A microgrid stability judgment method based on a second-order singular perturbation reduced-order model

Abstract

The application discloses a micro-grid system stability judgment method based on a second-order singular perturbation reduced model, is applied to a micro-grid system composed of a distributed power supply, an LCL filter, an inverter and a control device, and comprises the following steps: 1, constructing a spatial equation of the micro-grid state; 2, establishing a singular perturbation equation of the micro-grid; 3, simplifying the micro-grid model; and 4, judging the large disturbance stability of the micro-grid. The application can fully consider the change condition of a fast variable in a dynamic stability recovery process of the micro-grid after the micro-grid is subjected to a large disturbance, so that an accurate simplified model of the micro-grid can be established, and the stability of the micro-grid can be analyzed and judged.

Description

Technical Field

[0001] This invention belongs to the field of microgrid stability analysis and judgment, specifically a method for judging the stability of microgrid systems based on a second-order singular perturbation reduced-order model. Background Technology

[0002] In response to the energy crisis and environmental problems, China is actively exploring new power systems based on new energy sources. Distributed renewable energy sources (RES) have gained increasing attention due to their advantages of low environmental pollution and sustainable utilization. In power systems, RES connected to the grid in the form of distributed generation (DG) offers advantages such as low cost, but it can also reduce the power quality of the system. To control the RES connected to the system, microgrid (MG) technology has developed rapidly. However, the large-scale integration of DG, energy storage devices, power electronic equipment, and loads makes microgrids exhibit highly nonlinear and high-dimensional characteristics, making the modeling process of microgrid systems more complex and stability analysis more difficult. Therefore, researching methods to simplify microgrid models and assess microgrid stability is of great significance.

[0003] Kron's method simplifies the model structure of microgrid systems by transforming complex power network structures into star or delta topologies. However, this method cannot simplify the nonlinear dynamic characteristics of power electronic devices in microgrids. Therefore, its stability analysis of microgrids is incomplete. Establishing an equivalent model of the microgrid system is also a common model simplification method; however, its parameters are affected by the time-varying composition of the power system load and the stochastic behavior of distributed generators. Therefore, using this method for stability analysis of microgrids lacks reliability.

[0004] When a microgrid is subjected to small disturbances, the singular perturbation method can effectively balance the accuracy and simplification of the simplified microgrid model. However, when the microgrid is subjected to large disturbances, the traditional singular perturbation method falls short in accuracy. This is because the traditional singular perturbation method is based on a "quasi-static assumption," under which the microgrid can only recover stability when its fast variables have completely stabilized. However, when the microgrid is about to stabilize, other phenomena exist besides the derivatives or accelerations of the fast variables being zero. When nonlinear characteristics dominate the microgrid, the "quasi-steady-state assumption" should be fully considered, as its insufficient accuracy may lead to conservative stability assessments. Summary of the Invention

[0005] The present invention addresses the shortcomings of the existing technology by proposing a method for judging the stability of microgrid systems based on a reduced-order nonlinear model of a microgrid with second-order singular perturbation. This method aims to fully consider the changes in rapidly changing variables during the dynamic stability recovery process of a microgrid after being subjected to a large disturbance, thereby establishing an accurate and simplified model of the microgrid and enabling rapid analysis and accurate judgment of its stability.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The present invention provides a method for determining the stability of a microgrid system based on a second-order singular perturbation reduced-order model. The method is applicable to a microgrid system consisting of distributed power sources, LCL filters, inverters, and control devices, and includes the following steps: Step 1, construct the spatial equations of the microgrid state: Step 1.1: Use equation (1) to establish the dynamic equations of distributed power sources in the microgrid system: (1) In equation (1), This refers to the DC-side current of the distributed power source. This refers to the DC-side capacitor voltage of the distributed power source. For the DC-side resistance of the distributed power source, For the DC-side inductor of a distributed power source, For the DC-side capacitor of the distributed power source, and They are respectively and Regarding time t The first derivative; Step 1.2, use equation (2) to establish the positive-sequence dynamic equation of the LCL filter in the microgrid system: (2) In equation (2), , These represent the positive-sequence components of the inverter output current on the d-axis and q-axis, respectively. , These represent the positive-sequence components of the capacitor voltage of the LCL filter on the d-axis and q-axis, respectively. , These represent the positive-sequence components of the LCL filter output current on the d-axis and q-axis, respectively. , , , , , They are respectively , , , , , Regarding time t The first derivative, For filtering resistors, For filtering inductors, For filtering capacitors, The output inductor of the LCL filter, The angular frequency of the inverter. , These represent the positive sequence components of the inverter on the d-axis and q-axis, respectively. , These are the positive-sequence components of the output voltage of the LCL filter on the d-axis and q-axis. The modulation scheme for the inverter, Let be the amplitude of the PWM modulation signal, and we have: ; Step 1.3: Construct the zero-sequence and negative-sequence dynamic equations of the LCL filter in the microgrid system using equation (3): (3) In equation (3), Let represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the d-axis. These represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the q-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the d-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the q-axis. , , , They are respectively , , , Regarding time t The first derivative, Let represent the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the d-axis. These are the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the q-axis. Step 2: Based on the speed at which the microgrid system recovers to stability after being disturbed, divide the state variables in the spatial equations of the microgrid state into a set of slow-moving variables. ={ x si | i =1,…, m} and fast variable sets ={ x fj | j =1,…, n},in,x si express The first in i A slow variable, x fj express The first in j A fast variable, thus obtaining equation (4) m + n Nonlinear state-space model of a microgrid system: (4) In equation (4), f s It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. f f It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. u This represents the input vector that drives the operation of the microgrid system. , express , In time t The first derivative; Step 3: Adjust both sides of equation (4) with respect to time. t Find the two derivatives and list the third derivatives of all state variables of the microgrid system with respect to... , , u The differential equations are obtained, and thus the fast variable sets are obtained using equations (5) and (6) respectively. Differential equations and slow variable sets The differential equations are used to construct a second-order singular perturbation model of the microgrid system: (5) (6) In equations (5) and (6), express Regarding time t The third derivative, express Regarding time t The third derivative; It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other. It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other; Step 4: Set equation (6) to zero and solve for the fast variable set in the state-space equation of the microgrid using equation (7). Quasi-steady-state expression: (7) In equation (7), It is represented by and , A set of continuously differentiable functions that have dynamic relationships with each other; Step 5: Using equation (8), the second-order singular perturbation reduced-order model of the microgrid system is obtained, thereby transforming the nonlinear state-space model of the microgrid system from... m + n Degraded to m Rank: (8) In equation (8), f si The state-space equation of a microgrid represents the first... i A slow variable x si and , Continuously differentiable equations relating the dynamic relationships between them; i =1,…, m ; Step 6: Decompose equation (8) to obtain the non-divergent component and the non-rotational component using equation (9): (9) In equation (9), for m The set of slow variables in the nonlinear state-space model of a microgrid system. This represents a set containing no diverging components. This represents a set containing no rotational components; Step 7, use equation (10) to establish a system of equations: (10) In equation (10), H represents the Hamiltonian function, and T represents the transpose. This represents the derivative of the Hamiltonian function with respect to time t. It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 8, for To solve, if If the value is positive, it means that the microgrid system can recover stability after being subjected to a large disturbance; otherwise, it means that the microgrid system cannot recover stability after being subjected to a large disturbance.

[0007] The present invention provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the microgrid stability determination method, and the processor is configured to execute the program stored in the memory.

[0008] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the microgrid stability judgment method.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a method for large-signal stability analysis of a simplified model of a microgrid system, which is used to determine the stability of a microgrid system after it has been subjected to large disturbances. This solves the problem of difficulty in determining the stability of a microgrid caused by the large-scale connection of distributed power sources, power electronic devices and other devices to the microgrid, improves the reliability of microgrid stability determination and reduces the complexity of microgrid stability determination.

[0010] 2. This invention simplifies the microgrid system model using a second-order singular perturbation method, fully considering the behavior of fast variables during the microgrid's recovery from large disturbances. Based on the established microgrid system model, this method processes fast variables, reducing the model's order and resolving the inaccuracies of simplified microgrid models under traditional singular perturbation methods. This improves the accuracy of the simplified microgrid model and reduces the difficulty of microgrid stability analysis. Attached Figure Description

[0011] Figure 1 This is a diagram of a microgrid structure that includes a DC power supply, inverter, filter, and three-phase load. Figure 2 This is a flowchart illustrating the implementation of the present invention; Figure 3a This is a d-axis positive sequence component diagram of the converter output current after filtering in the simplified microgrid model of this invention; Figure 3b This is the d-axis positive sequence component diagram of the converter output current in the original microgrid model after filtering; Figure 3c The positive sequence d-axis component of the converter output current after filtering in a simplified model of a traditional singular perturbation in a microgrid. Detailed Implementation

[0012] like Figure 1 The diagram illustrates a simple microgrid structure. This microgrid includes distributed power sources such as photovoltaic power generation and loads connected to the system via power electronic devices. Due to the integration of nonlinear devices, the microgrid exhibits high-dimensional and highly nonlinear characteristics, making stability analysis difficult.

[0013] Based on this, the stability judgment method for a microgrid system based on a second-order singular perturbation reduced-order model in this embodiment is applied to a microgrid system composed of distributed power sources, LCL filters, inverters, and control devices, such as... Figure 2 As shown, and includes the following steps: Step 1, construct the spatial equations of the microgrid state: Step 1.1: Using photovoltaic power generation as the distributed power source in the microgrid, establish the dynamic equation of the distributed power source in the microgrid system using equation (1): (1) In equation (1), This refers to the DC-side current of the distributed power source. This refers to the DC-side capacitor voltage of the distributed power source. For the DC-side resistance of the distributed power source, For the DC-side inductor of a distributed power source, For the DC-side capacitor of the distributed power source, and They are respectively and Regarding time t The first derivative; Step 1.2, the function of the filter is to reduce harmonics in the AC power after DC power is inverted, and improve the power quality at the load end. The positive sequence dynamic equation of the LCL filter in the microgrid system is established using equation (2): (2) In equation (2), , These represent the positive-sequence components of the inverter output current on the d-axis and q-axis, respectively. , These represent the positive-sequence components of the capacitor voltage of the LCL filter on the d-axis and q-axis, respectively. , These represent the positive-sequence components of the LCL filter output current on the d-axis and q-axis, respectively. , , , , , They are respectively , , , , , Regarding time t The first derivative, For filtering resistors, For filtering inductors, For filtering capacitors, The output inductor of the LCL filter, The angular frequency of the inverter. , These represent the positive sequence components of the inverter on the d-axis and q-axis, respectively. , These are the positive-sequence components of the output voltage of the LCL filter on the d-axis and q-axis. The modulation scheme for the inverter, Let be the amplitude of the PWM modulation signal, and we have: ; Step 1.3: Construct the zero-sequence and negative-sequence dynamic equations of the LCL filter in the microgrid system using equation (3): (3) In equation (3), Let represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the d-axis. These represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the q-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the d-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the q-axis. , , , They are respectively , , , Regarding time t The first derivative, Let represent the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the d-axis. These are the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the q-axis. Step 2: The commissioning and disconnection of distributed power sources. The operation of high-power loads will cause large disturbances to the microgrid. Based on the speed at which the microgrid system recovers to stability after being disturbed, the state variables in the space equation of the microgrid state are divided into a set of slow-speed variables. ={ x si | i =1,…, m} and fast variable sets ={ xfj | j =1,…, n},in, x si express The first in i A slow variable, x fj express The first in j A fast variable, thus obtaining equation (4) m + n Nonlinear state-space model of a microgrid system: (4) In equation (4), f s It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. f f It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. u This represents the input vector that drives the operation of the microgrid system. , express , In time t The first derivative; Step 3: In microgrid systems dominated by nonlinearity, the assumption that the microgrid can only recover stability when the fast variables cease to change after a disturbance no longer holds, and the changes in the fast variables need to be reconsidered. Regarding both sides of equation (4) with respect to time... t Find the two derivatives and list the third derivatives of all state variables of the microgrid system with respect to... , , u The differential equations are obtained, and thus the fast variable sets are obtained using equations (5) and (6) respectively. Differential equations and slow variable sets The differential equations are used to construct a second-order singular perturbation model of the microgrid system: (5) (6) In equations (5) and (6), express Regarding time t The third derivative, express Regarding time t The third derivative; It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other. It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other; Step 4: Set equation (6) to zero and solve for the fast variable set in the state-space equation of the microgrid using equation (7). Quasi-steady-state expression: (7) In equation (7), It is represented by and , A set of continuously differentiable functions that have dynamic relationships with each other; Step 5: Using equation (8), the second-order singular perturbation reduced-order model of the microgrid system is obtained, thereby transforming the nonlinear state-space model of the microgrid system from... m+n Degraded to m Rank: (8) In equation (8), f si The state-space equation of a microgrid represents the first... i A slow variable x si and , Continuously differentiable equations relating the dynamic relationships between them; i =1,…, m Simulations were performed on the simplified microgrid model established in this invention, the original model, and the simplified model obtained by the traditional singular perturbation method. The simulation results are as follows: Figure 3a , Figure 3b and Figure 3c As shown, comparing the stable process of the positive sequence component of the output current on the d-axis under the three models, the simplified model obtained by this method maintains the dynamic process of the original microgrid system, while the model obtained by the traditional simplification method has the problem of increased oscillation amplitude and ripple size during the stable process.

[0014] Step 6: Decompose equation (8) to obtain the non-divergent component and the non-rotational component using equation (9): (9) In equation (9), for mThe set of slow variables in the nonlinear state-space model of a microgrid system. This represents a set containing no diverging components. This represents a set containing no rotational components; Step 7, use equation (10) to establish a system of equations: (10) In equation (10), H represents the Hamiltonian function, and T represents the transpose. This represents the derivative of the Hamiltonian function with respect to time t. It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 8, for To solve, if If the value is positive, it means that the microgrid system can recover stability after being subjected to a large disturbance; otherwise, it means that the microgrid system cannot recover stability after being subjected to a large disturbance.

[0015] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor in executing the microgrid stability determination method described above. The processor is configured to execute the program stored in the memory.

[0016] In this embodiment, a computer-readable storage medium stores a computer program, which, when executed by a processor, performs the steps of the microgrid stability judgment method described above.

Claims

1. A method for judging the stability of a microgrid system based on a second-order singular perturbation reduced-order model, characterized in that, It is applied to microgrid systems consisting of distributed power sources, LCL filters, inverters, and control devices, and includes the following steps: Step 1, construct the spatial equations of the microgrid state: Step 1.1: Use equation (1) to establish the dynamic equations of distributed power sources in the microgrid system: (1) In equation (1), This refers to the DC-side current of the distributed power source. This refers to the DC-side capacitor voltage of the distributed power source. For the DC-side resistor of the distributed power source, For the DC-side inductor of a distributed power source, For the DC-side capacitor of the distributed power source, and They are respectively and Regarding time t The first derivative; Step 1.2, use equation (2) to establish the positive-sequence dynamic equation of the LCL filter in the microgrid system: (2) In equation (2), , These represent the positive-sequence components of the inverter output current on the d-axis and q-axis, respectively. , These are the positive-sequence components of the capacitor voltage of the LCL filter on the d-axis and q-axis, respectively. , These represent the positive-sequence components of the LCL filter output current on the d-axis and q-axis, respectively. , , , , , They are respectively , , , , , Regarding time t The first derivative, For filtering resistors, For filtering inductors, For filtering capacitors, The output inductor of the LCL filter, The angular frequency of the inverter. , These represent the positive sequence components of the inverter on the d-axis and q-axis, respectively. , These are the positive-sequence components of the output voltage of the LCL filter on the d-axis and q-axis. The modulation scheme for the inverter, Let be the amplitude of the PWM modulation signal, and we have: ; Step 1.3: Construct the zero-sequence and negative-sequence dynamic equations of the LCL filter in the microgrid system using equation (3): (3) In equation (3), Let represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the d-axis. These represent the zero-sequence and negative-sequence components of the capacitor voltage of the LCL filter on the q-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the d-axis. Let represent the zero-sequence and negative-sequence components of the output current of the LCL filter on the q-axis. , , , They are respectively , , , Regarding time t The first derivative, Let represent the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the d-axis. These are the zero-sequence and negative-sequence components of the output voltage of the LCL filter on the q-axis. Step 2: Based on the speed at which the microgrid system recovers to stability after being disturbed, divide the state variables in the spatial equations of the microgrid state into a set of slow-moving variables. ={ x si | i =1,…, m } and fast variable sets ={ x fj | j =1,…, n },in, x si express The first in i A slow variable, x fj express The first in j A fast variable, thus obtaining equation (4) m + n Nonlinear state-space model of a microgrid system: (4) In equation (4), f s It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. f f It is represented by A set of continuously differentiable functions that have dynamic relationships with state variables. u This represents the input vector that drives the operation of the microgrid system. , express , In time t The first derivative; Step 3: Adjust both sides of equation (4) with respect to time. t Find the two derivatives and list the third derivatives of all state variables of the microgrid system with respect to... , , u The differential equations are obtained, and thus the fast variable sets are obtained using equations (5) and (6) respectively. Differential equations and slow variable sets The differential equations are used to construct a second-order singular perturbation model of the microgrid system: (5) (6) In equations (5) and (6), express Regarding time t The third derivative, express Regarding time t The third derivative; It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other. It is represented by and , , A set of continuously differentiable functions that have dynamic relationships with each other; Step 4: Set equation (6) to zero and solve for the fast variable set in the state-space equation of the microgrid using equation (7). The quasi-steady-state expression is: (7) In equation (7), It is represented by and , A set of continuously differentiable functions that have dynamic relationships with each other; Step 5: Using equation (8), the second-order singular perturbation reduced-order model of the microgrid system is obtained, thereby transforming the nonlinear state-space model of the microgrid system from... m + n Degraded to m Rank: (8) In equation (8), f si The state-space equation of a microgrid represents the first... i A slow variable x si and , Continuously differentiable equations relating the dynamic relationships between them; i =1,…, m ; Step 6: Decompose equation (8) to obtain the non-divergent component and the non-rotational component using equation (9): (9) In equation (9), for m The set of slow variables in the nonlinear state-space model of a microgrid system. This represents a set containing no diverging components. This represents a set containing no rotational components; Step 7, use equation (10) to establish a system of equations: (10) In equation (10), H represents the Hamiltonian function, and T represents the transpose. This represents the derivative of the Hamiltonian function with respect to time t. It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 8, for To solve, if If the value is positive, it means that the microgrid system can recover stability after being subjected to a large disturbance; otherwise, it means that the microgrid system cannot recover stability after being subjected to a large disturbance.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the microgrid stability determination method of claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to perform the steps of the microgrid stability judgment method of claim 1.

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