Active power distribution network discrete-continuous unified modeling method based on hybrid system theory

Abstract

The invention discloses an active power distribution network discrete-continuous unified modeling method based on a hybrid system theory, and the method comprises the steps: building an active power distribution network discrete-continuous layered modeling frame which comprises an information system layer and a physical equipment layer and is used for uniformly describing the hybrid dynamic behavior characteristics of an active power distribution network; secondly, considering discrete continuous characteristics in the operation process of the active power distribution network, and dividing an active power distribution network information system layer and an active power distribution network physical equipment layer into a continuous dynamic subsystem layer and a discrete event subsystem layer respectively; secondly, respectively establishing mathematical models of a continuous dynamic subsystem layer and a discrete event subsystem layer by adopting different methods; and finally, considering the interaction of the continuous dynamic subsystem layer and the discrete event subsystem layer, and establishing an interaction model to obtain an active power distribution network discrete-continuous unified model. Compared with the prior art, the model provided by the invention is beneficial to analyzing a hybrid dynamic process of interaction between physical equipment and an information system. And meanwhile, the built model framework is high in universality and can be expanded to any complex dynamic system.

Description

Technical Field

[0001] The present invention belongs to the technical field of active distribution network modeling, and in particular relates to a discrete-continuous unified modeling method for active distribution networks based on hybrid system theory. Background Art

[0002] As a crucial component of the power system, the operating state of the active distribution network directly impacts its safety and stability. With the widespread integration of distributed power sources, energy storage devices, and electric vehicles, the operational characteristics of active distribution networks have become increasingly complex, making it difficult for traditional static modeling methods to accurately describe their dynamic behavior. Furthermore, active distribution networks contain a large number of power electronic converters that perform power conversion. The switching on and off of IGBTs within these converters, as well as changes in external input commands, can cause changes in the active distribution network's operating mode. Furthermore, the switching on and off of various devices, such as circuit breakers and switches, can also alter the microgrid's operating mode, demonstrating that active distribution networks exhibit the characteristics of discrete event subsystems. When the active distribution network is in a specific operating mode, the output of distributed power sources and other devices within the network continuously changes over time, demonstrating that it also exhibits the characteristics of a continuous dynamic subsystem. These characteristics make the active distribution network a typical hybrid system, making it difficult for existing modeling methods to accurately describe its hybrid dynamic behavior.

[0003] Although a variety of modeling methods have been proposed to describe the dynamic behavior characteristics of active distribution networks, the following problems still need to be solved:

[0004] 1) Existing modeling mostly starts from specific application scenarios, so the established models are not very universal.

[0005] 2) Existing modeling methods for active distribution networks mainly focus on a single discrete model or a single continuous dynamic model, lacking a unified description of the discrete-continuous characteristics of the system. Summary of the Invention

[0006] To address the above technical issues, the present invention proposes a unified discrete-continuous modeling method for active distribution networks based on hybrid system theory. This method applies the hybrid system theory framework to active distribution network modeling, proposing a universal modeling framework for active distribution networks. The physical system in the active distribution network is represented by the continuous system states in the hybrid system, while the information system is represented by the discrete system states in the hybrid system. This achieves a unified description of the dynamic discrete-continuous characteristics of the active distribution network. The active distribution network model established by this method is highly universal and can be extended to arbitrarily complex dynamic systems.

[0007] The technical solution adopted by the present invention is:

[0008] The discrete-continuum unified modeling method for active distribution networks based on hybrid system theory includes the following steps:

[0009] Step 1: Unify the discrete and continuous dynamic characteristics of the active distribution network and establish a discrete-continuous hierarchical modeling framework for the active distribution network based on hybrid system theory;

[0010] Step 2: Considering the discrete-continuous characteristics of the active distribution network during operation, the active distribution network information system layer and the active distribution network physical equipment layer are divided into the continuous dynamic subsystem layer and the discrete event subsystem layer respectively;

[0011] Step 3: Use differential equations to describe the continuous dynamic behavior characteristics of the continuous dynamic subsystem layer in the active distribution network information system layer and the active distribution network physical device layer, and use a state machine model to describe the discrete event characteristics of the discrete event subsystem layer in the active distribution network information system layer and the active distribution network physical device layer;

[0012] Step 4: Establish the interface function model of the continuous dynamic subsystem layer and the discrete event subsystem layer to obtain the discrete-continuous unified model of the active distribution network.

[0013] In step 1, the hybrid system consists of a continuous dynamic subsystem, a discrete event subsystem, and an interface between the continuous and discrete systems. The discrete-continuous system interface converts discrete variables in the discrete event subsystem into continuous variables and uses them as input to the continuous dynamic subsystem. Conversely, the continuous-discrete system interface converts continuous variables in the continuous dynamic subsystem into discrete variables and uses them as input to the discrete event subsystem.

[0014] The step 1 comprises the following steps:

[0015] 1): The hybrid system theory is described in the form of multiple groups, as shown below:

[0016] H={I,M,Σ,Q,P,δ,R,X} (1);

[0017] In formula (1), I is the input set, which represents the input set of the external active distribution network, including the continuous input signal u in , discrete input signal d in and external input event signal e in , as shown below:

[0018] I=[u in ,d in ,e in ] (2);

[0019] M represents the set of discrete states (also called system operation modes) of the active distribution network. For any discrete state, m=m(t)∈M, where m(t) represents the discrete state of the active distribution network at time t.

[0020] Σ={e1,e2,…,e N} represents the discrete event set of the active distribution network, e1, e2,…, e N They represent different discrete events generated by the active distribution network. For any discrete event, it can be expressed as e = e(t)∈Σ, where e is the symbol used to describe the discrete event generated by the active distribution network, e(t) represents the discrete event of the active distribution network at time t, and Σ represents the set of discrete events of the active distribution network.

[0021] Q={q1,q2,…q k} represents a set of discrete variables; q1,q2,…q k They represent a discrete variable of the active distribution network. P represents the parameter variable of the active distribution network; δ represents the discrete state transition function of the active distribution network; R represents the reset function, which determines the continuous variable state after the discrete state transition of the active distribution network;

[0022] X={H (m)} m∈M represents the continuous state space set of the active distribution network under different operation modes, m represents the symbol used to describe the discrete state of the active distribution network (also called the system operation mode), and M represents the set of discrete states of the active distribution network (also called the system operation mode). (m) =(X (m) ,G (m) ,f (m) ,λ (m) ), H (m) The meaning of each element is as follows: X (m) represents the continuous state space of the active distribution network in mode m, x(t)∈X (m) Represents the state variable of the active distribution network; G (m) represents the transition condition of the active distribution network in mode m∈M; f (m) represents the evolution rule of the active distribution network under mode m, characterizing the dynamic behavior characteristics of the active distribution network; λ (m) represents the output function of the active distribution network.

[0023] 2) The equations describing the dynamic and static characteristics of the active distribution network using hybrid system theory are as follows:

[0024]

[0025] In formula (3), “-” and “+” represent the time before and after the event e respectively; m- (t) and They represent the state mode and continuous state before event e occurs; y(t) represents the output of the active distribution network. represents the state variable control law of the active distribution network in operation mode m; x (m) (t) represents the state variable of the active distribution network in operation mode m; u(t) represents the input control variable of the active distribution network; p represents the disturbance variable of the active distribution network; m + (t) represents the state mode of the active distribution network after the event e occurs; e represents the symbol used to describe the discrete events generated by the active distribution network, Represents the state variables of the active distribution network after event e occurs.

[0026] 3): The discrete-continuous hierarchical modeling framework of the active distribution network is divided into the information system layer and the physical device layer, and the two interact through event functions.

[0027] The physical device layer is the entity part of the active distribution network, including distribution transformers, distribution lines, switchgear, distributed power sources, energy storage equipment, load equipment, protection equipment and reactive power compensation equipment, etc., responsible for the transmission and distribution of electric energy, stable system operation, energy supply and demand balance, and voltage and frequency regulation. Figure 5 As shown in the figure, the entire physical system is connected via distribution lines. Distributed power sources (such as photovoltaics and wind turbines) and energy storage devices are integrated into the grid through these lines. The power is then stepped down by distribution transformers and supplied to the load devices. Reactive power compensation devices (such as SVGs and capacitors) are connected in parallel to the lines to regulate voltage stability. Switching devices (such as circuit breakers and section switches) are connected in series to control on / off switching to change the topology. Protection devices monitor line current and voltage in real time and control the switching devices through trip signals to achieve fault isolation.

[0028] The information system layer is the "brain" of the active distribution network, including the Supervisory Control and Data Acquisition System (SCADA), smart meters, communication networks, energy management systems (EMS), distribution automation systems (DAS), information processing platforms, and network security equipment. It is responsible for data acquisition and monitoring, optimized scheduling and control, fault detection and recovery, etc. The diagram of the information system layer is as follows: Figure 6As shown. Smart meters collect voltage, current, power and other data from the physical device layer in real time and upload them to the SCADA system through the communication network (fiber / 5G / PLC). The SCADA system then integrates data from all network points to provide a visual monitoring interface and transmits key information to the energy management system (EMS) and information processing platform. The EMS and information processing platform generate control strategies based on optimization algorithms. Finally, the distribution automation system (DAS) receives EMS instructions and sends control signals to switches, energy storage, etc. at the physical device layer through the communication network. Throughout the process, network security devices (firewalls, encryption gateways) are used to protect the integrity and confidentiality of data transmission.

[0029] In step 2, the continuous dynamic subsystem layer and the discrete event subsystem layer interact with each other through interface functions, wherein the interface functions include the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer and the action function of the discrete event subsystem layer on the continuous dynamic subsystem layer;

[0030] The action function of the continuous dynamic subsystem layer on the discrete event subsystem layer is expressed as F ccd Indicates that F ccd It is manifested as the state trajectory of the continuous state variable x crossing the hypersurface h m Event e will be triggered when cc and through the event e cc Acting on the discrete event subsystem layer, thereby changing the value of q, as shown below;

[0031]

[0032] In formula (4): H m (x(t),u(t)) represents the hypersurface h m The expression of F ccd (x(t),h m ) represents the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer.

[0033] The action function of the discrete event subsystem layer on the continuous dynamic subsystem layer is expressed as F cdc It is composed of the following two parts.

[0034] F cdc =[f cdx ,f cdm ](5);

[0035] In formula (5): f cdm It represents the function that affects the dynamic change relationship of the continuous variable x through the discrete state q. Its expression is

[0036]

[0037] In formula (6): m-(t) and Respectively represent the state mode and continuous state before the event e occurs, m + (t) represents the state mode after event e occurs.

[0038] f cdx The function f that represents the change in the value of the continuous state variable x when the system undergoes state transition cdx , its expression is as follows.

[0039]

[0040] In formula (7): Represents the continuous state after event e occurs.

[0041] In step 3, the continuous dynamic subsystem layer of the active distribution network physical device layer mainly describes the continuous dynamic behavior characteristics of the physical devices, and is described by the following differential equation:

[0042]

[0043] In formula (8): represents the state variables of the physical device layer of the active distribution network in mode m, Represents the continuous dynamic change relationship function of the physical device layer of the active distribution network in mode m, represents the output function of the physical device layer of the active distribution network, represents the continuous state variable of the physical device layer of the active distribution network, the superscript m represents the operation mode of the active distribution network; u(t) is the control variable generated by the physical device layer of the active distribution network; y c (t) represents the output variable of the physical device layer of the active distribution network; p represents the disturbance variable of the active distribution network;

[0044] The discrete event subsystem of the physical device layer of the active distribution network is used to describe the transition process of the device between different discrete states q, using the state transition condition function g c and the state transition function δ c describe;

[0045] State transition condition function g c :

[0046] g c :Cond={true,false},cond=g c (q,x) (9);

[0047] In formula (9), Cond represents the judgment result of the state transition condition function, {true, false} represents the symbol used to describe whether the judgment condition is true or false, true represents the symbol used to describe whether the judgment condition is true, and false represents the symbol used to describe whether the judgment condition is false. cond = g c (q,x) represents the expression used to describe the judgment result of the state transition condition function, cond represents the judgment result of the state transition condition function, g c (q,x) represents the judgment expression of the state transition condition function, q represents a discrete variable, and x represents a continuous variable.

[0048] Formula (9) indicates whether the discrete event subsystem satisfies the function g under the conditions of discrete state q and continuous state x. c The operating state transition conditions.

[0049] State transition function δ c :

[0050] δ c :δ c (q - ,e,cond)=q + ,{e cd1 ,e cd2 ,…,e cdn} (10);

[0051] In formula (10), δ c represents the state transition function, δ c (q - ,e,cond) represents the physical device layer from discrete state q - Transfer to discrete state q + The state transition function expression of .

[0052] {e cd1 ,e cd2 ,…,e cdn} indicates that the physical device layer is from discrete state q - Transfer to discrete state q + The set of discrete events generated, e cd1 ,e cd2 ,…,e cdn Respectively represent the physical device layer from discrete state q - Transfer to discrete state q + , resulting in a series of discrete events.

[0053] In formula (10), event e is the state event e generated by the continuous dynamic subsystem layer cc , or the internal control input event e of the discrete event subsystem de , or an event generated by the environment ecin ;

[0054] Formula (10) indicates that when event e occurs and the state transition condition cond is true, the system will change from discrete state q - Transfer to discrete state q + , and generates a series of discrete events e cdi ; The superscripts “-” and “+” represent the time before and after the event e occurs, respectively.

[0055] The step 4 comprises the following steps:

[0056] S4.1: Define F ccd is the continuous-discrete subsystem layer interface function, which represents the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer; define F dcd It is the discrete-continuous subsystem layer interface function, which represents the function of the discrete event subsystem layer on the continuous dynamic subsystem layer;

[0057] S4.2: Establish a discrete-continuous unified model of the active distribution network:

[0058] By integrating the continuous dynamic subsystem layer model, the discrete event subsystem layer model, and the interface function model between the continuous dynamic subsystem layer and the discrete event subsystem layer in the physical device layer of the active distribution network, the discrete-continuous unified model of the active distribution network is obtained, as shown below:

[0059]

[0060] Similarly, the discrete-continuous unified model of the active distribution network information system layer can be obtained as follows:

[0061]

[0062] The meaning of each variable in formula (12) is the same as that in formula (11).

[0063] The present invention provides a discrete-continuous unified modeling method for active distribution networks based on hybrid system theory, and the technical effects are as follows:

[0064] 1) Step 1 of the present invention realizes a unified description of discrete events (such as switching actions) and continuous dynamics (such as voltage fluctuations) through a hybrid system theoretical framework, solving the problem of separation between discrete and continuous parts in traditional models.

[0065] 2) Step 2 of the present invention further divides the active distribution network into a continuous dynamic subsystem layer and a discrete event subsystem layer, which is conducive to analyzing the interaction process between the discrete part and the continuous part.

[0066] 3) Step 3 of the present invention uses differential equations to accurately characterize continuous dynamics, combined with a state machine to describe discrete logic processes, which can clearly present the state transition process of the device and improve the observability of the system.

[0067] 4) The discrete-continuous unified model of the active distribution network established in step 4 of the present invention can provide a universal modeling basis for multi-time scale analysis and coordinated control of the active distribution network.

[0068] 5) Compared with existing technologies, the model proposed in this paper helps analyze the hybrid dynamic processes of interactions between physical devices and information systems. At the same time, the model framework is highly universal and can be extended to arbitrarily complex dynamic systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0070] Figure 1 Flow chart of the method of the present invention.

[0071] Figure 2 This is the structural block diagram of the hybrid system.

[0072] Figure 3 Block diagram of hierarchical modeling of active distribution network.

[0073] Figure 4 This is the simulation waveform of the active distribution network.

[0074] Figure 5 Schematic diagram of the physical device layer structure of the active distribution network.

[0075] Figure 6 This is a schematic diagram of the information system layer structure of the active power distribution network. DETAILED DESCRIPTION

[0076] The following is a detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0077] like Figure 1 As shown, the present invention discloses a discrete-continuous unified modeling method for active distribution network based on hybrid system theory, and its specific steps are as follows:

[0078] Step 1: Based on the hybrid system theoretical framework, a discrete-continuous hierarchical modeling framework for active distribution networks is established, which is divided into the information system layer and the physical device layer;

[0079] Figure 2This is a block diagram of a hybrid system structure, consisting of a continuous dynamic subsystem, a discrete event subsystem, and an interface between the continuous and discrete systems. The discrete-continuous system interface converts discrete variables in the discrete event subsystem into continuous variables and uses them as input to the continuous dynamic subsystem. Conversely, the continuous-discrete system interface converts continuous variables in the continuous dynamic subsystem into discrete variables and uses them as input to the discrete event subsystem.

[0080] Figure 3 The steps for establishing a hierarchical modeling framework for active distribution networks based on hybrid system theory are as follows:

[0081] 1): The hybrid system theory is described in the form of multiple groups, as shown below:

[0082] H={I,M,Σ,Q,P,δ,R,X}(1);

[0083] Where:

[0084] I: Input set, representing the input set of the external active distribution network, mainly including the continuous input signal u in , discrete input signal d in and external input event signal e in , as shown below:

[0085] I=[u in ,d in ,e in ](2);

[0086] M represents the set of discrete states of the active distribution network (also called system operation mode). For any discrete state, m = m(t)∈M;

[0087] Σ={e1,e2,…,e N} represents the set of discrete events of the active distribution network. For any discrete event, it can be expressed as e = e(t)∈Σ;

[0088] Q={q1,q2,…q k} represents a set of discrete variables;

[0089] P represents the parameter variable of the active distribution network;

[0090] δ represents the discrete state transition function of the active distribution network;

[0091] R represents the reset function, which determines the state of the continuous variables after the discrete state transition of the active distribution network;

[0092] X={H (m)} m∈Mrepresents the continuous state space set of the active distribution network under different operation modes, where H (m) =(X (m) ,G (m) ,f (m) ,λ (m) ), H (m) The meaning of each element is as follows:

[0093] X (m) represents the continuous state space of the active distribution network in mode m, x(t)∈X (m) Represents the state variables of the active distribution network.

[0094] G (m) Indicates the transition condition of the active distribution network in mode m∈M;

[0095] f (m) It represents the evolution rule of the active distribution network under mode m and characterizes the dynamic behavior characteristics of the active distribution network;

[0096] λ (m) represents the output function of the active distribution network.

[0097] 2) Establish a set of equations that describe the dynamic and static characteristics of the active distribution network using hybrid system theory, as shown below:

[0098]

[0099] Where: “-” and “+” represent the time before and after the event e respectively, m - (t) and Respectively represent the state mode and continuous state before the event e occurs, m + (t) and The meaning is similar. y(t) represents the output of the active distribution network.

[0100] 3): The dynamic and static modeling framework of the active distribution network is divided into the information system layer and the physical equipment layer, and the two interact through event functions.

[0101] The physical equipment layer is the physical component of the active distribution network, including distribution transformers, distribution lines, switchgear, distributed power sources, energy storage equipment, load equipment, protection devices, and reactive power compensation equipment. It is responsible for the transmission and distribution of electrical energy, stable system operation, energy supply and demand balance, and voltage and frequency regulation. The information system layer is the "brain" of the active distribution network and includes supervisory control and data acquisition (SCADA) systems, smart meters, communication networks, energy management systems (EMS), distribution automation systems (DAS), information processing platforms, and network security equipment. It is responsible for data acquisition and monitoring, optimized scheduling and control, and fault detection and recovery.

[0102] Step 2: Divide the active distribution network information system layer and the active distribution network physical equipment layer into the continuous dynamic subsystem layer and the discrete event subsystem layer respectively;

[0103] The continuous dynamic subsystem layer and the discrete event subsystem layer interact through interface functions, which include the action functions of the continuous dynamic subsystem layer on the discrete event subsystem layer and the action functions of the discrete event subsystem layer on the continuous dynamic subsystem layer.

[0104] Step 3: Use different methods to establish mathematical models of the continuous dynamic subsystem layer and the discrete event subsystem layer respectively. The specific process is as follows:

[0105] The continuous dynamic subsystem layer of the active distribution network physical equipment layer mainly describes the continuous dynamic behavior characteristics of the physical equipment, which is described by the following differential equations:

[0106]

[0107] In the above formula: Represents the continuous dynamic change relationship function of the physical equipment layer of the active distribution network, Represents the output function of the physical device layer of the active distribution network. represents the continuous state variable of the physical device layer of the active distribution network, and u(t) is the output control variable generated by the physical device layer of the active distribution network.

[0108] The discrete event subsystem of the physical device layer of the active distribution network is used to describe the transition process of the device between different discrete states q. The available state transition condition function g c and the state transition function δ c describe:

[0109] State transition condition function g c :

[0110] g c :Cond={true,false},cond=g c (q,x)(9);

[0111] Formula (5) indicates whether the discrete event subsystem satisfies the function g under the conditions of discrete state q and continuous state x. c The operating state transition conditions.

[0112] State transition function δ c :

[0113] δ c :δ c (q - ,e,cond)=q + ,{e cd1 ,e cd2,…,e cdn}(10);

[0114] Where: Event e can be the state event e generated by the continuous dynamic subsystem layer cc , or it can be the internal control input event e of the discrete event subsystem de , or an event generated by the environment e cin Formula (6) indicates that when event e occurs and the state transition condition cond is true, the system will change from state q to state q. - Transfer to state q + , and generates a series of discrete events e cdi .

[0115] Step 4: Establish the interaction model between the continuous dynamic subsystem layer and the discrete event subsystem layer to obtain the discrete-continuous unified model of the active distribution network. The specific steps are as follows:

[0116] 1) Define F ccd is the interface function between the continuous and discrete subsystem layers, which represents the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer. Define F dcd It is the discrete-continuous subsystem layer interface function, which represents the action function of the discrete event subsystem layer on the continuous dynamic subsystem layer.

[0117] 2):F ccd It is manifested as the state trajectory of the continuous state variable x crossing the hypersurface h m Event e will be triggered when cc and through the event e cc Acting on the discrete event subsystem layer, thereby changing the value of q, as shown below:

[0118]

[0119] 3):F cdc It represents the effect of the discrete event subsystem layer on the continuous dynamic subsystem layer and consists of the following two parts.

[0120] F cdc =[f cdx ,f cdm ](5);

[0121] Where: f cdm It represents the function that affects the dynamic change relationship of the continuous variable x through the discrete state q. Its expression is

[0122]

[0123] f cdx The function f that represents the change in the value of the continuous state variable x when the system undergoes state transition cdx , its expression is as follows.

[0124]

[0125] 4) Establish a discrete-continuous unified model of the active distribution network

[0126] By integrating the continuous dynamic subsystem layer model, the discrete event subsystem layer model, and the interface function model between the continuous dynamic subsystem layer and the discrete event subsystem layer in the physical equipment layer of the active distribution network, the discrete-continuous unified model of the active distribution network is obtained, as shown below.

[0127]

[0128] Similarly, the discrete-continuous unified model of the active distribution network information system layer can be obtained as shown below.

[0129]

[0130] The meaning of each variable in formula (12) is the same as that in formula (11).

[0131] This paper applies the proposed modeling method to power quality optimization control in active distribution networks. This optimization is primarily achieved by fully utilizing the interconnected converters (ILCs) connecting the DC and AC buses. Power quality control objectives include balancing AC bus voltage imbalances, balancing output current imbalances of the interconnected converters, and suppressing DC bus voltage ripple.

[0132] The continuous variables in the embodiment of the present invention are the AC bus voltage, the output current of the interconnected converter and the DC bus voltage, and the discrete variables are the operating status of the interconnected converter. Figure 4 As shown. Figure 4 It can be seen that when the proposed model achieves a specific optimization goal for the active distribution network, the entire active distribution network's operational control process and the operating state transition process of each device are clearly presented, improving the observability of the active distribution network's optimization and control. Furthermore, it can be seen that by controlling the transition of the interconnected converters between different operating states, the three optimization goals of controlling the imbalance of the AC bus voltage, balancing the output current imbalance of the interconnected converters, and suppressing ripple in the DC bus voltage can be achieved, respectively. This verifies the feasibility of the discrete-continuous unified model for active distribution networks.

Claims

1. A unified discrete-continuous modeling method for active distribution networks based on hybrid system theory, characterized by The following steps are involved: Step 1: Unify the discrete and continuous dynamic characteristics of the active distribution network and establish a discrete-continuous hierarchical modeling framework for the active distribution network based on hybrid system theory; Step 2: Considering the discrete-continuous characteristics of the active distribution network during operation, the active distribution network information system layer and the active distribution network physical equipment layer are divided into the continuous dynamic subsystem layer and the discrete event subsystem layer respectively; Step 3: Use differential equations to describe the continuous dynamic behavior characteristics of the continuous dynamic subsystem layer in the active distribution network information system layer and the active distribution network physical device layer, and use a state machine model to describe the discrete event characteristics of the discrete event subsystem layer in the active distribution network information system layer and the active distribution network physical device layer; Step 4: Establish the interface function model of the continuous dynamic subsystem layer and the discrete event subsystem layer to obtain the discrete-continuous unified model of the active distribution network.

2. The discrete-continuous unified modeling method for active distribution network based on hybrid system theory according to claim 1 is characterized by: In step 1, the hybrid system consists of a continuous dynamic subsystem, a discrete event subsystem, and an interface between the continuous and discrete systems; the discrete-continuous system interface converts discrete variables in the discrete event subsystem into continuous variables and serves as input to the continuous dynamic subsystem; In contrast, the continuous-discrete system interface converts the continuous variables in the continuous dynamic subsystem into discrete variables and uses them as input to the discrete event subsystem.

3. The discrete-continuous unified modeling method for active distribution network based on hybrid system theory according to claim 1 is characterized by: The step 1 comprises the following steps: 1): The hybrid system theory is described in the form of multiple groups, as shown below: H={I,M,Σ,Q,P,δ,R,X} (1); In formula (1), I is the input set, which represents the input set of the external active distribution network, including the continuous input signal u in , discrete input signal d in and external input event signal e in , as shown below: I=[u in ,d in ,e in ] (2); M represents the set of discrete states of the active distribution network. For any discrete state, m = m(t)∈M, where m(t) represents the discrete state of the active distribution network at time t; Σ = {e1, e2, …, e N } represents the discrete event set of the active distribution network, e1, e2,…, e N They represent different discrete events generated by the active distribution network; any discrete event can be expressed as e=e(t)∈Σ; e represents the symbol used to describe the discrete event generated by the active distribution network, e(t) represents the discrete event of the active distribution network at time t, Σ represents the discrete event set of the active distribution network; Q={q1,q2,…q k } represents a set of discrete variables; q1,q2,…q k They represent a discrete variable of the active distribution network respectively; P represents the parameter variable of the active distribution network; δ represents the discrete state transition function of the active distribution network; R represents the reset function, which determines the continuous variable state after the discrete state transition of the active distribution network; X={H (m) } m∈M represents the continuous state space set of the active distribution network under different operation modes, m represents the symbol used to describe the discrete state of the active distribution network, and M represents the set of discrete states of the active distribution network; Among them, H (m) =(X (m) ,G (m) ,f (m) ,λ (m) ), H (m) The meaning of each element is as follows: X (m) represents the continuous state space of the active distribution network in mode m, x(t)∈X (m) Represents the state variable of the active distribution network; G (m) represents the transition condition of the active distribution network in mode m∈M; f (m) represents the evolution rule of the active distribution network under mode m, characterizing the dynamic behavior characteristics of the active distribution network; λ (m) represents the output function of the active distribution network; 2) The equations describing the dynamic and static characteristics of the active distribution network using hybrid system theory are as follows: In formula (3), "-" and "+" represent the time before and after the event e respectively; m - (t) and They represent the state mode and continuous state before the event e occurs, respectively; y(t) represents the output of the active distribution network; represents the state variable control law of the active distribution network in operation mode m; x (m) (t) represents the state variable of the active distribution network in operation mode m; u(t) represents the input control variable of the active distribution network; p represents the disturbance variable of the active distribution network; m + (t) represents the state mode of the active distribution network after the event e occurs; e represents the symbol used to describe the discrete events generated by the active distribution network, represents the state variables of the active distribution network after event e occurs; 3): The discrete-continuous hierarchical modeling framework of the active distribution network is divided into the information system layer and the physical device layer, and the two interact through event functions.

4. The method for unified discrete-continuous modeling of active distribution networks based on hybrid system theory according to claim 3 is characterized by: The physical equipment layer is the physical part of the active distribution network, including distribution transformers, distribution lines, switchgear, distributed power sources, energy storage equipment, load equipment, protection equipment and reactive power compensation equipment. The physical equipment is connected through distribution lines, and the distributed power sources and energy storage equipment are connected to the grid through the lines. The electric energy is supplied to the load equipment after being stepped down by the distribution transformer; the reactive power compensation equipment is connected in parallel on the line to adjust the voltage stability; the switchgear is connected in series in the line to control the on and off to change the topology; the protection equipment monitors the line current / voltage in real time and controls the switchgear through trip signals to achieve fault isolation.

5. The discrete-continuous unified modeling method for active distribution network based on hybrid system theory according to claim 4 is characterized by: The information system layer includes a supervisory control and data acquisition (SCADA) system, smart meters, communication networks, an energy management system (EMS), a distribution automation system (DAS), an information processing platform, and network security equipment. Smart meters collect real-time data such as voltage, current, and power from the physical device layer and upload it to the SCADA system via the communication network. The SCADA system then integrates data from all network points to provide a visual monitoring interface and transmits key information to the energy management system (EMS) and information processing platform. The EMS and information processing platform generate control strategies based on optimization algorithms. Finally, the distribution automation system (DAS) receives EMS instructions and sends control signals to switches and energy storage devices at the physical device layer through the communication network. Throughout the process, network security equipment is used to protect the integrity and confidentiality of data transmission.

6. The method for unified discrete-continuous modeling of active distribution networks based on hybrid system theory according to claim 1 is characterized by: In step 2, the continuous dynamic subsystem layer and the discrete event subsystem layer interact with each other through interface functions, wherein the interface functions include the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer and the action function of the discrete event subsystem layer on the continuous dynamic subsystem layer; The action function of the continuous dynamic subsystem layer on the discrete event subsystem layer is expressed as F ccd Indicates that F ccd It is manifested as the state trajectory of the continuous state variable x crossing the hypersurface h m Event e will be triggered when cc and through the event e cc Acting on the discrete event subsystem layer, thereby changing the value of q, as shown below; In formula (4): H m (x(t),u(t)) represents the hypersurface h m The expression of F ccd (x(t),h m ) represents the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer; The action function of the discrete event subsystem layer on the continuous dynamic subsystem layer is expressed as F cdc It is composed of the following two parts: F cdc =[f cdx ,f cdm ] (5); In formula (5): f cdm It represents the function that affects the dynamic change relationship of the continuous variable x through the discrete state q. Its expression is In formula (6): m - (t) and Respectively represent the state mode and continuous state before the event e occurs, m + (t) represents the state pattern after event e occurs; f cdx The function f that represents the change in the value of the continuous state variable x when the system undergoes state transition cdx , its expression is as follows; In formula (7): Represents the continuous state after event e occurs.

7. The method for unified discrete-continuous modeling of active distribution networks based on hybrid system theory according to claim 1 is characterized by: In step 3, the continuous dynamic subsystem layer of the active distribution network physical device layer is used to describe the continuous dynamic behavior characteristics of the physical device, and is described by the following differential equation: In formula (8): represents the state variables of the physical device layer of the active distribution network in mode m, Represents the continuous dynamic change relationship function of the physical device layer of the active distribution network in mode m, represents the output function of the physical device layer of the active distribution network, represents the continuous state variable of the physical device layer of the active distribution network, the superscript m represents the operation mode of the active distribution network; u(t) is the control variable generated by the physical device layer of the active distribution network; y c (t) represents the output variable of the physical device layer of the active distribution network; p represents the disturbance variable of the active distribution network.

8. The discrete-continuum unified modeling method for active distribution network based on hybrid system theory according to claim 7 is characterized by: The discrete event subsystem of the physical device layer of the active distribution network is used to describe the transition process of the device between different discrete states q, using the state transition condition function g c and the state transition function δ c describe; State transition condition function g c : g c :Cond={true,false},cond=g c (q,x) (9); In formula (9), Cond represents the judgment result of the state transition condition function, {true, false} represents the symbol used to describe whether the judgment condition is true or false, true represents the symbol used to describe whether the judgment condition is true, and false represents the symbol used to describe whether the judgment condition is false. cond = g c (q,x) represents the expression used to describe the judgment result of the state transition condition function, cond represents the judgment result of the state transition condition function, g c (q,x) represents the judgment expression of the state transition condition function, q represents a discrete variable, and x represents a continuous variable; Formula (9) indicates whether the discrete event subsystem satisfies the function g under the conditions of discrete state q and continuous state x. c The operating state transition conditions; State transition function δ c : δ c :δ c (q - ,e,cond)=q + ,{And cd1 ,And cd2 ,…,And cdn } (10); In formula (10), δ c represents the state transition function, δ c (q - ,e,cond) represents the physical device layer from discrete state q - Transfer to discrete state q + The state transition function expression of {e cd1 ,e cd2 ,…,e cdn } indicates that the physical device layer is from discrete state q - Transfer to discrete state q + The set of discrete events generated, e cd1 ,e cd2 ,…,e cdn Respectively represent the physical device layer from discrete state q - Transfer to discrete state q + , a series of discrete events generated; In formula (10), event e is the state event e generated by the continuous dynamic subsystem layer cc , or the internal control input event e of the discrete event subsystem de , or an event generated by the environment e cin ; Formula (10) indicates that when event e occurs and the state transition condition cond is true, the system will change from discrete state q - Transfer to discrete state q + , and generates a series of discrete events e cdi ; The superscripts "-" and "+" represent the time before and after the event e occurs, respectively.

9. The method for unified discrete-continuous modeling of active distribution networks based on hybrid system theory according to claim 1 is characterized by: The step 4 comprises the following steps: S4.1: Define F ccd is the continuous-discrete subsystem layer interface function, which represents the action function of the continuous dynamic subsystem layer on the discrete event subsystem layer; define F dcd It is the discrete-continuous subsystem layer interface function, which represents the function of the discrete event subsystem layer on the continuous dynamic subsystem layer; S4.2: Establish a discrete-continuous unified model of the active distribution network: By integrating the continuous dynamic subsystem layer model, the discrete event subsystem layer model, and the interface function model between the continuous dynamic subsystem layer and the discrete event subsystem layer in the physical device layer of the active distribution network, the discrete-continuous unified model of the active distribution network is obtained, as shown below:

10. The method for unified discrete-continuous modeling of active distribution networks based on hybrid system theory according to claim 9, characterized in that: The discrete-continuous unified model of the active distribution network information system layer is as follows:

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