An optimized algorithm for determining the maximum phase advance depth of a generator

Abstract

This invention discloses an optimized algorithm for calculating the maximum phase advance depth of a generator. First, it uses real-time operating data from the generator synchronous phasor measurement unit (PMU) to identify the equivalent contact reactance x between the generator and the infinite bus. s Then, based on the principle of power flow calculation, the functional relationships between five variables—generator terminal voltage, high-voltage station bus voltage, low-voltage station bus voltage, power angle, and generator terminal current—and system voltage and generator reactive power are calculated. Finally, an optimal mathematical model for solving the maximum reactive power advance depth of the generator is established, and the maximum reactive power advance depth of the generator under different active power conditions is obtained. This invention solves the problems of complex procedures, time-consuming processes, and inability to adapt to online applications in existing simulation calculation methods.

Description

Technical Field

[0001] This invention belongs to the field of generator control technology, specifically relating to an optimized algorithm for calculating the maximum leading depth of a generator. Background Technology

[0002] As the scale of ultra-high voltage and extra-high voltage long-distance power transmission continues to expand and the power grid structure becomes increasingly complex, the problem of excessive reactive power during periods of low local power grid load, leading to higher voltage at the central point, is becoming increasingly prominent.

[0003] Generators operating in a leading-phase mode, employing underexcitation, can absorb excess reactive power while generating active power. This has become an important voltage regulation method for power grids, effectively addressing high-voltage issues. Due to its simple operation and lack of additional investment, it has been widely adopted.

[0004] The leading-phase capability of a generator is constrained by safety conditions. To determine the maximum leading-phase depth for safe generator operation, it is usually necessary to obtain it through on-site testing. To ensure the safe conduct of the leading-phase test, it is often necessary to estimate the maximum leading-phase depth of the generator under various typical active power output conditions before the test, in order to prevent excessive leading-phase capability from causing the unit to trip due to loss of excitation. Leading-phase capability estimation is achieved by offline simulation of various leading-phase operating conditions using power grid simulation software. This process calculates the generator terminal voltage, station service voltage, power angle, system transient stability, etc., under each condition, and identifies limiting conditions, ultimately determining the maximum leading-phase depth of the generator under each condition. Because it uses offline simulation and requires multiple calculations for various operating conditions, the calculation accuracy is limited by the model and parameters. Therefore, this method is relatively complex, time-consuming, and unsuitable for online monitoring of the generator's safe leading-phase capability. Summary of the Invention

[0005] The purpose of this invention is to provide an optimized algorithm for calculating the maximum phase advance depth of a generator, which solves the problems of complex and time-consuming procedures and inability to adapt to online applications in existing simulation calculation methods.

[0006] The technical solution adopted in this invention is an optimized algorithm for calculating the maximum leading depth of a generator, which is implemented according to the following steps:

[0007] Step 1: Use the real-time operating data of the generator synchronous phasor measurement unit (PMU) to identify the equivalent bonding reactance x between the generator and the infinite bus online. s ;

[0008] Step 2: Based on the power flow calculation principle, calculate the functional relationship between the five variables—generator terminal voltage, high-voltage station bus voltage, low-voltage station bus voltage, power angle, and generator terminal current—and the system voltage and generator reactive power.

[0009] Step 3: Establish an optimal mathematical model for solving the maximum advance depth of the generator, and solve it to obtain the maximum advance depth of the reactive power of the generator under different active power conditions.

[0010] The invention is further characterized in that,

[0011] Step 1 is as follows:

[0012] Step 1.1, Simplifying generator connection to the system:

[0013] The external power grid to which the generator is connected is considered an infinite system. The equivalent calculation circuit for the infinite system is based on the generator's synchronous reactance x. d x q , step-up transformer reactance x T1 Transmission line reactance x L Series connection, with the equivalent impedance x of the plant service transformer connected in parallel at the generator outlet side. T2 Branch circuit composition, where: E q For the generator's internal potential, U G For generator output voltage, U T Main transformer high voltage side voltage, U s The voltage of the infinite equivalent bus; x T2 These are the equivalent branch reactances of the plant service transformer, and are known values; x s The equivalent interconnecting reactance between the generator and the infinite busbar;

[0014] Step 1.2, Generator Equivalent Co-current x s The online identification process is as follows:

[0015] Real-time operating data of the generator's generator unit (PMU) under generator disturbance conditions was selected as samples for online identification of the generator's equivalent tie reactance. The real-time operating data of the PMU included: generator terminal voltage, generator terminal current, and reactive power. A mathematical model for identifying the generator's equivalent tie reactance was established.

[0016]

[0017] In the formula: U Gi I Gi Q Gi These represent the generator terminal voltage, generator terminal current, and reactive power corresponding to the i-th sample in the sample data, respectively; N is the total number of data samples.

[0018] Solving the optimal mathematical model of equation (1), we obtain x. s and U s The identification results.

[0019] Step 2 is as follows:

[0020] Step 2.1, Generator terminal voltage U G Its reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0021] (1) Generator terminal - plant service transformer branch, i.e., the equivalent branch reactance x of the plant service transformer T2 Location of the side road:

[0022] The reactive power loss of this branch is:

[0023]

[0024] In the formula: P L and Q L These are the active and reactive loads of the transformer branch used in the generator plant, respectively, and are known values, with units of MW and MVar, respectively; U L1N The voltage at the primary side tap of the plant service transformer is a known value, and the unit is kV.

[0025] The reactive power of this branch is:

[0026]

[0027] (2) The generator terminal - step-up transformer branch, i.e., the step-up transformer reactance x T1 Location of the side road:

[0028] The reactive power loss of this branch is:

[0029]

[0030] In the formula: P G The generator's active power is a known value, expressed in MW; S GN U represents the generator's rated apparent power, a known value, in MVA; T1 U T1N These are the tap voltage and rated voltage on the high-voltage side of the step-up transformer, respectively, both of which are known values ​​in kV.

[0031] The reactive power of this branch is:

[0032]

[0033] The transverse component of the voltage drop in this branch is:

[0034]

[0035] The longitudinal component of the voltage drop in this branch is:

[0036]

[0037] The generator terminal voltage is calculated as follows:

[0038]

[0039] In the formula: U T2 This refers to the actual tap voltage on the low-voltage side of the step-up transformer.

[0040] Then we have: x s ≈x T1 U T ≈U S ;

[0041] Substituting equations (3) to (7) into equation (8) in turn, we can derive U. G With Q G U T That is U s The functional relationship between the two is denoted as:

[0042] U G =f1(Q G U s (9)

[0043] Step 2.2, High-voltage plant bus voltage U LTL With generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0044] (1) Transverse component of voltage drop in branch circuit of plant service transformer:

[0045]

[0046] (2) Longitudinal component of voltage drop in branch circuit of plant service transformer:

[0047]

[0048] (3) Voltage of the high-voltage plant service transformer bus:

[0049]

[0050] In the formula: U L1 U L2 These are the primary and secondary tap voltages of the high-voltage plant service transformer, respectively, both of which are known values ​​in kV.

[0051] Substituting equations (10) and (11) into equation (12), we obtain U. LTL With Q G U s The functional relationship between the two is denoted as:

[0052] U LTL =f2(Q G U s(13)

[0053] Step 2.3, Low-voltage plant bus voltage U FL With generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0054]

[0055] In the formula: U F1 U F2 These are the high and low voltage taps of the low-voltage plant service transformer, respectively, both of which are known values ​​in kV.

[0056] Step 2.4, Generator power angle δ and generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0057]

[0058] In the formula: x q U GN The generator's q-axis synchronous reactance and rated terminal voltage are both known values, with units of Ω and kV, respectively.

[0059] Step 2.5, Generator terminal current I G With generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0060]

[0061] Step 3 is as follows:

[0062] Step 3.1: Establish the optimal mathematical model for solving the maximum advance depth of the generator:

[0063] (1) Construct the objective function:

[0064] Based on the equations of a synchronous generator, we derive:

[0065]

[0066] According to the principle of leading phase operation, when the generator reaches its maximum leading phase depth, the terminal voltage will be at its minimum. Therefore, the optimal objective function model for solving the maximum leading phase depth of the generator is as follows:

[0067]

[0068] (2) Constructing constraints:

[0069] Combining the upper and lower limits of each variable from step 2, the following constraints are obtained:

[0070]

[0071] In the formula: U Gmin U represents the lower limit of the generator terminal voltage, a known value, in kV. LTLmax U LTLmin These are the upper and lower limits of the voltage of the high-voltage station service transformer bus, respectively. These are known values, and the unit is kV; U FLmax U FLmin These are the upper and lower limits of the low-voltage plant auxiliary transformer bus voltage, respectively. These are known values, and the unit is kV; δ max I represents the upper limit of the generator's power angle, a known value, in degrees. Gmax U represents the upper limit of the generator terminal current, a known value, in kA; smax U smin These are the upper and lower limits of the system voltage, which are known values, and the unit is kV;

[0072] (3) By combining equations (18) and (19), the above optimization mathematical model can be solved to obtain the known generator active power P. G The corresponding reactive power Q G This is the maximum phase advance depth of the generator.

[0073] The beneficial effects of this invention are that it provides an optimization algorithm for determining the maximum advance depth of a generator, which transforms the determination of the maximum advance depth of a generator into an optimization problem. The algorithm automatically calculates the maximum advance depth under different active power output conditions through programming. It has the advantages of simple procedures, ease of implementation, and convenient online calculation. Attached Figure Description

[0074] Figure 1 The present invention provides a structural diagram of a single-machine infinite equivalent system with load at the machine end;

[0075] Figure 2 The present invention provides a circuit diagram of a single-machine infinite equivalent system;

[0076] Figure 3 The flowchart of the algorithm for optimizing the maximum phase advance depth of a generator provided by this invention is shown in the figure. Detailed Implementation

[0077] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0078] Figure 1 This is a structural diagram of an infinitely large equivalent system with load at the generator terminals. Figure 2 According to Figure 1A simplified equivalent calculation circuit is obtained. Based on this circuit, the equivalent interconnection reactance between the generator and the infinite bus is identified online using real-time operating data of the PMU (Synchronous Phasor Measurement Unit) under generator disturbance conditions. Based on the power flow calculation principle, the functional relationship between five variables—generator terminal voltage, high-voltage station service bus voltage, low-voltage station service bus voltage, power angle, and generator terminal current—and the generator reactive power and system voltage is calculated. An optimal mathematical model for solving the maximum phase advance depth of the generator is established, and the maximum reactive phase advance depth of the generator under different active power conditions can be obtained by using the optimal solution method. The above process is programmed to achieve automatic calculation.

[0079] This invention provides an optimized algorithm for calculating the maximum phase advance depth of a generator, the flowchart of which is shown below. Figure 3 As shown, please follow these steps:

[0080] Step 1, based on Figure 2 The equivalent calculation circuit for a single-unit infinite bus system with load shown uses real-time operating data from the generator synchronous phasor measurement unit (PMU) to identify the equivalent interconnect reactance x between the generator and the infinite bus online. s (Hereinafter referred to as generator equivalent interconnect reactance);

[0081] Step 1 is as follows:

[0082] Step 1.1, Simplifying generator connection to the system:

[0083] In modern power systems, generators typically supply power to loads via long-distance transmission systems. To simplify the analysis, the external power grid to which the generator is connected is considered an infinitely large system, and its equivalent calculation circuit is as follows: Figure 2 As shown. The equivalent calculation circuit for an infinite system consists of the synchronous reactance x of the generator. d x q , step-up transformer reactance x T1 Transmission line reactance x L Series connection, with the equivalent impedance x of the plant service transformer connected in parallel at the generator outlet side. T2 Branch circuit composition, where: E q For the generator's internal potential, U G For generator output voltage, U T Main transformer high voltage side voltage, U s The system voltage is the infinite equivalent bus voltage; x T2 These are the equivalent branch reactances of the plant service transformer, and are known values; x s This is the equivalent interconnecting reactance between the generator and the infinite busbar.

[0084] Step 1.2, Generator Equivalent Co-current x s The online identification process is as follows:

[0085] To improve calculation accuracy, real-time PMU operating data under generator disturbance conditions was selected as samples for online identification of generator equivalent interconnection reactance. The real-time PMU operating data includes: generator terminal voltage, terminal current, and reactive power. Figure 2 The equivalent circuit is used to establish a mathematical model for identifying the equivalent interconnect reactance of the generator:

[0086]

[0087] In the formula: U Gi I Gi Q Gi These represent the generator terminal voltage, generator terminal current, and reactive power corresponding to the i-th sample in the sample data, respectively; N is the total number of data samples.

[0088] The optimal mathematical model of equation (1) is solved using optimization algorithms such as genetic algorithms, and x is calculated. s and U s The identification results.

[0089] Step 2: Based on the power flow calculation principle, calculate the functional relationship between the five variables—generator terminal voltage, high-voltage station bus voltage, low-voltage station bus voltage, power angle, and generator terminal current—and the system voltage and generator reactive power.

[0090] Step 2 is as follows:

[0091] Step 2.1, Generator terminal voltage U G Its reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0092] (3) Generator terminal - plant service transformer branch, i.e., the equivalent branch reactance x of the plant service transformer T2 Location of the side road:

[0093] The reactive power loss of this branch is:

[0094]

[0095] In the formula: P L and Q L These are the active and reactive loads of the transformer branch used in the generator plant, respectively, and are known values, with units of MW and MVar, respectively; U L1N The voltage at the primary side tap of the plant service transformer is a known value, and the unit is kV.

[0096] The reactive power of this branch is:

[0097]

[0098] (4) Generator terminal - step-up transformer branch, i.e., step-up transformer reactance x T1 Location of the side road:

[0099] The reactive power loss of this branch is:

[0100]

[0101] In the formula: P G The generator's active power is a known value, expressed in MW; S GN U represents the generator's rated apparent power, a known value, in MVA; T1 U T1N These are the tap voltage and rated voltage on the high-voltage side of the step-up transformer, respectively, both of which are known values ​​in kV.

[0102] The reactive power of this branch is:

[0103]

[0104] The transverse component of the voltage drop in this branch is:

[0105]

[0106] The longitudinal component of the voltage drop in this branch is:

[0107]

[0108] The generator terminal voltage is calculated as follows:

[0109]

[0110] In the formula: U T2 This refers to the actual tap voltage on the low-voltage side of the step-up transformer.

[0111] Considering the reactance x of the generator's output transmission line in actual engineering practice L After calculation, it is usually much smaller than the reactance x of the step-up transformer. T1 Therefore, it can be ignored, so we have: x s ≈x T1 U T ≈U S ;

[0112] Substituting equations (3) to (7) into equation (8) in turn, we can derive U. G With Q G U T That is U s The functional relationship between the two is quite complex, so it is denoted here as:

[0113] U G =f1(Q GU s (9)

[0114] Step 2.2, High-voltage plant bus voltage U LTL With generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0115] (1) Transverse component of voltage drop in branch circuit of plant service transformer:

[0116]

[0117] (2) Longitudinal component of voltage drop in branch circuit of plant service transformer:

[0118]

[0119] (3) Voltage of the high-voltage station service transformer bus (secondary side voltage of the high-voltage station service transformer):

[0120]

[0121] In the formula: U L1 U L2 These are the primary and secondary tap voltages of the high-voltage plant service transformer, respectively, both of which are known values ​​in kV.

[0122] Substituting equations (10) and (11) into equation (12), we obtain U. LTL With Q G U s The functional relationship between the two; similarly, this relationship is more complex and is denoted here as:

[0123] U LTL =f2(Q G U s (13)

[0124] Step 2.3, Low-voltage plant bus voltage U FL (Secondary voltage of high-voltage station service transformer) and generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0125]

[0126] In the formula: U F1 U F2 These are the high and low voltage taps of the low-voltage plant service transformer, respectively, both of which are known values ​​in kV.

[0127] Step 2.4, Generator power angle δ and generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0128]

[0129] In the formula: x q U GN The generator's q-axis synchronous reactance and rated terminal voltage are both known values, with units of Ω and kV, respectively.

[0130] Step 2.5, Generator terminal current I G With generator reactive power Q G System voltage U s Derivation of the functional relationship between them:

[0131]

[0132] Step 3: Establish an optimal mathematical model for solving the maximum advance depth of the generator, and use genetic algorithms, particle swarm optimization, etc. to solve the maximum advance depth of the reactive power of the generator under different active power conditions.

[0133] Step 3 is as follows:

[0134] Step 3.1: Establish the optimal mathematical model for solving the maximum advance depth of the generator:

[0135] (4) Construct the objective function:

[0136] Based on the equations of a synchronous generator, we derive:

[0137]

[0138] According to the principle of leading phase operation, when the generator reaches its maximum leading phase depth, the terminal voltage will be at its minimum. Therefore, the optimal objective function model for solving the maximum leading phase depth of the generator is as follows:

[0139]

[0140] (5) Constructing constraints:

[0141] Combining the upper and lower limits of each variable from step 2, the following constraints are obtained:

[0142]

[0143] In the formula: U Gmin U represents the lower limit of the generator terminal voltage, a known value, in kV. LTLmax U LTLmin These are the upper and lower limits of the voltage of the high-voltage station service transformer bus, respectively. These are known values, and the unit is kV; U FLmax U FLmin These are the upper and lower limits of the low-voltage plant auxiliary transformer bus voltage, respectively. These are known values, and the unit is kV; δmax I represents the upper limit of the generator's power angle, a known value, in degrees. Gmax U represents the upper limit of the generator terminal current, a known value, in kA; smax U smin These are the upper and lower limits of the system voltage, which are known values, and the unit is kV;

[0144] (6) By combining equations (18) and (19), and using intelligent optimization algorithms such as genetic algorithm and particle swarm optimization to solve the above optimization mathematical model, the known generator active power P can be obtained. G The corresponding reactive power Q G This is the maximum phase advance depth of the generator.

Claims

1. An optimized algorithm for determining the maximum leading depth of a generator, characterized in that, The specific steps are as follows: Step 1: Use the real-time operating data of the generator synchronous phasor measurement unit (PMU) to identify the equivalent interconnect reactance between the generator and the infinite bus online. x s ; Step 1 is described in detail as follows: Step 1.1, Simplifying generator connection to the system: The external power grid to which the generator is connected is considered an infinite system. The equivalent calculation circuit for the infinite system is based on the synchronous reactance of the generator. x d、 x q Step-up transformer reactance x T1、 Transmission line reactance x L Series connection, with the equivalent impedance of the plant service transformer connected in parallel at the generator outlet side. x T2 Branch road structure, Step 1.2, Generator Equivalent Coordinate Reactance x s The online identification process is as follows: Real-time operating data of the generator's generator unit (PMU) under generator disturbance conditions was selected as samples for online identification of the generator's equivalent tie reactance. The real-time operating data of the PMU included: generator terminal voltage, generator terminal current, and reactive power. A mathematical model for identifying the generator's equivalent tie reactance was established. （1） In the formula: U Gi , I Gi , Q Gi The first and second parts of the sample data are respectively i The generator terminal voltage, terminal current, and reactive power corresponding to each sample; N The total number of data samples; Solving the optimal mathematical model of equation (1), we obtain the following results: x s and U s The identification results; Step 2: Based on the power flow calculation principle, calculate the functional relationship between the five variables—generator terminal voltage, high-voltage station bus voltage, low-voltage station bus voltage, power angle, and generator terminal current—and the system voltage and generator reactive power. Step 2 is described in detail below: Step 2.1, Generator Terminal Voltage U G Rather than reactive power Q G System voltage U s Derivation of the functional relationship between them: (1) Generator terminal - plant service transformer branch, i.e., the equivalent branch reactance of the plant service transformer x T2 Location of the side road: The reactive power loss of this branch is: （2） In the formula: P L and Q L These are the active and reactive loads of the transformer branch used in the generator plant, respectively, and are known values, with units of MW and MVar, respectively; U L1N The voltage at the primary side tap of the plant service transformer is a known value, and the unit is kV. The reactive power of this branch is: （3） (2) The generator terminal - step-up transformer branch, i.e., the step-up transformer reactance x T1 Location of the side road: The reactive power loss of this branch is: （4） In the formula: P G The generator's active power is a known value, expressed in MW. S GN The rated apparent power of the generator is a known value, and the unit is MVA; U T1 , U T1N These are the tap voltage and rated voltage on the high-voltage side of the step-up transformer, respectively, both of which are known values ​​in kV. The reactive power of this branch is: （5） The transverse component of the voltage drop in this branch is: （6） The longitudinal component of the voltage drop in this branch is: （7） U T The voltage on the high-voltage side of the main transformer; The generator terminal voltage is calculated as follows: （8） In the formula: U T2 This refers to the actual tap voltage on the low-voltage side of the step-up transformer. Then we have: x s ≈x T1， U T ≈U S ; U s The voltage is the infinite equivalent bus voltage; Substituting equations (3) to (7) into equation (8) in sequence, we derive the following: U G and Q G , U T Right now U s The functional relationship between the two is denoted as: （9） Step 2.2, Voltage of High-Voltage Plant Busbar U LTL With generator reactive power Q G System voltage U s Derivation of the functional relationship between them: (1) Transverse component of voltage drop in the branch of the plant service transformer: （10） (2) Longitudinal component of voltage drop in the branch of the plant service transformer: （11） (3) Voltage of the high-voltage plant service transformer bus: （12） In the formula: U L1 , U L2 These are the primary and secondary tap voltages of the high-voltage plant service transformer, respectively, both of which are known values ​​in kV. Substituting equations (10) and (11) into equation (12), we derive the following: U LTL and Q G , U s The functional relationship between the two is denoted as: （13） Step 2.3, Low-voltage plant bus voltage U FL Without generator Power Q G System voltage U s Derivation of the functional relationship between them: （14） In the formula: U F1 , U F2 These are the high and low voltage taps of the low-voltage plant service transformer, respectively, both of which are known values ​​in kV. Step 2.4, Generator Power Angle With generator reactive power Q G System voltage U s Derivation of the functional relationship between them: （15） In the formula: x q , U GN The generator's q-axis synchronous reactance and rated terminal voltage are both known values, with units of Ω and kV, respectively. Step 2.5, Generator Terminal Current I G With generator reactive power Q G System voltage U s between Derivation of the functional relationship: （16）； in: E q For the internal electromotive force of the generator, U G For generator output voltage, U T Main transformer high voltage side voltage, U s The voltage is the infinite equivalent bus voltage; x T2 These are the equivalent branch reactances of the plant service transformer, and are known values. x s The equivalent interconnecting reactance between the generator and the infinite busbar; Step 3: Establish an optimal mathematical model for solving the maximum advance depth of the generator, and solve it to obtain the maximum advance depth of the reactive power of the generator under different active power conditions.

2. The optimization algorithm for determining the maximum leading depth of a generator according to claim 1, characterized in that, Step 3 is as follows: Step 3.1: Establish the optimal mathematical model for solving the maximum advance depth of the generator: (1) Construct the objective function: Based on the equations of a synchronous generator, we derive: （17） According to the principle of leading phase operation, when the generator reaches its maximum leading phase depth, the terminal voltage will be at its minimum. Therefore, the optimal objective function model for solving the maximum leading phase depth of the generator is as follows: （18） (2) Constructing constraints: Combining the upper and lower limits of each variable from step 2, the following constraints are obtained: （19） In the formula: U Gmin This is the lower limit of the generator terminal voltage, a known value, in kV. U LTLmax , U LTLmin These are the upper and lower limits of the voltage of the high-voltage plant auxiliary transformer bus, which are known values ​​and are in kV. U FLmax , U FLmin These are the upper and lower limits of the low-voltage plant auxiliary transformer bus voltage, which are known values ​​and are in kV. δ max This is the upper limit of the generator's power angle, a known value, in degrees. I Gmax This is the upper limit of the generator terminal current, a known value, in kA. U smax , U smin These are the upper and lower limits of the system voltage, which are known values, and the unit is kV; (3) By solving equations (18) and (19) simultaneously, the above optimization mathematical model can be obtained to obtain the known active power of the generator. P G Corresponding reactive power Q G This is the maximum phase advance depth of the generator.

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