A method for tracking and identifying instability modes by considering load characteristics of a thévenin equivalent

Abstract

The application discloses a method for tracking and discriminating unstable modes of Thevenin equivalence considering load characteristics, which comprises the following steps: defining an equivalent load node, calculating equivalent impedance of the equivalent load node, calculating parameters of the equivalent load node of Thevenin equivalence considering load characteristics, and discriminating unstable modes, and the method is based on a traditional Thevenin equivalence tracking algorithm and a load model of the equivalent node to improve the Thevenin equivalence tracking algorithm, improve the precision of Thevenin equivalence under dynamic load or heavy load, improve the accuracy of discriminating unstable modes of a system, expand the application range of the Thevenin equivalence tracking algorithm for discriminating unstable modes of a system, and play a more efficient role in subsequent discrimination of unstable modes or other purposes.

Description

Technical Field

[0001] This invention relates to the field of power system instability mode identification, and in particular to a method for identifying instability modes using Thevenin equivalent tracking that takes into account load characteristics. Background Technology

[0002] With the diversification of power source types on the generation side and load types on the supply side of the power grid, the transient stability problem of the power system is becoming increasingly complex. After a grid fault occurs, it is often accompanied by two manifestations: power angle instability and voltage instability. These two phenomena occur simultaneously or sequentially. Power angle instability may cause voltage instability, and voltage collapse may also lead to power angle instability. Their mutual influence is usually described by coupled instability modes. However, judging whether a system has experienced a single instability or coupled instability solely based on the instability mode is inaccurate. Accurately identifying the instability mode of the power system and quickly taking effective measures to disconnect generators or loads to restore system stability is the focus of power system stability control research. Traditional Thevenin equivalent tracking algorithms do not fully consider the influence of equivalent node load models on Thevenin equivalent parameters. When the equivalent nodes are dynamic loads or heavy loads, the Thevenin parameter equivalent tracking results have large errors and cannot accurately determine the system instability mode. Currently, no literature proposes a method to solve this problem. Summary of the Invention

[0003] This invention addresses the problems existing in the prior art by creatively conceiving a method for identifying instability modes based on Thevenin equivalent tracking considering load characteristics. Based on the traditional Thevenin equivalent tracking algorithm and the load model of equivalent nodes, this invention improves the Thevenin equivalent tracking algorithm, thereby increasing the accuracy of Thevenin equivalent tracking under dynamic or heavy load conditions and improving the accuracy of identifying system instability modes.

[0004] The technical solution adopted to realize this invention is: a method for identifying instability modes by Thevenin equivalent tracking considering load characteristics, characterized in that it includes the following steps:

[0005] 1) Define equivalent load nodes:

[0006] In a power system, a load node is selected as the Thevenin equivalent load node. The Thevenin equivalent load node is a dynamic load node, and its equivalent load impedance is a non-fixed value that changes with time.

[0007] 2) Calculate the equivalent impedance of the equivalent load node:

[0008] The induction motor is simulated as a T-type mechanical transient equivalent circuit. The equivalent impedance of the induction motor at any given time is calculated using the T-type equivalent circuit of the induction motor:

[0009]

[0010] In the formula: R1 and X1 are the resistance and leakage reactance of the stator winding, R2 and X2 are the resistance and leakage reactance of the rotor winding, and R m X m Here, j represents the excitation resistance and excitation reactance, j is the imaginary unit of the induction motor impedance, and s is the rotor slip of the induction motor. After the power system is disturbed, the rotor slip is a constant that changes with time, denoted by s(t).

[0011] When the power system is operating stably or the voltage changes slowly, the induction motor maintains stable operation and its power remains basically unchanged, which can be approximated as a constant power load.

[0012] 3) Calculation of Thevenin equivalent parameters for equivalent load nodes considering load characteristics:

[0013] At any time t, looking into the power system from the equivalent load node, the power system is equivalently represented as a voltage source, a two-node Thevenin equivalent system supplying power to the load through an impedance. At time t, the node admittance matrix Y and the node voltage vector are generated through the system transient stability procedure.

[0014] The node admittance matrix is ​​corrected by adjusting the self-admittance Y of the remaining load nodes j (excluding the equivalent node i). jj With equivalent impedance Z ij The form is merged into the admittance matrix to form a new nodal admittance Y′. ij As shown in equation (2);

[0015]

[0016] In the formula: P Lj Q represents the active power at the load node. Lj U represents the reactive power at the load node. j This refers to the load node voltage;

[0017] When the load characteristics of the induction motor under different operating conditions of the power system are in steady state, the induction motor load is regarded as a constant power load. At this time, the slip of the power system does not change abruptly, and the equivalent impedance is determined by the slip. The induction motor load is included in the system node admittance matrix in the same way as other static loads of the power system, as shown in Equation (3). The equivalent load node voltage, active power and reactive power are calculated according to the calculation steps obtained by the quasi-stability procedure:

[0018]

[0019] In the formula: Y ii Y′ is the self-admittance of the isostat node i. ii For the corrected admittance, Z Li Let P be the equivalent impedance of node i. LiQ represents the equivalent nodal active power. Li U represents the equivalent nodal reactive power. i This refers to the equivalent node voltage;

[0020] Injecting a unit current at node i, while injecting zero current at the other nodes, the voltage vector at node i is then given by...

[0021] Then the equivalent node composite impedance Z iT Represented as equation (4):

[0022]

[0023] With the equivalent node open-circuited, a current source is added at node i using the compensation method. Find the open-circuit voltage at node i, which is the Thevenin equivalent potential E of the system at time t. ti，thev Then, short-circuit node i, and calculate the short-circuit current of node i using the superposition principle. The ratio of the open-circuit voltage to the short-circuit current is the Thevenin equivalent potential Z of the system at time t. ti，thev The equivalent parameters of Thevenin calculated using the compensation method are expressed as equation (5):

[0024]

[0025] In the formula: Z t，Mi Let be the equivalent impedance of the node induction motor at time t; Z is the equivalent node voltage vector at time t. iT Equivalent node composite impedance;

[0026] 4) Instability mode identification:

[0027] When the power system becomes unstable and the voltage drops significantly, based on the changes in Thevenin equivalent potential and the power angle difference, when the system's Thevenin equivalent potential decreases below the instability critical value as the power angle difference increases, it can be determined that the system has experienced power angle instability.

[0028] When the power system reaches its maximum transmission power, the magnitude of the Thevenin equivalent impedance is equal to the magnitude of the load impedance.

[0029] When the power transmission limit of the power system is less than the power required by the load, the voltage at the load point collapses. At this time, the Thevenin impedance at the equivalent node is greater than the load impedance, indicating that the system has experienced voltage instability.

[0030] The beneficial effects of the Thevenin equivalent tracking method for identifying instability modes considering load characteristics, as described in this invention, are as follows:

[0031] 1. A method for identifying instability modes by Thevenin equivalent tracking considering load characteristics. Based on the traditional Thevenin equivalent tracking time-domain simulation algorithm, this method considers the load model of the equivalent node, ensuring the rationality of the data used in the Thevenin equivalent tracking algorithm. The voltage curve calculated by Thevenin equivalent tracking basically matches the actual voltage curve, and the accuracy of Thevenin equivalent tracking is significantly improved. As a result, the accuracy of this method in identifying system instability modes is also improved.

[0032] 2. A method for identifying instability modes by Thevenin equivalent tracking considering load characteristics, which takes into account the dynamic load characteristics of the system under different operating conditions, processes the static load impedance and dynamic load impedance before and after the fault separately, and avoids the negative impact of load characteristics on the accuracy of Thevenin equivalent results when the equivalent node is a dynamic load or a heavy load scenario.

[0033] 3. A Thevenin equivalent tracking method for identifying instability modes that considers load characteristics solves the problem that when the equivalent node is a constant impedance model, the load impedance magnitude remains unchanged after transient voltage instability, making the impedance magnitude index unusable and unable to determine if the system has experienced voltage instability. The equivalent node adopts a dynamic load model, expanding the applicability of the Thevenin equivalent tracking algorithm for identifying system instability modes, and playing a more efficient role in subsequent instability mode identification or other applications. Attached Figure Description

[0034] Figure 1 This is a flowchart of the Thevenin equivalent tracking algorithm considering load characteristics in the embodiment;

[0035] Figure 2 This is a flowchart illustrating the instability mode determination using Thevenin equivalent parameters in this embodiment.

[0036] Figure 3 This is an example of an equivalent circuit diagram of a T-type mechanical transient induction motor with an equivalent node.

[0037] Figure 4 This is the electrical wiring diagram of the IEEE 9-node system in the embodiment;

[0038] Figure 5 In this embodiment, a comparison chart of the voltage curves calculated by Thevenin equivalent parameters considering load characteristics and those not considering load characteristics during the equivalent process, and the actual voltage curves;

[0039] Figure 6 In this embodiment, the Thevenin equivalent potential curve and the power angle curve of generator 3 relative to generator 1 are shown.

[0040] Figure 7 In this embodiment, the Thevenin equivalent impedance curve and the voltage curve of bus B6 are shown. Detailed Implementation

[0041] The following is in conjunction with the appendix Figures 1-7 The present invention will be further described in detail with reference to specific embodiments. The specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0042] As attached Figure 1 and attached Figure 2 As shown, a method for identifying instability modes using Thevenin equivalent tracking considering load characteristics includes the following steps:

[0043] 1) Define equivalent load nodes:

[0044] In a power system, a load node is selected as the Thevenin equivalent load node. The Thevenin equivalent load node is a dynamic load node, and its equivalent load impedance is a non-fixed value that changes with time.

[0045] 2) Calculate the equivalent impedance of the equivalent load node:

[0046] The induction motor is simulated as a T-type mechanical transient equivalent circuit, as shown in the attached diagram. Figure 3 As shown, the equivalent impedance of the induction motor at any given time, calculated using the T-type equivalent circuit of the induction motor, is:

[0047]

[0048] In the formula: R1 and X1 are the resistance and leakage reactance of the stator winding, R2 and X2 are the resistance and leakage reactance of the rotor winding, and R m X m Here, j represents the excitation resistance and excitation reactance, j is the imaginary unit of the induction motor impedance, and s is the rotor slip of the induction motor. After the power system is disturbed, the rotor slip is a constant that changes with time, denoted by s(t).

[0049] When the power system is operating stably or the voltage changes slowly, the induction motor maintains stable operation and its power remains basically unchanged, which can be approximated as a constant power load.

[0050] 3) Calculation of Thevenin equivalent parameters for equivalent load nodes considering load characteristics:

[0051] At any time t, looking into the power system from the equivalent load node, the power system is equivalently represented as a voltage source, a two-node Thevenin equivalent system supplying power to the load through an impedance. At time t, the node admittance matrix Y and the node voltage vector are generated through the system transient stability procedure.

[0052] The node admittance matrix is ​​corrected by adjusting the self-admittance Y of the remaining load nodes j (excluding the equivalent node i). jj With equivalent impedance Z ijThe form is merged into the admittance matrix to form a new nodal admittance Y′. ij As shown in equation (2);

[0053]

[0054] In the formula: P Lj Q represents the active power at the load node. Lj U represents the reactive power at the load node. j This refers to the load node voltage;

[0055] When the load characteristics of the induction motor under different operating conditions of the power system are in steady state, the induction motor load is regarded as a constant power load. At this time, the slip of the power system does not change abruptly, and the equivalent impedance is determined by the slip. The induction motor load is included in the system node admittance matrix in the same way as other static loads of the power system, as shown in Equation (3). The equivalent load node voltage, active power and reactive power are calculated according to the calculation steps obtained by the quasi-stability procedure:

[0056]

[0057] In the formula: Y ii Y is the self-admittance of the isostat node i. ii For the corrected admittance, Z Li Let P be the equivalent impedance of node i. Li Q represents the equivalent nodal active power. Li U represents the equivalent nodal reactive power. i This refers to the equivalent node voltage;

[0058] Injecting a unit current at node i, while injecting zero current at the other nodes, the voltage vector at node i is then given by... Then the equivalent node composite impedance Z iT Represented as equation (4):

[0059]

[0060] With the equivalent node open-circuited, a current source is added at node i using the compensation method. Find the open-circuit voltage at node i, which is the Thevenin equivalent potential E of the system at time t. ti , thev Then, short-circuit node i, and calculate the short-circuit current of node i using the superposition principle. The ratio of the open-circuit voltage to the short-circuit current is the Thevenin equivalent potential Z of the system at time t. ti，thev The equivalent parameters of Thevenin calculated using the compensation method are expressed as equation (5):

[0061]

[0062] In the formula: Z t，Mi Let be the equivalent impedance of the node induction motor at time t; Z is the equivalent node voltage vector at time t. iT Equivalent node composite impedance;

[0063] 4) Instability mode identification:

[0064] When the power system becomes unstable and the voltage drops significantly, based on the changes in Thevenin equivalent potential and the power angle difference, when the system's Thevenin equivalent potential decreases below the instability critical value as the power angle difference increases, it can be determined that the system has experienced power angle instability.

[0065] When the power system reaches its maximum transmission power, the magnitude of the Thevenin equivalent impedance is equal to the magnitude of the load impedance.

[0066] When the power transmission limit of the power system is less than the power required by the load, the voltage at the load point collapses. At this time, the Thevenin impedance at the equivalent node is greater than the load impedance, indicating that the system has experienced voltage instability.

[0067] Example:

[0068] A method for identifying instability modes using Thevenin equivalent tracking that considers load characteristics, and data analysis in the instability mode identification process;

[0069] 1. Data Description:

[0070] This embodiment uses the IEEE 9-node system, as shown in the attached diagram. Figure 4 As shown, node 6 is replaced with a 100% induction motor model. At 1.0 second, a three-phase short circuit fault occurs at the midpoint between nodes 4 and 6. The fault is cleared at 1.45 seconds, and the system becomes unstable.

[0071] 2. Thevenin equivalent parameter tracking calculation considering load characteristics:

[0072] After a fault occurs, the monitoring system identifies the load node with the lowest voltage following the fault. In this example, the monitoring point is node 6. Based on the Thevenin equivalent tracking algorithm considering load characteristics, the voltage of node 6 and the equivalent voltage calculated by Thevenin tracking are plotted as curves. The step size in this example is 0.01s. Figure 5 It can be seen that after considering the load characteristics, the error of the proposed algorithm is significantly improved compared with the traditional algorithm, and the curves basically overlap, which fully proves the accuracy of the proposed algorithm in tracking and obtaining the Thevenin equivalent parameters.

[0073] 3. Instability mode identification:

[0074] As can be seen from the load impedance and Thevenin equivalent impedance curves at node 6, after the fault occurs, the Thevenin equivalent impedance, considering the load characteristics, is always less than the load impedance, failing to meet the voltage instability criterion of impedance modulus, as shown in the attached figure. Figure 6As shown in the figure; from the Thevenin equivalent potential results at node 6, it can be seen that the Thevenin equivalent potential continues to decrease, and after 1.01 seconds it is less than the critical value of the Thevenin equivalent potential for power angle instability, as shown in the attached figure. Figure 7 As shown, it can be determined that the voltage drop at node 2 is caused by the power angle instability of the system, and this result is more consistent with the actual instability situation.

[0075] Using the IEEE 9-bus system as an example, the active and reactive power of the equivalent node 6 were gradually increased by multiples λ under a constant power factor, while the power of other loads and the active power output of generators remained unchanged, until the power flow no longer converged. The transient fault time was taken as the critical value of the system's voltage instability time. The Thevenin equivalent parameter tracking comparison results after considering load characteristics are shown in the table below:

[0076] Equivalent node B6 <![CDATA[λ1]]> <![CDATA[λ2]]> <![CDATA[λ3]]> P / pu 1.8 2.7 3.6 Q / pu 0.6 0.9 1.2 Fault duration / s 0.1504 0.0741 0.0051 Error ε / % not considering load characteristics 19.134 27.728 39.210 Error ε / % considering load characteristics 3.967 3.844 1.872

[0077] The Thevenin equivalent parameter error obtained by this algorithm is significantly improved compared with the traditional algorithm, which fully demonstrates the accuracy of the Thevenin equivalent parameter obtained by this algorithm under different load scenarios.

[0078] The above description is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for identifying instability modes using Thevenin equivalent tracking considering load characteristics, characterized in that, It includes the following steps: 1) Define equivalent load nodes: In a power system, a load node is selected as the Thevenin equivalent load node. The Thevenin equivalent load node is a dynamic load node, and its equivalent load impedance is a non-fixed value that changes with time. 2) Calculate the equivalent impedance of the equivalent load node: The induction motor is simulated as a T-type mechanical transient equivalent circuit. The equivalent impedance of the induction motor at any given time is calculated using the T-type equivalent circuit of the induction motor: In the formula: R1 and X1 are the resistance and leakage reactance of the stator winding, R2 and X2 are the resistance and leakage reactance of the rotor winding, and R m X m Here, j represents the excitation resistance and excitation reactance, j is the imaginary unit of the induction motor impedance, and s is the rotor slip of the induction motor. After the power system is disturbed, the rotor slip is a constant that changes with time, denoted by s(t). When the power system is operating stably or the voltage changes slowly, the induction motor maintains stable operation and its power remains basically unchanged, which can be approximated as a constant power load. 3) Calculation of Thevenin equivalent parameters for equivalent load nodes considering load characteristics: At any time t, looking into the power system from the equivalent load node, the power system is equivalently represented as a voltage source, a two-node Thevenin equivalent system supplying power to the load through an impedance. At time t, the node admittance matrix Y and the node voltage vector are generated through the system transient stability procedure. The node admittance matrix is ​​corrected by adjusting the self-admittance Y of the remaining load nodes j (excluding the equivalent node i). jj With equivalent impedance Z Lj The form is merged into the admittance matrix to form a new nodal admittance Y′. jj As shown in equation (2); In the formula: P Lj Q represents the active power at the load node. Lj U represents the reactive power at the load node. j This refers to the load node voltage; When the load characteristics of the induction motor under different operating conditions of the power system are in steady state, the induction motor load is regarded as a constant power load. At this time, the slip of the power system does not change abruptly, and the equivalent impedance is determined by the slip. The induction motor load is included in the system node admittance matrix in the same way as other static loads of the power system, as shown in Equation (3). The equivalent load node voltage, active power and reactive power are calculated according to the calculation steps obtained by the quasi-stability procedure: In the formula: Y ii Y is the self-admittance of the isostat node i. ii For the corrected admittance, Z Li Let P be the equivalent impedance of node i. Li Q represents the equivalent nodal active power. Li U represents the equivalent nodal reactive power. i This refers to the equivalent node voltage; Injecting a unit current at node i, while injecting zero current at the other nodes, the voltage vector at node i is then given by... Then the equivalent node composite impedance Z iT Represented as equation (4): With the equivalent node open-circuited, a current source is added at node i using the compensation method. Find the open-circuit voltage at node i, which is the Thevenin equivalent potential of the system at time t. E ti，thev Then, short-circuit node i, and calculate the short-circuit current of node i using the superposition principle. The ratio of the open-circuit voltage to the short-circuit current is the Thevenin equivalent potential Z of the system at time t. ti，thev The equivalent parameters of Thevenin calculated using the compensation method are expressed as equation (5): In the formula: Z t，Mi Let be the equivalent impedance of the node induction motor at time t; Z is the equivalent node voltage vector at time t. iT Equivalent node composite impedance; 4) Instability mode identification: When the power system becomes unstable and the voltage drops significantly, based on the changes in Thevenin equivalent potential and the power angle difference, when the system's Thevenin equivalent potential decreases below the instability critical value as the power angle difference increases, it can be determined that the system has experienced power angle instability. When the power system reaches its maximum transmission power, the magnitude of the Thevenin equivalent impedance is equal to the magnitude of the load impedance. When the power transmission limit of the power system is less than the power required by the load, the voltage at the load point collapses. At this time, the Thevenin impedance at the equivalent node is greater than the load impedance, indicating that the system has experienced voltage instability.

Images