Grid-connected load flow calculation method for doubly-fed pumped storage unit based on optimal rotating speed

Abstract

The invention discloses a grid-connected load flow calculation method of a doubly-fed pumped storage unit based on an optimal rotating speed. The grid-connected load flow calculation method comprises the following steps: 1, fitting an efficiency curve of the doubly-fed pumped storage unit into a polynomial function of flow and the rotating speed based on a recursive least square method with a discount factor; 2, establishing an analytical expression between the mechanical power and the flow when the unit operates at the optimal rotating speed; 3, introducing the unit internal constraint equation set into a power grid power flow equation, and establishing a grid-connected power flow model; 4, converting the grid-connected power flow model into a least square model; and 5, introducing twice approximate iteration steps, providing a four-order Levenberg Marquardt method for solving, and solving the problem of non-convergence of power flow caused by positive and negative switching of a rotor voltage phase angle. According to the method, the influence of variable-speed operation of the doubly-fed pumped storage unit on internal loss is considered, a grid-connected power flow model in which an internal constraint equation set and a power grid power flow equation are simultaneous is established, and a four-order Levenberg Marquardt method is adopted for solving, so that the accuracy of grid-connected power flow calculation of the doubly-fed pumped storage unit is improved.

Description

Technical Field

[0001] The invention belongs to the field of grid-connected power flow calculation and optimal dispatching of a doubly-fed pumped storage unit, and in particular relates to a grid-connected power flow calculation method of a doubly-fed pumped storage unit based on an optimal speed. Background Art

[0002] Doubly-fed pumped-storage units can not only change the frequency of the excitation current to achieve continuous regulation of the unit speed and improve the operating efficiency and regulation range of the reversible pump-turbine; but also achieve rapid power control, which has great advantages in promoting the consumption of new energy and smoothing power fluctuations.

[0003] At present, the research on the participation of doubly-fed pumped storage units in power grid flow calculation at home and abroad focuses more on the power generation cost of the entire system and the amount of wind and solar power abandoned. The doubly-fed pumped storage units are simply equivalent to adjustable power sources like batteries, while ignoring the working characteristics of the reversible pump-turbine and the internal structure of the doubly-fed induction motor. The influence of the variable speed operation of the unit on its internal loss is not taken into account, and the problem that the positive and negative switching of the rotor voltage phase angle easily leads to the oscillation and non-convergence of the flow iteration process is not solved. The calculation results of the simplified doubly-fed pumped storage unit flow model have a large deviation from the actual operation. Therefore, a grid-connected flow calculation method for doubly-fed pumped storage units based on the optimal speed is needed to improve the accuracy of the calculation. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned technology and propose a grid-connected power flow calculation method for a doubly-fed pumped-storage unit based on an optimal speed, in order to fully consider the influence of variable speed operation of the doubly-fed pumped-storage unit on internal losses, so as to improve the precision and accuracy of the grid-connected power flow calculation of the doubly-fed pumped-storage unit, thereby providing strong support for the optimal scheduling of the energy storage system.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on an optimal speed of the present invention is characterized in that it comprises the following steps:

[0007] Step S1: using the recursive least square method with a discount factor to fit the steady-state efficiency curve polynomial of the doubly-fed pumped storage unit when it is running at a variable speed under a fixed water head;

[0008] Step S2: Solve the steady-state efficiency curve polynomial according to the partial derivative of the steady-state efficiency curve polynomial with respect to the speed, and obtain the optimal speed corresponding to different flow rates of the double-fed pumped storage unit during variable frequency speed regulation operation. , thus establishing an analytical expression between mechanical power and flow rate when operating at the optimal speed;

[0009] Step S3: using a simultaneous iterative solution method to introduce the internal constraint equations of the doubly-fed pumped storage unit into the power grid flow equation, thereby establishing its grid-connected power flow model;

[0010] Step S4: Perform a first-order Taylor expansion on the grid-connected power flow model of the doubly-fed pumped storage unit and introduce a damping factor to construct a least squares model;

[0011] Step S5: using a fourth-order convergent Levenberg Marquardt algorithm to iteratively solve the least squares model, and obtain the power flow calculation results taking into account the internal losses of the doubly-fed pumped storage unit, including the approximate power flow solution of the doubly-fed pumped storage unit when the slip rate is 0.

[0012] The method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on an optimal speed according to the present invention is also characterized in that step S1 is performed according to the following steps:

[0013] Step S1-1: Use equation (1) to establish a fitting polynomial for the doubly-fed pumped storage unit:

[0014] (1)

[0015] In formula (1), They are the flow rate, efficiency and speed of the doubly-fed pumped storage unit when it is running at variable speed under fixed water head; are 6 curve fitting coefficients, and ; is the impeller radius of the doubly-fed pumped storage unit; is the impeller swept area; is an intermediate variable;

[0016] Step S1-2: Taking the minimum sum of squares of the residuals between the data sampling points and the fitting polynomial as the objective function, the recursive least squares method with a discount factor is used to perform curve fitting on equation (1) to obtain 6 curve fitting coefficients that meet a certain accuracy. The corresponding estimated value ;

[0017] Step S1-3: The estimated values ​​of the six curve fitting coefficients Substituting into equation (1), we can use equation (2) to obtain the steady-state efficiency curve polynomial of the doubly-fed pumped storage unit when running at variable speed under fixed water head:

[0018] (2)

[0019] Furthermore, step S2 is performed as follows:

[0020] Step S2-1: Using equation (3) to obtain the steady-state efficiency curve polynomial versus speed The partial derivative of :

[0021] (3)

[0022] Step S2-2: Set equation (3) to 0, and then use equation (4) to obtain the optimal speed corresponding to different flow rates of the double-fed pumped storage unit during variable frequency speed regulation operation: :

[0023] (4)

[0024] Step S2-3: Use equation (5) to establish the optimal speed of the doubly-fed pumped storage unit Its mechanical power during operation With flow The analytical expression between:

[0025] (5)

[0026] In formula (5), is the specific gravity of water, is the acceleration due to gravity, For the water head.

[0027] Furthermore, step S3 is performed as follows:

[0028] Step S3-1: Use equation (6) to establish the stator node of the doubly-fed pumped storage unit The active power constraint equation is:

[0029] (6)

[0030] In formula (6), They represent the stator nodes of the doubly-fed pumped storage unit. Active unbalance, active output, voltage value, and current conjugate value; Represents the grid-side converter node of the doubly-fed pumped storage unit The conjugate value of the current; Re means taking the real part, Im means taking the imaginary part;

[0031] Step S3-2: Use equation (7) to establish the stator node of the doubly-fed pumped storage unit The reactive power constraint equations are:

[0032] (7)

[0033] In formula (7), They represent the stator nodes of the doubly-fed pumped storage unit. Reactive power imbalance between the power grid and the unit; They represent the stator nodes of the doubly-fed pumped storage unit. Reactive power output and virtual nodes The current conjugate value of

[0034] Step S3-3: Use equation (8) to establish the virtual node of the double-fed pumped storage unit The power constraint equations are:

[0035] (8)

[0036] In formula (8), They represent the virtual nodes of the double-fed pumped storage units. Active unbalance and reactive unbalance; They represent the virtual nodes of the double-fed pumped storage units. The voltage value of the rotor node The current conjugate value of

[0037] Step S3-4: Use equation (9) to establish the grid-side converter node of the doubly-fed pumped storage unit The power constraint equations are:

[0038] (9)

[0039] In formula (9), They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance; They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Reactive power setting value and voltage value; Represents the rotor node of the doubly-fed pumped storage unit Voltage value;

[0040] Step S3-5: Use equation (10) to obtain the optimal speed of the doubly-fed pumped storage unit Slip rate during operation :

[0041] (10)

[0042] In formula (10), is the number of pole pairs of the doubly-fed induction motor; is the speed increase ratio of the gearbox; is the per unit value of the rated frequency of the power grid;

[0043] Step S3-6: Use equation (11) to establish the optimal speed of the doubly-fed pumped storage unit Mechanical power during operation With electromagnetic power The equilibrium relationship, that is, the torque constraint equation:

[0044] (11)

[0045] In formula (11), Indicates the torque unbalance of the doubly-fed pumped storage unit;

[0046] Step S3-7: Combine equations (6) to (11) with the power grid flow equation, and use equation (12) to establish a grid-connected power flow model for the doubly-fed pumped storage unit:

[0047] (12)

[0048] In formula (12), Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage amplitude correction value; Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage phase angle correction value; They represent the stator nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance of AC power grid nodes; represents the expanded Jacobian matrix.

[0049] Further, step S4 is performed as follows:

[0050] Step S4-1: Perform a first-order Taylor expansion on the grid-connected power flow model of the doubly-fed pumped storage unit, and then use equation (13) to construct the first The objective function of the iteration :

[0051] (13)

[0052] In formula (13), is the number of iterations; represents transpose; Respectively represent The power imbalance between the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration; For the The Jacobian matrix of the iteration; Respectively represent The voltage correction amount of the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration;

[0053] Step S4-2: Using formula (14) to obtain For The voltage correction value of the iteration The partial derivative of :

[0054] (14)

[0055] Step S4-3: Set equation (14) to 0 and introduce the Damping factor for iterations , and then use formula (15) to establish the least squares model:

[0056] (15).

[0057] Further, step S5 is performed as follows:

[0058] Step S5-1: Initialization , , and The voltage value of the AC power grid node under the iteration and Voltage values ​​of internal nodes of the doubly-fed pumped storage unit under iteration , set the convergence accuracy ;

[0059] Step S5-2: Based on The voltage value of the AC power grid node under the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit under iteration , use formula (12) to calculate the The Jacobian matrix of the iteration;

[0060] Step S5-3: Calculate the first Damping factor for iterations :

[0061] (16)

[0062] In formula (16), For the The adaptive factor of the iteration, and ;

[0063] Step S5-4: Use formula (17) to obtain The voltage value of the AC grid node corrected for the first time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the first time in the iteration , and The voltage correction of the AC grid node introduced for the first time in the iteration With The voltage correction value of the internal node of the doubly-fed pumped storage unit introduced for the first time in the iteration :

[0064] (17)

[0065] In formula (17), is the power balance equation including the AC grid nodes and the internal nodes of the doubly-fed pumped storage unit;

[0066] Step S5-5: Use formula (18) to obtain The voltage value of the AC grid node corrected for the second time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the second time in the iteration , and The voltage correction of the AC grid node introduced for the second time in the iteration With Voltage correction of the internal nodes of the double-fed pumped storage unit introduced for the second time in the iteration :

[0067] (18)

[0068] Step S5-6: Combine equation (15), equation (17) and equation (18), and use equation (19) to obtain Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration :

[0069] (19)

[0070] Step S5-7: Based on and , calculate the Active unbalance of each node in the iteration Reactive unbalance ,like , then stop the calculation and output the Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration ; Otherwise, execute step S5-8;

[0071] Step S5-8: Use formula (20) to obtain Adaptive factor of the iteration :

[0072] (20)

[0073] In formula (20), For the The evaluation index of the descent effect in the iteration, is the upper threshold of the evaluation index; is the lower threshold of the evaluation index; is the lower threshold of the adaptive factor;

[0074] Step 5-9: Assign to Then, return to step S5-2 and execute sequentially.

[0075] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the grid-connected power flow calculation method, and the processor is configured to execute the program stored in the memory.

[0076] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the grid-connected power flow calculation method when the computer program is executed by a processor.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] 1. The present invention uses the recursive least square method with a discount factor to fit the steady-state efficiency curve of the doubly-fed pumped storage unit into a polynomial of flow rate and speed, and derives an analytical expression between its mechanical power and flow rate when the unit runs at the optimal speed, laying a theoretical foundation for constructing its grid-connected power flow model.

[0079] 2. Based on the traditional power flow equation and least squares model, the present invention innovatively introduces the internal constraint equations of the doubly-fed pumped-storage unit into the power grid power flow equation, expands the traditional Jacobian matrix, and constructs a grid-connected power flow model of the doubly-fed pumped-storage unit, which can take into account the impact of its variable speed operation on internal losses and improve the accuracy and convergence of the power flow calculation.

[0080] 3. The grid-connected power flow model of the doubly-fed pumped-storage unit of the present invention is subjected to first-order Taylor expansion, an adaptive damping factor is introduced, a linear least squares model is constructed, and a fourth-order convergent Levenberg Marquardt algorithm is used for solving the problem. This can reduce the dependence of the grid-connected power flow calculation of the doubly-fed pumped-storage unit on the initial value of the power flow, solve the problem that the positive and negative switching of the rotor voltage phase angle easily leads to oscillation and non-convergence of the power flow iteration process, and obtain the power flow calculation results taking into account the internal losses of the doubly-fed pumped-storage unit, including the approximate power flow solution of the doubly-fed pumped-storage unit when the slip rate is 0. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a flow chart of the present invention;

[0082] Figure 2 It is the steady-state efficiency-speed curve at different flow rates;

[0083] Figure 3 This is the principle diagram of the least squares method;

[0084] Figure 4 It is a structural schematic diagram of a doubly-fed pumped storage unit;

[0085] Figure 5 Schematic diagram of rotor voltage phase angle mutation. DETAILED DESCRIPTION

[0086] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0087] In this embodiment, a method for calculating the grid-connected power flow of a doubly-fed pumped-storage unit based on the optimal speed is proposed. Taking into account the impact of the variable speed operation of the doubly-fed pumped-storage unit on the internal losses and the problem that the positive and negative switching of the rotor voltage phase angle easily leads to the oscillation and non-convergence of the power flow iteration process, an analytical expression between the mechanical power and flow of the doubly-fed pumped-storage unit when it is running at the optimal speed is proposed. After establishing a grid-connected power flow model that combines its internal constraint equations with the power grid power flow equation, it is converted into a least squares model and iteratively solved using the fourth-order convergent Levenberg Marquardt algorithm, which effectively solves the problem that the positive and negative switching of the rotor voltage phase angle easily leads to the oscillation and non-convergence of the power flow iteration process, and improves the accuracy and convergence of the grid-connected power flow calculation of the doubly-fed pumped-storage unit. Specifically, Figure 1 As shown, the method comprises the following steps:

[0088] Step S1: The efficiency of the pump turbine is highly dependent on its turbine design and operating conditions. It is difficult to determine its analytical expression through theoretical analysis. In addition, the steady-state efficiency curve of the doubly fed pumped storage unit with variable speed operation under fixed water head has a single peak shape. As the flow rate changes, the steady-state efficiency-speed curve at different flow rates is as follows: Figure 2Therefore, the recursive least square method with discount factor is used to fit its efficiency curve into a polynomial function of flow rate and speed.

[0089] Step S1-1: The steady-state efficiency curve of the doubly-fed pumped storage unit running at variable speed under a fixed water head has a single peak shape and changes with the flow rate. The steady-state efficiency curve is fitted into a polynomial of flow rate and speed:

[0090] (1)

[0091] In formula (1), They are the flow rate, efficiency and speed of the doubly-fed pumped storage unit when it is running at variable speed under fixed water head; are 6 curve fitting coefficients, and ; is the impeller radius of the doubly-fed pumped storage unit; is the impeller swept area; is an intermediate variable.

[0092] Step S1-2: The undetermined parameters appear in a nonlinear form in the constructed polynomial function, and are linearized by variable substitution, so that a fitting polynomial satisfying the recursive least squares method is established using formula (2) to simplify the calculation process.

[0093] (2)

[0094] Step S1-3: Taking the minimum sum of squares of the residuals between the data sampling points and the fitting polynomial as the objective function, the recursive least squares method with a discount factor is used to perform curve fitting on equation (2) to obtain 6 curve fitting coefficients that meet a certain accuracy. The corresponding estimated value , its schematic diagram is as follows Figure 3 shown.

[0095] Step S1-3-1: Rewrite equation (2) into a vector form that satisfies the sample data:

[0096] (3)

[0097] In formula (3), is the vector form of measurable output data; is the vector form of measurable input data; is the vector form of the curve fitting coefficients; is the added white noise; represents transpose; Respectively represent The efficiency, flow rate and speed corresponding to each data sampling point.

[0098] Step S1-3-2: Use formula (4) to construct the objective function of the recursive least squares method with discount factor :

[0099] (4)

[0100] Step S1-3-3: Use equation (5) to derive the objective function Curve fitting coefficients The partial derivative of :

[0101] (5)

[0102] Step S1-3-4: Set equation (5) equal to 0 and obtain the estimated value of the curve fitting coefficient :

[0103] (6)

[0104] Step S1-3-5: Use formula (7) to perform variable substitution to make the recursive least square method with discount factor inheritable, so as to reduce the amount of calculation and storage of the system and avoid matrix inversion operations.

[0105] (7)

[0106] In formula (7), For the The covariance matrix of the iterations, For the The adaptive gain matrix of the iterations, both of which will change with the number of iterations The increase gradually approaches 0; is the identity matrix; For the The vector form of the input data for the iteration.

[0107] Step S1-3-6: Combine equations (6) and (7) to obtain an estimated value of the curve fitting coefficient using equation (8):

[0108] (8)

[0109] In formula (8), For the The estimated values ​​of the curve fitting coefficients in iterations; For the The vector form of the input data for the iteration.

[0110] Step S1-3-7: In order to weaken the influence of data saturation and overcome the contradiction between fast convergence speed and small parameter estimation error, the effects of weighting factor and forgetting factor are comprehensively considered and the objective function is Introducing dynamic discount factor :

[0111] (9)

[0112] In formula (9), For the Weighting factors; For the The forgetting factor in the iteration is usually between 0.9 and 1.0.

[0113] Step S1-3-8: Combine equations (5), (8) and (9), and then use equation (10) to establish the recursive relationship of the recursive least squares method with a discount factor:

[0114] (10)

[0115] Step S1-3-9: Set initial value , ,in, is a sufficiently small positive real vector, is a sufficiently large positive real number.

[0116] Step S1-3-10: By continuously acquiring the sampling data of the steady-state efficiency curve of the pump-turbine when running at a fixed water head and at a variable speed, the data is substituted into formula (10) for iterative calculation until a certain accuracy requirement is met, and the curve fitting coefficient is obtained. The corresponding estimated value .

[0117] Step S1-4: Estimated values ​​of the six curve fitting coefficients Substituting into equation (2), we can use equation (11) to obtain the steady-state efficiency curve polynomial of the doubly-fed pumped storage unit when operating at variable speed under fixed water head:

[0118] (11)

[0119] Step S2: In order to give full play to the advantages of variable frequency speed regulation of the doubly fed pumped storage unit, the partial derivative of its steady-state efficiency curve polynomial with respect to the speed is derived, and the optimal speed corresponding to different flow rates under the variable frequency speed regulation condition is obtained, thereby establishing an analytical expression between the mechanical power and flow rate of the doubly fed pumped storage unit when it operates at the optimal speed.

[0120] Step S2-1: When the pump-turbine deviates from the optimal efficiency, the wear, vibration, cavitation and other phenomena of the unit are aggravated, and the operating efficiency is greatly reduced. Therefore, it is necessary to adjust the converter and the speed governor to make the doubly fed pumped storage unit always operate at the optimal efficiency. The polynomial of the steady-state efficiency curve of the doubly fed pumped storage unit versus speed is derived using formula (12): The partial derivative of :

[0121] (12)

[0122] Step S2-2: Set equation (12) to 0, and then use equation (13) to obtain the flow rates of the double-fed pumped storage unit under variable frequency speed regulation conditions: The corresponding optimal speed :

[0123] (13)

[0124] Step S2-3: Use equation (14) to obtain the mechanical power of the reversible pump turbine :

[0125] (14)

[0126] In formula (14), is the specific gravity of water, is the acceleration due to gravity, For the water head.

[0127] Step S2-4: Combine equations (11), (13) and (14), and then use equation (15) to establish the mechanical power of the doubly-fed pumped storage unit when it runs at the optimal speed: With flow The analytical expression between:

[0128] (15)

[0129] Step S3: Considering the influence of the change of internal loss during the variable speed operation of the doubly-fed pumped storage unit, the simultaneous iterative solution method is selected to introduce its power / torque constraint equations into the power grid flow equation, expand the traditional Jacobian matrix, and establish a grid-connected power flow model to improve the accuracy of power flow calculation. Figure 4 shown.

[0130] Step S3-1: Considering that the active output of the doubly-fed pumped storage unit is not only related to the mechanical power, but also affected by the winding losses of the stator, rotor, and grid-side converter. As shown in formula (16), it is not a constant, so it is impossible to establish the active balance equation of the stator node of the doubly fed pumped storage unit before solving the power grid flow.

[0131] (16)

[0132] In formula (16), They represent the stator nodes of the doubly-fed pumped storage unit. , Virtual Node Grid-side converter node Voltage value; They represent the stator nodes of the doubly-fed pumped storage unit. , rotor node Grid-side converter node The current conjugate value; They respectively represent the stator impedance, rotor impedance and grid-side converter impedance of the doubly-fed pumped storage unit; Re represents the real part, and Im represents the imaginary part.

[0133] Step S3-2: Combine the stator node of the doubly fed pumped storage unit with the power grid and the power constraint equation inside the unit to establish its stator node The power constraint equations.

[0134] Step S3-2-1: According to the active power flow relationship between the double-fed pumped storage unit and the power grid, use equation (17) to establish its stator node Active power constraint equations for the power grid and the internal units:

[0135] (17)

[0136] In formula (17), They represent the stator nodes of the doubly-fed pumped storage unit. The active output and its set value.

[0137] Step S3-2-2: Based on equation (17), use equation (18) to establish the stator node of the doubly-fed pumped storage unit The active power constraint equation is:

[0138] (18)

[0139] In formula (18), Represents the stator node of the doubly-fed pumped storage unit The active unbalance amount.

[0140] Step S3-2-3: Both the rotor-side converter and the grid-side converter can adjust the reactive output, so that the doubly-fed pumped storage unit operates in a constant reactive mode. According to the reactive power flow relationship between it and the grid, the stator node is established using equation (19): The reactive power constraint equations are:

[0141] (19)

[0142] In formula (19), They represent the stator nodes of the doubly-fed pumped storage unit. Reactive power imbalance between the power grid and the unit; Virtual node representing a doubly-fed pumped storage unit The current conjugate value.

[0143] Step S3-3: To distinguish the stator and rotor circuits, add an excitation circuit and use equation (20) to establish its virtual node Active and reactive power constraint equations:

[0144] (20)

[0145] In formula (20), They represent the virtual nodes of the double-fed pumped storage units. The active unbalance and reactive unbalance.

[0146] Step S3-4: When the doubly-fed pumped storage unit is in steady-state operation, the DC voltage of the back-to-back converter is constant, that is, the sum of the active outputs of the rotor-side converter and the grid-side converter is zero, and the grid-side converter can be independently controlled and output reactive power. The grid-side converter node is established using equation (21): Active and reactive power constraint equations:

[0147] (twenty one)

[0148] In formula (21), They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance; They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Reactive power setpoint and rotor node Voltage value.

[0149] Step S3-5: To maintain torque The active power balance relationship between the reversible pump-turbine and the doubly-fed induction motor is established.

[0150] Step S3-5-1: Ignore the excitation branch resistance and define the electromagnetic power from the right side of the air gap , using equation (22) to establish the balance relationship between the stator and rotor of the doubly fed pumped storage unit:

[0151] (twenty two)

[0152] In formula (22), is the slip rate; is the number of pole pairs of the doubly-fed induction motor; is the gearbox speed ratio; is the per unit value of the rated frequency of the power grid; is the torque unbalance of the doubly-fed pumped storage unit.

[0153] Step S3-5-2: Substitute equation (13) into equation (22), and use equation (23) to obtain the optimal speed of the doubly-fed pumped storage unit: Slip rate during operation :

[0154] (twenty three)

[0155] Step S3-5-3: Combine equation (15), equation (23) and equation (22), and then use equation (24) to establish the torque constraint equation of the doubly-fed pumped storage unit:

[0156] (twenty four)

[0157] Step S3-6: Select the simultaneous iterative solution method to combine the power / torque constraint equations of the doubly-fed pumped storage unit with the power grid flow equation, expand the traditional Jacobian matrix, and use equation (25) to establish its grid-connected power flow model:

[0158] (25)

[0159] In formula (25), Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage amplitude correction value; Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage phase angle correction value; They represent the stator nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance of AC power grid nodes; represents the expanded Jacobian matrix.

[0160] Step S4: To solve the problem that the positive and negative switching of the rotor voltage phase angle of the doubly-fed pumped storage unit easily leads to the oscillation and non-convergence of the power flow iteration process, the grid-connected power flow model is expanded by the first-order Taylor, the damping factor is introduced, and the least squares model is established. Figure 5 shown.

[0161] Step S4-1: In order to overcome the problem that the positive and negative switching of the rotor voltage phase angle of the doubly fed pumped storage unit easily leads to the oscillation and non-convergence of the traditional power flow iteration process, the grid-connected power flow model is constructed using equation (26). The objective function of the iteration :

[0162] (26)

[0163] In formula (26), is the number of iterations; Respectively represent The power imbalance between the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration; Respectively represent The voltage correction amount of the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration.

[0164] Step S4-2: Perform a first-order Taylor expansion on equation (26) and use equation (27) to construct the first The new objective function for the iteration :

[0165] (27)

[0166] In formula (27), For the The Jacobian matrix of the iteration.

[0167] Step S4-3: Using formula (28) to obtain For The voltage correction value of the iteration The partial derivative of :

[0168] (28)

[0169] Step S4-4: Set equation (28) to 0 and introduce Damping factor for iterations In order to overcome the problem that the Jacobian matrix cannot be inverted when it is singular or approximately singular, the least squares model is established using formula (29):

[0170] (29)

[0171] Step S5: To improve the convergence of the power flow calculation and solve the problem that the positive and negative switching of the rotor voltage phase angle easily leads to the oscillation and non-convergence of the power flow iteration process, the damping factor is improved. The selection strategy of the proposed method is adopted, two approximate Levenberg-Marquardt iteration steps are introduced, and the least squares model is iteratively solved using the Levenberg-Marquardt algorithm with fourth-order convergence. The power flow calculation results taking into account the internal losses of the doubly-fed pumped-storage unit are obtained, including the approximate power flow solution of the doubly-fed pumped-storage unit when the slip rate is 0.

[0172] Step S5-1: Initialization , , and The voltage value of the AC power grid node under the iteration and Voltage values ​​of internal nodes of the doubly-fed pumped storage unit under iteration , set the convergence accuracy ε.

[0173] Step S5-2: Based on The voltage value of the AC power grid node under the iteration The voltage value of the internal node of the double-fed pumped storage unit , use formula (25) to calculate the The Jacobian matrix for the iteration.

[0174] Step S5-3: In order to make the Levenberg Marquardt algorithm have both the global optimization characteristics of the gradient descent method and the local fast convergence characteristics of the Gauss-Newton method, the damping factor Improve the selection strategy.

[0175] Step S5-3-1: In order to change the step size and direction of the node voltage amplitude and phase angle correction at the same time and overcome the problem that the power flow equation is sensitive to the initial value, equation (30) is used to obtain Adaptive damping factor for iterations :

[0176] (30)

[0177] In formula (30), For the The adaptive factor of the iteration, and .

[0178] Step S5-3-2: In order to meet the requirement that the adaptive damping factor changes with the iteration process and verify the effectiveness of the current iteration step, the first Evaluation index of the effect of iterative descent :

[0179] (31)

[0180] In formula (31), For the The voltage value of the AC grid node in the iteration, For the The voltage value of the internal node of the doubly-fed pumped storage unit at the iteration; is the power balance equation including the AC grid nodes and the internal nodes of the doubly-fed pumped storage unit; when When it is close to 1, the model has a good approximation effect. The value is appropriate.

[0181] Step S5-4: To improve the convergence of power flow calculation, two approximate Levenberg-Marquardt iteration steps are introduced, and a Levenberg-Marquardt algorithm with fourth-order convergence is proposed. Using equation (33), the first The voltage value of the AC grid node corrected for the first time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the first time in the iteration , and The voltage correction of the AC grid node introduced for the first time in the iteration With The voltage correction value of the internal node of the doubly-fed pumped storage unit introduced for the first time in the iteration :

[0182] (33)

[0183] Step S5-5: Use formula (34) to obtain The voltage value of the AC grid node corrected for the second time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the second time in the iteration , and respectively represent the The voltage correction of the AC grid node introduced for the second time in the iteration With The voltage correction value of the internal node of the doubly-fed pumped storage unit introduced for the second time in the iteration :

[0184] (34)

[0185] Step S5-6: Combine equation (29), equation (33) and equation (34), and then use equation (35) to obtain Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration :

[0186] (35)

[0187] Step S5-7: Based on and , calculate the Active unbalance of each node in the iteration Reactive unbalance ,like , then stop the calculation and output the Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration ; Otherwise, execute step S5-8.

[0188] Step S5-8: Use equation (36) to obtain Adaptive factor of the iteration :

[0189] (36)

[0190] In formula (36), is the upper threshold of the evaluation index; is the lower threshold of the evaluation index; is the lower threshold of the adaptive factor.

[0191] Step 5-9: Assign to Then, return to step S5-2 and execute sequentially.

[0192] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0193] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on optimal speed, characterized in that: The following steps are involved: Step S1: using the recursive least square method with a discount factor to fit the steady-state efficiency curve polynomial of the doubly-fed pumped storage unit when it is running at a variable speed under a fixed water head; Step S2: Solve the steady-state efficiency curve polynomial according to the partial derivative of the steady-state efficiency curve polynomial with respect to the speed, and obtain the optimal speed corresponding to different flow rates of the double-fed pumped storage unit during variable frequency speed regulation operation. , thus establishing an analytical expression between mechanical power and flow rate when operating at the optimal speed; Step S3: using a simultaneous iterative solution method to introduce the internal constraint equations of the doubly-fed pumped storage unit into the power grid flow equation, thereby establishing its grid-connected power flow model; Step S4: Perform a first-order Taylor expansion on the grid-connected power flow model of the doubly-fed pumped storage unit and introduce a damping factor to construct a least squares model; Step S5: using a fourth-order convergent Levenberg Marquardt algorithm to iteratively solve the least squares model, and obtain the power flow calculation results taking into account the internal losses of the doubly-fed pumped storage unit, including the approximate power flow solution of the doubly-fed pumped storage unit when the slip rate is 0.

2. A method for calculating grid-connected power flow of a doubly-fed pumped storage unit based on optimal speed according to claim 1, characterized in that: The step S1 is performed as follows: Step S1-1: Use equation (1) to establish a fitting polynomial for the doubly-fed pumped storage unit: (1) In formula (1), They are the flow rate, efficiency and speed of the doubly-fed pumped storage unit when it is running at variable speed under fixed water head; are 6 curve fitting coefficients, and ; is the impeller radius of the doubly-fed pumped storage unit; is the impeller swept area; is an intermediate variable; Step S1-2: Taking the minimum sum of squares of the residuals between the data sampling points and the fitting polynomial as the objective function, the recursive least squares method with a discount factor is used to perform curve fitting on equation (1) to obtain 6 curve fitting coefficients that meet a certain accuracy. The corresponding estimated value ; Step S1-3: The estimated values ​​of the six curve fitting coefficients Substituting into equation (1), we can use equation (2) to obtain the steady-state efficiency curve polynomial of the doubly-fed pumped storage unit when operating at variable speed under fixed water head: (2)。 3. The method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on an optimal speed according to claim 2, characterized in that: The step S2 is performed as follows: Step S2-1: Using equation (3) to obtain the steady-state efficiency curve polynomial versus speed The partial derivative of : (3) Step S2-2: Set equation (3) to 0, and then use equation (4) to obtain the optimal speed corresponding to different flow rates of the double-fed pumped storage unit during variable frequency speed regulation operation: : (4) Step S2-3: Use equation (5) to establish the optimal speed of the doubly-fed pumped storage unit Its mechanical power during operation With flow The analytical expression between: (5) In formula (5), is the specific gravity of water, is the acceleration due to gravity, For the water head.

4. The method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on an optimal speed according to claim 3, characterized in that: The step S3 is performed as follows: Step S3-1: Use equation (6) to establish the stator node of the doubly-fed pumped storage unit The active power constraint equation is: (6) In formula (6), They represent the stator nodes of the doubly-fed pumped storage unit. Active unbalance, active output, voltage value, and current conjugate value; Represents the grid-side converter node of the doubly-fed pumped storage unit The current conjugate value; Re means taking the real part, Im means taking the imaginary part; Step S3-2: Use equation (7) to establish the stator node of the doubly-fed pumped storage unit The reactive power constraint equations are: (7) In formula (7), They represent the stator nodes of the doubly-fed pumped storage unit. Reactive power imbalance between the power grid and the unit; They represent the stator nodes of the doubly-fed pumped storage unit. Reactive power output and virtual nodes The current conjugate value of Step S3-3: Use equation (8) to establish the virtual node of the double-fed pumped storage unit The power constraint equations are: (8) In formula (8), They represent the virtual nodes of the double-fed pumped storage units. Active unbalance and reactive unbalance; They represent the virtual nodes of the double-fed pumped storage units. The voltage value of the rotor node The current conjugate value of Step S3-4: Use equation (9) to establish the grid-side converter node of the doubly-fed pumped storage unit The power constraint equations are: (9) In formula (9), They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance; They represent the grid-side converter nodes of the doubly-fed pumped storage unit. Reactive power setting value and voltage value; Represents the rotor node of the doubly-fed pumped storage unit Voltage value; Step S3-5: Use equation (10) to obtain the optimal speed of the doubly-fed pumped storage unit Slip rate during operation : (10) In formula (10), is the number of pole pairs of the doubly-fed induction motor; is the speed increase ratio of the gearbox; is the per unit value of the rated frequency of the power grid; Step S3-6: Use equation (11) to establish the optimal speed of the doubly-fed pumped storage unit Mechanical power during operation With electromagnetic power The equilibrium relationship, that is, the torque constraint equation: (11) In formula (11), Indicates the torque unbalance of the doubly-fed pumped storage unit; Step S3-7: Combine equations (6) to (11) with the power grid flow equation, and use equation (12) to establish a grid-connected power flow model for the doubly-fed pumped storage unit: (12) In formula (12), Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage amplitude correction value; Represents the AC grid node and the virtual node of the double-fed pumped storage unit , rotor node , grid-side converter node The voltage phase angle correction value; They represent the stator nodes of the doubly-fed pumped storage unit. Active unbalance and reactive unbalance of AC power grid nodes; represents the expanded Jacobian matrix.

5. A method for calculating grid-connected power flow of a doubly-fed pumped storage unit based on optimal speed according to claim 4, characterized in that: The step S4 is performed as follows: Step S4-1: Perform a first-order Taylor expansion on the grid-connected power flow model of the doubly-fed pumped storage unit, and then use equation (13) to construct the first The objective function of the iteration : (13) In formula (13), is the number of iterations; represents transpose; Respectively represent The power imbalance between the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration; For the The Jacobian matrix of the iteration; Respectively represent The voltage correction amount of the AC grid nodes and the internal nodes of the double-fed pumped storage unit in the iteration; Step S4-2: Using formula (14) to obtain For The voltage correction value of the iteration The partial derivative of : (14) Step S4-3: Set equation (14) to 0 and introduce the Damping factor for iterations , and then use formula (15) to establish the least squares model: (15)。 6. The method for calculating the grid-connected power flow of a doubly-fed pumped storage unit based on optimal speed according to claim 5, characterized in that: The step S5 is performed as follows: Step S5-1: Initialization , , and The voltage value of the AC power grid node under the iteration and Voltage values ​​of internal nodes of the doubly-fed pumped storage unit under iteration , set the convergence accuracy ; Step S5-2: Based on The voltage value of the AC power grid node under the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit under iteration , use formula (12) to calculate the The Jacobian matrix of the iteration; Step S5-3: Calculate the first Damping factor for iterations : (16) In formula (16), For the The adaptive factor of the iteration, and ; Step S5-4: Use formula (17) to obtain The voltage value of the AC grid node corrected for the first time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the first time in the iteration , and The voltage correction of the AC grid node introduced for the first time in the iteration With The voltage correction value of the internal node of the doubly-fed pumped storage unit introduced for the first time in the iteration : (17) In formula (17), is the power balance equation including the AC grid nodes and the internal nodes of the doubly-fed pumped storage unit; Step S5-5: Use formula (18) to obtain The voltage value of the AC grid node corrected for the second time in the iteration With The voltage value of the internal node of the doubly-fed pumped storage unit corrected for the second time in the iteration , and The voltage correction of the AC grid node introduced for the second time in the iteration With Voltage correction of the internal nodes of the double-fed pumped storage unit introduced for the second time in the iteration : (18) Step S5-6: Combine equation (15), equation (17) and equation (18), and use equation (19) to obtain Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration : (19) Step S5-7: Based on and , calculate the Active unbalance of each node in the iteration Reactive unbalance ,like , then stop the calculation and output the Voltage values ​​of AC grid nodes in the iteration With Voltage values ​​of internal nodes of the doubly-fed pumped storage unit in the iteration ; Otherwise, execute step S5-8; Step S5-8: Use formula (20) to obtain Adaptive factor of the iteration : (20) In formula (20), For the The evaluation index of the descent effect in the iteration, is the upper threshold of the evaluation index; is the lower threshold of the evaluation index; is the lower threshold of the adaptive factor; Step 5-9: Assign to Then, return to step S5-2 and execute sequentially.

7. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the grid-connected power flow calculation method described in any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the grid-connected power flow calculation method described in any one of claims 1 to 6 are executed.

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