CN117251971A - Distributed load recovery method for multi-energy coupling power distribution network - Google Patents
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Abstract
A distributed load recovery method of a multi-energy coupling distribution network belongs to the technical field of electric-gas comprehensive energy control, and a load recovery model of an electric-gas comprehensive energy system is established by coordinating load recovery of the electric-gas comprehensive energy system based on a consensus ADMM and interacting information of operation of a gas DG and a compressor in the system in consideration of the cooperative action of the electric system and the natural gas system in the electric-gas comprehensive energy system; the load recovery model of the electric-gas comprehensive energy system is solved by adopting an ADMM algorithm, the load recovery problem of the whole system is decomposed into an electric sub-problem and a natural gas sub-problem which are solved independently, and independent decision and coordination optimization of the electric-gas comprehensive energy system are realized by adopting an ADMM algorithm acceleration, so that the electric-gas comprehensive energy system has higher precision and efficiency. The invention effectively reduces the load loss of the electric-gas comprehensive energy system while protecting the information privacy of the electric subsystem and the natural gas subsystem, and has important significance for improving the operation stability of the system.
Description
Technical Field
The invention belongs to the technical field of electric-gas comprehensive energy control, and particularly relates to a distributed coincidence recovery method of a multi-coupling power distribution network.
Background
In recent years, due to natural disasters and frequent occurrence of extreme weather events, power systems face increasing risks of power failure, and bring about huge economic losses to the power systems. The distribution system (power distribution system, PDS) is a weak part of the power infrastructure, and is more prone to extreme disasters and large-scale power failure [2] . Furthermore, the rapidly increasing power demands and the complexity of modern distributed networks increase the risk of failure. The corresponding protection device can isolate faults in the PDSBut areas without faults are also affected to power down. Therefore, an effective restoration scheme should protect the critical load as much as possible. Due to the high operational flexibility and low carbon emissions of natural gas, the gas turbine has an increased permeability in PDS, which also increases the interaction between PDS and the natural gas system (natural gas systems, NGS) [3] . The increasing dependence between PDS and NGS can present operational risks to both subsystems and can cause large-scale load loss [4] . Therefore, the load recovery method for the electric-gas integrated energy system should be studied [5] 。
However, most of the existing researches are performed by adopting a centralized solution method, and the method considers that a central operator can ignore the obstacle of information exchange and management between the power system and the natural gas subsystem, so that the two energy subsystems can be monitored. Different utility companies may own the power network and the natural gas network and be managed by their operators. Furthermore, the centralized approach cannot protect the information privacy of each energy subsystem because the central operator exchanges large amounts of private data.
Therefore, the conventional centralized optimization method may not be suitable for practical situations, and a new method is required to solve the above problems.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the distributed load recovery method of the multi-energy coupling power distribution network is provided, load recovery is independently carried out through two energy subsystems to minimize load loss, and cooperative operation can be realized in a distributed mode through adopting an Alternate Direction Multiplier Method (ADMM); the method has the advantages that the information privacy of the electric subsystem and the natural gas subsystem is protected, meanwhile, the load loss of the electric-gas comprehensive energy system is effectively reduced, and the method has important significance for improving the operation stability of the system.
The distributed load recovery method of the multi-energy coupling power distribution network comprises the following steps of:
step one, taking the synergistic effect of an electric power system and a natural gas system in an electric-gas comprehensive energy system into consideration, and establishing a load recovery model of the electric-gas comprehensive energy system according to network operation constraint in a power distribution system, various distributed power supply operation constraint, network reconstruction constraint and operation constraint in a natural gas network; relaxing the non-convex nonlinear constraint into a second order conical constraint using a conical relaxation technique;
and secondly, solving a load recovery model of the proposed electric-gas comprehensive energy system by adopting an ADMM algorithm, decomposing the load recovery problem of the whole system into a PDS electric sub-problem and an NGS natural gas sub-problem which are independently solved by interacting information of active power output of gas DG and operation of an electric compressor in the system, and independently deciding and coordinately optimizing the electric-gas comprehensive energy system by adopting an accelerating ADMM algorithm.
The load recovery model of the first step of the electric-gas comprehensive energy system has the objective function of minimum total coincidence loss cost, and the objective function is as follows:
in the method, in the process of the invention,and->Load loss cost coefficients of the power system and the natural gas system respectively; />And->The load loss percentages of the power system and the natural gas system are respectively; />And->Active loads and of power systems, respectivelyThe load of the natural gas system.
The PDS electric power sub-problem of the step two is constructed in an extended Lagrangian function form, and coupling constraint is added;
wherein lambda is 1,G And lambda (lambda) 1,C Is the vector of Lagrangian multipliers, z G And z C Is a consistent change, ρ is a penalty parameter, P G And P C Is the vector of the active power output of the gas DG in the PDS and the power consumption of the compressor;
the sub-problem model of NGS is constructed as:
wherein lambda is 2,G And lambda (lambda) 2,C Is the vector of lagrange multipliers; e (E) G And E is C Is the active power output of the gas DG in NGS and the power consumption vector of the compressor.
The PDS power sub-problem model constraint comprises a PDS node power balance constraint, a voltage drop equation constraint, a voltage constraint, a branch current constraint, a power flow constraint, a DG operation constraint and a network reconstruction constraint.
The sub-problem model constraint of the NGS is NGS node flow balance constraint, and comprises a load loss percentage limit of each gas node, a gas node pressure and a gas supply limit of a gas well, a compression ratio and a gas flow of a movable pipeline are limited, and a gas flow direction of natural gas flowing from a high-pressure node to the node is ensured after the natural gas pipeline fails.
Through the design scheme, the invention has the following beneficial effects:
1. compared with the existing method, the method considers the reconstruction strategy of the distribution network, the coupling effect of the distributed power sources (distributed generation, DG) and the power and natural gas subsystems, and provides a distributed load recovery strategy of the multi-energy coupling distribution network;
2. the invention constructs a system load recovery optimal model based on network operation constraint and various distributed power supply operation constraint in a typical electric-gas comprehensive energy system; in mathematical modeling of a natural gas pipeline, the invention adopts a bidirectional gas flow direction model, which is different from a fixed gas flow direction under normal operation, and can obtain a more accurate load recovery result when considering faults occurring in a natural gas network;
3. compared with the existing centralized method, the load recovery model provided by the invention adopts the ADMM algorithm based on consensus to solve in a distributed mode, so that information exchange is reduced, and the information privacy of the electric subsystem and the natural gas subsystem is protected.
Drawings
The invention is further described with reference to the drawings and detailed description which follow:
fig. 1 is a schematic diagram of an information interaction framework constructed by a distributed load recovery method of a multi-energy coupling power distribution network.
Fig. 2 is a system topology diagram of coupling between an IEEE13 node power distribution network and a 7 node natural gas network according to a specific embodiment of a distributed load recovery method for a multi-energy coupling power distribution network of the present invention.
Fig. 3 is a schematic diagram of an optimal topology after load recovery according to an embodiment of the distributed load recovery method for a multi-energy coupled power distribution network.
Fig. 4 is a schematic diagram of load loss of a power system and a natural gas system according to an embodiment of a distributed load recovery method for a multi-energy coupled power distribution network.
Fig. 5 is a schematic diagram of DG output in a specific embodiment of a distributed load recovery method for a multi-energy coupled power distribution network according to the present invention.
Fig. 6 is a schematic voltage diagram of each node in a specific embodiment of a distributed load recovery method for a multi-energy coupled power distribution network according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below.
Because the permeability of gas turbines consuming natural gas energy to generate electricity in power systems has increased year by year and extreme disasters have frequently occurred in recent years, the embodiments of the present invention consider coupled operation of power systems and natural gas systems, network reconfiguration of power distribution systems, and optimized operation of DG. The two energy subsystems are independently load restored to minimize the load loss of the overall system and use the ADMM algorithm to achieve co-operation in a distributed manner. In modeling of a natural gas system, the embodiment of the invention adopts a bidirectional airflow model, and can obtain more accurate load recovery results when faults occurring in a natural gas pipe network are considered, unlike the fixed airflow direction under normal operation.
Example 1
A distributed load restoration strategy for a multi-energy coupled power distribution network, the method comprising the steps of:
101: considering the synergistic effect of an electric power system and a natural gas system in an electric-gas comprehensive energy system, coordinating load recovery of the electric-gas comprehensive energy system based on a consensus ADMM, and interacting information of gas DG and compressor operation in the system, wherein the frame of the interaction information is shown in figure 1;
102: based on a typical electric-gas comprehensive energy system, according to network operation constraint in a power distribution system, various distributed power supply operation constraint, network reconstruction constraint and operation constraint in a natural gas network, a load recovery model of the electric-gas comprehensive energy system is established by considering reconfiguration of a power distribution network and DG and coupling characteristics of the electric system and the natural gas system;
103: relaxing the non-convex nonlinear constraint into a second order conical constraint using a conical relaxation technique;
the load recovery problem according to the embodiment of the invention is designed as a mixed integer nonlinear model, which is difficult to solve due to non-convexity and nonlinearity. In order to effectively solve the proposed mixed integer nonlinear model, a cone relaxation technique is used to relax the non-convex nonlinear constraint into a second order cone constraint, so that the model proposed by the embodiment of the invention can be further solved by adopting an ADMM algorithm.
104: the load recovery model of the electric-gas comprehensive energy system is solved by adopting an ADMM algorithm, the load recovery problem of the whole system is decomposed into an electric sub-problem and a natural gas sub-problem which are solved independently, and independent decision and coordination optimization of the electric-gas comprehensive energy system are realized by adopting an ADMM algorithm acceleration, so that the electric-gas comprehensive energy system has higher precision and efficiency.
In summary, the embodiment of the invention obtains the distributed coordination optimization decision of the electric-gas comprehensive energy system through the steps 101-104, thereby effectively reducing the system load loss.
Example 2
The scheme of example 1 is further described below in conjunction with specific formulas and examples, as described below:
201: considering the synergistic effect of an electric power system and a natural gas system in an electric-gas comprehensive energy system, coordinating an information exchange framework for load recovery of the electric-gas comprehensive energy system through an ADMM based on consensus, wherein the framework is shown in figure 1;
in the embodiment of the invention, the load recovery problem of the electric-gas integrated energy system is decomposed into PDS and NGS sub-problems by using an ADMM algorithm. The two subsystems independently perform load recovery so as to reduce load loss in the respective systems to the greatest extent, realize coordination optimization of the electric-gas comprehensive energy system through information interaction between the coupling elements, and obtain an optimal load recovery result. In the proposed ADMM approach, each operator only has complete information about its subsystems, and cannot access detailed information of other subsystems. The only information exchanged is the active power output of the gas DG and the power consumption of the electric compressor.
202: based on a typical electric-gas comprehensive energy system, according to network operation constraint in a power distribution system, various distributed power supply operation constraint, network reconstruction constraint and operation constraint in a natural gas network, a load recovery model of the electric-gas comprehensive energy system is established by considering reconfiguration of a power distribution network and DG and coupling characteristics of the electric system and the natural gas system;
wherein, this step 202 includes:
1) Objective function:
for a given set of faults, the load recovery method should minimize the total load loss of the overall system. The unit load loss cost is introduced as an energy load weight coefficient in the objective function, and the objective function of the proposed load recovery model is to minimize the total load loss cost in equation (1). The objective function is shown in formula (1):
in the formula (1), the components are as follows,and->The load loss cost coefficients of the power system and the natural gas system, respectively. />And->The percentage of load loss for the power system and the natural gas system, respectively. />And->The active load of the power system and the load of the natural gas system are respectively.
2) PDS operation constraints:
PDS node power balancing constraints:
in the formulas (2) and (3),and->Active power output and reactive power output of DG, respectively; p (P) ni And Q ni Active power flow and reactive power flow of branch ni respectively; i.e ni A square value of the current on the path ni; r is R ij And X ij The resistance and reactance values of the branches ij are respectively; p (P) ij And Q ij Active power flow and reactive power flow of the branch ij are respectively; />Active power consumed for compressor k; the set Θ (i) is a set of DGs connected to the node i; set b 1 (i) And set b 2 (i) A set of initial and terminal nodes having branches of terminal node i and initial node i, respectively; set ψ c (i) Is a collection of electric compressors. Set B is a set of nodes in the PDS. The formula (2) and the formula (3) respectively represent an active power balance equation and a reactive power balance equation of each node; equation (4) represents a limit range of the load loss percentage of each node.
The voltage drop equation is constrained as follows:
in the formula (5), M is a constant; mu (mu) ij Is a binary variable representing the state of branch ij; u (u) i Is the square value of the voltage at node i; i.e ij Is the square value of the current on branch ij; and the set omega is a set of branches in the power distribution network.Equation (5) represents the voltage drop across each leg.
Branch tidal current equation:
the voltage constraints, branch current constraints and power flow constraints are as follows:
in the formula (7), x i A binary state variable for node i;and->Respectively the minimum value and the maximum value of the voltage value on the node i; in formula (8), ->And->Respectively the minimum value and the maximum value of the current flowing through the branch ij; in the formula (9), a->And->Respectively, the branch ij flows active powerAnd the maximum value of reactive power.
Operating constraints of DG:
in the formula (10), the amino acid sequence of the compound,and->Minimum and maximum active power outputs of DG, respectively; />And->The minimum reactive power output and the maximum reactive power output of DG, respectively. The active and reactive power outputs of DG are limited in equation (10).
Network reconfiguration constraints:
in the formula (11), beta ij And beta ji Binary variable representing the flow direction of branch ij, beta if the power in the branch flows from node i to node j ij 1, if power in the branch flows from node j to node i, then β ji 1 is shown in the specification; constraint (11) - (13) ensures that the power distribution network is restored to its spokeRadial topology.
Constraint (14) represents a network connection of the system, (14) indicates that the leg can be powered only when both the initial node and the end node of the leg are powered. Constraints (16) define binary decision variables.
3) NGS operation constraints:
NGS node flow balance equation:
in the formula (17), the amino acid sequence of the compound,the gas yield of the gas well r; />Is the gas flow in the passive pipe pm; />And->Is the gas flow in the movable pipeline k; />Is the gas flow in the passive pipe mq; the set R (m) is a gas well set connected with a natural gas node m; set N 1 (m) and set N 2 (m) is the initial or terminal node set of the pipe with terminal and initial end node m, respectively; theta (theta) gf (m) is a gas DG set connected to gas node m. Constraint (17) provides a gas flow balance equation for each gas node. Set N is a set of natural gas nodes.
Constraint (18) represents the limit of the percentage of load loss for each gas node:
equation (19) is the passive conduit's weymouth gas flow equation, where the conduit gas flow direction is assumed to be fixed under normal operating conditions.
In the formula (19), C pm Coefficients of the weymouth equation; pi p And pi m The pressure of the node p and the pressure of the node m are respectively; set ψ pl Is a collection of passive pipes.
Constraint (20) and constraint (21) represent the limits of gas node pressure and gas supply, respectively, of a gas well, specifically as follows:
in the formula (20), the amino acid sequence of the compound,and->The minimum and maximum pressure values for node m, respectively. And(21) In (I)>And->The minimum and maximum gas production of gas well r, respectively.
The compression ratio and the gas flow rate of the movable pipeline are limited by the constraint (22) and the constraint (23), and the specific steps are as follows:
in the formula (22), pi com,k,t And pi com,k,f The node pressures before/after compressor k, respectively; in the formula (23), the amino acid sequence of the compound,is the maximum gas flow allowed in the compressor k.
In natural gas networks, the direction of the gas flow in the system is unchanged in daily normal operation, and the direction of each pipeline is fixed [6]-[7] . For example, natural gas in conduit pm flows from node p, where the pressure is higher, to node m, where the pressure is lower (i.e., in equation (19),). However, when the natural gas pipe fails, a bidirectional gas flow model should be considered. The method comprises the following steps:
wherein τ pm A binary variable representing the direction of gas flow;and->The higher or lower pressure of nodes p and m, respectively. Constraints (24) - (28) ensure that natural gas flows from high pressure node to low pressure node, wherein a binary variable τ is introduced pm To indicate the direction of gas flow. Thus, equation (19) can be converted to (29).
4) Coupling constraints
The main coupling elements of the electric-gas integrated energy system are the gas DG and the electric compressor, the following coupling constraints should be considered.
In the formula (30), beta g Is gas fuelThe gas power conversion coefficient of DG; in the formula (31), xi k Is a compressor power consumption coefficient. Equation (30) represents the energy consumption relationship of the gas DG, and (31) represents the relationship between the energy consumption of the electric compressor and the natural gas flow. It should be noted that in the embodiment of the present invention, due to the coupling effect of the electricity-gas integrated energy system, a fault in NGS may cause a gas load shortage of gas DG, while a fault in PDS may cause the electric compressor to be out of operation. Thus, the coupling effect of the electrical-electrical integrated energy system can affect the load recovery strategy for different faults.
203: the load recovery problem provided by the embodiment of the invention is designed into a mixed integer nonlinear model, and is difficult to solve due to the non-convexity and nonlinearity of the mixed integer nonlinear model; to effectively solve the proposed model, a cone relaxation technique is used to relax the non-convex nonlinear constraint to a second order cone constraint; wherein step 203 comprises:
equation (6) translates into:
equation (32) can be re-expressed as:
similarly, equation (29) can be restated as:
thus, the proposed load recovery model can be restated as (35), which is a mixed integer second order cone programming problem.
In the above model, by converting the nonlinear and non-convex constraints (6) and (19) intoConvex constraints achieve second order cone relaxation. Note that the relaxation is accurate only when equations (6) and (19) are satisfied; however, the second order cone relaxation (34) may not always be accurate in the solution process. Thus, the linear penalty termAdded to equation (1), the accuracy of the second order cone relaxation is ensured, where σ is a positive penalty factor.
204: and solving the load recovery model of the proposed electric-gas comprehensive energy system by adopting an ADMM algorithm, and decomposing the load recovery problem of the whole system into an electric sub-problem and a natural gas sub-problem which are independently solved. And the independent decision and coordination optimization of the electric-gas comprehensive energy system are realized by adopting an accelerating ADMM algorithm, and the method has higher precision and efficiency.
Wherein step 204 comprises:
in practice, the load recovery problem should not be solved using a centralized approach. In one aspect, NGS may not be uniformly managed by a single central operator. Alternatively, the centralized solution approach results in a large amount of information being transmitted in the subsystems, which leaves the information privacy of each energy subsystem unprotected. Therefore, the embodiment of the invention provides a distributed method for solving the load recovery problem of the electric-gas comprehensive energy system, which decomposes the load recovery problem of the electric-gas comprehensive energy system into independent solving sub-problems.
The solving idea of ADMM is to decompose the original variable in the convex problem into different variables x and y, and the objective function is also decomposed into two parts to ensure the decomposability of the optimization process, and the standard form of the algorithm is as follows:
where f (x) is the objective function and g (z) is the indicator function. A is that 1 、A 2 And B is a coefficient matrix of the coupling constraint. If the variables x and z satisfy A 1 x+A 2 z=b, g (z) =0, otherwise g (z) () = + infinity. Dividing the objective function and constraint in equation (36)Solutions are in the form of (37) and (38), where the global variable z ensures consistency of boundary information between subsystems.
Wherein f n (x n ) Is a convex objective function of subsystem n. Equation (38) is a consistency constraint. The method effectively ensures the information privacy and decision independence of each subsystem, and simplifies the information exchange process.
To resolve the original load recovery problem, variablesAnd->Is introduced into the sub-problem of NGS and satisfies the following relationship.
For distributed recovery problems of an electro-pneumatic integrated energy system, a consistency-based ADMM can be employed by introducing consistency variationsTo perform collaborative optimization between PDS and NGS.
Wherein equations (41) and (42) are contained in models of the power and natural gas subsystems, respectively, ensuring that the same variables repeated in the different subsystems are equal.
1) Sub-problem of PDS: the PDS sub-problem of load recovery may be constructed in the form of an augmented lagrangian function, as shown in equation (43), with the addition of coupling constraints (41).
s.t.Constraints(2)—(5),(7)—(16),(33) (44)
Wherein lambda is 1,G And lambda (lambda) 1,C Is the vector of Lagrangian multipliers, z G And z C Is a vector of consistent variables, ρ is a penalty parameter. P (P) G And P C Is a vector of active power output of the gas DG in the PDS and compressor power consumption.
2) Sub-problem of NGS: similar to equation (43), NGS load recovery sub-problems may also be constructed as:
wherein lambda is 2,G And lambda (lambda) 2,C Is a vector of lagrange multipliers. E (E) G And E is C Is the active power output of the gas DG in NGS and the power consumption vector of the compressor.
In summary, in the embodiment of the present invention, through the steps 201 to 204, the load recovery problem of the proposed electric-electric integrated energy system is decomposed into the PDS and NGS sub-problems by using the ADMM algorithm, and the two sub-systems independently perform load recovery, so as to reduce the load loss in the respective systems to the maximum extent, and realize information communication through the coupling element; solving the load recovery model by adopting the ADMM algorithm can reduce information exchange and protect the information privacy of the electric power subsystem and the natural gas subsystem.
Example 3
The schemes in examples 1 and 2 were validated in conjunction with specific examples, as described in detail below:
in the embodiment of the invention, the 13-node power distribution network and the 7-node natural gas network are used for carrying out simulation analysis by taking the example, the effectiveness of the method is verified, and in the process of solving the 13-7-node electric-gas comprehensive energy system by using the ADMM, the punishment parameter rho is set to be 20, and the threshold epsilon is stopped relatively P And εD is 10 -6 . The model was solved using a CPLEX solver with the YALMIP toolbox in MATLAB R2016a on a PC equipped with Intel Core i510210UCPU and 8GB RAM. For each case study, the embodiments of the present invention assume that after an extreme disaster has occurred, the PDS is unable to obtain power from the upper power transmission network due to severe damage to the power infrastructure.
The topology diagram of the 13-7 node electricity-gas integrated energy system is shown in the figure 2. The total power load provided by the system is 5.22MW+3.33MVar and 2750Sm 3 Total gas load per h. Three DG are located at nodes 1, 2 and 7, where G2 and G3 are gas DG. The 7-node NGS includes: an electric compressor, 2 gas wells and 5 passive pipelines. The detailed parameters of DG and network can be found in literature [8 ]]Is found.
To verify the accuracy of the embodiments of the present invention, the following calculation analyses were performed:
1) And (5) recovering the result analysis, and adopting four cases to analyze the recovery result.
Case 1-1: and 2-5 branch faults of the power distribution network.
Cases 1-2: and 7-10 branch faults of the power distribution network.
Cases 1-3: and the branches of the power distribution network 2-5 and 7-10 are failed.
Case 2: branches 2-5 and 7-10 in the distribution network fail the 2-5 pipes in the natural gas network.
Figure 3 shows the best topology in four cases. The power supply paths of all the nodes are restored, and the radial state of the restored power network is ensured. In order to further analyze the switching actions after different fault locations, several other faults are set in the PDS for case study. Table 1 lists the switching actions in several fault conditions. It can be seen from the table that the network reconfiguration is achieved by closing or opening the switches on the branches to obtain an optimal power supply path, so that the power supply to the blackout nodes can be restored and the radial topology of the power grid is ensured.
Table 1 results of switching actions under different fault conditions in PDS
Table 2 shows the load recovery results for cases 1-3 and example 2. Fig. 4 shows the load loss results for the power system node and the natural gas system node. Fig. 5 shows the active power output of each DG. In cases 1-3, the recovered electrical load has only a loss of 0.56MW, because closing the tie-switch can keep the entire grid connected, while the gas DG can consume natural gas and convert it into electricity to supply the electrical load. For nodes 7, 8, 9 and 10 with lower load cut costs, the amount of cut-off in the power load carried on these nodes occurs because the system guarantees a preferential supply of important loads in case of limited DG output. The natural gas supplied by the gas DG and the natural gas load is quite sufficient, so that there is no natural gas load loss. As can be seen from fig. 5, the output of DG 2 is very small due to the limitation of the natural gas network and the consideration of the natural gas load loss cost. The total output of DG cannot power all the power loads and thus the power loads cannot be fully recovered. In case 2, the power load shedding is greater than cases 1-3 because the total output of DG in case 2 is even smaller. Failure on conduit 2-5 prevents natural gas from flowing from node 5 to node 2, gas supplied by gas well 7 being preferentially used to supply natural gas network loads; thus, there is no excess gas on the natural gas node 2 to provide consumption of gas DGThus fig. 5 shows that the active power output of station 2 is zero. In case 2, there is more power load loss at nodes 7, 8, 9 and 10. In the natural gas network, the natural gas flow to node 1 is insufficient, resulting in 380Sm 3 Load loss per h, represents 57.5% of the natural gas load at node 1. Fig. 6 shows the node voltage results for each node after recovery in 4 cases. All nodes are powered back up. The above results demonstrate the effectiveness of the proposed load recovery model of the electric-gas integrated energy system.
Table 2 load recovery results for cases 1-3 and case 2
Case 2: and (3) analyzing the influence of the coupling effect between the power system and the natural gas system.
In this case study, the effect of the coupling effect between the power system and the natural gas system on the recovery result was analyzed, assuming two cases.
In case 3, the power and natural gas systems are independent, and in case 4, the two subsystems are coupled by a gas DG. In both cases the pipeline 3-5 in the natural gas system is assumed to be in a faulty condition. Table 3 shows the switching actions of cases 3 and 4 and the load loss results for the power system and the natural gas system. In case 3, the failure on pipe 3-5 results in all natural gas load loss at node 3. Since the two subsystems are independent, faults in the natural gas network do not affect the distribution system, there is no loss of power load, nor is the network need to be reconfigured by a switching operation to achieve load recovery. However, in case 4, except for 350.00Sm 3 In addition to the natural gas load losses per h, there are also power load losses in the distribution network, since the gas DG connected to the natural gas node 3 is not supplied with natural gas and cannot supply power to the distribution network. Thus, despite no faults in the distribution network, there is also a load shedding of 0.57MW, because the remaining two DGs are not able to meet all the power loads, and thus a negative power can occurLoad loss. The new power functional path must be formed by opening the switches on branch 7-8 and closing the switches on branches 5-8, 6-9 and 4-10. The above results indicate that faults in NGS may result in loss of electrical load in PDS.
Table 3 repair results for cases 3 and 4
Case 3: and (5) comparing and analyzing the ADMM method and the centralized method.
Table 4 compares the results obtained using the ADMM and centralized approach. According to the active power output and load loss of DG in table 4, the proposed ADMM recovery method is essentially identical to the result of the centralized method, with a relative error of less than 0.1%. This result verifies the accuracy of the proposed distributed load restoration strategy for the multi-energy coupled distribution network.
Table 4 comparison of results for centralized and distributed methods
In table 4: PG 1 : active power output (MW) of gas DG; PC: active power consumption (MW) of the compressor; PL: power load loss (MW); GL: gas load loss (MW).
The embodiment of the invention provides a distributed load recovery strategy of a multi-energy coupling power distribution network so as to minimize the cost of total load loss in PDS and NGS. Reconstruction after a power distribution network fault and coupling effects between power and gas systems are considered. The proposed load recovery model is converted to a MISOCP formulation and the proposed distributed recovery model is solved using an ADMM algorithm. The method can effectively reduce the system load loss and realize independent decision and coordination optimization of the electric-gas comprehensive energy system through the analysis of the calculation example.
The embodiment of the invention does not limit the types of other devices except the types of the devices, so long as the devices can complete the functions.
Those skilled in the art will appreciate that the drawings are schematic representations of only one preferred embodiment, and that the above-described embodiment numbers are merely for illustration purposes and do not represent advantages or disadvantages of the embodiments.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A distributed load recovery method of a multi-energy coupling power distribution network is characterized by comprising the following steps: the method comprises the following steps in sequence:
step one, taking the synergistic effect of an electric power system and a natural gas system in an electric-gas comprehensive energy system into consideration, and establishing a load recovery model of the electric-gas comprehensive energy system according to network operation constraint in a power distribution system, various distributed power supply operation constraint, network reconstruction constraint and operation constraint in a natural gas network; relaxing the non-convex nonlinear constraint into a second order conical constraint using a conical relaxation technique;
and secondly, solving a load recovery model of the proposed electric-gas comprehensive energy system by adopting an ADMM algorithm, decomposing the load recovery problem of the whole system into a PDS electric sub-problem and an NGS natural gas sub-problem which are independently solved by interacting information of active power output of gas DG and operation of an electric compressor in the system, and independently deciding and coordinately optimizing the electric-gas comprehensive energy system by adopting an accelerating ADMM algorithm.
2. The distributed load recovery method for a multi-energy coupled power distribution network according to claim 1, wherein the method comprises the following steps: the load recovery model of the first step of the electric-gas comprehensive energy system has the objective function of minimum total coincidence loss cost, and the objective function is as follows:
in the method, in the process of the invention,and->Load loss cost coefficients of the power system and the natural gas system respectively; r is (r) i p And->The load loss percentages of the power system and the natural gas system are respectively; p (P) i D And->The active load of the power system and the load of the natural gas system are respectively.
3. The distributed load recovery method for a multi-energy coupled power distribution network according to claim 1, wherein the method comprises the following steps: the PDS electric power sub-problem of the step two is constructed in an extended Lagrangian function form, and coupling constraint is added;
wherein lambda is 1,G And lambda (lambda) 1,C Is the vector of Lagrangian multipliers, z G And z C Is a consistent change, ρ is a penalty parameter, P G And P C Is the vector of the active power output of the gas DG in the PDS and the power consumption of the compressor;
the sub-problem model of NGS is constructed as:
wherein lambda is 2,G And lambda (lambda) 2,C Is Lagrangian multiplicationVector of the son; e (E) G And E is C Is the active power output of the gas DG in NGS and the power consumption vector of the compressor.
4. A method for distributed load restoration of a multi-energy coupled power distribution network as defined in claim 3, wherein: the PDS power sub-problem model constraint comprises a PDS node power balance constraint, a voltage drop equation constraint, a voltage constraint, a branch current constraint, a power flow constraint, a DG operation constraint and a network reconstruction constraint.
5. A method for distributed load restoration of a multi-energy coupled power distribution network as defined in claim 3, wherein: the sub-problem model constraint of the NGS is NGS node flow balance constraint, and comprises a load loss percentage limit of each gas node, a gas node pressure and a gas supply limit of a gas well, a compression ratio and a gas flow of a movable pipeline are limited, and a gas flow direction of natural gas flowing from a high-pressure node to the node is ensured after the natural gas pipeline fails.
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