Power distribution network-microgrid-traffic network robust optimization method under multiple uncertainties

Abstract

The invention provides a power distribution network-microgrid-traffic network robust optimization method under multiple uncertainty, belongs to the technical field of distributed energy transaction, is used for energy transaction among an NMG, an SPL and an EDN based on a P2P energy transaction framework of DRO, simulates multiple uncertainty behaviors of RES in the NMG, the SPL and the EDN, and provides a power distribution network-microgrid-traffic network robust optimization method. And the influence of the charging electric vehicle is considered in the power distribution network-micro-grid-traffic network distributed robust optimization regulation and control method. Firstly, a distributed double-layer optimization method is put forward, and optimal energy transactions among NMG, SPL and EDN are modeled by utilizing a P2P interaction energy concept. Modeling of LEM (EDN) of liquidation is at a lower level problem, while development of P2P transactions between NMG and SPL is at an upper level. And then, based on a DLMP model, researching the interaction between the animator and the LEM. The decentralized double-layer problem proposed on the solving strategy is generally balanced through the ADMM algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of distributed energy trading, and more specifically, relates to a robust optimization method for a distribution network-microgrid-transportation network under multiple uncertainties. Background Art

[0002] Distributed energy, mainly green new energy, has become an important part of the energy trading market. With the increasing demand for new energy power in social and economic development, the field of P2P interactive energy trading in multiple microgrids (MGs) has been widely studied in recent years. However, the main problems in existing research are:

[0003] First, in some studies, the focus is mainly on decentralized or P2P transactions between multiple MGs. However, the impact of distribution network (EDN) or local electricity market (LEM) on P2P energy trading has been ignored. Under normal operating conditions, EDN plays an important role in supplying power to networked microgrid (NMG) loads. Therefore, the role of EDN and distributed location marginal price (DLMP) in P2P transactions of MGs is very important.

[0004] Second, in some studies, P2P interactive energy trading between MG and EDN is conducted in a decentralized approach. However, the impact of independent power producers (SPLs) participating in the trade between MG and EDN is not investigated. With the increasing popularity of electric vehicles and V2G technology (V2G is the abbreviation of Vehicle-to-grid), SPLs are becoming strategic players in the P2P interactive energy market. Therefore, their presence in the transactional energy market will be inevitable.

[0005] Third, the multiple uncertainties of renewable energy sources (RES) are interrelated, increasing the complexity of system analysis and prediction. Multiple uncertainties are not just the superposition of single uncertainties, but may also involve interactions between uncertainties. In many studies, the uncertain behavior of RES is usually modeled based on stochastic programming (SP) or robust optimization (RO). The SP method may be useful if there is an exact probability distribution. But in most cases, the exact probability distribution is not available. In addition, the SP method cannot provide a robust solution to the fluctuating behavior of RES. In the RO method, probability distribution is not required, and the solution obtained is robust. However, the solution provided by RO is too conservative and may cause operators to incur additional costs. At the same time, both schemes do not have a good solution for multiple uncertainties. Summary of the invention

[0006] In view of the problems existing in the prior art, the purpose of the present invention is to provide a robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties, a P2P energy trading framework based on distributed robust optimization (DRO), which is used for energy trading between NMG, SPL and EDN, and a distributed robust optimization control method for distribution network-microgrid-transportation network taking into account the impact of smart charging electric vehicles.

[0007] To achieve the above object, the present invention adopts the following technical solution: a robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties, comprising:

[0008] Step 1: Construct a UE traffic flow model coupled with transportation and power distribution, and consider the optimal pricing of electric vehicle charging stations in which transportation and power systems are coupled. The UE traffic flow model coupled with transportation and power distribution is a basic UE model that incorporates electric vehicles and electric vehicle charging stations.

[0009] Step 2: Considering the uncertainty of electric vehicle energy consumption, a P2P energy trading framework based on the DRO method is used to conduct energy trading between NMG, SPL and EDN, and a P2P energy trading mathematical model in which EDN, NMG and SPL interact with each other in a decentralized manner is constructed;

[0010] Step 3: The ADMM algorithm is used to solve the convex optimization problem of the constructed P2P energy trading mathematical model in which EDN, NMG and SPL interact with each other in a decentralized manner. At this point, the robust optimization method of distribution network-microgrid-transportation network under multiple uncertainties is completed.

[0011] Through the above-mentioned design scheme, the present invention can bring the following beneficial effects: The present invention provides a distributed robust optimization and control method for distribution network-microgrid-transportation network considering multiple uncertainties. The method proposes a decentralized two-layer optimization method, which uses the concept of P2P interactive energy to model the optimal energy transaction between NMG, SPL and EDN. In the proposed method, the modeling of the cleared LEM (EDN) is a problem at a lower level, while the development of P2P transactions between NMG and SPL is at an upper level. The interaction between prosumers (NMG and SPL) and LEM is studied based on the DLMP model. In terms of solution strategy, the proposed decentralized two-layer problem reaches general equilibrium through the ADMM algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The accompanying drawings herein are used to provide a further understanding of the present invention and constitute a part of the present application. The exemplary embodiments of the present invention and their descriptions are used to understand the present invention and do not constitute improper limitations of the present invention. In the accompanying drawings:

[0013] Figure 1Flowchart of the robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties.

[0014] Figure 2 The proposed flow chart for P2P energy trading based on ADMM algorithm. DETAILED DESCRIPTION

[0015] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0016] The present invention proposes a robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties, such as Figure 1 As shown, the following steps are included:

[0017] Step 1: Optimal pricing of public electric vehicle charging stations considering the coupled operation of transportation and power systems.

[0018] The User Equilibrium (UE) model is widely used in the field of traffic research to describe urban traffic systems. Given a traffic network and traffic demand, the UE model outputs the current traffic state, that is, the traffic flow distribution on the road. In the basic UE model, the urban traffic system is represented by a connected directed graph. To describe, where T N and T A Denote the node set and link set respectively. However, the basic UE model was originally designed to analyze the stable traffic flow distribution containing conventional vehicles (GVs), without considering the potential impact of EV charging demand. In order to overcome this shortcoming, in the present invention, electric vehicles (EVs) and EV charging stations (EVCSs) are incorporated into the basic UE model. First, the “virtual” arcs such as charging station entrance arcs and bypass arcs are used to simulate T A It is extended to describe the charging choices of EVs during driving, and virtual links are used to unify the behavior of GVs and EVs, and attempt to determine the network balance of the traffic-distribution coupling system. Links are divided into three types, namely ordinary links, charging links, and bypass links. Ordinary links are physical road links, and charging and bypass links are virtual links (charging links correspond to electric vehicle queuing and charging events in EVCS, and bypass links represent electric vehicle bypass events in EVCS). The traffic flow of charging links represents the number of electric vehicles that choose to charge in the corresponding EVCS, while bypass links represent non-selection. The introduction of virtual links transforms the traffic network into an extended graph, making it possible to describe the behavior of GVs and EVs in a unified way.

[0019] The traffic system model of the present invention is based on the improved hybrid UE traffic flow model proposed above. By allowing one EVCS to provide services for electric vehicles from multiple links, the interaction between EVs from these competing links is explicitly simulated. The improved hybrid UE traffic flow model (improved to (1-2d), (1-3b), (1-3c), (1-7)) is a nonlinear complementarity problem (NCP) consisting of four constraint sets:

[0020] UE-NCP:{Cons-Flow(1-2),Cons-Time(1-3)

[0021] Cons-Cost (1-4), Cons-CP (1-5)} (1-1) The constraint set in formula (1-1) is expressed as follows:

[0022] Cons-Flow:

[0023]

[0024] in, and represents the travel rate of GV and EV between OD pairs, ρ represents the available path, and Respectively represent the path and GV / EV flow on, (r,s) is the departure-destination (OD) pair, and represent the available paths between GV and EV in OD pairs, and They refer to the set of available paths between OD pairs for GV and EV, respectively; and are the GV / EV association matrix elements of the OD pair link a and path ρ, respectively, T A Refers to a group of links in the urban transportation network UTN. and a refer to the link of the mth EVCS and UTN respectively, x a refers to the traffic flow of link a, Refers to the traffic flow of the mth EVCS.

[0025] Cons-Time:

[0026]

[0027] where t a and They refer to the travel time of link a and the charging time in EVCS, respectively. and They are the empirical coefficients for link driving and EVCS charging time approximation, J() represents the corresponding approximate function; c a and They represent the capacity of link a and EVCS respectively; Refers to a group of normal / charging / bypass links in UTN respectively. Cons-Cost:

[0028]

[0029] in and Indicates GV / EV on the path and The driving time on and Indicates that GV and EV are respectively on the path and The travel cost on the road, ω represents the economic value of travel time, Indicates the value set by CNO Charge price, is a column vector consisting of 0 and 1, indicating the relationship between EVCS and path The corresponding relationship, E B Indicates the charging demand of electric vehicles.

[0030] Cons-CP:

[0031]

[0032] in, and denote the GV and EV travel costs of the OD pair, respectively.

[0033] Constraint set Cons-Flow mainly describes the traffic demand of GV / EV according to different departure-destination (OD) pairs (r, s). Formula (1-2c) Link traffic flow x a By path GV traffic on and path EV traffic on Cons-Time gives the estimated link running time for different link types. Constraint (1-3a) uses the most widely used BPR function to express the running time t of link a a Traffic flow x on link a aThe expected time (the time spent in queuing and charging) is modeled in the EVCS using the Davidson function developed based on queuing theory in constraint (1-3b). For each connection to the same EVCS, Charging chain Constraint (1-3c) ensures that the travel time through a is equal to Because the virtual charging chain a is The constraints (1-3b) and (1-3c) together describe the link The charging time is not determined by the link traffic flow x a is determined not by the connected electric vehicle charging stations Charging flow For bypass link The driving (charging) time is 0, as shown in equation (1-3d). The constraint set Cons-Cost shows that the travel cost of the GV is and travel time Proportional to the EV travel cost Also affected by the charging energy cost Finally, Cons-CP uses the complementary constraint to determine the total travel cost of GV / EV for each OD pair based on the fact that the solution of the UE model obeys the Wardrop equilibrium principle.

[0034] In the present invention, an electric vehicle charging station (EVCS) is provided From the distribution network (EDN) k The price of electricity purchased Determined by the local EDN electricity market clearing price DLMP. k , based on the future base load forecast and EVCS charging load forecast, the distribution company (DSO) can optimize the output power of local generators and the power purchased from the upper grid to minimize the total operating cost. The bus / branch set in EDN is represented as E N / E L , let busbar j∈E N The power generation cost of the generator on in is the power generation, a j 、b j and c j is the power generation cost coefficient. k The DLMP in is calculated according to the convex optimization ACOPF model based on branch flow as follows (the subscript symbol of EDN is omitted here for brevity): EDN-DLMP:

[0035]

[0036] st

[0037]

[0038] In formula (1-6a) to formula (1-6h), λ LMP represents the price of electricity purchased by EDN from the upper power grid, π(j) represents the set of sub-buses related to bus j in EDN, and π(0) represents the set of sub-buses related to the root bus in EDN. It represents the line l∈E from bus i to bus j, bus j to bus k, bus 0 to bus j in EDN L The active power, It represents the line l∈E from bus i to bus j and bus j to bus k in EDN L of reactive power. and are the active power and reactive power generated at bus i and bus j in the EDN, respectively. and for their respective changing areas. and Denotes the busbar j∈E N The active power and reactive power of the reference load at the location, the dual variable λ j is the corresponding DLMP at busbar j, U i , and They are respectively the busbar i∈E N The square value of the voltage amplitude at and its upper and lower limits, U j represents the square value of the voltage amplitude at bus j, Denotes the busbar j∈E N EV charging power, and Represents the line l∈E connecting buses i and j in EDN L The resistance and reactance, its impedance and For line l∈E L The square value of the medium current amplitude and its upper limit.

[0039] The AC Power Optimal Power Flow (ACOPF) model is a branch flow model relaxed in the form of a second order cone (SOC). The operating cost of the EDN (1-6a) includes the cost of generating electricity within the EDN and the cost of purchasing electricity from the upper grid. Constraints (1-6e) represent the SOC relaxation of the original equality constraints and convexify the feasible region. Constraints (1-6f) prevent reverse active power flow in the EDN, making the convex relaxation exact and efficiently solved by off-the-shelf solvers such as IBM CPLEX and Gurobi. The dual variable λ of the bus power balance constraint (1-6b) is j is the corresponding DLMP at busbar j, obtained by a solver such as Gurobi.

[0040] In this invention, the charging network operator CNO is assumed to be grid profit-oriented, and its optimal pricing problem (at a given electric vehicle charging station Electricity purchase price In the case of ( ) is expressed as the following two-level optimization model: CNO-OP:

[0041]

[0042] st

[0043]

[0044] In the formula, represents the allocated charging load, They represent the EDN power purchase price of EVCS and its upper and lower limits (corresponding to DLMP at the same time), and Respectively refer to the upper / lower power limit of the transformer connected to the EVCS, is the basic load power of EVCS, M k It represents the set of EVCS in EDN, and UE represents the user balance model.

[0045] In the two-layer optimization model, the upper layer adjusts the price of electric vehicle charging stations (EVCS) and charging load distribution To maximize CNO grid profit (1-7a). The upper constraints include electric vehicle charging stations Charging power range constraints (1-7b), electric vehicle charging stations The charging price range constraint (1-7c) and the EV charging station pricing level constraint (1-7d) (i.e., the average charging price of all EV charging stations is fixed at price level C, which is selected by the CNO after considering factors such as local consumption levels and average electricity purchase prices). Constraint (1-7e) indicates that each EV charging station Charging load Distribution of electric vehicle flows in the transportation system It is decided that these distributions are computed in the lower level problems (1-7f).

[0046] Step 2: A P2P energy trading framework based on distributionally robust optimization (DRO) is established for energy trading between NMG, SPL, and EDN, and the impact of smart charging EVs is considered.

[0047] Step 2.1: Modeling the mathematical model of the distribution network;

[0048] 1) Objective function: The objective function of EDN is shown in equation (2-1); the objective of the distribution network operator DNO is to minimize the total grid operating cost;

[0049]

[0050] The first term in the equation is represents the cost of distributed generation DG, and the second item is represents the cost of purchasing electricity from the wholesale electricity market WEM, and the third item is represents the interruptible load cost of EDN, and the fourth item is Represents NMG's operating expenses, item 5, namely represents the service cost of SPL; the subscripts t, g, b, m, and c represent the index of the time period, the index of the DG, the index of the EDN power bus, the index of the EVCS in the EDN, and the index of the IL, respectively;

[0051] 2) Constraints of EDN: The constraints of distributed generation DG in EDN are expressed by equations (2-2)-(2-4); the nonlinear conditions are maintained by equations (2-5)-(2-14), and EDN is modeled as a second-order quadratic programming SOCP model in convex space; for this purpose, in equations (2-5)-(2-6), the variable U b,t and Specified as the square of the node voltage and the feeder current. Equation (2-7) represents the active power exchanged between the EDN and the NMG. The active power exchanged between the SPL and the EDN is also expressed by equation (2-8), and the active and reactive balance equations are satisfied by equations (2-9)-(2-10). Equation (2-11) represents the voltage value, and its limit is expressed by equation (2-12). Equation (2-11) is a nonlinear term and causes significant problems when solving the problem. Therefore, it is replaced by equation (2-13) through SOCP relaxation. Equation (2-14) also expresses the range of values ​​of the apparent power in the EDN feeder.

[0052]

[0053]

[0054] In formula (2-2) to formula (2-14), and is the DG active power in period t and period t-1, is the upper limit of DG active power, is the DG reactive power in period t, It represents the lower limit of DG reactive power in period t; is the power change rate limit of the DG ramp-up and ramp-down process, is the power of the wth WT and its upper power limit, V b,t is the voltage of the EDN power bus, is the current in the EDN power bus; Respectively represent the active power and reactive power flow of different power buses in NMG and EDN, and They refer to the active power of the b,b′ bus and the b,f bus in the l branch of the EDN, respectively. and They refer to the reactive power of bus b, b′ and bus b, f in branch l in EDN, respectively. Subscript l is the branch index in EDN, and b, b′, f are the indexes of power bus in EDN. and denote the target and response variables of active power exchanged between peers in NMG and EDN, respectively, and denote the target and response variables of active power exchanged between SPL and EDN peers, respectively, and Respectively represent the active power and reactive power purchased in the power system, and represents the active power and reactive power of IL, and represents the active power and reactive power of DG, and Indicates the active power and reactive power of the load; w is the index of WT, e is the index of SPL, and They represent the power output to the set of WT, IL, DG, DM and f buses on the b bus in the EDN; qv is the index of the static VAR compensator SVC, Indicates the power output to the set of SVCs on bus b in the EDN; U b,t , U b They represent the voltage, upper voltage limit and lower voltage limit of the EDN power bus respectively; DLMP for EDN, is the bus index of the power bus in END, is the power of the static VAR compensator, and is the reactance and impedance of the power bus line in the EDN; S l To represent the maximum apparent power limit associated with line l; in equations (2-5)-(2-6), the variable U b,t and Specified as the square of the node voltage and the feeder current; Equation (2-7) represents the active power exchanged between EDN and NMG; the active power exchanged between SPL and EDN is expressed by Equation (2-8), and the active and reactive balance equations are satisfied by Equations (2-9)-(2-10). Equation (2-11) represents the voltage value, and its limit is expressed by Equation (2-12). Equation (2-11) is a nonlinear term, so it is replaced by Equation (2-13) through SOCP relaxation. Equation (2-14) expresses the complex apparent power boundary in the EDN feeder.

[0055] Step 2.2: Mathematical modeling of networked microgrid

[0056] 1) Operating costs of NMG: Operating costs of NMG The expression of is shown in formula (2-15). The first, second and third items represent the operation, startup and shutdown costs of micro turbines (MTs), respectively.

[0057]

[0058] in, and represent the operation, startup and shutdown costs of microturbine MTs, respectively.

[0059] Constraints of NMG: The constraints of MT are modeled by equations (2-16)-(2-20). The constraints of WT and PV power generation are expressed by equations (2-21)-(2-22). Equation (2-23) represents the electric power flow in NMG. The bus voltage limit of NMG is implemented by equation (2-24). Equation (2-25) represents the active power exchange between NMGs. The active power exchanged between NMG and SPL is also expressed by equation (2-26). The active and reactive balance equations of the NMG system are satisfied by equations (2-27)-(2-28). The constraints of active and reactive power flows are expressed by equations (2-29)-(2-30). Finally, the power transfer limit between connected NMGs is contained in equation (2-31).

[0060]

[0061]

[0062] In formula (2-16) to formula (2-31), and They are the upper and lower limits of the active power of the MT obtained by the EVCS in the EDN. and are the active power of MT acquired by EVCS in EDN in period t and period t-1 respectively; and They refer to the reactive power of MT and its upper and lower limits obtained by EVCS in EDN. is the reactive power of MT acquired by EVCS in EDN during period t; is the power increase rate limit of MT in NMG, SU u,m and SD u,m Refers to the start and stop of MT and EVCS respectively. and They refer to the WT active power required by EVCS and its upper limit, and They refer to the PV active power required by EVCS and its upper limit respectively; V i,m 、V i,m,t 、V j,m,t and They represent the bus voltage lower limit, bus voltage, root bus voltage and bus voltage upper limit of the EVCS power bus in the EDN respectively; and They represent the active power flowing through the root voltage bus in the EDN and its upper and lower limits, and They represent the reactive power flowing through the root voltage bus in the EDN and its upper and lower limits, and They represent the active power and reactive power flowing through the voltage bus in the EDN, respectively, where i, j, r represent the index of the bus in the EDN, and l represents the branch index of the EDN; and Indicates the active power and reactive power of the EVCS load in the EDN; v is the index of PV, m′ is the NMG index different from m, They represent the set of NMG m, WT, PV, MT, NMG m′, SPL e, NMG bus r, and IL connected to NMG bus i respectively; and are the line resistance and line reactance in EDN respectively; and They refer to the active power target value and its upper and lower limits exchanged between EVCS peers in the EDN; It represents the response of EVCS exchanging power between NMGs; and It indicates the active power of WT, MT and PV acquired by EVCS in EDN; and Indicates the reactive power in the off state, the reactive power exchanged between NMG and EDN, the static VAR compensator reactive power required by IL, and the reactive power of MT obtained by EVCS; a u,m 、b u,m and c u,m I is the power grid operation cost coefficient of MT; u,m,t is the current of EDN and MG; x u,m,t is the locking status of MT in MG, u u,m,t and v u,m,t It indicates the start and stop status of MT in MG.

[0063] Step 2.3: Mathematical model of the operating cost of SPL. The operating cost of SPL is modeled by equation (2-32). This equation represents the cost of electric vehicle battery loss in SPL.

[0064]

[0065] in is the operating cost of SPL, represents the daily degradation of the electric vehicle battery. The model uses the K-means clustering method to model all electric vehicles located in the SPL under a convex optimization framework. In addition, the random behavior of their arrival / departure from the SPL is simulated by the scenario scenarios generated by the specific empirical distribution. Equations (2-33) to (2-34) represent the state of charge (SOC) at the time of arrival and departure of the electric vehicle. The initial SOC of the electric vehicle is modeled by equation (35). Equation (2-36) ensures that the final SOC of the electric vehicle is acceptable. The upper / lower bounds of the SOC are modeled by equation (2-37). In addition, equations (2-38) to (2-39) represent the charging and discharging limitations of the electric vehicle, respectively. Therefore, equation (2-40) declares PDe,t to be a negative variable. The battery cycle depth is defined by equation (2-41). The limitation in equation (2-42) establishes the cycle depth degradation function of the electric vehicle battery. The marginal degradation cost of the battery is modeled by the chain derivative using equation (2-43). Equations (2-44)-(2-45) represent the power generation limitations of PV and WT in SPL respectively.

[0066]

[0067]

[0068] In formula (2-33) to formula (2-45), SOC e,t and SOC e,t-1 is the state of charge of the electric vehicle in period t and period t-1, SOC e and The upper and lower limits of the state of charge of the electric vehicle; η c and η e They are respectively the charging and discharging efficiency of electric vehicles; EB e is the battery capacity, BC e For battery cost, and are the initial and maximum SOC of the electric vehicle, is the expected electric vehicle SOC, a0 is the electric vehicle cycle depth degradation function coefficient, ψ e,t () is the cycle depth degradation function, MD e,t The marginal degradation of energy storage for electric vehicles, and They are the charging and discharging power of electric vehicles, TA e and TD e They are the charging process and end time of electric vehicles, DT e and Cr e They represent the daily mileage of electric vehicles and the nominal charging rate of electric vehicles, ECPM e Indicates the energy consumption of electric vehicles, PD e,t represents the power exchanged between SPL and EDN, σ e,t and σ e,t-1 They represent the charging cycle depth of the electric vehicle battery at cycle t and cycle t-1 respectively, and represents the active WT power of SPL and its upper limit, and Indicates the PV active power and its upper limit of the SPL.

[0069]

[0070]

[0071] In formula (2-46) to formula (2-49), is the daily decay reference value of EV, and Respectively represent the battery daily degradation coefficient under different conditions, is the ambient temperature of the electric vehicle, SOC e,s,t Indicates the state of charge of the EV, and the subscript s indicates different working environments. and Respectively represent the power exchanged between the two SPLs, The power targets exchanged between peers in SPL and EDN, is the response of the power exchanged between NMG and SPL, and Represent the power of WT, PV, EV charging and EV discharging, respectively, Represents the SPL load power; it can be seen from formula (2-46) that the calendar model of battery degradation is directly related to the temperature and SOC of the electric vehicle battery; by setting the positive matrix specific coefficient, that is, the above-mentioned battery daily degradation coefficient, the battery daily degradation equation of the electric vehicle is a convex quadratic equation, which is converted into the SOCP model (precise conversion), as shown in formula (2-47); formula (2-48) represents the active power exchange between SPLs; the power balance equation in SPL is modeled by formula (2-49).

[0072] Step 2.4: Perform distributed robust optimization on the above framework. In most existing studies, two approaches, SP or RO, are used to simulate the uncertain behavior of RES. The SP model does not provide robust behavior in its solution and requires an accurate probability distribution. To generate scenarios, Ω represents the sample space, which may not be feasible in many real-world situations. On the other hand, the uncertainty modeling of the RO method leads to overly conservative solutions. At the same time, both methods do not have a good way to deal with the multiple uncertainties of RES. In this paper, a moment-based DRO method is proposed to simulate the multiple uncertainties of RES in NMG, SPL and EDN. In the DRO method, the present invention is to convert the worst-case probability distribution of the fuzzy set D to the estimated distribution To minimize the expected operating cost. Formula (2-50) is a general representation of the fuzzy set D, which considers all possible distributions, with the mean matrix μ and the standard deviation matrix σ.

[0073]

[0074] in express The set of all valid probability distributions in , It is called the support set, and its task is to realize multiple uncertainties in a finite set; represents the expected value of the uncertainty parameter ξ. In addition, Γ1≥0 and Γ2≥1 are multiple uncertainty control parameters that control the volume of the fuzzy set. In the present invention, the DRO method is used to simulate the uncertain behavior of renewable energy in EDN, NMG and SPL, which is restated by Equation (2-51).

[0075]

[0076] OF EDN is the objective function of EDN, and formula (2-51) represents OF EDNThe minimization of the maximum expected penalty is constrained by equations (2-1)-(2-50). It can be clearly seen from equation (2-51) that the minimum-maximum problem cannot be solved normally by commercial solvers. To this end, the present invention uses duality theory to convert the double-layer minimum-maximum problem into a minimum-minimum problem, and uses commercial solvers to easily solve the problem.

[0077] Step 2.5: Establish a decentralized P2P energy trading model. In the proposed mathematical model, EDN is coupled with NMG and smart SPL through equations (2-7) and (2-8). In addition, NMG and SPL are coupled to each other through equations (2-25), (2-26) and (2-48) for P2P energy trading. However, in the proposed method, each NMG and SPL cannot make the optimal decision alone with privacy protection. In other words, the ownership of NMG and SPL is not observed, and the main decision maker is EDN or the local electricity market. To solve this problem, the ADMM distributed algorithm is adopted. The implementation of the ADMM algorithm enables EDN, NMG and SPL to interact with each other in a decentralized manner. In addition, in P2P energy trading, the ownership and privacy of each strategic participant are fully protected.

[0078] Step 3: Alternating Direction Method of Multipliers. Using ADMM algorithm to solve convex optimization problems, the decomposition format is as follows:

[0079]

[0080] s.tAx+Bz=c (3-2)

[0081] Among them, f(x) and g(z) are convex functions, A and B are known matrices, and c represents the constant vector in the constraint condition. Applying the Lagrangian relaxation of equation (3-2) to equation (3-1), the augmented Lagrangian function is expressed as equation (54), where λ represents the Lagrangian coefficient, is the penalty factor, and is expressed in the form of a second norm vector. The ADMM algorithm consists of iterative repetitions of equations (3-3)-(3-6), where k is the iteration index of the ADMM algorithm. Therefore, the optimal values ​​of the x and z variables are calculated by equations (3-4) and (3-5), respectively. By decomposing the decentralized problem into equation (3-6), this makes the ADMM algorithm an effective method for solving decentralized problems.

[0082]

[0083] λ(k+1)=λ(k)+ρ(Ax(k+1)+Bz(k+1)-c) (3-6)

[0084] The convergence criterion of the ADMM method is based on the original residual representation and is established as follows:

[0085] ||λ(k+1)-λ(k)||≤ε (3-7)

[0086] ε represents the tolerance for judging the convergence of the ADMM method. The method is considered to have converged when it satisfies formula (3-7).

[0087] Step 3.1: Now, in this section, the integration problem proposed in the present invention is transformed into a decentralized P2P energy trading method using the ADMM algorithm. It is obvious that in the proposed method, there are three types of strategic participants (i.e., EDN, NMG, and SPL). Therefore, the general decision variables of ADMM are x, z1, and z2, which belong to sets X, Z1, and Z2, respectively, where z in equation (3-6) is divided into z1 and z2, and the set Z is divided into Z1 and Z2 accordingly. In the P2P trading problem proposed in the present invention, x, z1, and z2 represent the decision variables of EDN, NMG, and SPL, respectively. Therefore, set X includes constraint equations (2-2)-(2-6) and equations (2-9)-(2-14), and set Z1 contains constraint equations (2-16)-(2-24) and equations (2-27)-(2-31). Finally, Z2 contains constraint equations (2-33)-(2-47) and equation (49). In addition, constraint equations (2-7)-(2-8), (2-25)-(2-26) and (2-48) are related to equation (3-2) of the ADMM method. The augmented Lagrangian function is:

[0088]

[0089] In formula (3-8), ρ is the penalty factor in the ADMM algorithm, and denote the DG active power and the constrained energy power, respectively, and denote the constrained energy price, IL energy price, DLMP energy price of EVCS within EDN, and DLMP energy price of SPL, respectively. and They are the NMG objective function and SPL objective function corresponding to each EVCS respectively.

[0090] As mentioned above, equation (3-8) is separable, and each strategic participant in the problem can optimize the decentralization. In this way, each NMG can make the optimal decision based on RO by solving equation (3-9) while protecting privacy.

[0091]

[0092] In the formula, and Indicates the opening and closing prices of MT. and are the agreed prices for energy exchange between NMG and SPLs, It represents the price of DLMP energy consumed by EVCS in EDN via the power bus. and are the target and response variables of the active power exchanged between the peers and NMGs, and are the target and response variables for the active power exchanged between the NMG and SPL by the peer, and The target and response variables for the active power exchanged between the NMG and EDN for the peers.

[0093] Subject to: Equations (2-16)-(24) and (2-27)-(2-31).

[0094] By further solving equation (3-10) under the decentralized method, the optimal RO-based decision for each SPL is determined.

[0095]

[0096] In the formula, represents the daily decay of EV, and Indicates the opening and closing prices of MT. and are the agreed prices for exchanging energy between NMG and SPLs, respectively. and are the target and response variables for the active power exchanged between peers in SPL, and are the target and response variables of the active power exchanged between the peers in SPLs and EDNs,

[0097] Subject to: Equations (2-33)-(2-47) and equation (2-49).

[0098] Finally, by solving the problem (3-11) under the decentralized method, the optimal RO-based decision of EDN is determined.

[0099]

[0100] Subject to: Equations (2-2)-(2-6) and (2-9)-(2-14).

[0101] Step 3.2: As mentioned above, the ADMM algorithm has been used for decentralized trading of MG, SPL, and EDN in the P2P energy trading conceptual framework. Using the ADMM algorithm, in energy trading, the privacy of peers is completely preserved because peers do not know the topological structure of other peers. The step-by-step implementation of the ADMM algorithm is as follows: Figure 2 shown.

[0102] Start with the first step: Initialization (NMGs): Get input parameters

[0103]

[0104] 1. Solve the first-level problem after receiving the parameters using equation (60) and calculate the total cost

[0105] 1-1. Update The value of and submit it to LEM (submit to step 3)

[0106] 1-2. Update The value is submitted to the connected NMG (submitted to step 1)

[0107] 1-3. Update The value is submitted to the connected SPLs. (Submitted to step 2)

[0108] Start the second step: Initialization (SPL): Get input parameters

[0109]

[0110] 2. Use equation (61) to solve the second-level problem after receiving the parameters and find the optimal value of the total cost

[0111] 2-1. Update and submit to LEM (submit to step 3)

[0112] 2-2. Update The value is submitted to the connected NMG (submitted to step 1)

[0113] 2-3. Update The value is submitted to the connected SPLs. (Submitted to step 2)

[0114] Start the third step: Initialization (LEM): Get input parameters

[0115]

[0116] 3. Use equation (62) to solve the third level problem after receiving the parameters, and the optimal value of the total cost is X(k+1)=OF EDN ;

[0117] 3-1. Update The value of and submit it to NMG (submit it to step 1)

[0118] 3-2. Update The value of and submit it to SPL (submit it to step 2)

[0119] 3-4. Check the convergence criteria of all strategy participants (i.e. NMG, SPL, LEM). If the convergence criteria are met, proceed to step 4. Otherwise, continue.

[0120] 4. Check the overall equilibrium point. If the problem reaches the equilibrium point, stop the algorithm. Otherwise, go back to step 1.

Claims

1. A robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties, characterized in that: include: Step 1: Construct a UE traffic flow model coupled with transportation and power distribution, and consider the optimal pricing of electric vehicle charging stations in which transportation and power systems are coupled. The UE traffic flow model coupled with transportation and power distribution is a basic UE model that incorporates electric vehicles and electric vehicle charging stations. Step 2: Considering the uncertainty of electric vehicle energy consumption, a P2P energy trading framework based on the DRO method is used to conduct energy trading between NMG, SPL and EDN, and a P2P energy trading mathematical model in which EDN, NMG and SPL interact with each other in a decentralized manner is constructed; Step 3: The ADMM algorithm is used to solve the convex optimization problem of the constructed P2P energy trading mathematical model in which EDN, NMG and SPL interact with each other in a decentralized manner. At this point, the robust optimization method of distribution network-microgrid-transportation network under multiple uncertainties is completed.

2. The robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties according to claim 1 is characterized in that: The UE traffic flow model coupled with traffic and power distribution is a nonlinear complementarity problem NCP consisting of four constraint sets: UE-NCP:{Cons-Flow(1-2),Cons-Time(1-3) Cons-Cost (1-4), Cons-CP (1-5)} (1-1) The constraint set in formula (1-1) is expressed as follows: Cons-Flow: in, and represents the travel rate of GV and EV between OD pairs, ρ represents the available path, and Respectively represent the path and GV / EV flow on, (r,s) is the departure-destination (OD) pair, and represent the available paths between GV and EV in OD pairs, and They refer to the set of available paths between OD pairs for GV and EV, respectively; and are the GV / EV association matrix elements of the OD pair link a and path ρ, respectively, T A Refers to a group of links in the urban transportation network UTN. and a refer to the link of the mth EVCS and UTN respectively, x a refers to the traffic flow of link a, refers to the traffic flow of the mth EVCS; Cons-Time: where t a and They refer to the travel time of link a and the charging time in EVCS, respectively. and They are the empirical coefficients for link driving and EVCS charging time approximation, J() represents the corresponding approximate function; c a and They represent the capacity of link a and EVCS respectively; Refers to a set of normal / charging / bypass links in UTN respectively; Cons-Cost: in and Indicates GV / EV on the path and The driving time on and Indicates that GV and EV are respectively on the path and The travel cost on the road, ω represents the economic value of travel time, Indicates the value set by CNO Charge price, is a column vector consisting of 0 and 1, indicating the relationship between EVCS and path The corresponding relationship, E B Indicates the charging demand of electric vehicles; Cons-CP: in, and denote the GV and EV travel costs of the OD pair, respectively.

3. The robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties according to claim 1 is characterized in that: In step 2, the moment-based DRO method is used to simulate the multiple uncertain behaviors of RES in NMG, SPL, and EDN. In the DRO method, the worst-case probability distribution in the fuzzy set D is converted to the estimated distribution P ξ to minimize the expected running cost, and the dual-level min-max problem is transformed into a min-min problem using duality theory and solved using a commercial solver.

4. The robust optimization method for distribution network-microgrid-transportation network under multiple uncertainties according to claim 1 is characterized in that: Step 2 includes: Step 2.1: Modeling the mathematical model of the distribution network; 1) Objective function: The objective function of EDN is shown in equation (2-1); the objective of the distribution network operator DNO is to minimize the total grid operating cost; The first term in the equation is represents the cost of distributed generation DG, and the second item is represents the cost of purchasing electricity from the wholesale electricity market WEM, and the third item is represents the interruptible load cost of EDN, and the fourth item is Represents NMG's operating expenses, item 5, i.e. represents the service cost of SPL; the subscripts t, g, b, m and c represent the index of the time period, the index of the DG, the index of the EDN power bus, the index of the EVCS in the EDN and the index of the IL, respectively; 2) Constraints of EDN: The constraints of distributed generation DG in EDN are expressed by equations (2-2)-(2-4); the nonlinear conditions are maintained by equations (2-5)-(2-14), and EDN is modeled as a second-order quadratic programming SOCP model in convex space; for this purpose, in equations (2-5)-(2-6), the variable U b,t and Specified as the square of the node voltage and the feeder current; Equation (2-7) represents the active power exchanged between EDN and NMG; The active power exchanged between SPL and EDN is expressed by Equation (2-8), and the active and reactive balance equations are satisfied by Equations (2-9)-(2-10); Equation (2-11) represents the voltage value, and its limit is expressed by Equation (2-12); Equation (2-11) is a nonlinear term, so it is replaced by Equation (2-13) through SOCP relaxation; Equation (2-14) expresses the range of apparent power in the EDN feeder; In formula (2-2) to formula (2-14), and is the DG active power in period t and period t-1, is the upper limit of DG active power, is the DG reactive power in period t, It represents the lower limit of DG reactive power in period t; is the power change rate limit of the DG ramp-up and ramp-down process, is the power of the wth WT and its upper power limit, V b,t is the voltage of the EDN power bus, is the current in the EDN power bus; Respectively represent the active power and reactive power flows of different power buses in NMG and EDN, and They refer to the active power of bus b,b′ and bus b,f in branch l of EDN, respectively. and They refer to the reactive power of bus b, b′ and bus b, f in branch l in EDN, respectively. Subscript l is the branch index in EDN, and b, b′, f are the indexes of power bus in EDN. and denote the target and response variables of active power exchanged between peers in NMG and EDN, respectively, and denote the target and response variables of active power exchanged between SPL and EDN peers, respectively, and Respectively represent the active power and reactive power purchased in the power system, and represents the active power and reactive power of IL, and represents the active power and reactive power of DG, and Indicates the active power and reactive power of the load; w is the index of WT, e is the index of SPL, and They represent the power output to the set of WT, IL, DG, DM and f buses on the b bus in the EDN; qv is the index of the static VAR compensator SVC, Indicates the power output to the set of SVCs on bus b in the EDN; U b,t , U b They represent the voltage, upper voltage limit and lower voltage limit of the EDN power bus respectively; DLMP for EDN, is the bus index of the power bus in END, is the power of the static VAR compensator, and is the reactance and impedance of the power bus line in the EDN; S l To represent the maximum apparent power limit associated with line l; in equations (2-5)-(2-6), the variable U b,t and Specified as the square of the node voltage and feeder current; Equation (2-7) represents the active power exchanged between EDN and NMG; the active power exchanged between SPL and EDN is expressed by Equation (2-8), and the active and reactive balance equations are satisfied by Equations (2-9)-(2-10). Equation (2-11) represents the voltage value, and its limit is expressed by Equation (2-12). Equation (2-11) is a nonlinear term, so it is replaced by Equation (2-13) through SOCP relaxation. Equation (2-14) expresses the complex apparent power boundary in the EDN feeder; Step 2.2: Mathematical modeling of networked microgrid 1) Operating costs of NMG: Operating costs of NMG The expression of is shown in formula (2-15); the first, second and third items represent the operation, startup and shutdown costs of micro-turbine MTs respectively; in, and They represent the operation, startup and shutdown costs of the microturbine MT respectively; 2) Constraints of NMG: The constraints of MT are modeled by equations (2-16)-(2-20); the constraints of WT and PV power generation are expressed by equations (2-21)-(2-22); equation (2-23) represents the electric power flow in NMG; the bus voltage limit of NMG is implemented by equation (2-24); equation (2-25) represents the active power exchange between NMGs; the active power exchanged between NMG and SPL is also expressed by equation (2-26); the active and reactive balance equations of the NMG system are satisfied by equations (2-27)-(2-28); the constraints of active and reactive power flows are expressed by equations (2-29)-(2-30); finally, the power transfer limit between connected NMGs is included in equation (2-31); In formula (2-16) to formula (2-31), and They are the upper and lower limits of the active power of the MT obtained by the EVCS in the EDN. and are the active power of MT acquired by EVCS in EDN in period t and period t-1 respectively; and They refer to the reactive power of MT and its upper and lower limits obtained by EVCS in EDN. is the reactive power of MT acquired by EVCS in EDN during period t; is the power increase rate limit of MT in NMG, SU u,m and SD u,m Refers to the start and stop of MT and EVCS respectively. and They refer to the WT active power required by EVCS and its upper limit, and They refer to the PV active power required by EVCS and its upper limit respectively; V i,m 、V i,m,t 、V j,m,t and They represent the bus voltage lower limit, bus voltage, root bus voltage and bus voltage upper limit of the EVCS power bus in the EDN respectively; and They represent the active power flowing through the root voltage bus in the EDN and its upper and lower limits, and They represent the reactive power flowing through the root voltage bus in the EDN and its upper and lower limits, and They represent the active power and reactive power flowing through the voltage bus in the EDN, respectively, where i, j, r represent the index of the bus in the EDN, and l represents the branch index of the EDN; and Indicates the active power and reactive power of the EVCS load in the EDN; v is the index of PV, m′ is the NMG index different from m, They represent the set of NMG m, WT, PV, MT, NMG m′, SPL e, NMG bus r, and IL connected to NMG bus i respectively; and are the line resistance and line reactance in EDN respectively; and They refer to the active power target value and its upper and lower limits exchanged between EVCS peers in the EDN; It represents the response of EVCS exchanging power between NMGs; and It indicates the active power of WT, MT and PV acquired by EVCS in EDN; and Indicates the reactive power in the off state, the reactive power exchanged between NMG and EDN, the static VAR compensator reactive power required by IL, and the reactive power of MT obtained by EVCS; a u,m 、b u,m and c u,m I is the power grid operation cost coefficient of MT; u,m,t is the current of EDN and MG; x u,m,t is the locking status of MT in MG, u u,m,t and v u,m,t The start and stop status of MT in MG; Step 2.3: Mathematical model of the operating cost of SPL; The operating cost of SPL is modeled by equation (2-32); This equation represents the cost of electric vehicle battery loss in SPL; in is the operating cost of SPL, represents the daily attenuation of the electric vehicle battery; the model uses the K-means clustering method to model all electric vehicles located in the SPL under a convex optimization framework; in addition, the scenario scenarios generated by the specific empirical distribution simulate the random behavior of their arrival / leaving the SPL; equations (2-33) to (2-34) represent the state of charge (SOC) of the electric vehicle at the time of arrival and departure; the initial SOC of the electric vehicle is modeled by equation (35); equation (2-36) ensures that the final SOC of the electric vehicle is acceptable; the SOC The upper / lower bounds are modeled by equation (2-37); in addition, equations (2-38) to (2-39) represent the charging and discharging limitations of electric vehicles, respectively; therefore, equation (2-40) declares PDe,t to be a negative variable; the battery cycle depth is defined by equation (2-41); the limitations in equation (2-42) establish the cycle depth degradation function of the electric vehicle battery; the marginal degradation cost of the battery is modeled by the chain derivative using equation (2-43); equations (2-44)-(2-45) represent the power generation limitations of PV and WT in SPL, respectively; In formula (2-33) to formula (2-45), SOC e,t and SOC e,t-1 is the state of charge of the electric vehicle in period t and period t-1, SOC e and is the upper and lower limits of the state of charge of the electric vehicle; η c and η e They are respectively the charging and discharging efficiency of electric vehicles; EB e is the battery capacity, BC e For battery cost, and are the initial and maximum SOC of the electric vehicle, is the expected electric vehicle SOC, a0 is the electric vehicle cycle depth degradation function coefficient, ψ e,t () is the cycle depth degradation function, MD e,t The marginal degradation of energy storage for electric vehicles, and They are the charging and discharging power of electric vehicles, TA e and TD e They are the charging process and end time of electric vehicles, DT e and Cr e They represent the daily mileage of electric vehicles and the nominal charging rate of electric vehicles, ECPM e Indicates the energy consumption of electric vehicles, PD e,t represents the power exchanged between SPL and EDN, σ e,t and σ e,t -1 represents the charging cycle depth of the electric vehicle battery at cycle t and cycle t-1, respectively. and represents the active WT power of SPL and its upper limit, and Indicates the PV active power of SPL and its upper limit; In formula (2-46) to formula (2-49), is the daily decay reference value of EV, and Respectively represent the battery daily degradation coefficient under different conditions, is the ambient temperature of the electric vehicle, SOC e,s,t Indicates the state of charge of the EV, and the subscript s indicates different working environments. and Respectively represent the power exchanged between the two SPLs, The power targets exchanged between peers in SPL and EDN, is the response of the power exchanged between NMG and SPL, and Represent the power of WT, PV, EV charging and EV discharging, respectively, Represents the SPL load power; From formula (2-46), it can be seen that the calendar model of battery degradation is directly related to the temperature and SOC of the electric vehicle battery; By setting the positive matrix specific coefficient, that is, the above-mentioned battery daily degradation coefficient, the battery daily degradation equation of the electric vehicle is a convex quadratic equation, which is converted into the SOCP model (precise conversion), as shown in formula (2-47); Formula (2-48) represents the active power exchange between SPLs; The power balance equation in SPL is modeled by formula (2-49); Step 2.4: Perform distributed robust optimization on the above framework; in the DRO method, the present invention is to obtain the estimated distribution through the probability distribution of the worst case in the fuzzy set D To minimize the expected operating cost; Formula (2-50) is the conventional expression of the fuzzy set D, which considers all possible distributions, with the mean matrix μ and the standard deviation matrix σ; in express The set of all valid probability distributions in , It is called the support set, and its task is to realize multiple uncertainties in a finite set; represents the expected value of the uncertainty parameter ξ; in addition, Γ1≥0 and Γ2≥1 are multiple uncertainty control parameters, which control the volume of the fuzzy set; in the present invention, the DRO method is used to simulate the uncertain behavior of renewable energy in EDN, NMG and SPL, which is restated by formula (2-51); OF EDN is the objective function of EDN, and formula (2-51) represents OF EDN Minimization of the maximum expected penalty; subject to: Equations (2-1)-(2-50); It can be clearly seen from equation (2-51) that the minimum-maximum problem cannot be solved normally by commercial solvers; for this reason, the duality theory is used to convert the two-level minimum-maximum problem into a minimum-minimum problem, and the problem is easily solved using commercial solvers; Step 2.5: Establish a decentralized P2P energy trading model; In the proposed mathematical model, EDN is coupled with NMG and smart SPL through Equations (2-7) and (2-8); In addition, NMG and SPL are coupled with each other through Equations (2-25), (2-26) and (2-48) for P2P energy trading.

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