as the active oscillation amplitude, the damping factor corresponding to the lowest point of the curve is taken as the value of r25, and r is the value of 25 ＝1.3。
And constructing a hydroelectric generating set operation simulation system with certain integrity. The speed regulator adopts a typical parallel PID structure, and the control parameters are as follows: k (K) P ＝5.0，K D ＝2.5，K I ＝1.5，b p =0.04; the excitation control system adopts PID control of the terminal voltage, K P1 ＝10，K I1 ＝5，K D1 =0.001. Inertial time constant T of unit j = 8.999 (seconds), generator equivalent damping coefficient d=5.
And substituting the hydroelectric generating set parameters into the formula (14) to carry out numerical calculation. In numerical calculation, the Hamiltonian model of the formula (14) is discretized into an iterative calculation format according to a second-order Dragon-Gregorian tower method, programming calculation is carried out in Matlab, and the iterative calculation time interval is 0.001(s).
Simulation working conditions: the hydroelectric generating set operates at 50% rated load, i.e. pe=0.5 (pu), draft tube pressure pulsation characteristics: the pressure pulsation amplitude is h pre =0.05 (pu), pressure pulsation frequency f pre ＝0.9(Hz)。
Fig. 2 is a graph of pressure pulsation induced hydraulic turbine head and mechanical power fluctuations. FIG. 3 compares the active output oscillations of the generator with or without Hamiltonian injection control. Obviously, the Hamiltonian additional damping injection control provided by the invention can obviously reduce the active oscillation amplitude of the generator.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (2)
1. A method for suppressing pressure pulsation induced active oscillation based on a Hamiltonian model is characterized by comprising the following steps of: introducing the pressure pulsation characteristic into a Hamiltonian model of the hydroelectric generating set, adopting a Hamiltonian structure correction theory to design an equivalent control law, and inhibiting the active oscillation amplitude by controlling input damping; the method specifically comprises the following steps:
step one: taking the power fluctuation of the water turbine induced by the draft tube pressure fluctuation head as additional excitation to obtain a Hamiltonian model containing the influence of the draft tube pressure fluctuation;
step two: modifying Hamiltonian damping matrix elements, adopting a Hamiltonian structure modification design theory, leading out a control law, and controlling the output of the hydroelectric generating set by controlling injection damping;
the specific steps of the first step are that
The induced turbine mechanical power fluctuation Δp of draft tube pressure pulsation is:
Δp＝A t h pre (q-q nl )sin(2πf pre t)
wherein A is t Is the coefficient, h pre Is the per-unit value of the amplitude of the pressure pulsation head of the draft tube, q and q nl The per unit value of the flow of the water turbine and the no-load flow is respectively;
taking the water turbine power fluctuation deltap induced by the draft tube pressure pulsation head as additional excitation, the Hamiltonian model containing the draft tube pressure pulsation influence is obtained as follows:
take x= [ x ] 1 x 2 x 3 x 4 x 5 ] T ＝[q y δ ω 1 E′ q ]The Hamiltonian of the unit is as follows:
wherein T is y Is the time constant of the servomotor, q nl Is no-load flow, omega is the angular speed of the unit; a is that t Is the gain coefficient of the water turbine; u (U) s Is the bus voltage, X' d∑ Is the d-axis transient reactance, X q∑ Is q-axis synchronous reactance, X f Is the reactance of the exciting winding, X ad Is the d-axis armature reaction reactance;
the hamilton equation is:
wherein algebraic equations are:
f (x) is the input stimulus, which is generated by the draft tube pressure pulsation head; wherein, the up (x) dissipation realizes the formed control, and u (x) is the input control of the main servomotor; t (T) w Is the water flow inertia time constant(s); t (T) j Is a unit inertia time constant(s); t (T) y Is a servomotor time constant(s); q, q nl Is the flow and no-load flow (pu); f (f) p Is the pipeline loss coefficient; h is a 0 Is the hydrostatic head (pu) of the water turbine; y, y 0 Is the opening degree of the guide vane and the opening degree initial value (pu); omega B Is the basic value (rad/s) of the angular velocity of the unit; omega 1 =ω -1, ω is unit angular velocity (pu); a is that t Is the gain coefficient of the water turbine; e (E) q ' is the q-axis transient electromotive force (pu); delta is the generator power angle (rad); d is the equivalent damping coefficient of the unit; t (T) d0 ' is d-axis open circuit transient time constant(s), U s Is the bus voltage (pu), X d ′ ∑ Is d-axis transient reactance (pu), X q∑ Is q-axis synchronous reactance (pu), X f Is the exciting winding reactance (pu), X ad Is the d-axis armature reaction reactance (pu); p is p m Is the turbine power (pu);
the specific steps of the second step are as follows
The constant structure correction matrix is selected as follows: j (J) a (x)＝0，R a (x) Is that
The control law after the structure correction is obtained is as follows:
and controlling the output of the hydroelectric generating set according to the control law.
2. The method for suppressing pressure pulsation induced active oscillations based on hamiltonian model according to claim 1, wherein: the r is 25 The value of the (c) is as follows: actually measuring the active oscillation amplitude under the pressure pulsation of the draft tube under a given working condition, calculating a damping factor under the corresponding amplitude, fitting a curve with the abscissa as the damping factor and the ordinate as the active oscillation amplitude, and taking the damping factor corresponding to the lowest point of the curve as r 25 Is a value of (2).
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| CN101915203A (en) * | 2010-08-06 | 2010-12-15 | 昆明理工大学 | Damping injection control method for improving power angle oscillation of water turbine generator set |
| CN113110023A (en) * | 2021-04-02 | 2021-07-13 | 昆明理工大学 | Structure correction control method based on diesel engine Hamilton model |
| CN115296330A (en) * | 2022-06-17 | 2022-11-04 | 昆明理工大学 | Hamilton damping cooperative control method in isolated network mode |
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| CN101915203A (en) * | 2010-08-06 | 2010-12-15 | 昆明理工大学 | Damping injection control method for improving power angle oscillation of water turbine generator set |
| CN113110023A (en) * | 2021-04-02 | 2021-07-13 | 昆明理工大学 | Structure correction control method based on diesel engine Hamilton model |
| CN115296330A (en) * | 2022-06-17 | 2022-11-04 | 昆明理工大学 | Hamilton damping cooperative control method in isolated network mode |
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| 曾云 ; 张立翔 ; 钱晶 ; 郭亚昆 ; .哈密顿结构修正的控制设计方法及其应用.电机与控制学报.2014,(第03期),第93-100页. * |
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