CN115929534B - Method for inhibiting pressure pulsation induced active oscillation based on Hamiltonian model - Google Patents

Abstract

The invention relates to a method for suppressing active power oscillation induced by pressure pulsation based on a Hamiltonian model, and belongs to the technical field of hydraulic turbine stability analysis and control. The pressure fluctuation characteristics are introduced into the Hamiltonian model of the hydroelectric unit, and the equivalent control law is designed by using the Hamiltonian structure modification theory. By controlling the input damping, the active power oscillation amplitude is suppressed; the turbine power fluctuation induced by the pressure fluctuation head of the draft tube is used as an additional excitation, and the obtained The Hamiltonian model including the influence of draft tube pressure fluctuations; the elements of the Hamiltonian damping matrix are modified, and the Hamiltonian structural modification design theory is used to derive the control law, and the output of the hydroelectric unit is controlled by controlling the injection damping. On the basis of the control structure of the traditional hydroelectric generating set, an additional Hamiltonian control unit is added to form a new control structure that obtains the coupling relationship between the mechanical and electrical parts. The active power oscillation is suppressed by controlling the injection damping, and the output of the hydroelectric generating set is controlled accordingly, which can effectively Suppress the active power oscillation amplitude of the unit.

Description

A method of suppressing active power oscillation induced by pressure pulsation based on Hamiltonian model

technical field

The invention relates to a method for suppressing active power oscillation induced by pressure pulsation based on a Hamiltonian model, and belongs to the technical field of hydraulic turbine stability analysis and control.

Background technique

The pressure pulsation of the draft pipe of the Francis turbine induces the active power oscillation of the unit, which is one of the limiting factors for the unit not to operate in the vibration area. However, under the background of dual carbon, in the power system with a high proportion of new energy, the hydroelectric unit is used as a regulating power source. In order to increase the active power regulation range of the hydroelectric unit, it may be inevitable to extend the operating area to the vibration area. The problem of oscillation suppression has become one of the key technologies to be solved urgently.

The fluctuation of unit active power in part-load operation of Francis turbine affects the stability of unit operation, which has been reported at home and abroad. The early solutions were mainly studied from the perspective of optimizing the design of the turbine and draft tube structure and reducing the pressure fluctuation of the draft tube. Although some effective results have been obtained from the structural design of turbines and draft tubes, as well as engineering measures, this problem has not been well resolved. In recent years, according to the characteristics of active power oscillation in partial load area, research on the problem of suppressing active power oscillation from the perspective of control strategy design can reduce the amplitude of active power oscillation to a certain extent and improve the stability of hydropower unit operation in partial load area. The use of control strategies as an auxiliary means for the expansion of the turbine's operating area has attracted attention from all sides.

From the perspective of dynamics, the core problem to be solved is to improve the active power oscillation damping of the unit system and suppress the oscillation amplitude for the problem of active power oscillation in the partial load area. Among the current control theories, the control design theory that clearly aims to improve the system damping is a generalized Hamiltonian control theory with strong systemicity.

CN101915203A discloses a damping injection control method for improving the power angle oscillation of a hydro-generator set. Based on the structural analysis of the damping matrix of the Hamiltonian model of a hydro-generator set, the self-correlation factor of the power angle of the unit is increased, and through the equivalent control law Applicability analysis, a variable structure control strategy is proposed to realize the control of the unit. However, the internal parameter association mechanism provided by the Hamiltonian model has not been fully utilized in the research.

CN103779870A discloses a hydroelectric island frequency suppression method considering the water pressure pulsation of the draft tube, which simulates the actual pulsation of the draft tube through a resonance function, and establishes a water turbine considering both the hydraulic pressure pulsation of the draft tube and the elastic water column The model is used to obtain the island frequency oscillation waveform of the high-voltage direct current sending end hydropower station caused by the water pressure fluctuation of the draft tube, and the island sending end frequency oscillation caused by the water pressure fluctuation of the draft tube is suppressed by the newly designed DC frequency limiter.

Contents of the invention

The purpose of the present invention is to provide a method for suppressing active power oscillations induced by pressure pulsations based on the Hamiltonian model, which solves the problem in the prior art that the internal parameter correlation is not considered and the control effect is poor.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions: a method for suppressing pressure pulsation-induced active power oscillation based on the Hamiltonian model, which is characterized in that: the characteristics of pressure pulsation are introduced into the Hamiltonian model of the hydroelectric unit, and the Hamiltonian structure is used to correct Theoretical design of equivalent control law suppresses the amplitude of active power oscillation by controlling the input damping; specifically, the following steps are included:

Step 1: Taking the power fluctuation of the turbine induced by the pressure fluctuation of the draft tube as an additional excitation, a Hamiltonian model including the influence of the pressure fluctuation of the draft tube is obtained;

Step 2: Modify the Hamiltonian damping matrix elements, use the Hamiltonian structure modification design theory, derive the control law, and use the control injection damping to control the output of the hydroelectric unit.

A further technical solution is that the specific steps of said step 1 are

The turbine mechanical power fluctuation Δp induced by the draft tube pressure fluctuation is:

Δp＝A _t h _pre (qq _nl )sin(2πf _pre t)

Among them, A _t is the coefficient, h _pre is the per unit value of draft tube pressure fluctuation head amplitude, q and q _nl are the per unit value of turbine flow rate and no-load flow rate respectively;

Taking the turbine power fluctuation Δp induced by draft tube pressure fluctuation head as an additional excitation, the Hamiltonian model including the influence of draft tube pressure fluctuation is obtained as follows:

Take x＝[x ₁ x ₂ x ₃ x ₄ x ₅ ] ^T ＝[qyδω ₁ E′ _q ], the Hamiltonian function of the unit is:

Among them, _Ty is the time constant of the servomotor, q _nl is the no-load flow, ω is the unit angular velocity; A _t is the gain coefficient of the turbine; U _s is the bus voltage, X _d ′ _∑ is the d-axis transient reactance, X _q∑ is the q-axis synchronous reactance, X _f is the excitation winding reactance, and X _ad is the d-axis armature reaction reactance;

Hamilton's equation is:

where the algebraic equations are:

F(x) is the input excitation, which is generated by the draft tube pressure fluctuation head; where up(x) is the control formed by dissipation, u(x) is the main servomotor input control; T _w is the water flow inertia Time constant (s); T _j is the unit inertia time constant (s); _Ty is the servomotor time constant (s); q, q _nl is the flow and no-load flow (pu); f _p is the pipeline loss coefficient; h ₀ is the static head of the turbine (pu); y, y ₀ are the opening of the guide vane and the initial value of the opening (pu); ω _B = 314.16 is the base value of the angular velocity of the unit (rad/s); ω ₁ = ω-1, ω is the unit angular velocity (pu); A _t is the turbine gain coefficient; E _q ' is the q-axis transient electromotive force (pu); δ is the generator power angle (rad); D is the equivalent damping coefficient of the unit; T _d0 ' is d Axis open-circuit transient time constant (s), U _s is bus voltage (pu), X _d ′ _∑ is d-axis transient reactance (pu), X _q∑ is q-axis synchronous reactance (pu), X _f is excitation Winding reactance (pu), X _ad is d-axis armature reaction reactance (pu); p _m is turbine power (pu);

A further technical scheme is that the specific steps of said step 2 are

The structure correction matrix is selected as: J _a (x) = 0, R _a (x) is

The modified control law is as follows:

According to the above control law, the output of the hydroelectric unit is controlled.

A further technical solution is that the steps for determining the value of r ₂₅ are as follows: Under a given working condition, the active oscillation amplitude under the pressure fluctuation of the draft tube is actually measured, and the damping factor under the corresponding amplitude is calculated, and the abscissa is fitted as Damping factor, the ordinate is the curve of active oscillation amplitude, take the damping factor corresponding to the lowest point of the curve as the value of _r25 .

The beneficial effects of the present invention are:

1. By using the turbine power fluctuation induced by the draft tube pressure fluctuation head as an additional excitation, the Hamiltonian model including the influence of the draft tube pressure fluctuation is obtained; the Hamiltonian damping matrix elements are modified, and the Hamiltonian structure is used to modify the design theory to derive the control law. By controlling the injection damping, the control method of the coupling relationship between the mechanical and electrical parts is obtained, and the output of the hydroelectric unit is controlled accordingly, which can effectively suppress the active power oscillation amplitude of the unit.

2. The control algorithm proposed by this discovery essentially increases the damping of the hydroelectric unit. In addition to being used to suppress the active power oscillation in the partial load area of the hydroelectric unit, it can also be used to suppress the unit’s operation adjustments such as the unit starting to cross the vibration area and the unit’s active power adjustment. Play a role in terms of active fluctuations.

Description of drawings

Fig. 1 is the Hamiltonian control structure of the hydroelectric unit in Embodiment 1 of the present invention.

Fig. 2 is the water head and mechanical power fluctuation of the water turbine in Embodiment 2 of the present invention.

Fig. 3 is a comparison of generator active power oscillations in Embodiment 2 of the present invention.

Fig. 4 is a variation curve of active oscillation amplitude with damping factor in Embodiment 2 of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Example 1

Using the Hamiltonian structural modification control design theory, by controlling the equivalent injection damping, the active power oscillation amplitude of the unit induced by the draft tube pressure fluctuation in the partial load area of the hydro-generator unit is suppressed, and the operating range of the unit is expanded. Specifically include the following steps:

Step 1: The mechanical power fluctuation induced by pressure fluctuation is used as an additional input excitation to construct a Hamiltonian model of the hydroelectric generator set including the influence of pressure fluctuation.

According to the periodic characteristics of draft tube pressure pulsation during partial load operation, combined with the definition of turbine head by IEEE Working Group, the turbine head is modified into the following form:

h＝h _t +h _pre sin(2πf _pre t)(1)

In the formula, h _t is the relative value of turbine head defined by IEEE Working Group, h _pre is the relative value of draft tube pressure fluctuation head amplitude, h is the relative value of turbine head after including pressure fluctuation head, f _pre is the frequency of pressure fluctuation (Hz ).

Under the above definition, the turbine power is:

p is the relative value of turbine power, A _t is the coefficient, q and q _nl are the relative values of turbine flow and no-load flow respectively, p _t is the relative value of turbine power defined by IEEE Working Group, Δp is the turbine power oscillation caused by pressure pulsation head, Δp = A _t h _pre (qq _nl ) sin(2πf _pre t).

The turbine power fluctuation Δp induced by draft tube pressure pulsation head is used as an additional excitation, which remains unchanged as an additional excitation input in the Hamiltonian transformation, and the original form of the hydraulic unit Hamilton remains unchanged, except that this excitation input is added , the 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 function of the unit is:

Hamilton's equation is:

in, u(x) is the main servomotor input control; ΔF(x) is the input excitation; T _w is the water flow inertia time constant (s); T _j is the unit inertia time constant (s); _Ty is the servomotor time constant (s ); f _p is the pipeline loss coefficient; h ₀ is the relative value of the static head of the turbine; y, y ₀ are the relative values of the guide vane opening and the initial opening; ω _B = 314.16 is the unit angular velocity base value (rad/s), ω ₁ ＝ω-1, ω is the relative value of unit angular velocity; E _q ' is the relative value of q-axis transient electromotive force; δ is generator power angle (rad); D is equivalent damping coefficient of unit; T _d0 ' is d-axis Open-circuit transient time constant (s); U _s is the relative value of bus voltage; X′ _d∑ is the relative value of d-axis transient reactance; X _q∑ is the relative value of q-axis synchronous reactance; X _f is the relative value of excitation winding reactance ; X _ad is the relative value of d-axis armature reaction reactance.

Step 2: Modify the Hamiltonian damping matrix elements, use the Hamiltonian structure modification design theory, derive the control law, and use the control to inject damping;

Let the Hamiltonian form be:

State variable x∈R ⁿ , control u∈R ^m , m<n, H(x) is the energy function of the system, structure matrix J(x) is antisymmetric, damping matrix R(x) is positive semi-definite symmetric matrix, g( x) is the input channel matrix.

Given the constant structure correction J _a and R _a of the system, the correction matrix is J _d (x)=J(x)+J _a , R _d (x)=R(x)+R _a , satisfying J _d (x) =-J _d (x) ^T , R _d (x) = R _d (x) ^T . If the input matrix g has full rank, then (g ^T g) is invertible, and the Hamiltonian equivalent control after structure modification is:

u(x)=v _* +α(x) (6)

v _* is the stabilizing control at a given equilibrium point x _* such that:

α(x) is the additional control resulting from structural modification, calculated using the following formula:

Combined with the Hamiltonian model of the hydroelectric generator set, the structure correction matrix is selected as: J _a (x) = 0, R _a (x) is

Substituting into formula (8), the additional control is obtained as follows:

Expand Hamiltonian partial derivatives, combined with formula (6), we get:

In the above formula, the state parameters of the generator and the state parameters of the turbine cross in the additional control part, that is, the coupling relationship between the mechanical and electrical parts is established.

According to the control law given by formula (11), the Hamiltonian control structure of the hydroelectric unit is obtained, as shown in Fig. 1 .

Step 3: The steps for determining the value of r ₂₅ are as follows: Under a given working condition, the active oscillation amplitude under the pressure fluctuation of the draft tube is actually measured, and the damping factor under the corresponding amplitude is calculated, and the abscissa is fitted as the damping factor, The ordinate is the curve of active oscillation amplitude, and the damping factor corresponding to the lowest point of the curve is taken as the value of _r25 .

Example 2

Calculation based on the data of a hydropower station.

Since the target system of the hydroelectric generating set of the present invention is a single-machine single-pipe system, it is necessary to convert the complex water diversion system into a single-machine single-pipe water diversion system based on the layout of the hydraulic system of the hydropower station and take the change of water head and flow at the inlet of the turbine as the core.

Main parameters of the system: pipe length L=517 (m), pipe diameter D=3.3 (m), rated flow Q _r ＝53.5 (m3/s), rated water head H _r ＝312 (m), water shock wave velocity α＝ 1100 (m/s), the main servomotor time constant _Ty = 0.5 (s).

Step 1: Taking the mechanical power fluctuation induced by pressure fluctuation as an additional input excitation, constructing a Hamiltonian model of the hydroelectric generator set including the influence of pressure fluctuation;

According to the derivation of the arrangement 1 of the content of the invention, the mechanical power fluctuation of the hydraulic turbine induced by the pressure fluctuation of the draft tube is obtained as:

Δp＝A _t h _pre (qq _nl )sin(2πf _pre t)(12)

Taking the turbine power fluctuation Δp induced by draft tube pressure fluctuation head as an additional excitation, the Hamiltonian model including the influence of draft tube pressure fluctuation is obtained as follows.

Take x＝[x ₁ x ₂ x ₃ x ₄ x ₅ ] ^T ＝[qyδω ₁ E′ _q ], the Hamiltonian function of the unit is:

Hamilton's equation is:

Step 2: Modify the Hamiltonian damping matrix elements, use the Hamiltonian structure modification design theory, derive the control law, and use the control to inject damping;

According to the physical meaning represented by the Hamiltonian damping matrix elements, combined with the purpose of the damping injection of the present invention, the selected structure correction matrix is: J _a (x)=0, _Ra (x) is

Substituting into formula (8), the additional control is obtained as follows:

Expanding the partial derivative of Hamilton, combined with formula (6), the control law after structure modification is obtained as follows:

According to the control law given by formula (11), the Hamiltonian control structure of the hydroelectric unit is obtained, as shown in Fig. 1 .

Step 3: Use the actual parameters of the hydroelectric unit to establish a simulation calculation model. Given the measured draft tube pressure fluctuation amplitude, water head and pulse frequency under a certain working condition, in order to use the simulation calculation method, determine the optimal value of the Hamiltonian damping matrix correction element r25 value.

Specifically, as shown in Figure 4, under a given working condition, the active power oscillation amplitude under the draft tube pressure pulsation is actually measured, and the damping factor under the corresponding amplitude is calculated, and the abscissa is the damping factor, and the ordinate is the active power For the curve of oscillation amplitude, the damping factor corresponding to the lowest point of the curve is taken as the value of r25, r ₂₅ =1.3.

Construct a simulation system for the operation of hydroelectric generating units with certain integrity. The governor adopts a typical parallel PID structure, the control parameters: K _P =5.0, K _D =2.5, K _I =1.5, b _p =0.04; the excitation control system adopts the PID control of the machine terminal voltage, K _P1 =10, K _I1 =5, K _D1 =0.001. Unit inertia time constant T _j =8.999 (seconds), generator equivalent damping coefficient D=5.

Substitute the parameters of the hydroelectric unit into formula (14) for numerical calculation. In the numerical calculation, the Hamiltonian model of formula (14) is discretized into an iterative calculation format according to the second-order Runge-Kutta method, and the calculation is programmed in Matlab, and the iterative calculation time interval is 0.001 (s).

Simulation working conditions: the hydroelectric unit operates at 50% of the rated load, that is, pe=0.5(pu), the pressure fluctuation characteristics of the draft tube: the pressure fluctuation amplitude is h _pre =0.05(pu), the pressure fluctuation frequency f _pre =0.9(Hz) .

Fig. 2 is the hydraulic head and mechanical power fluctuations of the turbine induced by pressure fluctuations. Figure 3 compares the generator active output oscillation under the control of Hamiltonian damping injection or not. Obviously, using the Hamiltonian additional damping injection control proposed by the present invention can significantly reduce the generator active oscillation amplitude.

The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Variations.

Claims (2)

1. A method for suppressing pressure pulsation-induced active power oscillations based on the Hamiltonian model, characterized in that: the pressure pulsation feature is introduced into the Hamiltonian model of the hydroelectric unit, and the equivalent control law is designed using the Hamiltonian structure modification theory. By controlling the input damping, Suppress active power oscillation amplitude; specifically include the following steps: Step 1: Taking the power fluctuation of the turbine induced by the pressure fluctuation of the draft tube as an additional excitation, a Hamiltonian model including the influence of the pressure fluctuation of the draft tube is obtained; Step 2: Modify the Hamiltonian damping matrix elements, use the Hamiltonian structure modification design theory, derive the control law, and use the control injection damping to control the output of the hydroelectric unit; The concrete steps of described step one are The turbine mechanical power fluctuation Δp induced by the draft tube pressure fluctuation is: Δp＝A _t h _pre (qq _nl )sin(2πf _pre t) Among them, A _t is the coefficient, h _pre is the per unit value of draft tube pressure fluctuation head amplitude, q and q _nl are the per unit value of turbine flow rate and no-load flow rate respectively; Taking the turbine power fluctuation Δp induced by draft tube pressure fluctuation head as an additional excitation, the Hamiltonian model including the influence of draft tube pressure fluctuation is obtained as follows: Take x＝[x ₁ x ₂ x ₃ x ₄ x ₅ ] ^T ＝[qy δ ω ₁ E′ _q ], the Hamiltonian function of the unit is: Among them, _Ty is the time constant of the servomotor, q _nl is the no-load flow, ω is the unit angular velocity; A _t is the gain coefficient of the turbine; U _s is the bus voltage, X′ _d∑ is the d-axis transient reactance, X _q∑ is the q-axis synchronous reactance, X _f is the excitation winding reactance, and X _ad is the d-axis armature reaction reactance; Hamilton's equation is: where the algebraic equations are: F(x) is the input excitation, which is generated by the draft tube pressure fluctuation head; where up(x) is the control formed by dissipation, u(x) is the main servomotor input control; T _w is the water flow inertia Time constant (s); T _j is the unit inertia time constant (s); _Ty is the servomotor time constant (s); q, q _nl is the flow and no-load flow (pu); f _p is the pipeline loss coefficient; h ₀ is the static head of the turbine (pu); y, y ₀ are the opening of the guide vane and the initial value of the opening (pu); ω _B is the base value of the angular velocity of the unit (rad/s); ω ₁ = ω-1, ω is the unit Angular velocity (pu); A _t is the turbine gain coefficient; E _q ' is the q-axis transient electromotive force (pu); δ is the generator power angle (rad); D is the equivalent damping coefficient of the unit; T _d0 ' is the d-axis open circuit Transient time constant (s), U _s is bus voltage (pu), X _d ′ _∑ is d-axis transient reactance (pu), X _q∑ is q-axis synchronous reactance (pu), X _f is excitation winding reactance (pu), X _ad is the d-axis armature reactance (pu); p _m is the turbine power (pu); The concrete steps of described step 2 are The constant structure correction matrix is selected as: J _a (x) = 0, R _a (x) is The modified control law is as follows: According to the above control law, the output of the hydroelectric unit is controlled. 2. A method for suppressing pressure pulsation-induced active power oscillations based on the Hamiltonian model according to claim 1, characterized in that: the value step of said r ₂₅ is as follows: Under a given working condition, the draft tube pressure pulsation is actually measured and calculate the damping factor at the corresponding amplitude, and fit a curve with the damping factor on the abscissa and the active oscillation amplitude on the ordinate, and take the damping factor corresponding to the lowest point of the curve as the value of r ₂₅ .