Calculation method for stability margin domain of isolated grid operation regulation of pumped storage power station

Abstract

The invention provides a method for calculating a stable margin domain of isolated network operation regulation of a pumped storage power station, which comprises the following steps of: constructing a simulation model of the pumped storage power station in an isolated network mode, and deducing a comprehensive transfer function based on the model so as to obtain a margin stability characteristic equation of a pumped storage power station regulation system; by adjusting various parameters in the pumped storage power station, any two parameters are selected as coordinate axes in a rectangular coordinate system, and the stability margin domain of the pumped storage power station adjusting system under different stability margins is calculated by utilizing the Hellzz criterion; and fitting the time domain simulation curves of the pumped storage power station at different stability margin domain boundaries by adopting a power function. The method can quantify the stability margin of the power station when the power station encounters disturbance, identifies the stability boundary of the system under the ultralow frequency oscillation condition by analyzing the stability margin under different operation conditions, can effectively prevent and reduce the instability phenomenon, and improves the overall safety and reliability of the pumped storage power station.

Description

Technical Field

[0001] The invention relates to the technical field of pumped storage power stations, and in particular to a method for calculating a stable margin domain for isolated grid operation regulation of a pumped storage power station. Background Art

[0002] With the continuous development and expansion of the global power system, pumped storage power stations, as an important power storage technology, are increasingly being used in grid dispatching and load balancing. Its main function is to achieve effective storage and release of electric energy through the regulation of peak and valley power, ensuring the safety and stability of the power grid. Especially in the context of large-scale access to intermittent renewable energy such as wind power and photovoltaic power, pumped storage power stations are particularly important in peak load shaving and valley filling and frequency regulation of the power grid. However, with the construction of more and more pumped storage power stations, the stability of the system has become increasingly complex, especially under high load and extreme operating conditions, instability has frequently occurred, which poses a threat to the safety of the power system. Therefore, research on the regulation stability of pumped storage power stations has become particularly urgent to enhance the robustness and stability of the power system.

[0003] Among the existing patents, some patents focus on the optimization of the speed regulation system of pumped storage power stations, especially the optimization of PI speed regulator parameters to improve the dynamic response speed and stability of the system; in addition, some patents involve frequency control methods, exploring how to achieve frequency stability through pumped storage units when the power grid fluctuates; and some patents study the control method of water hammer phenomenon, which contributes to improving system safety. However, none of the above patents conduct research and analysis on the stability margin domain of pumped storage power station regulation under isolated grid conditions. In summary, patents in this field lack systematic methods and quantitative analysis, resulting in challenges in ensuring the stability of pumped storage power stations under isolated grid operation conditions. Summary of the invention

[0004] In response to the above problems, the present invention provides a method for calculating the stability margin domain of isolated grid operation regulation of a pumped-storage power station. The method can quantify the stability margin of the pumped-storage power station when encountering disturbances, and by analyzing the stability margin under different operating conditions, identify the stability boundary of the system under different oscillation conditions, thereby filling the gap in the prior art and providing theoretical support and practical basis for the safe and stable operation of the pumped-storage power station.

[0005] In order to realize the above technical features, the object of the present invention is achieved as follows: a method for calculating the stability margin domain of isolated grid operation regulation of a pumped storage power station comprises the following steps:

[0006] Step 1, constructing a simulation model of a pumped storage power station in an isolated grid mode;

[0007] Step 2, deriving a comprehensive transfer function based on the simulation model established in step 1;

[0008] Step 3, calculating the residual stability characteristic equation of the pumped storage power station based on the comprehensive transfer function in step 2;

[0009] Step 4, calculating the stability margin domain of the pumped storage power station regulation system under different stability margins;

[0010] Step 5: Use a power function to fit the time domain simulation curve of the pumped storage power station regulation system at different stability margin domain boundaries to quantify the stability margin of the regulation system when encountering disturbances.

[0011] Preferably, the step 1 specifically includes:

[0012] Step 1.1, establish the models of each subsystem of the governor, water diversion system, pump-turbine and generator respectively according to the transfer function method;

[0013] Step 1.2, the pumped storage power station adopts the speed control mode, and the speed governor uses a PI type controller to achieve precise control of the speed change;

[0014] The PI controller is responsible for adjusting the hydraulic actuator, thereby controlling the opening of the guide vanes.

[0015] Preferably, the step 2 specifically includes:

[0016] Step 2.1, determine the transfer functions of the subsystem models of the governor, water diversion system, pump-turbine and generator respectively;

[0017] Step 2.2, based on the transfer functions of each subsystem model, derive the comprehensive transfer function of the entire pumped storage power station.

[0018] Preferably, the step 3 specifically includes:

[0019] Step 3.1, the denominator of the integrated transfer function is used as the characteristic equation of the pumped storage power station regulation system, as shown in equation (1), where s is the Laplace operator, a n is the coefficient of s raised to the nth power;

[0020] a n s n +a n-1 s n-1 +…+a0=0(1);

[0021] Step 3.2, when the stability margin domain of the pumped storage power station regulation system is m, the residual stability characteristic equation must satisfy that the real parts of all characteristic roots are less than -m. Let s = Ym to calculate the residual stability characteristic equation as shown in formula (2), and expand it to obtain formula (3), where cn is the coefficient obtained by expanding the coefficients in formula (2) and combining similar terms;

[0022] a n (Ym) n +a n-1 (Ym) n-1 +...+a0=0(2);

[0023] c n Y n +c n-1 Y n-1 +...+c0=0(3).

[0024] The step 4 is to obtain the stability condition under the stability margin m of the pumped storage power station regulation system by using the Hurwitz criterion according to the margin stability characteristic equation calculated in the step 3.

[0025] Preferably, the step 4 specifically includes:

[0026] Step 4.1, among the control parameters of the PI speed regulator, the water flow inertia time constant, the water flow elastic time constant and the main relay time constant, any two parameters are selected as the coordinate axes of the rectangular coordinate system, the selected parameters are varied, and the stability margin domain of the pumped storage system under the stability margin m is obtained by using the Hurwitz criterion;

[0027] Step 4.2, select the points in the coordinate system in step 4.1 and input them into the simulation model of the pumped storage power station established in step 1 for simulation verification to verify the correctness of the proposed stability margin domain.

[0028] Preferably, the step 5 specifically includes:

[0029] Step 5.1, according to the time domain simulation curves of different stability margin domain boundaries obtained by simulation in step 4, a power function is used for fitting;

[0030] Step 5.2, extract each peak value and corresponding time of each response change separately, and use the exponential function expression y=de fx The envelope of the speed response is fitted, and the power coefficient f in the fitting expression is equal to the stability margin m.

[0031] Preferably, the control mode in the simulation model established in step 1.1 adopts a speed control mode;

[0032] The speed regulator is implemented by a pump turbine regulating system, where ω is the speed, ω ref is a given speed, T y is the main servomotor time constant, K p and K iare the proportional and integral gain coefficients of the speed regulator, b p is the negative feedback regulation coefficient, y PI is the governor control signal, y is the guide vane opening, s is the Laplace operator, the pump-turbine model adopts a linear model with 6 transfer coefficients; the water diversion system adopts a second-order elastic water hammer model and ignores friction loss; the generator model adopts the first-order rotor motion equation.

[0033] The transfer function of the speed regulator model determined in step 2.1 is:

[0034]

[0035] The transfer function of the water diversion system model is:

[0036]

[0037] Where, T w is the water flow inertia time constant, T e is the elastic time constant of water flow, α is the parameter describing the damping characteristics of the system;

[0038] The transfer function of the pump-turbine and water delivery system is:

[0039]

[0040] The transfer function of the generator and load model is:

[0041]

[0042] In the formula, e y is the transfer coefficient of turbine torque to guide vane opening, e x is the transmission coefficient of turbine torque to speed, e h is the transfer coefficient of turbine torque to water head, e qy is the transfer coefficient of turbine flow to guide vane opening, e qx is the transfer coefficient of turbine flow to speed, e qh is the transfer coefficient of turbine flow to water head, T a is the unit inertia time constant, e n is the generator self-regulation coefficient.

[0043] Preferably, the comprehensive transfer function of the entire system in step 2.2 is:

[0044]

[0045] In the formula, a n is the coefficient of the Laplace operator s raised to the power of n in the denominator, b n are the coefficients of the numerator Laplace operator s raised to the power of n.

[0046] The present invention has the following beneficial effects:

[0047] 1. The present invention designs a method for calculating the stability margin domain of isolated grid operation regulation of a pumped storage power station. By establishing a comprehensive transfer function and a margin stability characteristic equation, the present method can quantify the stability margin of the power station when encountering disturbances and provide a more accurate stability assessment.

[0048] 2. The present invention allows adjustment of multiple key parameters, including control parameters of the PI speed regulator and water flow time constant, etc., and can adapt to different operating conditions.

[0049] 3. The present invention can effectively prevent and reduce instability and improve the overall safety and reliability of the pumped storage power station. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0051] Figure 1 The figure is a flow chart of the overall method of the present invention.

[0052] Figure 2 This is a structural block diagram of the pumped storage power station model of the present invention.

[0053] Figure 3 This is a structural block diagram of the speed regulator of the pumped storage power station of the present invention.

[0054] Figure 4 It is the stability margin domain under different stability margins of the pumped storage power station of the present invention.

[0055] Figure 5 Graphs 1 and 2 are the time domain responses of four different stability margins m of the present invention.

[0056] Figure 6 This is the power function fitting envelope curve of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with embodiments. It is necessary to point out that the following embodiments are only used to further illustrate the present invention and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technical personnel in the field based on the above invention content still fall within the scope of protection of the present invention.

[0058] Embodiment 1:

[0059] See also Figure 1-3 A method for calculating a stable margin region for isolated grid operation regulation of a pumped storage power station comprises the following steps:

[0060] Step 1, constructing a simulation model of a pumped storage power station in an isolated grid mode;

[0061] Step 1.1, establish the models of each subsystem of the governor, water diversion system, pump-turbine and generator respectively according to the transfer function method;

[0062] Step 1.2, the pumped storage power station adopts the speed control mode, and the speed governor uses a PI type controller to achieve precise control of the speed change;

[0063] The PI controller is responsible for adjusting the hydraulic actuator, thereby controlling the opening of the guide vanes.

[0064] Step 2, deriving a comprehensive transfer function based on the simulation model established in step 1;

[0065] Step 2.1, determine the transfer functions of the subsystem models of the governor, water diversion system, pump-turbine and generator respectively;

[0066] Step 2.2, based on the transfer functions of each subsystem model, derive the comprehensive transfer function of the entire pumped storage power station.

[0067] Step 3, calculating the residual stability characteristic equation of the pumped storage power station based on the comprehensive transfer function in step 2;

[0068] Step 3.1, the denominator of the integrated transfer function is used as the characteristic equation of the pumped storage power station regulation system, as shown in equation (1), where s is the Laplace operator, a n is the coefficient of s raised to the nth power;

[0069] a n s n +a n-1 s n-1 +...+a0=0(1);

[0070] Step 3.2, when the stability margin domain of the pumped storage power station regulation system is m, the residual stability characteristic equation must satisfy that the real parts of all characteristic roots are less than -m. Let s = Ym to calculate the residual stability characteristic equation as shown in formula (2), and expand it to obtain formula (3), where c n is the coefficient obtained by expanding the coefficients in formula (2) and combining similar terms;

[0071] a n (Ym) n +a n-1 (Ym) n-1 +...+a0=0(2);

[0072] c n Y n +c n-1 Y n-1+...+c0=0(3).

[0073] Step 4, calculating the stability margin domain of the pumped storage power station regulation system under different stability margins;

[0074] According to the margin stability characteristic equation calculated in step 3, the Hurwitz criterion is used to obtain the stability condition of the pumped storage power station regulation system when the stability margin is m.

[0075] Step 4.1, among the control parameters of the PI speed regulator, the water flow inertia time constant, the water flow elastic time constant and the main relay time constant, any two parameters are selected as the coordinate axes of the rectangular coordinate system, the selected parameters are varied, and the stability margin domain of the pumped storage system under the stability margin m is obtained by using the Hurwitz criterion;

[0076] Step 4.2, select the points in the coordinate system in step 4.1 and input them into the simulation model of the pumped storage power station established in step 1 for simulation verification to verify the correctness of the proposed stability margin domain.

[0077] Step 5: Use a power function to fit the time domain simulation curve of the pumped storage power station regulation system at different stability margin domain boundaries to quantify the stability margin of the regulation system when encountering disturbances.

[0078] Step 5.1, according to the time domain simulation curves of different stability margin domain boundaries obtained by simulation in step 4, a power function is used for fitting;

[0079] Step 5.2, extract each peak value and corresponding time of each response change separately, and use the exponential function expression y=de fx The envelope of the speed response is fitted, and the power coefficient f in the fitting expression is equal to the stability margin m.

[0080] Embodiment 2:

[0081] The following describes the method of the present invention in detail by taking a pumped storage power station for calculating the stability margin domain as an embodiment of the present invention:

[0082] See also Figure 2 ,In this virtual simulation system, the operation condition of the pumped storage power station is ,isolated grid mode, and the control mode adopts the ,speed control mode.

[0083] Step 1: Build a simulation model of a pumped storage power station.

[0084] The specific block diagram of the speed regulator control is as follows: Figure 3 As shown, all are implemented by the pump turbine regulation system, where ω is the speed, ω ref is a given speed, T y is the main servomotor time constant, K pand K i are the proportional and integral gain coefficients of the speed regulator, b p is the negative feedback regulation coefficient, y PI is the governor control signal, y is the guide vane opening, and s is the Laplace operator. The pump turbine model uses a linear model with 6 transfer coefficients. The water diversion system uses a second-order elastic water hammer model and ignores friction losses. The generator model uses the first-order rotor motion equation.

[0085] Step 2: Derive the comprehensive transfer function based on the simulation model established in step 1.

[0086] Step 2.1, determine the transfer functions of the subsystem models of the governor, water diversion system, pump-turbine and generator respectively;

[0087] The transfer function of the speed regulator model is:

[0088]

[0089] The transfer function of the water diversion system model is:

[0090]

[0091] Where, T w is the water flow inertia time constant, T e is the elastic time constant of water flow, α is the parameter describing the damping characteristics of the system;

[0092] The transfer function of the pump-turbine and water delivery system is:

[0093]

[0094] The transfer function of the generator and load model is:

[0095]

[0096] In the formula, e y is the transfer coefficient of turbine torque to guide vane opening, e x is the transmission coefficient of turbine torque to speed, e h is the transfer coefficient of turbine torque to water head, e qy is the transfer coefficient of turbine flow to guide vane opening, e qx is the transfer coefficient of turbine flow to speed, e qh is the transfer coefficient of turbine flow to water head, T a is the unit inertia time constant, e n is the generator self-regulation coefficient.

[0097] Step 2.2, based on the transfer functions of each subsystem model in step 2.1, derive the comprehensive transfer function of the entire pumped storage power station.

[0098] The comprehensive transfer function of the entire system is:

[0099]

[0100] In the formula, a n is the coefficient of the Laplace operator s raised to the power of n in the denominator, b n are the coefficients of the numerator Laplace operator s raised to the power of n.

[0101] Step 3, calculating the residual stability characteristic equation of the pumped storage power station based on the comprehensive transfer function in step 2;

[0102] Step 3.1, take the denominator of the transfer function as the characteristic equation of the pumped storage regulation system:

[0103] a5s 5 +a4s 4 +a3s 3 +a2s 2 +a1s+a0=0(9);

[0104] Step 3.2: When the system's stability margin domain is m, the residual stability characteristic equation must satisfy that the real parts of all characteristic roots are less than -m. Let s = Ym to calculate the residual stability characteristic equation as shown in equation (10), and expand it to obtain equation (11).

[0105] a5(Ym) 5 +a4(Ym) 4 +a3(Ym) 3 +a2(Ym) 2 +a1(Ym)+a0=0(10);

[0106] 5c 5 +c4Y 4 +c3Y 3 +c2Y 2 +c1Y+c0=0(11);

[0107] Step 4: According to the residual stability characteristic equation calculated in step 3, the Hurwitz criterion is used to obtain the stability condition of the pumped storage power station regulation system when the stability margin is m.

[0108] Step 4.1, select the control parameter K of the PI speed regulator p and K i As the coordinate axis of the rectangular coordinate system, the stability margin domain of the pumped storage power station regulation system under the stability margin of m is obtained by using the Hurwitz criterion as follows Figure 4 ;

[0109] Step 4.2, select Figure 4 The points in “×” are input into the pumped storage power station model established in step 1 for simulation verification, and the time domain responses are obtained as follows: Figure 5 (a)~(d).

[0110] Step 5: Use a power function to fit the time domain simulation curve of the pumped storage power station regulation system at different stability margin domain boundaries to quantify the stability margin of the regulation system when encountering disturbances.

[0111] Select the point where the margin domain m value is 0.02, extract each peak value and corresponding time of each response change separately, and use the exponential function expression y=de 0.02x Fit the envelope of the speed response, and the fitting curve is as follows: Figure 6 The power coefficient f in the fitting expression is equal to the stability margin m.

[0112] The present invention is the embodiment of the present invention as described above. The above embodiments and the specific parameters in the embodiments are only for the purpose of clearly describing the invention verification process, and are not used to limit the protection scope of the present invention. The protection scope of the present invention is still subject to its claims, and any equivalent structural changes made by using the description and drawings of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station, characterized in that: The following steps are involved: Step 1, constructing a simulation model of a pumped storage power station in an isolated grid mode; Step 2, deriving a comprehensive transfer function based on the simulation model established in step 1; Step 3, calculating the residual stability characteristic equation of the pumped storage power station based on the comprehensive transfer function in step 2; Step 4, calculating the stability margin domain of the pumped storage power station regulation system under different stability margins; Step 5: Use a power function to fit the time domain simulation curve of the pumped storage power station regulation system at different stability margin domain boundaries to quantify the stability margin of the regulation system when encountering disturbances.

2. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1, establish the models of each subsystem of the governor, water diversion system, pump-turbine and generator respectively according to the transfer function method; Step 1.2, the pumped storage power station adopts the speed control mode, and the speed governor uses a PI type controller to achieve precise control of the speed change; The PI controller is responsible for adjusting the hydraulic actuator, thereby controlling the opening of the guide vanes.

3. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 2 is characterized in that: The step 2 specifically includes: Step 2.1, determine the transfer functions of the subsystem models of the governor, water diversion system, pump-turbine and generator respectively; Step 2.2, based on the transfer functions of each subsystem model, derive the comprehensive transfer function of the entire pumped storage power station.

4. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 3 is characterized in that: The step 3 specifically includes: Step 3.1, the denominator of the integrated transfer function is used as the characteristic equation of the pumped storage power station regulation system, as shown in equation (1), where s is the Laplace operator, a n is the coefficient of s raised to the nth power; a n s n +a n-1 s n-1 +…+a0=0(1); Step 3.2, when the stability margin domain of the pumped storage power station regulation system is m, the residual stability characteristic equation must satisfy that the real parts of all characteristic roots are less than -m. Let s = Ym to calculate the residual stability characteristic equation as shown in formula (2), and expand it to obtain formula (3), where c n is the coefficient obtained by expanding the coefficients in formula (2) and combining similar terms; to n (Ym) n +a n-1 (Ym) n-1 +...+a0=0(2); c n Y n +c n-1 Y n-1 +…+c0=0(3)。 5. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 4 is characterized in that: The step 4 is to obtain the stability condition under the stability margin m of the pumped storage power station regulation system by using the Hurwitz criterion according to the margin stability characteristic equation calculated in the step 3.

6. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 5 is characterized in that: The step 4 specifically includes: Step 4.1, among the control parameters of the PI speed regulator, the water flow inertia time constant, the water flow elastic time constant and the main relay time constant, any two parameters are selected as the coordinate axes of the rectangular coordinate system, the selected parameters are varied, and the stability margin domain of the pumped storage system under the stability margin m is obtained by using the Hurwitz criterion; Step 4.2, select the points in the coordinate system in step 4.1 and input them into the simulation model of the pumped storage power station established in step 1 for simulation verification to verify the correctness of the proposed stability margin domain.

7. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 6 is characterized in that: The step 5 specifically includes: Step 5.1, according to the time domain simulation curves of different stability margin domain boundaries obtained by simulation in step 4, a power function is used for fitting; Step 5.2, extract each peak value and corresponding time of each response change separately, and use the exponential function expression y=de fx The envelope of the speed response is fitted, and the power coefficient f in the fitting expression is equal to the stability margin m.

8. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 4, characterized in that: The control mode in the simulation model established in step 1.1 adopts the speed control mode; The speed regulator is implemented by a pump turbine regulating system, where ω is the speed, ω ref is a given speed, T y is the main servomotor time constant, K p and K i are the proportional and integral gain coefficients of the speed regulator, b p is the negative feedback regulation coefficient, y PI is the governor control signal, y is the guide vane opening, s is the Laplace operator, the pump-turbine model adopts a linear model with 6 transfer coefficients; the water diversion system adopts a second-order elastic water hammer model and ignores friction loss; the generator model adopts the first-order rotor motion equation.

9. The method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 8, characterized in that: The transfer function of the speed regulator model determined in step 2.1 is: The transfer function of the water diversion system model is: Where, T w is the water flow inertia time constant, T e is the elastic time constant of water flow, α is the parameter describing the damping characteristics of the system; The transfer function of the pump-turbine and water delivery system is: The transfer function of the generator and load model is: In the formula, e y is the transfer coefficient of turbine torque to guide vane opening, e x is the transmission coefficient of turbine torque to speed, e h is the transfer coefficient of turbine torque to water head, e qy is the transfer coefficient of turbine flow to guide vane opening, e qx is the transfer coefficient of turbine flow to speed, e qh is the transfer coefficient of turbine flow to water head, T a is the unit inertia time constant, e n is the generator self-regulation coefficient.

10. A method for calculating the stability margin region of isolated grid operation regulation of a pumped storage power station according to claim 9, characterized in that: The comprehensive transfer function of the entire system in step 2.2 is: In the formula, a n is the coefficient of the Laplace operator s raised to the power of n in the denominator, b n are the coefficients of the numerator Laplace operator s raised to the power of n.

Images