Method for judging large disturbance stability of unbalanced microgrid based on caputo fractional order singular perturbation

Abstract

The application discloses a method for judging large-disturbance stability of an unbalanced micro-grid based on Caputo fractional order singular perturbation, and steps of the method comprise the following steps: 1, establishing a state space model of the micro-grid system; 2, simplifying the micro-grid model based on Caputo fractional order singular perturbation; 3, judging the large-disturbance stability of the micro-grid based on an energy equation of the micro-grid.The application can establish a simplified model of the micro-grid system by fully considering dynamic performance in a stable process of the micro-grid system, so that the complexity of judging the stability of the micro-grid system can be reduced while the accuracy of the judgment is maintained.

Description

Technical Field

[0001] This invention belongs to the field of microgrid stability assessment, specifically a method for assessing the stability of unbalanced microgrids under large disturbances based on Caputo fractional singular perturbations. Background Technology

[0002] A microgrid (MG) is a small-scale power generation and distribution system that effectively eliminates fluctuations in the power output of renewable energy sources (RES) through the large-scale integration of energy storage devices. This technology has become a highly efficient means of integrating renewable energy power generation devices.

[0003] Microgrids typically consist of numerous power electronic devices, which exhibit high nonlinearity. This characteristic manifests as high-order differential equations in the microgrid system's state-space model, hindering stability assessment. When a microgrid operates in a three-phase unbalanced state, the system model cannot describe the dynamic characteristics of all three phases based on single-phase scenarios; the order of the differential equations in the state-space model is three times that of the balanced state. These ultra-high-order differential equations in the microgrid system's state-space model pose significant challenges to the quantitative analysis of microgrid stability. The goal of microgrid stability assessment is to accurately quantify the maximum disturbance the microgrid can withstand, providing a quantitative standard for the design of control schemes and equipment selection to achieve stable operation. Stability assessment places strict requirements on the accuracy and nonlinearity of the microgrid system model. If the model is oversimplified, reducing its accuracy, the stability assessment will deviate significantly from reality and become unreliable. Conversely, an overly complex model will make the stability assessment process difficult to solve. Therefore, while fully preserving the accuracy of the microgrid system model, effectively simplifying the microgrid system model is an important means of judging the stability of the microgrid system.

[0004] The Dynamic Phasor (DP) method is a feature extraction approach for systems using Fourier decomposition, suitable for analyzing the dynamic characteristics of systems across various frequency bands. This method can be used to construct a first-order DP model of a system, which can then be further simplified using a first-order Taylor approximation. It can also be used to construct DP models of unbalanced microgrids, with further simplification achieved using structure-preserving methods. The DP method can balance the accuracy and simplification of the simplified model; however, decoupling characteristics in different frequency bands may lead to the loss of frequency-coupled features, which are primarily composed of the complex and nonlinear characteristics of electronically interfaced microgrids.

[0005] The singular perturbation method is a model simplification approach focusing on the quasi-steady state of dynamic systems. This method reduces the order of the system model by converting the differential equations of fast variables in the system into algebraic equations when the derivatives of these fast variables are equal to zero. For microgrids with small disturbances, the singular perturbation method can simplify the microgrid system model while maintaining its accuracy. Traditional singular perturbation methods are based on the traditional "quasi-static assumption," which states that the microgrid system can only recover stability when the fast variables are completely stable. However, during the recovery process after a large disturbance, when the derivatives of fast variables are zero, the microgrid system will still exhibit other phenomena due to its inertia. Ignoring these phenomena reduces the accuracy of the simplified microgrid model and the accuracy of stability assessments. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention proposes a method for judging the stability of unbalanced microgrids under large disturbances based on Caputo fractional singular perturbations. The aim is to reduce the complexity of microgrid stability judgment while maintaining its accuracy by establishing a simplified model of the microgrid system that fully considers the dynamic performance during the stability process.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The present invention provides a method for judging the stability of unbalanced microgrids under large disturbances based on Caputo fractional singular perturbations. This method is applicable to microgrid systems composed of distributed power sources, converters, filters, controllers, and loads, and includes the following steps: Step 1: Establish the state-space model of the microgrid system; 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:

[0008] 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: Use equation (4) to obtain the integrated microgrid system. m + n + l State-space equations: (4) In equation (4), x This represents the set of all state variables in the state-space model of the microgrid system. u This represents the set of all input variables in the state-space model of a microgrid system. f This represents the set of dynamic relationships between all state variables and input variables in the state-space model of a microgrid system; Based on the speed at which the system recovers to stability after being disturbed, all state variables in the state-space model of the microgrid system are divided into a set of slow variables consisting of slow variables. x s ={ x si | i =1,…, m A set of fast variables consisting of fast variables. x f ={ x fj | j =1,…, n} and the set of rapid variables consisting of rapid variables x v ={ x vk | k =1,…, l};in, x si Indicates the first i A slow variable, x fj Indicates the first j A fast variable, x vk Indicates the first k A fast variable, m This represents the total number of slow variables. n This indicates the total number of fast variables. l This represents the total number of rapid variables, and x = xs ∪ x f ∪ x v ; Using equation (5), the state-space equation of the microgrid is obtained: (5) In equation (5), f s This represents the set of dynamic relationships between slow variables and all state variables of the system. f f This represents the set of dynamic relationships between fast variables and all state variables of the system. f v A set representing the dynamic relationships between rapid variables and all state variables of the system; Step 3, using equation (6a) to obtain the first... j A fast variable x fj of p Second Caputo derivative Thus, we obtain all the fast variables. p The set of Caputo derivatives ; p Let represent the order of the Caputo derivative of the fast variable, and p Belongs to [0,1]; The kth rapid variable is obtained using equation (6b). x vk of q Second Caputo derivative Thus, we obtain all the rapid variables. q The set of Caputo derivatives ; q This represents the order of the Caputo derivative of the slow variable, and q Belongs to [0,1] q>p ; (6a) (6b) In equations (6a) and (6b), Represents the Gamma function; Step 4, let set and After all variables are equal to 0, use equation (7) to establish the algebraic expressions for the fast and rapid variables; (7) (8) In equations (7) and (8),r f It is a set of dynamic relationships between fast variables and slow variables and input variables. r v It is a set of dynamic relationships between rapidly changing variables and slow and input variables; (9) Step 7, use equation (10) to obtain the sum of the non-divergent component and the non-rotational component: (10) In equation (10), This represents a set containing no diverging components. This represents a set containing no rotational components; Step 8, use equation (11) to establish a system of equations: (11) In equation (11), H Represents the Hamiltonian function. T Indicates transpose. Representing the Hamiltonian function H Regarding time t The derivative, It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 9, 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.

[0009] 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 large disturbance stability judgment method for the unbalanced microgrid, and the processor is configured to execute the program stored in the memory.

[0010] The present invention provides 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 method for determining the stability of an unbalanced microgrid under large disturbances.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention fully considers the dynamic performance of fast variables in the steady-state process of a microgrid system after a large disturbance, and simplifies the microgrid model by using Caputo's fractional singular perturbation method. Through this method, the differential equations of fast and rapid variables in the state-space equations of the microgrid system are transformed into algebraic equations. Compared with the traditional singular perturbation scheme that directly sets the first derivatives of fast and rapid variables to zero, this invention avoids neglecting the dynamic characteristics of fast variables in the steady-state process of the microgrid system after a large disturbance, thus improving the accuracy of the simplified microgrid system model.

[0012] 2. This invention uses a simplified model of a microgrid system to determine the stability of a microgrid system under large disturbances. By establishing a stability criterion on the reduced-order microgrid system model, compared with directly establishing a stability criterion on the microgrid system model, the difficulty of establishing a stability criterion due to the high-order characteristics of the microgrid system is avoided. The accuracy of the simplified model in this invention ensures the accuracy of the stability determination. Attached Figure Description

[0013] Figure 1 This is a basic structural diagram of a microgrid system, which includes distributed power sources, converters, filters, and loads.

[0014] Figure 2 This is a flowchart illustrating the implementation of the present invention. Detailed Implementation

[0015] In this embodiment, as Figure 1 The diagram shows the basic structure of a microgrid system. The microgrid system includes distributed power sources, converters, filters, and loads. Due to the presence of a large number of power electronic devices in the microgrid system, and the fact that the microgrid often operates under a three-phase unbalanced state, the state-space model of the microgrid system exhibits a high order, which complicates the stability assessment of the microgrid system.

[0016] Based on this, the method for judging the stability of unbalanced microgrids under large disturbances based on Caputo fractional singular perturbations in this embodiment is applied to a microgrid system composed of distributed power sources, converters, filters, controllers, and loads, such as... Figure 2 As shown, and includes the following steps: Step 1: Establish the state-space model of the microgrid system; Step 1.1, assuming the distributed power sources in the microgrid are DC power sources, establish the dynamic equations of the distributed power sources 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 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: The filter can reduce the harmonic content in the AC power converted from DC power generated by the distributed power source through inverter, thereby improving 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: Organize the state variable differential equations of the microgrid system in Step 1, and use equation (4) to obtain the integrated microgrid system. m + n + l State-space equations: (4) In equation (4), x This represents the set of all state variables in the state-space model of the microgrid system. u This represents the set of all input variables in the state-space model of a microgrid system. f This represents the set of dynamic relationships between all state variables and input variables in the state-space model of a microgrid system; The connection and disconnection of distributed generation sources in a microgrid system can cause significant disturbances. Based on the speed at which the system recovers to stability after being disturbed, all state variables in the state-space model of the microgrid system are divided into a set of slow variables consisting of slow variables. x s ={ x si | i =1,…, m A set of fast variables consisting of fast variables. x f ={ x fj | j =1,…, n} and the set of rapid variables consisting of rapid variables xv ={ x vk | k =1,…, l};in, x si Indicates the first i A slow variable, x fj Indicates the first j A fast variable, x vk Indicates the first k A fast variable, m This represents the total number of slow variables. n This indicates the total number of fast variables. l This represents the total number of rapid variables, and x = x s ∪ x f ∪ x v ; Using equation (5), the state-space equation of the microgrid is obtained: (5) In equation (5), f s This represents the set of dynamic relationships between slow variables and all state variables of the system. f f This represents the set of dynamic relationships between fast variables and all state variables of the system. f v A set representing the dynamic relationships between rapid variables and all state variables of the system; Step 3: The traditional quasi-steady-state assumption orders the first derivatives of the fast and rapid variables in equation (5) to be 0, and performs singular perturbation reduction on the microgrid system. Since the dynamic characteristics of these state variables are ignored, this quasi-steady-state assumption affects the accuracy of the reduced-order model. This patent adopts a simplified scheme for these state variables with non-integer derivatives of 0. The orders of these derivatives are all greater than 1 and less than 2. According to the properties of Caputo fractional derivatives, this simplified scheme describes the following state of the state variables: acceleration is 0, that is, the external disturbance has disappeared, but they will continue to move for a period of time with the inertia of the system. Therefore, their derivatives are not 0. The dynamic characteristics of the microgrid system in the stabilization process after a large disturbance are fully considered. Using equation (6a), the first... j A fast variable x fj of p Second Caputo derivative Thus, we obtain all slow variables. pThe set of Caputo derivatives ; The kth rapid variable is obtained using equation (6b). x vk of q Second Caputo derivative Thus, we obtain all the fast variables. q The set of Caputo derivatives ; In this embodiment, the golden ratio system is introduced, and the 1.309th derivative of the rapidly changing quantity is set to 0. p =0.309, and setting the 1.618th derivative of the rapidly changing quantity to 0, q =0.618; (6a) (6b) in, Represents the Gamma function, and ; Step 4, let set and After all variables are equal to 0, use equation (7) to establish the algebraic expressions for the fast and rapid variables: (7) (8) In equations (7) and (8), r f It is a set of dynamic relationships between fast variables and slow variables and input variables. r v It is a set of dynamic relationships between rapidly changing variables and slow and input variables; Step 6: Use equation (9) to obtain the microgrid system m Order-state space model: (9) Step 7, use equation (10) to obtain the sum of the non-divergent component and the non-rotational component: (10) In equation (10), This represents a set containing no diverging components. This represents a set containing no rotational components; Step 8, use equation (11) to establish a system of equations: (11) In equation (11), H Represents the Hamiltonian function. T Indicates transpose. Representing the Hamiltonian function H Regarding time t The derivative, It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 9, 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.

[0017] 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 above-described method for determining the stability of unbalanced microgrids under large disturbances. The processor is configured to execute the program stored in the memory.

[0018] In this embodiment, a computer-readable storage medium stores a computer program, which, when executed by a processor, performs the steps of the above-described method for judging the stability of unbalanced microgrids under large disturbances.

Claims

1. A method for judging the stability of an unbalanced microgrid under large disturbances based on Caputo fractional singular perturbations, characterized in that, It is applied to microgrid systems consisting of distributed power sources, converters, filters, controllers, and loads, and includes the following steps: Step 1: Establish the state-space model of the microgrid system; 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 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: Use equation (4) to obtain the integrated microgrid system. m + n + l State-space equations: (4) In equation (4), x This represents the set of all state variables in the state-space model of the microgrid system. u This represents the set of all input variables in the state-space model of a microgrid system. f This represents the set of dynamic relationships between all state variables and input variables in the state-space model of a microgrid system; Based on the speed at which the system recovers to stability after being disturbed, all state variables in the state-space model of the microgrid system are divided into a set of slow variables consisting of slow variables. x s ={ x si | i =1,…, m A set of fast variables consisting of fast variables. x f ={ x fj | j =1,…, n } and the set of rapid variables consisting of rapid variables x v ={ x vk | k =1,…, l };in, x si Indicates the first i A slow variable, x fj Indicates the first j A fast variable, x vk Indicates the first k A fast variable, m This represents the total number of slow variables. n This indicates the total number of fast variables. l This represents the total number of rapid variables, and x = x s ∪ x f ∪ x v ; Using equation (5), the state-space equation of the microgrid is obtained: (5) In equation (5), f s This represents the set of dynamic relationships between slow variables and all state variables of the system. f f This represents the set of dynamic relationships between fast variables and all state variables of the system. f v A set representing the dynamic relationships between rapid variables and all state variables of the system; Step 3, using equation (6a) to obtain the first... j A fast variable x fj of p Second Caputo derivative Thus, we obtain all the fast variables. p The set of Caputo derivatives ; p Let represent the order of the Caputo derivative of the fast variable, and p Belongs to [0,1]; The kth rapid variable is obtained using equation (6b). x vk of q Second Caputo derivative Thus, we obtain all the rapid variables. q The set of Caputo derivatives ; q This represents the order of the Caputo derivative of the slow variable, and q Belongs to [0,1] q> p ; (6a) (6b) In equations (6a) and (6b), Represents the Gamma function; Step 4, let set and After all variables are equal to 0, use equation (7) to establish the algebraic expressions for the fast and rapid variables; (7) (8) In equations (7) and (8), r f It is a set of dynamic relationships between fast variables and slow variables and input variables. r v It is a set of dynamic relationships between rapidly changing variables and slow and input variables; Step 6: Use equation (9) to obtain the microgrid system m Order-state space model: (9) Step 7, use equation (10) to obtain the sum of the non-divergent component and the non-rotational component: (10) In equation (10), This represents a set containing no diverging components. This represents a set containing no rotational components; Step 8, use equation (11) to establish a system of equations: (11) In equation (11), H Represents the Hamiltonian function. T Indicates transpose. Representing the Hamiltonian function H Regarding time t The derivative, It is a Hamiltonian operator, and , x si Indicates the first A slow variable; Step 9, 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 large disturbance stability judgment method for unbalanced microgrids as described in 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, When the computer program is run by the processor, it executes the steps of the method for judging the stability of unbalanced microgrids under large disturbances as described in claim 1.

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