CN116667424A - Two-stage robust fault recovery method for power distribution network based on toughness improvement - Google Patents
Two-stage robust fault recovery method for power distribution network based on toughness improvement Download PDFInfo
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Abstract
A two-stage robust fault recovery method for a power distribution network based on toughness improvement belongs to the field of power distribution network fault recovery. The method comprises the steps of combining important load recovery time in the fault recovery process of the power distribution network and load shedding time possibly caused by output fluctuation of a distributed power supply, and constructing a power distribution network toughness assessment method; an ellipsoid uncertainty set is introduced to fully consider the characteristics of randomness, volatility and the like of the distributed power supply output; and taking the optimal toughness index as an objective function, completing the establishment of a two-stage robust optimization model, and adopting an improved C & CG algorithm based on a limit scene to complete the solution of the fault recovery model. Aiming at the influence of extreme disasters on the power distribution network, the characteristics of randomness and fluctuation of the output of the distributed power supply are fully considered from the viewpoint of load recovery after the power distribution network fails, the power supply to the key load is met to the greatest extent, and the toughness of the power distribution network under the influence of the extreme disasters can be ensured. The method can be widely applied to the fields of operation management and fault emergency treatment of the power distribution network.
Description
Technical Field
The invention belongs to the field of power distribution network fault recovery, and particularly relates to a two-stage robust fault recovery method for a power distribution network based on toughness improvement.
Background
In recent years, with the frequent occurrence of extreme disasters such as typhoons, the power system is greatly destroyed, and meanwhile, as the power distribution network is directly connected with a secondary load, the power distribution network has important significance in ensuring the stable operation under the extreme disasters. In addition, as the installed capacity of the distributed power supply increases, the damage of extreme disasters is increased by taking the characteristics of fluctuation and randomness of the output of the distributed power supply into consideration.
In this context, toughness is introduced to express the ability of the distribution network to minimize load losses under extreme disaster effects, to guarantee as much as possible important load power supply during extreme weather effects.
Therefore, how to improve the toughness of the power distribution network is a key to ensure safe and stable operation of the power distribution network in extreme weather.
The invention patent application with application publication number of CN 113705964A, whose application publication date is 2021.11.26, discloses a method and a device for preparing a pre-disaster plan for toughness recovery of a power distribution network, comprising: establishing a toughness recovery contract model of the power distribution network; establishing a topology reconstruction model of a power distribution network fault scene set according to preset disaster information, wherein the topology reconstruction model is used for representing a reconstructed topology structure of the post-disaster power distribution network toughness recovery; determining a confidence parameter, wherein the confidence parameter is used for representing the risk preference of the power distribution network; under the topology of the topology reconstruction model, optimizing the constraint model according to the confidence parameters and preset disaster information to obtain a pre-disaster planning result of the toughness recovery of the power distribution network. The public traffic resource is reasonably utilized in the toughness recovery of the power distribution network so as to improve the toughness recovery capability of the power distribution network; and a reasonable contract model is formulated and a pre-disaster plan result is obtained by solving, so that a basis is provided for the overall decision of the toughness improvement of the power distribution network. The technical scheme is focused on pre-disaster planning and toughness recovery of the power distribution network, less consideration is given to the randomness and fluctuation of the distributed power supply output, and the randomness problem of the distributed power supply output is not involved.
The application publication date is 2022.09.30, and the application publication number is CN 115130378A, and discloses a method for evaluating the toughness of a power distribution network based on a Monte Carlo algorithm under typhoon disasters, which comprises the following steps: s1: according to the rule that wind speeds are distributed in an eddy mode under typhoon disasters, a typhoon wind field model is built by taking the maximum wind speed radius as a boundary; s2: according to the mechanical effect of the power distribution network element under typhoon disasters, a power distribution network element fault probability model based on a mechanical load effect theory is established; s3: obtaining fault probability data through a fault probability model, simulating by using a Monte Carlo method, and determining a random fault scene of the power distribution network element; s4: taking the integral of the difference value between the total load and the running load under typhoon disasters as a toughness evaluation index of the power distribution network, and calculating to obtain a toughness evaluation index value; the method provided by the invention only needs to consider the influence of the elements of the power distribution network on the load points of the power distribution network, can effectively solve the calculation amount problem caused by excessive elements in the system, is suitable for large-scale toughness evaluation calculation of the power distribution network, and has good comprehensiveness and operability for the toughness evaluation of the power distribution network. The technical scheme is focused on the evaluation of the failure probability of the power distribution network element under typhoon disasters, and the problem of how to realize the failure recovery of the power distribution network based on toughness improvement on the basis of fully considering the randomness of the output of the distributed power supply is not related.
Disclosure of Invention
The invention aims to solve the technical problem of providing a two-stage robust fault recovery method for a power distribution network based on toughness improvement. The method is focused on the aspects of load recovery after the power distribution network faults, the toughness of the power distribution network is improved, the power supply to the key load is met to the greatest extent, the characteristics of the randomness and the fluctuation of the output of the distributed power supply can be fully considered, and compared with the traditional fault recovery method, the method can ensure the toughness of the power distribution network under the influence of extreme disasters due to the fact that the robust optimization model considers the worst case.
The technical scheme of the invention is as follows: the utility model provides a two-stage robust fault recovery method of a power distribution network based on toughness improvement, which is characterized by comprising the following steps:
step 1: constructing a power distribution network toughness evaluation method by combining important load recovery time in the power distribution network fault recovery process and load shedding time possibly caused by the output fluctuation of a distributed power supply;
step 2: for effectively analyzing the problems of uncertainty and the like of the output force of the distributed power supply, introducing an ellipsoid uncertainty set to fully consider the characteristics of the output force of the distributed power supply, including randomness and fluctuation;
step 3: and taking the optimal toughness index as an objective function, completing the establishment of a two-stage robust optimization model, and adopting an improved C & CG algorithm based on a limit scene to complete the solution of the fault recovery model.
Specifically, the two-stage robust fault recovery method of the power distribution network aims at the influence of extreme disasters on the power distribution network, considers the characteristics of randomness and fluctuation of the output of the distributed power supply fully from the viewpoint of load recovery after the power distribution network has faults, adopts an improved C & CG algorithm based on a limiting scene to complete the solution of the established two-stage robust fault recovery model, satisfies the power supply to the key load to the greatest extent, and can ensure the toughness of the power distribution network under the influence of the extreme disasters.
Further, in step 1, by giving out a specific expression formula of important load recovery time and load shedding time possibly caused by output fluctuation of the distributed power supply in the fault recovery process of the power distribution network, the evaluation of the toughness of the power distribution network is completed;
wherein the important load recovery time T 1 Load shedding time T 2 The specific expression formulas are respectively as follows:
where L is all load sets, T is all period sets, T\ {1} is a period set other than the first period, ω i For each level of load weight coefficient,indicating whether the load i is restored during period T, T int C for each equal interval of the whole recovery process i Load shedding penalty coefficient for each class of load, gamma i,t Characterizing whether the load i is cut off during period t,respectively indicate->γ i,t The value of (2) is 1.
Specifically, in step 2, in order to effectively analyze the problems of uncertainty and the like of the output force of the distributed power supply, an ellipsoid uncertainty set is introduced to fully consider the randomness and fluctuation characteristics of the output force of the distributed power supply;
the construction method of the data-driven ellipsoid uncertainty set is as follows:
1): constructing a distributed power supply historical output matrix omega according to historical data:
let a total of N in the region p A photovoltaic power station, setting the number of days of the collected historical data as N s The method comprises the steps of carrying out a first treatment on the surface of the The expression for ω can be written as:
2): data-driven high-dimensional ellipsoid set construction:
based on MVEE data driving algorithm, a high-dimensional ellipsoid is constructed to wrap all historical scenes:
wherein: ρ is a constant representing N p Volume of unit sphere of dimension T; q is the deviation direction of the symmetry axis of the ellipsoid from the coordinate axis:
the above formula is solved by using a lift-and-project algorithm, and finally the expression of the high-dimensional ellipsoid is obtained as follows:
n described in the formula p T-dimensional ellipsoid uncertainty set together 2N p T vertices;
3): solving the model to obtain vertex coordinates of an ellipsoid set:
first, Q is subjected to orthogonalization decomposition: q=p T DP＝P -1 DP, noteP is a transformation matrix; in order to obtain the vertex corresponding to the high-dimensional ellipsoid, the ellipsoid is rotationally translated to enable the symmetry axis to coincide with the coordinate axis, and the rotation change equation is as follows:
ω′＝P×(ω-c)
wherein omega' is the coordinate value of the vertex after rotation; e' (. Cndot.) is a high-dimensional ellipsoidal expression obtained after rotation; omega e ′ ,1 ,…,ω e ′,N e The method comprises the steps of carrying out a first treatment on the surface of the The vertex coordinates of the rotated high-dimensional ellipsoid are obtained; n (N) e The number of vertexes;
obtaining the high-dimensional ellipsoid E vertex omega e,i Coordinates, thereby creating a data driven uncertainty set based on the ellipsoidal vertices.
Further, in the step 3, the toughness index is optimized as an objective function, the establishment of a two-stage robust optimization model is completed, and the solution of the established two-stage fault recovery robust model based on toughness improvement is completed by adopting an improved C & CG algorithm based on a limit scene;
the two-stage power distribution network fault recovery optimization model determines data including all load recovery states, line opening and closing states and pre-dispatching output values of the controllable distributed power supply in each period;
the fault recovery decision process of the power distribution network is divided into two stages:
the first stage, according to the predictive value of the distributed power supply of each period, deciding the pre-dispatching output value, load recovery state and line open-close state of each controllable distributed power supply; in order to reduce the line switch operation in the load recovery process of the power distribution network, the network topology is not changed once being determined at the beginning of the recovery process;
and in the second stage, the actual output value of the controllable distributed power supply is correspondingly adjusted according to the actual output value of the distributed power supply.
Specifically, on the basis of the two-stage fault recovery model and the established ellipsoid uncertainty set, the construction of the two-stage robust fault recovery model is completed, and the matrix is expressed as follows:
wherein h is a limit scene number; omega shape 1 、Ω 2 、Ω 3 The method comprises the steps of respectively obtaining a first stage decision variable set, a distributed power output uncertainty variable set and a second stage decision variable set; A. b is a coefficient matrix; x and y are the first stage and second stage decision variables, respectively;
the extremum in convex optimization can only be obtained at the vertex of the polyhedron space, so that the ultimate scene of robust optimization is positioned at the vertex of an ellipsoid;
for the determined first stage decision variable x, only the second stage decision variable y is adjusted to adapt to all limit scenes omega e,h Then the robustness of fault recovery can be ensured, and the improvement C based on the limit scene is adopted&The CG algorithm solves the two-stage data driving robust planning model;
the form of the improved C & CC algorithm sub-problem SP is:
in the method, in the process of the invention,the solution result of the main problem decision variable in the nth iteration is as follows:
the form of the main problem MP of the improved C & CG algorithm is:
wherein n is the current C&CG algorithm iteration number; η maximum running cost; w (w) h The method comprises the steps of selecting a limit scene for the h iteration;for extreme scene w h Lower run decision variables; />For extreme scene w h The variable is valued at the following uncertainty.
Further, the steps of the improved C & CG algorithm flow based on the limit scene method are as follows:
step 7-1: setting lower limit L B = - ≡, upper bound U B = + infinity of the two points, algorithm iteration number n=1;
step 7-2: solving the main problem to obtain an optimal solution of the main problemMaximum controllable distributed power supply output adjustment valueAnd update the lower bound->
Step 7-3: fixingSolving the sub-problem by enumerating limit scenes; if the sub-problem is solved, the maximum value f of the output adjustment value of the controllable distributed power supply is obtained SP And the corresponding worst limit scene h, updating the upper bound U B ＝min(U B ,f SP ) The method comprises the steps of carrying out a first treatment on the surface of the If the sub-problem has no feasible solution, selecting a limit scene h for enabling the sub-problem to have no solution as a worst scene;
step 4: if U B -L B If epsilon is less than epsilon, ending the iteration and outputting a main problem decisionOtherwise, adding the constraint corresponding to the worst limit scene h to the main problem, wherein n=n+1, and returning to the step 7-2.
Compared with the prior art, the invention has the advantages that:
1. according to the technical scheme, aiming at the influence of extreme disasters on a power distribution network, the two-stage robust fault recovery method based on toughness promotion is provided from the perspective of toughness, the characteristics of randomness and volatility of the output of a distributed power supply can be fully considered, meanwhile, the solution of an established two-stage robust fault recovery model is creatively provided by an improved C & CG algorithm based on a limit scene, and compared with the traditional fault recovery method, the toughness of the power distribution network under the influence of the extreme disasters can be ensured due to the fact that the worst case is considered by the robust optimization model;
2. according to the technical scheme, from the point of load recovery after power distribution network faults, the toughness of the power distribution network is improved, power supply to key loads is met to the greatest extent, and the characteristics of randomness and fluctuation of the distributed power supply output can be fully considered.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a two-stage fault recovery model established;
FIG. 3 is a block diagram of a flow of an adopted data-driven robust optimization algorithm;
FIG. 4 is a schematic diagram of a photovoltaic interval uncertainty set and an ellipsoid uncertainty set;
FIG. 5 is a schematic diagram of an example of an improved IEEE33 node power distribution network system;
FIG. 6 is a schematic diagram of the load condition and load class of each node;
FIG. 7 is a schematic diagram of a distributed power access scenario for a power distribution network;
FIG. 8 is a schematic diagram of a power distribution network line fault condition in typhoon weather;
FIG. 9 is a schematic diagram of a line repair sequence;
FIG. 10 is a schematic diagram of a load recovery scenario;
FIG. 11 is a schematic diagram of real-time day-ahead output of a micro gas turbine.
Detailed Description
The invention is further described below with reference to the drawings and examples.
According to the technical scheme, from the perspective of load recovery after power distribution network faults, the toughness of the power distribution network is improved, power supply to key loads is met to the greatest extent, and the two-stage robust fault recovery method of the power distribution network based on the toughness improvement is provided on the basis of fully considering the randomness of the distributed power supply output.
As shown in fig. 1, the specific technical scheme of the invention is a two-stage robust fault recovery method of a power distribution network based on toughness improvement, which comprises the following steps:
step 1: and constructing a power distribution network toughness evaluation method by combining important load recovery time in the power distribution network fault recovery process and load shedding time possibly caused by the output fluctuation of the distributed power supply.
Step 2: in order to effectively analyze the problems of uncertainty of the output force of the distributed power supply, an ellipsoid uncertainty set is introduced to fully consider the characteristics of randomness, fluctuation and the like of the output force of the distributed power supply.
Step 3: and taking the optimal toughness index as an objective function, completing the establishment of a two-stage robust optimization model, and adopting an improved C & CG algorithm based on a limit scene to complete the solution of the fault recovery model.
The technical scheme is further specifically described as follows:
step 1: and (3) providing a concrete expression formula of important load recovery time and load shedding time possibly caused by the fluctuation of the output of the distributed power supply in the fault recovery process of the power distribution network, thereby completing the evaluation of the toughness of the power distribution network.
As mentioned initially, the main goal of power distribution network fault recovery is to recover as much critical load as possible according to load recovery priority and continue to power the recovered load until the main network is available to power the loads in the power distribution network. However, the output power regulation capability of the controllable distributed power supply is limited, so that the energy imbalance caused by fluctuation of the output power of the distributed power supply cannot be compensated, and the secondary power failure, namely load shedding, of the recovered important load is most likely caused. Therefore, it is also considered to minimize the number of load shedding during the fault recovery. Considering the effect of reducing the number of load shedding, there are mainly two reasons: (1) Frequent load shedding actions necessarily increase the risk of instability of the power distribution network system and even lead to failure of the recovery process; (2) Cutting the load necessarily directly reduces the power reliability and user satisfaction. In addition to the above-mentioned time-wise toughness indicators, also toughness indicators from the load point of view are included, but here, for simplicity of analysis, only time-wise considerations are made in terms of fault recovery.
Time of important load recovery T 1 Load shedding time T 2 The specific expression formulas are respectively as follows:
where L is all load sets, T is all period sets, and t\ {1} is a period set other than the first period. Omega i The weight coefficient is used for each grade of load.Indicating whether the load i is restored during the t period. T (T) int For each equal interval of the overall recovery process. c i And (5) a load shedding penalty coefficient for each grade of load. Gamma ray i,t It is characterized whether the load i is cut off at time t.Respectively indicate->γ i,t The value of (2) is 1.
Step 2: in order to effectively analyze the problems of uncertainty of the output force of the distributed power supply, an ellipsoid uncertainty set is introduced to fully consider the characteristics of randomness, fluctuation and the like of the output force of the distributed power supply.
The interval uncertainty set is a method which is frequently adopted by most students in researching the uncertainty of the output of the distributed power supply at present, and the expression of the interval uncertainty set is as follows:
the interval uncertainty set is the simplest uncertainty set, but as the subsequent robust optimization is an optimization solution method under the worst condition, aiming at the condition that all uncertainty parameters are optimized on the upper and lower boundaries of the interval uncertainty set in a robust optimization model, the probability of occurrence of the condition is extremely low or cannot occur in practice, so that the condition of excessive conservation is easy to occur. That is, the interval uncertainty set depends only on the maximum and minimum output forces in the robust optimization model, but the consideration method really ignores the real situation of the distributed power supply output, so that the interval uncertainty set is too conservative, and more unlikely scenes are considered.
The interval uncertainty set and the ellipsoid uncertainty set are shown in fig. 4, from which it can be seen that ellipsoids are more suitable for modeling non-uniform data sets than interval uncertainty sets. General ellipsoid setThe combined expression is E= { (ω -c) T θ -1 (ω -c), 1, where c is the center of the ellipsoid, θ is the weighted variable covariance, ω is the distributed power source historical output matrix.
Aiming at the construction of an ellipsoid uncertainty set, a minimum closed volume algorithm adopts a data driving method to construct a minimum volume ellipsoid uncertainty set capable of wrapping all historical data according to the distribution condition of the history data of the uncertainty variable, and the uncertainty output space surrounded by the set is smaller and the conservation is smaller.
The construction method of the data-driven ellipsoid uncertainty set is as follows:
1): and constructing a distributed power supply historical output matrix omega according to the historical data. Let a total of N in the region p A photovoltaic power station, setting the number of days of the collected historical data as N s . The expression of ω can be written as
2): and constructing a high-dimensional ellipsoid set based on data driving. Based on MVEE data driving algorithm, a high-dimensional ellipsoid is constructed to wrap all historical scenes.
Wherein: ρ is a constant representing N p Volume of unit sphere of dimension T; q is the deviation direction of the symmetry axis of the ellipsoid from the coordinate axis.
The above formula can be solved by using a lift-and-project algorithm, and finally the expression of the obtained high-dimensional ellipsoid is
N described by p T-dimensional ellipsoid uncertainty set together 2N p T vertices.
3): solving forAnd (5) obtaining the vertex coordinates of the ellipsoid set by the model. First, Q is subjected to orthogonalization decomposition: q=p T DP＝P - 1 DP, noteP is the transform matrix. In order to obtain the vertex corresponding to the high-dimensional ellipsoid, the ellipsoid is rotationally translated to enable the symmetry axis to coincide with the coordinate axis, and the rotation change equation is as follows:
ω′＝P×(ω-c)
wherein omega' is the coordinate value of the vertex after rotation; e' (. Cndot.) is a high-dimensional ellipsoidal expression obtained after rotation; omega e ′ ,1 ,…,ω e ′,N e . The vertex coordinates of the rotated high-dimensional ellipsoid are obtained; n (N) e The number of vertices.
Obtaining the high-dimensional ellipsoid E vertex omega e,i Coordinates, thereby creating a data driven uncertainty set based on the ellipsoidal vertices.
Step 3: and taking the optimal toughness index as an objective function, completing the establishment of a two-stage robust optimization model, and adopting an improved C & CG algorithm based on a limit scene to complete the solution of the established two-stage fault recovery robust model based on toughness improvement.
In the fault recovery, the distributed power supply is considered, but the actual output specific value cannot be accurately predicted by the existing prediction tool, and the actual value and the predicted value always have a certain deviation. Thus, the randomness of the distributed power supply will further increase the risk of unintended load shedding during load restoration. To reduce the risk of unintended load shedding during load restoration, the pre-scheduled output value of the controllable distributed power source (such as a micro gas turbine) is determined in advance, and the remaining part which does not reach the maximum value of the controllable distributed power source output is used as the standby power of the controllable distributed power source. The power deviation caused by the randomness of the actual output of the intermittent energy source is compensated by further adjusting the output of the controllable distributed power source. Of course, when the load recovery strategy of the power distribution network is formulated, the balance between the two aims of recovering as much key load as possible and reducing the load shedding times in the recovery process should be made. Setting redundant controllable distributed power supply standby power for avoiding occurrence of load shedding conditions is against the goal of achieving recovery of as much load as possible; but a small number of load shedding operations with non-essential loads are acceptable to ensure restoration of the essential loads and their continued power supply. The recovery model will be differentiated by setting different weight coefficients for the two targets.
The two-stage power distribution network fault recovery optimization model provided by the technical scheme is used for determining all load recovery states, line opening and closing states, pre-dispatching output values of the controllable distributed power supply and the like in each period. The power distribution network fault recovery decision process is divided into two stages, as shown in fig. 2.
And in the first stage, according to the predicted value of the distributed power supply in each period, the pre-dispatching output value, the load recovery state and the line opening and closing state of each controllable distributed power supply are decided. To reduce line switching during a power distribution network load restoration process, the restoration process is started and once the network topology is determined, the network topology is not changed. And in the second stage, the actual output value of the controllable distributed power supply is correspondingly adjusted according to the actual output value of the distributed power supply.
On the basis of the two-stage fault recovery model and the established ellipsoid uncertainty set, the construction of the two-stage robust fault recovery model can be completed, and the matrix is expressed as follows:
wherein h is a limit scene number; omega shape 1 、Ω 2 、Ω 3 Respectively, a first stage decision variable set and uncertainty of distributed power supply outputA set of qualitative variables and a set of second stage decision variables; A. b is a coefficient matrix; x and y are the first stage and second stage decision variables, respectively.
Since extremum in convex optimization can only be taken at vertices of polyhedral space, the limiting scene of robust optimization is located at the vertices of ellipsoids. For the determined first stage decision variable x, only the second stage decision variable y is adjusted to adapt to all limit scenes omega e,h Then the robustness of the fault recovery can be guaranteed. But due to the tradition C by Lagrangian dual&CG algorithm is too complex, taking into account characteristics of data driven uncertainty sets, using limit scene based modification C&And the CG algorithm solves the two-stage fault recovery model.
The sub-problem SP is the worst scenario of controllable DG power adjustment due to uncertainty in distributed power supply output, given the optimal solution of the main problem MP.
The form of the improved C & CC algorithm subproblem SP is
In the method, in the process of the invention,and the result is the solving result of the main problem decision variable in the nth iteration.
The main problem MP is to solve the coordination of the prescheduled output value, load recovery state and line open-close state of the controllable distributed power supply given the uncertainty set of the distributed power supply output ellipsoids.
The main problem MP of the improved C & CG algorithm is in the form of
Wherein n is the current C&CG algorithm iteration number; η maximum power adjustment cost; w (w) h The method comprises the steps of selecting a limit scene for the h iteration;for extreme scene w h A lower sub-problem decision variable; />For extreme scene w h The variable is valued at the following uncertainty.
The improved C & CG algorithm flow based on the limit scene method is shown in figure 3, and the steps are as follows:
step 1: setting lower limit L B = - ≡, upper bound U B = + infinity of the two points, algorithm iteration number n=1.
Step 2: solving the main problem to obtain an optimal solution of the main problemMaximum controllable distributed power supply output adjustment valueAnd update the lower bound->
Step 3: fixingThe sub-problem is solved by enumerating the limit scenarios. If the sub-problem is solved, the maximum value f of the output adjustment value of the controllable distributed power supply is obtained SP And the corresponding worst limit scene h, updating the upper bound U B ＝min(U B ,f SP ) The method comprises the steps of carrying out a first treatment on the surface of the If the sub-problem has no feasible solution, selecting a limit scene h for making the sub-problem have no solution as the worst scene.
Step 4: if U B -L B If epsilon is less than epsilon, ending the iteration and outputting a main problem decisionOtherwise, adding the constraint corresponding to the worst limit scene h to the main problem, wherein n=n+1, and returning to the step 2.
Examples:
here, only the distributed power source of photovoltaic is considered for simplifying the calculation analysis, but the application object of the present invention is not limited to the power distribution network including only the distributed power source of photovoltaic.
The established two-stage fault recovery robust optimization model is as follows:
where L is all load sets, T is all period sets, and t\ {1} is a period set other than the first period. Omega i The weight coefficient is used for each grade of load.Indicating whether the load i is restored during the t period. T (T) int For each equal interval of the overall recovery process. c i And (5) a load shedding penalty coefficient for each grade of load. Gamma ray i,t It is characterized whether the load i is cut off at time t.Respectively indicate->γ i,t The value of (2) is 1. Lambda (lambda) 1 And lambda (lambda) 2 Is a weight coefficient. />Representing the active power adjustment quantity of the controllable distributed power supply according to the photovoltaic random output value, which is shaped like +.>The variables of (a) all represent random variables. c ± The cost of the output adjustment for the controllable distributed power supply.
The technical scheme adopts an improved IEEE33 node power distribution network system, as shown in figure 5. The line numbers are based on the principle that the serial numbers at the start and end are smaller, for example, (1-2) is line 1, (2-3) is line 2, (2-19) is line 3, and the rest line numbers are the same.
The load conditions and load levels of the nodes are shown in fig. 6.
The photovoltaic and micro gas turbine access conditions are shown in fig. 7. The photovoltaic access capacities of all the nodes of the photovoltaic are equal and are 621.7463kW, and the capacities of the miniature gas turbines are 800kW.
In addition, in the extreme weather, typhoon is taken as an example, and the power transmission line, the pole tower and the photovoltaic of the power distribution network are likely to fail under the influence of typhoon weather, so that in order to simplify analysis, in a fault recovery calculation example, the photovoltaic failure rate is directly 40%, and meanwhile, the photovoltaic output in typhoon weather is similar to the photovoltaic output in rainy days.
The line fault condition of the distribution network in typhoon weather is shown in fig. 8.
In order to facilitate smooth repair of the transmission line of the power distribution network, a line repair sequence is given according to the magnitude of the line disconnection loss load, as shown in fig. 9.
And finally determining a line repair sequence according to the load loss condition after the disconnection of each line, and respectively obtaining line numbers 18, 9, 5 and 12.
Assuming that the power outage time after disconnection is 2 hours in total, the time is divided into 10 time periods, namely 12 minutes for each time period, and the load recovery situation is shown in fig. 10.
All primary loads can be restored within 10 time periods; while the secondary load 25 is not restored eventually, in practice the secondary load 25 is restored in the first 6 time periods, but is cut off in the 7 th time period, and only once is allowed to change the load state in order to avoid the frequent change of the load state from adversely affecting the restoration process, so that the secondary load 25 is not restored in the subsequent time periods. The three-level load is not restored all the time except that the load 12 is restored in the 7 th period and the loads 14, 15, 22 are restored in the 8 th period.
The real-time day-ahead output of the micro gas turbine is shown in FIG. 11.
Aiming at the influence of extreme disasters on a power distribution network, the characteristics of randomness and fluctuation of the output of a distributed power supply are fully considered from the perspective of load recovery after the power distribution network fails, the technical scheme of the invention provides an improved C & CG algorithm based on a limit scene to complete the solution of an established two-stage fault recovery robust model, and compared with the traditional fault recovery method, the robust optimization model can ensure the toughness of the power distribution network under the influence of the extreme disasters due to the consideration of the worst case; and the toughness of the power distribution network is improved, the power supply to the key load is met to the greatest extent, and the characteristics of randomness and fluctuation of the output of the distributed power supply can be fully considered.
The invention can be widely applied to the fields of operation management and fault emergency treatment of the power distribution network.
Claims (7)
1. A two-stage robust fault recovery method for a power distribution network based on toughness improvement is characterized by comprising the following steps:
step 1: constructing a power distribution network toughness evaluation method by combining important load recovery time in the power distribution network fault recovery process and load shedding time possibly caused by the output fluctuation of a distributed power supply;
step 2: for effectively analyzing the problems of uncertainty and the like of the output force of the distributed power supply, introducing an ellipsoid uncertainty set to fully consider the characteristics of the output force of the distributed power supply, including randomness and fluctuation;
step 3: and taking the optimal toughness index as an objective function, completing the establishment of a two-stage robust optimization model, and adopting an improved C & CG algorithm based on a limit scene to complete the solution of the fault recovery model.
2. The two-stage robust fault recovery method for the power distribution network based on toughness promotion is characterized in that the two-stage robust fault recovery method for the power distribution network is aimed at the influence of extreme disasters on the power distribution network, the characteristics of randomness and fluctuation of the output of a distributed power supply are fully considered from the viewpoint of load recovery after the power distribution network faults, the built two-stage robust fault recovery model is solved by adopting an improved C & CG algorithm based on a limiting scene, the power supply to a key load is met to the greatest extent, and the toughness of the power distribution network under the influence of the extreme disasters can be ensured.
3. The two-stage robust fault recovery method for the power distribution network based on toughness promotion according to claim 1 is characterized in that in step 1, the evaluation of the toughness of the power distribution network is completed by giving out a specific expression formula of important load recovery time and load shedding time possibly caused by the fluctuation of the output of a distributed power supply in the fault recovery process of the power distribution network;
wherein the important load recovery time T 1 Load shedding time T 2 The specific expression formulas are respectively as follows:
where L is all load sets, T is all period sets, T\ {1} is a period set other than the first period, ω i For each level of load weight coefficient,indicating whether the load i is restored during period T, T int C for each equal interval of the whole recovery process i Load shedding penalty coefficient for each class of load, gamma i,t Characterizing whether load i is cut off during period t, < >>Respectively indicate->γ i,t The value of (2) is 1.
4. The two-stage robust fault recovery method for the power distribution network based on toughness promotion according to claim 1 is characterized in that in step 2, an ellipsoid uncertainty set is introduced to fully consider the randomness and fluctuation characteristics of the distributed power supply output in order to effectively analyze the problems of uncertainty and the like of the distributed power supply output;
the construction method of the data-driven ellipsoid uncertainty set is as follows:
1): constructing a distributed power supply historical output matrix omega according to historical data:
let a total of N in the region p A photovoltaic power station, setting the number of days of the collected historical data as N s The method comprises the steps of carrying out a first treatment on the surface of the The expression for ω can be written as:
2): data-driven high-dimensional ellipsoid set construction:
based on MVEE data driving algorithm, a high-dimensional ellipsoid is constructed to wrap all historical scenes:
wherein: ρ is a constant representing N p Volume of unit sphere of dimension T; q is the deviation direction of the symmetry axis of the ellipsoid from the coordinate axis:
the above formula is solved by using a lift-and-project algorithm, and finally the expression of the high-dimensional ellipsoid is obtained as follows:
n described in the formula p T-dimensional ellipsoid uncertainty set together 2N p T vertices;
3): solving the model to obtain vertex coordinates of an ellipsoid set:
first, Q is orthogonalizedSolution: q=p T DP＝P -1 DP, noteP is a transformation matrix; in order to obtain the vertex corresponding to the high-dimensional ellipsoid, the ellipsoid is rotationally translated to enable the symmetry axis to coincide with the coordinate axis, and the rotation change equation is as follows:
ω′＝P×(ω-c)
wherein omega' is the coordinate value of the vertex after rotation; e' (. Cndot.) is a high-dimensional ellipsoidal expression obtained after rotation; omega e ′ ,1 ,…,ω e ′,N e The method comprises the steps of carrying out a first treatment on the surface of the The vertex coordinates of the rotated high-dimensional ellipsoid are obtained; n (N) e The number of vertexes;
obtaining the high-dimensional ellipsoid E vertex omega e,i Coordinates, thereby creating a data driven uncertainty set based on the ellipsoidal vertices.
5. The two-stage robust fault recovery method for the power distribution network based on toughness promotion according to claim 1, wherein in the step 3, the establishment of a two-stage robust optimization model is completed by taking the toughness index optimization as an objective function, and the solution of the established two-stage robust fault recovery model based on toughness promotion is completed by adopting an improved C & CG algorithm based on a limit scene;
the two-stage power distribution network fault recovery optimization model determines data including all load recovery states, line opening and closing states and pre-dispatching output values of the controllable distributed power supply in each period;
the fault recovery decision process of the power distribution network is divided into two stages:
the first stage, according to the predictive value of the distributed power supply of each period, deciding the pre-dispatching output value, load recovery state and line open-close state of each controllable distributed power supply; in order to reduce the line switch operation in the load recovery process of the power distribution network, the network topology is not changed once being determined at the beginning of the recovery process;
and in the second stage, the actual output value of the controllable distributed power supply is correspondingly adjusted according to the actual output value of the distributed power supply.
6. The two-stage robust fault recovery method for the power distribution network based on toughness promotion according to claim 1, wherein the construction of the two-stage robust fault recovery model is completed on the basis of the two-stage fault recovery model and the established ellipsoid uncertainty set, and the matrix is expressed as:
wherein h is a limit scene number; omega shape 1 、Ω 2 、Ω 3 The method comprises the steps of respectively obtaining a first stage decision variable set, a distributed power output uncertainty variable set and a second stage decision variable set; A. b is a coefficient matrix; x and y are the first stage and second stage decision variables, respectively;
the extremum in convex optimization can only be obtained at the vertex of the polyhedron space, so that the ultimate scene of robust optimization is positioned at the vertex of an ellipsoid;
for the determined first stage decision variable x, only the second stage decision variable y is adjusted to adapt to all limit scenes omega e,h Then the robustness of fault recovery can be ensured, and the improvement C based on the limit scene is adopted&The CG algorithm solves the two-stage data driving robust planning model;
the form of the improved C & CC algorithm sub-problem SP is:
in the method, in the process of the invention,the solution result of the main problem decision variable in the nth iteration is as follows:
the form of the main problem MP of the improved C & CG algorithm is:
wherein n is the current C&CG algorithm iteration number; η maximum running cost; w (w) h The method comprises the steps of selecting a limit scene for the h iteration;for extreme scene w h Lower run decision variables; />For extreme scene w h The variable is valued at the following uncertainty.
7. The two-stage robust fault recovery method for the power distribution network based on toughness promotion according to claim 1 is characterized in that the steps of the improved C & CG algorithm flow based on the limit scene method are as follows:
step 7-1: setting lower limit L B = - ≡, upper bound U B = + infinity of the two points, algorithm iteration number n=1;
step 7-2: solving the main problem to obtain an optimal solution of the main problemMaximum controllable distributed power supply output adjustment value +.>And update the lower bound->
Step 7-3: fixingSolving the sub-problem by enumerating limit scenes; if the sub-problem is solved, the maximum value f of the output adjustment value of the controllable distributed power supply is obtained SP And the corresponding worst limit scene h, updating the upper bound U B ＝min(U B ,f SP ) The method comprises the steps of carrying out a first treatment on the surface of the If the sub-problem has no feasible solution, selecting a limit scene h for enabling the sub-problem to have no solution as a worst scene;
step 4: if U B -L B If epsilon is less than epsilon, ending the iteration and outputting a main problem decisionOtherwise, adding the constraint corresponding to the worst limit scene h to the main problem, wherein n=n+1, and returning to the step 7-2.
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