Alternating current and direct current hybrid power distribution network dynamic operation envelope characterization method based on distributed robust optimization and generative learning

Abstract

The invention relates to the field of AC / DC power distribution network operation regulation and control, and discloses an AC / DC hybrid power distribution network dynamic operation envelope characterization method based on distributed robust optimization and generative learning, and the method comprises the steps: constructing an AC / DC hybrid power distribution network active and reactive power operation envelope model; constructing an AC / DC hybrid power distribution network uncertainty fuzzy set based on a second moment; constructing an energy storage power and energy reservation model based on distributed robust optimization; calculating the active power regulation capability of time decoupling of the AC / DC hybrid power distribution network by using an approximation technology in a hyperrectangle; and constructing and training an AC / DC hybrid power distribution network operation envelope representation model based on mathematical model hybrid driving by using the generative adversarial network. According to the method, the defect of a traditional optimization model in calculation efficiency can be overcome so as to adapt to the real-time operation requirement of a large-scale power grid, the uncertain real distribution characteristics can be accurately captured, and the operation potential of the power grid can be mined to the maximum extent on the premise that safety and reliability are guaranteed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of AC / DC power distribution network operation regulation, in particular to a dynamic operation envelope representation method for AC / DC hybrid power distribution network based on distributed robust optimization and generative learning. BACKGROUND

[0002] With the increasing penetration of distributed energy in AC / DC hybrid power distribution network, the accurate representation of dynamic operation envelope of the power distribution network has become a core technical prerequisite for improving the utilization efficiency of power grid assets, ensuring the consumption of high proportion of renewable energy, and maintaining the safe and stable operation of the power grid. However, the existing technology faces serious technical bottlenecks in representing the dynamic operation envelope, which not only limits the operation potential of the power grid, but also may cause safety risks.

[0003] Firstly, the existing methods cannot balance the contradiction between calculation efficiency and large-scale application. Traditional model-based optimization methods need to model and solve a large number of operation scenarios and complex nonlinear constraints when dealing with increasingly large and complex AC / DC hybrid power distribution networks, which leads to an exponential increase in calculation amount. The calculation time is often measured in hours, which makes it completely unable to meet the real-time requirements of power grid dispatching and control for minute-level or even second-level decision-making, and lacks application value in actual engineering.

[0004] Secondly, in terms of coping with uncertainty, the existing methods are trapped in the dilemma of "conservative" and "aggressive". In order to cope with the strong uncertainty of load fluctuation and renewable energy output, traditional methods mostly rely on simple probability distribution assumption for stochastic optimization, or use conservative deterministic method. The assumption of the former is seriously inconsistent with the non-Gaussian characteristics of actual renewable energy, which leads to insufficient reliability of the operation envelope, and easily causes overrun risk in extreme scenarios; the latter has to greatly compress the operation boundary in order to ensure absolute safety, which leads to overly conservative operation envelope, causing insufficient scheduling of flexible resources, and seriously affecting the economic benefit of the power grid.

[0005] Thirdly, the existing methods have inherent limitations in the accuracy of representation ability. The operation envelope of AC / DC hybrid power distribution network is a high-dimensional complex set determined by a large number of time-coupled constraints. Existing methods often rely on the assumption of convexity or pre-set geometric shape to simplify the model, which leads to a large deviation between the representation result and the real operation boundary, misleading the decision-making of the operation personnel.

[0006] In view of the problems in the related art, no effective solution has been proposed so far. SUMMARY

[0007] (I) Technical problems solved

[0008] In view of the deficiencies of the prior art, the application provides a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning, which has the advantages of adapting to real-time operation requirements of a large-scale power grid, accurately capturing real distribution characteristics of uncertainties, and maximizing the operation potential of the power grid, thereby solving the problem of calculation efficiency of a traditional optimization model.

[0009] The technical scheme

[0010] To achieve the above-mentioned advantages of adapting to real-time operation requirements of a large-scale power grid, accurately capturing real distribution characteristics of uncertainties, and maximizing the operation potential of the power grid, the application adopts the following specific technical scheme:

[0011] A dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning, the method comprising:

[0012] A power active and reactive power operation envelope model for the AC-DC hybrid distribution network is constructed by taking into account a heterogeneous flexible resource mathematical model and network power flow constraints;

[0013] An uncertainty fuzzy set for the AC-DC hybrid distribution network based on the second moment is constructed by taking into account unimodality and skewness information of the probability distribution form of random variables;

[0014] An energy storage power and energy reservation model based on distribution robust optimization is constructed;

[0015] The power active and reactive power operation envelope model for the AC-DC hybrid distribution network and the uncertainty fuzzy set for the AC-DC hybrid distribution network based on the second moment are combined to solve the energy storage power and energy reservation model, so as to obtain an energy storage power and energy reservation strategy resisting the worst probability distribution;

[0016] Based on the energy storage power and energy reservation strategy, the active power regulation capability of the AC-DC hybrid distribution network in time decoupling is calculated by using the hyper-rectangle inner approximation technique;

[0017] Based on the active power regulation capability, a generative adversarial network is used to construct and train a mathematical model hybrid-driven operation envelope representation model for the AC-DC hybrid distribution network, so as to represent the operation envelope of the AC-DC hybrid distribution network.

[0018] Preferably, the power active and reactive power operation envelope model for the AC-DC hybrid distribution network is constructed by taking into account the heterogeneous flexible resource mathematical model and the network power flow constraints, and comprises:

[0019] A heterogeneous flexible resource mathematical model is established based on preset constraint conditions of the heterogeneous flexible resource;

[0020] The AC / DC hybrid power distribution network power flow model is established based on preset upper and lower limits of node voltage amplitude and upper and lower limits of branch capacity, and the AC / DC hybrid power distribution network power flow model comprises an AC node active power balance equation, an AC node reactive power balance equation, an AC branch voltage drop equation, an AC node active power injection equation, an AC node reactive power injection equation, a second-order cone relaxation AC branch capacity equation, a DC node active power balance equation, a DC branch voltage drop equation, a DC node active power injection equation, and a second-order cone relaxation DC branch capacity equation;

[0021] The VSC mathematical model is established based on preset reactive power compensation constraints, and the VSC mathematical model comprises a VSC active power balance equation and an operating capacity equation;

[0022] The AC / DC hybrid power distribution network active and reactive power operating envelope model is generated by combining the heterogeneous flexible resource mathematical model, the AC / DC hybrid power distribution network power flow model, and the VSC mathematical model.

[0023] Preferably, the heterogeneous flexible resource comprises a combined heat and power unit, a distributed photovoltaic, an energy storage system, an electric vehicle, and a heating, ventilation and air conditioning.

[0024] Preferably, the heterogeneous flexible resource mathematical model is established based on preset constraints of the heterogeneous flexible resource, and comprises:

[0025] The combined heat and power unit mathematical model is constructed based on active power constraints, reactive power constraints, power factor constraints, and ramping constraints of the combined heat and power unit;

[0026] The distributed photovoltaic mathematical model is constructed based on active power constraints, reactive power constraints, and active and reactive power coupling constraints of the distributed photovoltaic;

[0027] The energy storage system mathematical model is constructed based on charge and discharge power constraints, reactive power constraints, active and reactive power coupling constraints, and energy constraints of the energy storage system;

[0028] The electric vehicle mathematical model is constructed based on charge and discharge power constraints, reactive power constraints, active and reactive power coupling constraints, energy constraints, charging target constraints, and access and exit time constraints of the electric vehicle;

[0029] The heating, ventilation and air conditioning mathematical model is constructed based on active power constraints, reactive power constraints, and temperature constraints of the heating, ventilation and air conditioning.

[0030] Preferably, the second-moment-based AC / DC hybrid power distribution network uncertainty fuzzy set is constructed by taking into account the unimodality and skewness information of the probability distribution form of the random variable, and comprises:

[0031] Generate equivalent net load error of AC / DC hybrid distribution network based on predefined power prediction error of distributed photovoltaic, heating, ventilation and air conditioning and electric vehicle;

[0032] Introduce second-moment fuzzy set based on unimodal and skewness information to represent uncertainty of equivalent net load error of AC / DC hybrid distribution network, and obtain uncertainty fuzzy set of AC / DC hybrid distribution network.

[0033] Preferably, after constructing the second-moment-based uncertainty fuzzy set of AC / DC hybrid distribution network and before constructing the energy storage power and energy reservation model based on distribution robust optimization, it further comprises:

[0034] Obtain the access time and disconnection time of electric vehicles and the access energy and disconnection required energy of electric vehicles within a preset time period, and construct an electric vehicle charging behavior probability model in combination with a Gaussian mixture model;

[0035] Based on the electric vehicle charging behavior probability model, generate the probability distribution functions of the access time and disconnection time of electric vehicles and the access energy and disconnection required energy of electric vehicles, respectively;

[0036] Obtain the total number of electric vehicles within a preset time period, and construct a dynamic change model of the number of electric vehicles based on the total number of electric vehicles;

[0037] Combine the electric vehicle charging behavior probability model, the probability distribution functions and the dynamic change model of the number of electric vehicles to construct an electric vehicle charging station operation model, and integrate the electric vehicle charging station operation model as a heterogeneous flexible resource mathematical model into the active and reactive power operation envelope model of the AC / DC hybrid distribution network.

[0038] Preferably, the calculation of the time-decoupled active power regulation capability of the AC / DC hybrid distribution network using the hyper-rectangle inner approximation technique comprises:

[0039] Based on the time-decoupled power interval, represent the active power boundary of the AC / DC hybrid distribution network operation envelope, and take the active power boundary of the AC / DC hybrid distribution network operation envelope as a hyper-rectangle in a preset dimensional space;

[0040] Take the maximum active power regulation capability of the AC / DC hybrid distribution network in the time domain as the objective function, take the upper bound trajectory greater than the lower bound trajectory as the constraint condition, establish a mathematical optimization model based on the hyper-rectangle inner approximation, and solve the mathematical optimization model based on the hyper-rectangle inner approximation to obtain the time-decoupled active power regulation capability of the AC / DC hybrid distribution network.

[0041] Preferably, a discriminator in the generative adversarial network is generated for learning the decision boundary of the active and reactive power envelope of the AC / DC hybrid distribution network from the labeled data set;

[0042] A generator in a generative adversarial network is configured to generate a candidate active and reactive power sample point on a decision boundary;

[0043] A labeling model in the generative adversarial network is configured to provide a feasibility label for the candidate active and reactive power sample point.

[0044] Preferably, the mathematical model hybrid-driven AC / DC hybrid power distribution network operation envelope representation model is constructed and trained by using the generative adversarial network, so as to represent the AC / DC hybrid power distribution network operation envelope, which comprises:

[0045] The discriminator is trained based on the pre-collected sample set, so that the discriminator learns and approximates the decision boundary of the active and reactive power envelope of the AC / DC hybrid power distribution network;

[0046] The generator generates active and reactive power sample points in the uncertain region of the discriminator based on the decision boundary output by the discriminator;

[0047] The active and reactive power sample points are input into the labeling model, and the labeling model labels the feasibility label to form a new sample set with labels; the new sample set is combined with the current sample set to obtain an expanded sample set as the input of the next iteration;

[0048] The iteration process is repeated until the decision boundary output by the discriminator converges or reaches a preset number of iterations, and the active and reactive power sample points of the feasible sample set are extracted from the final sample set, and the convex hull of the active and reactive power sample points is obtained to obtain the operation envelope of the AC / DC hybrid power distribution network.

[0049] Preferably, the mathematical model hybrid-driven AC / DC hybrid power distribution network operation envelope representation model is constructed and trained by using the generative adversarial network, so as to represent the AC / DC hybrid power distribution network operation envelope, which comprises:

[0050] A composite loss function is constructed by using a geometric regularization technique, and the composite loss function is used to solve the mode collapse of the generative adversarial network in the training process;

[0051] The composite loss function comprises a standard adversarial loss and a geometric loss composed of a pair distance loss and an angle variance loss.

[0052] The pair distance loss is an average Euclidean distance between a plurality of active and reactive power sample points; and the angle variance loss is used to capture the curvature and two-dimensional shape of the active power boundary.

[0053] (Three) beneficial effects

[0054] Compared with the prior art, the AC / DC hybrid power distribution network dynamic operation envelope representation method based on distribution robust optimization and generative learning has the following beneficial effects:

[0055] The application provides a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0057] Figure 1 is a flowchart of a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0058] Figure 2 is a schematic diagram of an over-rectangle inner approximation method in a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0059] Figure 3 is a schematic diagram of a data model hybrid driving AC-DC hybrid distribution network operation envelope representation model in a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0060] Figure 4 is a schematic diagram of an AC-DC hybrid distribution network in a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0061] Figure 5 is a schematic diagram of an electric vehicle charging station operation range in a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0062] Figure 6 is a schematic diagram of a time-decoupled robust active power boundary in a dynamic operation envelope representation method for an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application;

[0063] Figure 7It is an active and reactive power dynamic operation envelope schematic diagram in a dynamic operation envelope representation method of an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application.

[0064] Figure 8 It is an adversarial learning process diagram of a dynamic operation envelope in a dynamic operation envelope representation method of an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application. DETAILED DESCRIPTION

[0065] To further illustrate the embodiments, the present application provides drawings, which are part of the disclosure of the present application, mainly used to illustrate the embodiments, and can explain the operating principle of the embodiments in conjunction with the related description of the specification. With reference to these contents, those skilled in the art should understand other possible implementations and advantages of the present application.

[0066] According to an embodiment of the present application, a dynamic operation envelope representation method of an AC-DC hybrid distribution network based on distribution robust optimization and generative learning is provided.

[0067] The present application will be further described in conjunction with the drawings and specific embodiments, as shown in Figure 1 The dynamic operation envelope representation method of an AC-DC hybrid distribution network based on distribution robust optimization and generative learning according to an embodiment of the present application includes:

[0068] A model of active and reactive power operation envelope of an AC-DC hybrid distribution network is constructed considering the mathematical model of heterogeneous flexible resources and network power flow constraints;

[0069] A second-moment-based uncertainty fuzzy set of an AC-DC hybrid distribution network is constructed considering the unimodality and skewness information of the probability distribution form of random variables;

[0070] A power and energy reservation model of energy storage based on distribution robust optimization is constructed;

[0071] The power and energy reservation model of energy storage is solved by combining the model of active and reactive power operation envelope of an AC-DC hybrid distribution network with the second-moment-based uncertainty fuzzy set of an AC-DC hybrid distribution network, to obtain a power and energy reservation strategy of energy storage resisting the worst probability distribution;

[0072] Based on the power and energy reservation strategy of energy storage, the active power regulation capability of time decoupling of an AC-DC hybrid distribution network is calculated using the hyper-rectangle inner approximation technique;

[0073] Based on the active power regulation capability, a representation model of operation envelope of an AC-DC hybrid distribution network based on mathematical model hybrid driving is constructed and trained using generative adversarial networks, to represent the operation envelope of an AC-DC hybrid distribution network.

[0074] In one embodiment, the active and reactive power operation envelope model of the AC / DC hybrid distribution network is constructed by taking into account the heterogeneous flexibility resource mathematical model and the network power flow constraints, comprising:

[0075] Based on the preset constraint conditions of the heterogeneous flexibility resource, a heterogeneous flexibility resource mathematical model is established; based on the preset upper and lower limit constraints of the node voltage amplitude and the upper and lower limit constraints of the branch capacity, an AC / DC hybrid distribution network power flow model is established, and the AC / DC hybrid distribution network power flow model comprises an AC node active power balance equation, an AC node reactive power balance equation, an AC branch voltage drop equation, an AC node active power injection equation, an AC node reactive power injection equation, a second-order cone relaxation AC branch capacity equation, a DC node active power balance equation, a DC branch voltage drop equation, a DC node active power injection equation, and a second-order cone relaxation DC branch capacity equation; based on the preset reactive power compensation constraint, a voltage source converter mathematical model is established, and the voltage source converter mathematical model comprises a voltage source converter active power balance equation and an operating capacity equation; the heterogeneous flexibility resource mathematical model, the AC / DC hybrid distribution network power flow model and the voltage source converter mathematical model are combined to generate an active and reactive power operation envelope model of the AC / DC hybrid distribution network.

[0076] In one embodiment, the heterogeneous flexibility resource includes a combined heat and power unit, a distributed photovoltaic, an energy storage system, an electric vehicle, and a heating, ventilation and air conditioning.

[0077] In one embodiment, based on the preset constraint conditions of the heterogeneous flexibility resource, the establishment of the heterogeneous flexibility resource mathematical model comprises:

[0078] Based on the active power constraint, the reactive power constraint, the power factor constraint and the ramping constraint of the combined heat and power unit, a combined heat and power unit mathematical model is constructed; based on the active power constraint, the reactive power constraint and the active and reactive power coupling constraint of the distributed photovoltaic, a distributed photovoltaic mathematical model is constructed; based on the charge and discharge power constraint, the reactive power constraint, the active and reactive power coupling constraint and the energy constraint of the energy storage system, an energy storage system mathematical model is constructed; based on the charge and discharge power constraint, the reactive power constraint, the active and reactive power coupling constraint, the energy constraint, the charging target constraint and the access and exit time constraint of the electric vehicle, an electric vehicle mathematical model is constructed; based on the active power constraint, the reactive power constraint and the temperature constraint of the heating, ventilation and air conditioning, a heating, ventilation and air conditioning mathematical model is constructed.

[0079] In one embodiment, the uncertainty fuzzy set of the AC / DC hybrid distribution network based on the second moment is constructed by taking into account the unimodality and skewness information of the probability distribution form of the random variable, comprising:

[0080] Generate equivalent net load error of AC / DC hybrid distribution network based on predefined power prediction error of distributed photovoltaic, heating, ventilation and air conditioning and electric vehicle; introduce second moment fuzzy set based on single peak and skewness information to represent uncertainty of equivalent net load error of AC / DC hybrid distribution network, and obtain uncertainty fuzzy set of AC / DC hybrid distribution network.

[0081] In one embodiment, after constructing the second moment based uncertainty fuzzy set of AC / DC hybrid distribution network and before constructing the energy storage power and energy reservation model based on distribution robust optimization, further comprising:

[0082] Obtain access time and exit time of electric vehicle and access energy and required exit energy of electric vehicle in a preset time period, and construct electric vehicle charging behavior probability model in combination with Gaussian mixture model; generate probability distribution functions of access time and exit time of electric vehicle and access energy and required exit energy of electric vehicle based on the electric vehicle charging behavior probability model; obtain total number of electric vehicles in the preset time period, and construct dynamic change model of electric vehicle number based on the total number of electric vehicles; combine the electric vehicle charging behavior probability model, the probability distribution functions and the dynamic change model of electric vehicle number to construct an electric vehicle charging station operation model, and integrate the electric vehicle charging station operation model as a heterogeneous flexible resource mathematical model into the active and reactive power operation envelope model of AC / DC hybrid distribution network.

[0083] In one embodiment, the active power regulation capability of the AC / DC hybrid distribution network time decoupling is calculated by using the hyperrectangle inner approximation technique, comprising:

[0084] The active power boundary of the AC / DC hybrid distribution network operation envelope is represented based on the time decoupled power interval, and the active power boundary of the AC / DC hybrid distribution network operation envelope is taken as a hyperrectangle in a preset dimension space; taking the maximum active power regulation capability of the AC / DC hybrid distribution network in the time domain as an objective function, and taking the upper boundary trajectory greater than the lower boundary trajectory as a constraint condition, a mathematical optimization model based on hyperrectangle inner approximation is established, and the mathematical optimization model based on hyperrectangle inner approximation is solved to obtain the active power regulation capability of the AC / DC hybrid distribution network time decoupling.

[0085] In one embodiment, a discriminator in the generative adversarial network is used to learn the decision boundary of the active and reactive power envelope of the AC / DC hybrid distribution network from the labeled data set; a generator in the generative adversarial network is used to generate candidate active and reactive power sample points on the decision boundary; and a labeling model in the generative adversarial network is used to provide a feasibility label for the candidate active and reactive power sample points.

[0086] In one embodiment, the mathematical model hybrid driven AC-DC hybrid power distribution network operation envelope representation model is constructed and trained by using a generative adversarial network to represent the AC-DC hybrid power distribution network operation envelope, which comprises:

[0087] The discriminator is trained based on the pre-collected sample set, so that the discriminator learns and approximates the decision boundary of the active and reactive power envelope of the AC-DC hybrid power distribution network; the generator generates active and reactive power sample points in the uncertain region of the discriminator based on the decision boundary output by the discriminator; the active and reactive power sample points are input into the labeling model, and the labeling model labels the feasibility label to form a new sample set with a label; the new sample set is combined with the current sample set to obtain an expanded sample set which is used as the input of the next iteration; the iteration process is repeated until the decision boundary output by the discriminator converges or the preset iteration number is reached, and the active and reactive power sample points of the feasible sample set are extracted from the final sample set, and the convex hull of the active and reactive power sample points is obtained to obtain the operation envelope of the AC-DC hybrid power distribution network.

[0088] In one embodiment, the mathematical model hybrid driven AC-DC hybrid power distribution network operation envelope representation model is constructed and trained by using a generative adversarial network to represent the AC-DC hybrid power distribution network operation envelope, which comprises:

[0089] A geometric regularization technique is used to construct a composite loss function to solve the mode collapse of the generative adversarial network in the training process; wherein the composite loss function includes a standard adversarial loss and a geometric loss composed of a pair distance loss and an angle variance loss; the pair distance loss is the average Euclidean distance between a plurality of active and reactive power sample points; the angle variance loss is used to capture the curvature and two-dimensional shape of the active power boundary.

[0090] In order to facilitate the understanding of the above technical solutions of the present application, the above technical solutions of the present application are further described from the aspects of architecture and principle as follows:

[0091] The AC-DC hybrid power distribution network dynamic operation envelope representation method provided by the present application comprises:

[0092] A, taking into account the mathematical model of heterogeneous flexible resources and network power flow constraints, an active and reactive power operation envelope model of the AC-DC hybrid power distribution network is constructed;

[0093] B, taking into account the unimodality and skewness information of the probability distribution shape of the random variable, a second moment based AC-DC hybrid power distribution network uncertainty fuzzy set is constructed;

[0094] C, considering the random charging behavior of electric vehicles, an electric vehicle charging station operation model is constructed;

[0095] D. Constructing energy storage power and energy reservation model based on distributionally robust optimization;

[0096] E. Constructing mathematical optimization model based on hyper-rectangle inner approximation to calculate the active power regulation capability of time-decoupled AC / DC hybrid distribution network;

[0097] F. Constructing AC / DC hybrid distribution network operation envelope representation model based on data model hybrid driving.

[0098] It should be noted that the "AC / DC hybrid distribution network active and reactive power operation envelope model" constructed in step A is the physical basis and constraint framework of the entire method. The system topology, power flow equation, operation limits of various devices, and other static and dynamic constraints are defined. The basic model is the object of all subsequent analysis and optimization, and its constraint conditions will run through the optimization models of steps E and F. At the same time, the "electric vehicle charging station operation model" constructed in step C is a key random load and flexibility resource model, and its specific constraints and variables are integrated into the overall model of step A to further improve the mathematical model of electric vehicles. Secondly, the "uncertainty fuzzy set" constructed in step B provides a mathematical description of the risks faced by the system, and this fuzzy set is used in step D distributionally robust optimization to find the energy storage power and energy reservation strategy against the worst probability distribution. Then, step D is the key to ensuring the reliability of the final envelope, which combines the basic model of step A with the uncertainty fuzzy set of step B to obtain the power and energy reservation values of the energy storage by solving the distributionally robust optimization problem. Then, step E efficiently calculates the active power regulation boundary of the AC / DC distribution network considering the uncertainty of flexible resources based on the results of step D through the hyper-rectangle inner approximation method. Finally, step F uses the fitting ability of the generative learning model to train an operation envelope representation model driven by a combination of data and physical models. By learning the complex nonlinear mapping relationship between system state and operation envelope boundary, the active and reactive power envelope boundary samples of the AC / DC distribution network are obtained. After training, the operation envelope convex hull is constructed based on the feasible power sample points to obtain the dynamic operation envelope of the AC / DC distribution network.

[0099] In step A, a heterogeneous flexibility resource mathematical model needs to be established, which includes combined heat and power units, distributed photovoltaic, energy storage systems, electric vehicles, and heating, ventilation, and air conditioning.

[0100] The mathematical model of combined heat and power units includes active power constraints, reactive power constraints, power factor constraints, and ramp constraints, as shown in equations (1)-(4):

[0101]

[0102]

[0103]

[0104]

[0105] In formula (1)-(4): and respectively represent the active and reactive power output of the cogeneration unit i at time t; and respectively represent the upper and lower limits of the active power output of the cogeneration unit i at time t; and respectively represent the upper and lower limits of the reactive power output of the cogeneration unit i at time t; represents the power factor angle of the cogeneration unit i; represents the maximum ramp rate of the cogeneration unit i; and respectively represent the active and reactive power output of the cogeneration unit i at time t; represents the active power output of the cogeneration unit i at time t-1.

[0106] The mathematical model of distributed photovoltaic includes active power constraints, reactive power constraints and active-reactive power coupling constraints, as shown in formula (5)-(7):

[0107]

[0108]

[0109]

[0110] In formula (5)-(7): and respectively represent the active and reactive power output of the distributed photovoltaic i at time t; and respectively represent the upper and lower limits of the active power output of the distributed photovoltaic i at time t; and respectively represent the upper and lower limits of the reactive power output of the distributed photovoltaic i at time t; represents the apparent power capacity of the distributed photovoltaic i.

[0111] The mathematical model of the energy storage system includes charge-discharge power constraints, reactive power constraints, active-reactive power coupling constraints, energy equations and energy constraints, as shown in formula (8)-(12):

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] In formulas (8)-(12): represents the charge-discharge power of the energy storage system i at time t; represents the reactive power of the energy storage system i at time t; represents the energy state of the energy storage system i at time t; represents the energy state of the energy storage system i at time t-1; and respectively represent the upper and lower limits of the charge-discharge power of the energy storage system i at time t; and respectively represent the upper and lower limits of the reactive power of the energy storage system i at time t; represents the apparent power capacity of the energy storage system i; represents the charge-discharge efficiency of the energy storage system i; and respectively represent the upper and lower limits of the energy state of the energy storage system i at time t.

[0118] The mathematical model of the electric vehicle includes charge-discharge power constraints, reactive power constraints, active-reactive power coupling constraints, energy equations, energy constraints, charging target constraints, and access-in and access-out time constraints, as shown in formulas (13)-(19):

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] In formulas (13)-(19): denotes the charging / discharging power of the electric vehicle j at time t; denotes the reactive power of the electric vehicle j at time t; denotes the energy state of the electric vehicle j at time t; denotes the energy state of the electric vehicle j at time t-1; and denote the upper and lower limits of the charging / discharging power of the electric vehicle j at time t, respectively; and denote the upper and lower limits of the reactive power of the electric vehicle j at time t, respectively; denotes the apparent power capacity of the electric vehicle j; denote the charging / discharging efficiency of the electric vehicle j, respectively; and denote the upper and lower limits of the energy state of the electric vehicle j at time t, respectively; denotes the charging target when the electric vehicle j is connected out; and denote the time when the electric vehicle is connected to the charging station and connected out of the charging station, respectively; denotes the time interval.

[0127] The mathematical model of the heating, ventilation and air conditioning includes active power constraints, reactive power constraints, temperature constraints and thermal effect equations, as shown in formulas (20)-(23):

[0128]

[0129]

[0130]

[0131]

[0132] In formulas (20)-(23): denotes the active power of the heating, ventilation and air conditioning i at time t; denotes the reactive power of the heating, ventilation and air conditioning i at time t; denotes the indoor temperature of the heating, ventilation and air conditioning i at time t; denotes the upper limit of the active power of the heating, ventilation and air conditioning i at time t; denotes the power factor angle of the heating, ventilation and air conditioning i; Tt represents the ambient temperature of the HVAC i at time t; and Tt represents the comfort temperature upper and lower limits of the HVAC i at time t; and Ct represents the thermal effect coefficient of the HVAC i at time t;

[0133] In Step A, the AC / DC hybrid power distribution network power flow model needs to be established, including AC node active power balance equation, AC node reactive power balance equation, AC branch voltage drop equation, AC node active power injection equation, AC node reactive power injection equation, second-order cone relaxation AC branch capacity equation, DC node active power balance equation, DC branch voltage drop equation, DC node active power injection equation, second-order cone relaxation DC branch capacity equation, node voltage amplitude upper and lower limit constraint and branch capacity upper and lower limit constraint, as shown in equations (24)-(35):

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] In equations (24)-(35): and These represent the active power and reactive power injected into AC node i, respectively. and These represent the active power and reactive power on AC branch ij, respectively. This represents the square of the current amplitude in the AC branch ki; This represents the square of the voltage magnitude at AC node i; This represents the active power injected from the main network at node i; This represents the active power injected into DC node i; This represents the active power on the DC branch ij; This represents the square of the current magnitude of the DC branch ki; This represents the square of the voltage magnitude at DC node i; and These represent the resistance and reactance of AC branch ij, respectively; This represents the resistance of the DC branch ij; Ω ac Represents the set of communication nodes; Ω dc Represents the set of DC nodes; Ω r Ω represents the set of end nodes of the branch whose first node is node i; s B represents the set of first nodes of a branch whose last node is node i; ac B represents the set of AC branches; dc Represents the set of DC branches; This represents the square of the voltage magnitude at node i; This represents the lower limit of the square of the voltage magnitude at node i; This represents the upper limit of the square of the voltage magnitude at node i; This represents the square of the amplitude of the current in branch ij; This represents the upper limit of the square of the current amplitude in branch ij.

[0147] Step A requires establishing a mathematical model of the voltage source converter, including active power balance equations, operating capacity equations, and reactive power compensation constraints, as shown in equations (36)-(38):

[0148]

[0149]

[0150]

[0151] In equations (36)-(38): and Let represent the active power and reactive power injected by voltage source converter i at the AC side node at time t, respectively; P0i(t) represents the active power injected by voltage source converter i at DC side node i at time t; Qi(t) represents the apparent capacity of voltage source converter i at time t; and Qi(t) represents the apparent capacity of voltage source converter i at time t;

[0152] In step A, the active and reactive power operation envelope model of AC / DC hybrid distribution network needs to be established, as shown in equations (39)-(40):

[0153]

[0154]

[0155] In equations (39)-(40): Pi(t) represents the controllable injected power vector of all flexibility resources at time t, and K∈{CHP, PV, ES, EVs, HVAC, VSC}; Pi(t) represents the controllable injected active power vector of node i; Qi(t) represents the controllable injected reactive power vector of node i; i represents the node of AC / DC hybrid network; Pi(t) represents the controllable injected power vector of all flexibility resources at time t, and K∈{CHP, PV, ES, EVs, HVAC, VSC}; 0,t t∈T and q0:=(q 0,t ) t∈T Pi(t) represents the controllable injected power vector of all flexibility resources at time t, and K∈{CHP, PV, ES, EVs, HVAC, VSC}; Xi(t) represents the uncertain parameter related to flexibility resources, Xi(t) represents the corresponding fuzzy set; x:=(x t t∈T Xi(t) represents the controllable injected power vector of flexibility resources at all times; matrices C, W, H, M and vectors c, w, h, m represent the corresponding system parameters; equation (40b) represents the second-order cone and apparent power capacity constraints of AC / DC network and flexibility resources; equation (40c) represents the linear constraint conditions of AC / DC network and flexibility resources; equations (40d) and (40e) respectively represent the coupling relationship between interactive power and flexibility resource injected power by using the power flow equation.

[0156] In step B, the uncertainty fuzzy set of AC / DC hybrid distribution network needs to be established. First, define the equivalent load error of AC / DC hybrid distribution network, as shown in equation (41):

[0157]

[0158] In equation (41): ​​This represents the net load prediction error at node i at time t; , , , represents the power prediction errors for photovoltaic, HVAC, load, and electric vehicle, respectively; T represents vector transpose.

[0159] Furthermore, a second-order moment fuzzy set based on single-peak and skewness information is introduced to characterize the uncertainty of the net load forecasting error of the AC / DC hybrid distribution network, as shown in Equation (42):

[0160]

[0161] In equation (42): Represents random variables probability distribution; parameters and The mode skewness and the mean were constrained respectively. Deviation; constraints Used to limit the upper bound of the mode skewness; constraint conditions Used to ensure the true covariance matrix is ​​bit Within a semi-fixed cone; It represents the mathematical expectation.

[0162] In step C, a probabilistic model of electric vehicle charging behavior is constructed based on a Gaussian mixture model, as shown in equation (43):

[0163]

[0164] In equation (43): t a and t d These represent the connection and disconnection times of electric vehicles, respectively; E a and E d These represent the energy required for the electric vehicle to connect and the energy required to disconnect, respectively; K represents the number of Gaussian components. Let the mixing ratio of the k-th Gaussian component satisfy the following condition: >0 and have ; Representing vectors The multidimensional Gaussian joint probability distribution is given by the mean vector. Covariance Matrix Characterization.

[0165] t a and t d The probability distribution function can be expressed as: The marginal probability distribution is shown in equations (44)-(45):

[0166]

[0167]

[0168] In formulas (44)-(45): μ a,k and μ d,k represent the mean of t a and t d , respectively, in the k-th Gaussian component; and represent the corresponding variances, extracted from the diagonal of the covariance matrix .

[0169] Let N i denote the total number of electric vehicles arriving at charging station i per day, then the dynamic change of the number of electric vehicles at charging station i at time t is represented as formulas (46)-(48):

[0170]

[0171]

[0172]

[0173] In formulas (46)-(48): denotes the number of on-station electric vehicles at charging station i at time t; and denote the number of electric vehicles arriving at and leaving charging station i at time t, respectively; and are the cumulative probability density functions of formulas (44) and (45), respectively.

[0174] The energy E a and E d required by the electric vehicle arriving at the charging station at time t to access and leave, respectively, are modeled by the conditional probability distribution of formula (43), as shown in formulas (49)-(50):

[0175]

[0176]

[0177] In formulas (49)-(50): denotes the conditional component weight; and denote the conditional mean of the arrival energy and the energy required when leaving, respectively; and denote the corresponding conditional variances, respectively.

[0178] Based on the probability models of electric vehicle charging behavior in step C, the charging station operation model is constructed as shown in equations (51)-(57).

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186] In equations (51)-(57): and denote the upper and lower energy limits of electric vehicle j at time t, respectively; denotes the charging and discharging power of electric vehicle j at time t; denotes the maximum charging and discharging power of electric vehicle; and denote the charging and discharging efficiency of electric vehicle j, respectively; and denote the active and reactive power of charging station i at time t, respectively; denotes the energy state of charging station i at time t; denotes the charging and discharging efficiency of electric vehicle; and denote the upper and lower energy limits of charging station i at time t, respectively; equations (51) and (52) define the upper and lower energy limits of each electric vehicle to ensure that its charging demand is met when it leaves; the active and reactive power of the charging station is constrained by equations (53) and (54); finally, this model describes the dynamic process of the aggregated energy of the charging station, equation (55) provides the energy state update rule, and equations (56) and (57) establish the upper and lower limits of this aggregated energy.

[0187] The energy storage power and energy reservation model based on distribution robust optimization needs to be constructed in Step D, as shown in equations (58)-(61):

[0188]

[0189]

[0190]

[0191]

[0192] In equations (58)-(61): represents the weight coefficient vector for proportionally allocating the reserved capacity to each energy storage; p R and E R respectively represent the energy storage reserved power matrix and the reserved energy vector; ξ t represents the net power prediction error of all nodes in the distribution network at time t; N ES represents the total number of energy storages in the distribution network; represents the confidence level; represents the lower bound of the probability distribution of the random variable when

[0193] After the energy storage reserved power and energy in Step D, the operating range of the energy storage is as shown in equations (62)-(63):

[0194]

[0195]

[0196] In equations (62)-(63): represents the reserved power capacity of energy storage i at time t; represents the reserved energy capacity of energy storage i.

[0197] In Step E, the time-decoupled power interval is used to describe the active power boundary of the operation envelope of the AC / DC hybrid distribution network, as shown in equation (64):

[0198]

[0199] In equation (64): represents the active power operation envelope; and ​respectively represent the upper and lower bounds of the interactive active power of the AC-DC hybrid distribution network at time t. In the T-dimensional space, the essence is a hyper-rectangle, where each dimension is defined by the power lower and upper bounds of a specific time period.

[0200] As shown in Figure 2 , step E requires the establishment of a mathematical optimization model based on the approximation within the hyper-rectangle to calculate the active power regulation capability of the AC-DC hybrid distribution network time decoupling, as shown in equations (65)-(70):

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207] In equations (65)-(70): represents the weight coefficient vector; and represent the decision variables, corresponding to the implementation of the power trajectory and .

[0208] Objective function (65) aims to maximize the active power regulation capability within time domain T. Constraint (66) stipulates that the upper bound trajectory must be strictly greater than the lower bound trajectory to ensure the formation of an effective, non-intersecting hyper-rectangle. Constraints (67)-(70) ensure the physical feasibility of the two boundary trajectories by ensuring that all underlying system operation constraints are satisfied and representing the coupling relationship between these boundary trajectories and the power injection of each independent device.

[0209] The AC / DC hybrid power distribution network operation envelope representation model based on data model hybrid driving in step F represents the active and reactive power envelope through the minimax game unfolded before the generator G and the discriminator D of the generative adversarial network, and provides label information for the training process of the generative adversarial network through the labeling model O: the discriminator D learns the decision boundary of the active and reactive power envelope of the AC / DC hybrid power distribution network from an ever-growing labeled data set; the generator G aims to directly generate novel and information-rich candidate active and reactive power sample points on the boundary currently estimated by the discriminator; the labeling model O serves as a computing resource to provide clear feasibility labels for the generated samples.

[0210] As shown in Figures 3-4 , the AC / DC hybrid power distribution network operation envelope representation model based on data model hybrid driving in step F identifies the unknown active and reactive power envelope in the two-dimensional power space at any time t using labeled power samples. For sample points u=(p0,q0)∈ in the space, there is a feasibility label y∈{+1,-1} (where +1 represents "feasible"), which is determined by querying the labeling model O. In the kth iteration process, the discriminator D is trained on the existing data set to approximate the decision boundary . Then, the generator adversarially synthesizes a new set of query points , which are concentrated in the area where the discriminator is most uncertain. These points are then labeled by the labeling model O and used to expand the data set = for the next iteration. After the iteration process is complete, the maximum active and reactive power envelope is defined by the convex hull of all feasible samples in the final data set .

[0211] The discriminator D(u;θ D ) is a neural network defined by the parameters θ D , which aims to accurately estimate the feasibility probability of the candidate power sample. The goal of the discriminator D is to minimize its classification error on the current existing labeled data set . Its loss function is shown in equation (71):

[0212]

[0213] In equation (71): is the output of the discriminator D, representing the probability that the sample u is predicted to have a label of +1 under the parameters , and its value is in the range (0, 1).

[0214] The generator G(z;θG is a neural network defined by parameters G that maps a latent vector z sampled from a prior distribution to a point u in the data space. The goal of G is to generate power samples that are maximally ambiguous to the discriminator, corresponding to points on the decision boundary of the active and reactive power operating envelope, at which the output of the discriminator is . To achieve this goal, the generator is trained to maximize the entropy of the discriminator's output. This objective is formalized by a loss function, as shown in equation (72):

[0215]

[0216] The generative adversarial network in step F is prone to mode collapse during training, i.e., the generated samples by the generator G lose diversity and cluster around a suboptimal portion of the boundary. To address this limitation, a geometric regularization method is proposed for the representation process of the active and reactive power envelope, and a composite loss function is designed as shown in equation (73):

[0217]

[0218] In equation (73), L ad represents the standard adversarial loss in equation (72); L dist and L angle represent the pairwise distance loss and the angle variance loss, respectively, which together constitute the geometric loss; λ dist and λ angle represent hyperparameters for balancing the contributions of the adversarial loss and the geometric loss.

[0219] The pairwise distance loss L dist aims to maximize the average Euclidean distance between the N generated sample points. If the generator produces a cluster of sample points that are tightly packed in space, this loss imposes a significant penalty, resulting in a gradient that guides the generator to map different inputs to a more diverse and widely distributed set of outputs, thereby effectively preventing mode collapse. Its main function is shown in equation (74):

[0220]

[0221] The angle variance loss L angle complements L dist , and its role is to maximize the variance of the angle distribution of the generated samples relative to their centroid, prompting the samples to spread out along the circumference, thereby capturing the curvature and two-dimensional morphology of the power boundary. In equation (75), the samples u (k)ordered from π to -π, the goal is to minimize the difference δ between each adjacent angle i from the ideal uniform difference δ ideal = 2π / N, as shown in equation (75):

[0222]

[0223] Step F, the mathematical optimization model shown in equations (76)-(81) is used to determine the feasibility of the active and reactive power samples. If there exists a solution that satisfies all network and device constraints (77)-(81), the optimal objective value is 1, and the point is marked as feasible; otherwise, the objective value is -∞, and the point is marked as infeasible.

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230] In equations (76)-(81), H t and M t represent the row sub-matrices of matrices H and M corresponding to time t, respectively; h t and m t represent the elements of vectors h and m corresponding to time t, respectively.

[0231] The implementation effect of the AC / DC hybrid distribution network dynamic operation envelope representation method based on distribution robust optimization and generative learning provided by the present application will be further described below in conjunction with specific embodiments.

[0232] According to 1000 historical charging data of four charging stations (CS), an electric vehicle charging station operation model is constructed to obtain the charging station operation range, and the result is shown in Figure 5 .

[0233] ​The active power feasible region of the AC / DC hybrid distribution network is approximated by using super-rectangle, and the robust active power boundary of the time-decoupled AC / DC hybrid distribution network is obtained, as shown in the result of Figure 6 The parameters of combined heat and power (CHP), photovoltaic (PV), energy storage (ES), and heating, ventilation, and air conditioning (HVAC) are shown in Tables 1-4.

[0234] Table 1. CHP parameters

[0235] Table 2. PV parameters

[0236] Table 3. ES parameters

[0237] Table 4. HVAC parameters

[0238] The active and reactive power dynamic operating envelope of the AC / DC hybrid distribution network is characterized by using the data model hybrid driving method, and the result is shown in Figure 7 The dynamic operating envelope at t=8:00 is shown in Figure 8

[0239] The above only describes the preferred embodiments of the present application and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.​

Claims

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comprises: The method comprises: The HVAC mathematical model is constructed based on active power constraints, reactive power constraints and temperature constraints of the HVAC.

5. The method of claim 1, wherein the method is characterized by, The single-peak and skewness information of the probability distribution form of the random variable is considered to construct the second-moment-based uncertainty fuzzy set of the AC / DC hybrid distribution network, which includes: Based on the predefined power prediction error of the distributed photovoltaic, HVAC and electric vehicle, the equivalent net load error of the AC / DC hybrid distribution network is generated; The second-moment-based fuzzy set is introduced to represent the uncertainty of the equivalent net load error of the AC / DC hybrid distribution network based on the single-peak and skewness information, and the uncertainty fuzzy set of the AC / DC hybrid distribution network is obtained.

6. The method of claim 1, wherein the method is characterized by, After the second-moment-based uncertainty fuzzy set of the AC / DC hybrid distribution network is constructed, and before the energy storage power and energy reservation model based on distribution robust optimization is constructed, it further includes: The access time and exit time of the electric vehicle in the preset time period, and the access energy and required exit energy of the electric vehicle are obtained, and a Gaussian mixture model is used to construct an electric vehicle charging behavior probability model; Based on the electric vehicle charging behavior probability model, the probability distribution functions of the access time and exit time of the electric vehicle, and the access energy and required exit energy of the electric vehicle are generated respectively; The total number of electric vehicles in the preset time period is obtained, and a dynamic change model of the number of electric vehicles is constructed based on the total number of electric vehicles; The electric vehicle charging station operation model is constructed by combining the electric vehicle charging behavior probability model, the probability distribution function and the dynamic change model of the number of electric vehicles, and the electric vehicle charging station operation model is integrated into the active and reactive power operation envelope model of the AC / DC hybrid distribution network as a heterogeneous flexible resource mathematical model.

7. The method of claim 1, wherein the method is characterized by, The active power regulation capability of the AC / DC hybrid distribution network is calculated by using the hyperrectangle inner approximation technique, which includes: Based on the time-decoupled power interval representing the active power boundary of the AC / DC hybrid distribution network operation envelope, the active power boundary of the AC / DC hybrid distribution network operation envelope is used as a hyperrectangle in a preset dimension space; The maximum active power regulation capability of the AC / DC hybrid distribution network in the time domain is used as the objective function, and the upper limit trajectory is greater than the lower limit trajectory as the constraint condition, and a mathematical optimization model based on hyperrectangle inner approximation is established, and the mathematical optimization model based on hyperrectangle inner approximation is solved to obtain the time-decoupled active power regulation capability of the AC / DC hybrid distribution network.

8. The method of claim 1, wherein the method is characterized by, The discriminator in the generative adversarial network is used to learn the decision boundary of the active and reactive power envelope of the AC / DC hybrid distribution network from the labeled data set; The generator in the generative adversarial network is used to generate candidate active and reactive power sample points on the decision boundary; The labeling model in the generative adversarial network is used to provide a feasibility label for the candidate active and reactive power sample points.

9. The method of claim 8, wherein the method is characterized by, The generative adversarial network is used to construct and train the mathematical model hybrid-driven AC / DC hybrid distribution network operation envelope representation model to represent the AC / DC hybrid distribution network operation envelope, which includes: The discriminator is trained based on the pre-collected sample set, so that the discriminator learns and approximates the decision boundary of the active and reactive power envelope of the AC / DC hybrid distribution network; The generator generates active and reactive power sample points in an uncertain region of the discriminator based on a decision boundary output by the discriminator; The active and reactive power sample points are input into the labeling model, and a feasibility label is labeled by the labeling model to form a new sample set with labels; the new sample set is combined with the current sample set to obtain an expanded sample set which is used as input for the next iteration; The iteration process is repeated until the decision boundary output by the discriminator converges or a preset number of iterations is reached, and the active and reactive power sample points of the feasible sample set are extracted from the final sample set, and the convex hull of the active and reactive power sample points is used to obtain the operation envelope of the AC / DC hybrid distribution network.

10. The method of claim 9, wherein the method is characterized by, The method for constructing and training the operation envelope representation model of the AC / DC hybrid distribution network based on the mathematical model hybrid driving by using the generative adversarial network to represent the operation envelope of the AC / DC hybrid distribution network further comprises: A compound loss function is constructed by using a geometric regularization technique, and the mode collapse of the generative adversarial network in the training process is solved by using the compound loss function; The compound loss function includes a standard adversarial loss and a geometric loss composed of a pair distance loss and an angle variance loss. The pair distance loss is the average Euclidean distance between a plurality of active and reactive power sample points, and the angle variance loss is used to capture the curvature and two-dimensional shape of the active power boundary.

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