CN111900722B - Construction method of bottom-preserving power grid backbone grid structure considering recovery capability - Google Patents

Construction method of bottom-preserving power grid backbone grid structure considering recovery capability Download PDF

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CN111900722B
CN111900722B CN202010637379.2A CN202010637379A CN111900722B CN 111900722 B CN111900722 B CN 111900722B CN 202010637379 A CN202010637379 A CN 202010637379A CN 111900722 B CN111900722 B CN 111900722B
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node
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CN111900722A (en
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赵洁
贾陈伊洋
张胜峰
刘涤尘
马宇辉
麻高源
方宇迪
何育钦
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Wuhan University WHU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract

The invention provides a construction method of a bottom-preserving power grid backbone grid structure considering recovery capacity. The invention divides a normal energy supply scene and a power failure recovery scene, and determines the initial conditions of each scene. Respectively defining a power supply capacity index, a safety margin index and a smooth power transmission index in a normal power supply scene, establishing a multi-objective optimization model of a backbone grid frame of a bottom-preserving power grid in the normal scene, and optimally solving fitness function values corresponding to the three indexes in the normal power supply scene by using a discrete particle swarm algorithm to obtain a Pareto non-dominated solution set in the normal scene; under the power failure recovery scene, defining a recovery success rate and a recovery time index; and establishing a network frame construction re-optimization model based on comprehensive recovery indexes in a power failure scene, and selecting an optimal bottom-preserving backbone network frame in the power failure scene from a Pareto non-dominated solution set in a normal scene. The invention can give consideration to the recovery time and the recovery success rate when the net rack is recovered in power failure, has the best comprehensive effect, effectively adjusts the optimal scheme and has strong practicability.

Description

Construction method of bottom-preserving power grid backbone grid structure considering recovery capability
Technical Field
The invention belongs to the technical field of power system planning, and particularly relates to a construction method of a bottom-preserving grid backbone grid structure considering recovery capacity.
Background
At present, the construction of a backbone grid frame of a bottom-protected power grid is an important issue in coastal typhoon-rich areas, ice-waterlogging areas and load-intensive areas, and is originally proposed by southern power grid companies in 2015, and the grid frame is formed by strengthening part of line nodes to guarantee the power supply and recovery of important loads. With the scale enlargement of a power grid, the complicated structure and frequent disasters, a blackout accident occurs, and once the bottom-protecting power grid backbone network can not successfully recover in a short time after the blackout, the huge influence on the social and economic stability can be generated; meanwhile, the bottom-protecting power grid backbone network frame only considers the units with high covering important loads and generating capacity in a normal scene, and time consumption is too much or even recovery failure is caused by complicated recovery steps in a power failure scene, so that the method for constructing the bottom-protecting power grid backbone network frame considering the recovery capacity is researched, and the method has important significance for reliably recovering the network frame in the power failure scene and reducing the power failure time of the important loads. Aiming at a backbone grid of a bottom-protecting power grid, two research directions mainly exist, firstly, the searching efficiency of a target grid in a large power grid is improved by an optimization solution algorithm, and therefore the calculation analysis time is reduced; secondly, by constructing a proper objective function, the method adapts to the trend of increasing the new energy proportion and enlarging the scale of the power grid, and researches focus on improving the new energy consumption, the important load proportion and the disaster resistance of the backbone grid frame of the bottom-preserving power grid and insufficient researches on the recovery capability of the bottom-preserving power grid.
In summary, optimization of the backbone grid of the bottom-protected power grid relates to energy supply to important loads in a normal scene and recovery capability in a power failure scene, and at present, in the grid optimization model at home and abroad, the power supply capability of the grid in the normal scene is improved mainly from important load coverage rate, new energy consumption and stable operation of the power grid to the goal, and the grid skeleton quality is biased. The study on the bottom-preserving performance of the net rack in the power failure scene is insufficient, the recovery indexes are analyzed only based on the load importance and the network structure, and the actual recovery steps and key factors such as black start power supply and equipment parameters influencing the recovery effect are not considered. According to the construction method of the bottom-preserving grid backbone network frame considering the recovery capability, on the basis of a normal scene optimization model, the recovery steps and key factors are analyzed, the network frame recovery time and the recovery success rate are quantized, the recovery indexes are increased, the conventional multi-target backbone network frame optimization obtaining scheme is optimized again, the recovery success rate of the network frame is improved, and the recovery time is shortened.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a construction method of a bottom-preserving grid backbone grid structure considering recovery capacity.
Step 1: dividing a normal energy supply scene and a power failure recovery scene, and setting initial conditions in the normal energy supply scene and the power failure recovery scene;
step 2: respectively defining a power supply capacity index, a safety margin index and a power transmission smoothness index in a normal power supply scene;
and step 3: according to the power supply capacity index, the safety margin index and the power transmission smoothness index, a multi-target optimization model of the backbone grid frame of the bottom-protected power grid under a normal scene is established, a discrete particle swarm algorithm is used for carrying out optimization solving on the fitness function values corresponding to the three indexes under the normal energy supply scene, and a Pareto non-dominated solution set under the normal scene of comprehensively considering the power supply capacity index, the safety margin index and the power transmission smoothness index is obtained;
and 4, step 4: under the power failure recovery scene, defining the recovery success rate and the recovery time;
and 5: establishing a comprehensive recovery index according to the recovery success rate and the recovery time, establishing a grid construction re-optimization model based on the recovery capacity in the power failure scene, and selecting an optimal bottom-preserving backbone grid in the power failure scene from a Pareto non-dominated solution set in the normal scene based on the comprehensive recovery index;
preferably, the initial condition in the normal energy supply scene in the step 1 is that each line and equipment in the net rack work normally, and the initial condition in the power failure recovery scene in the step 1 is that the net rack is completely black;
preferably, the power supply capacity indexes in the step 2 comprise important load storage rate and power supply storage rate in the backbone network frame of the bottom-guaranteed power grid;
the power supply capacity index f1Can be expressed as:
f1＝a1+β1a2
in the formula, a1The power conservation rate; a is2Important load retention rate; beta is a1To a significant load retention rate a2And (4) weighting.
a1、a2Standardized processing is carried out, and the standard processing is in the same order of magnitude; when beta is1When the load is more than 1, the important load is reserved by the grid frame in preference to the reserved power supply when the grid frame is selected; otherwise, the power source node is reserved preferentially. From the power balance, take beta here11 corresponds to the actual operating situation.
The power conservation rate is as follows:
Figure GDA0003339551890000021
in the formula, bgThe total number of the power generation nodes in the net rack;
Figure GDA0003339551890000022
the rated power generation amount of the kth power generation node in the net rack is obtained; n isgThe total number of the nodes of the power generation group in the net rack before reconstruction;
Figure GDA0003339551890000023
the rated power generation amount of the ith power generation node in the reconstructed front net rack is obtained;
the important load retention rate is as follows:
Figure GDA0003339551890000024
in the formula, blThe total number of the load nodes in the net rack;
Figure GDA0003339551890000025
the power consumption of the kth load node in the net rack; alpha is alphakSelecting the weight of the load node in the net rack based on the power consumer grade, thereby distinguishing the user importance grade; n islThe total number of load nodes in the net rack before reconstruction;
Figure GDA0003339551890000026
the rated power generation amount of the ith power generation node in the reconstructed front net rack is obtained;
step 2, the safety margin indexes comprise the average electric energy transmission distance and the transmission power margin of a line;
safety margin index f2Comprises the following steps:
f2＝s1+β2s2
in the formula, s1Is the node voltage margin; s2Is the power margin of the power generation node; beta is a2For the power margin s of the power generation node2And (4) weighting.
In the computing sectionDot voltage margin s1Power margin s of power generation node2Then, a standardization process is performed, s1And s2Are all in the same order of magnitude; when beta is2When the voltage is more than 1, the power margin of the node is ensured more importantly than the voltage margin of the node; otherwise, the voltage margin is more emphasized, beta2The selection can be carried out between 0.5 and 1.5 according to actual requirements;
the node voltage margin s1Comprises the following steps:
Figure GDA0003339551890000027
Figure GDA0003339551890000028
in the formula, b is the total number of nodes in the net rack;
Figure GDA0003339551890000029
the weight of the kth node in the net rack is determined by the active power injected into the node;
Figure GDA00033395518900000210
is the voltage margin of the kth node; u shapemax,kIs the allowable upper voltage limit of the kth node; u shapemin,kIs the allowable lower voltage limit of the kth node; u shapekNIs the rated voltage value of the kth node.
The power margin s of the power generation node2Comprises the following steps:
Figure GDA00033395518900000211
in the formula (I), the compound is shown in the specification,
Figure GDA00033395518900000212
the maximum active output of the ith power generation node in the net rack is obtained;
Figure GDA00033395518900000213
the rated power generation amount of the ith power generation node in the net rack is obtained; bgThe total number of the power generation nodes in the net rack.
Step 2, the unobstructed index of transmission of electricity, including power generation reserve, rack node voltage, the formula of calculating is as follows:
Figure GDA00033395518900000214
wherein:
Figure GDA0003339551890000031
in the formula, npathReserving the number of lines in the net rack;
Figure GDA0003339551890000032
the weight occupied by the kth line in the net rack is calculated;
Figure GDA0003339551890000033
the active transmission limit of the kth line in the net rack is set;
Figure GDA0003339551890000034
and transmitting active power for the kth line in the net rack in a normal power supply scene.
Preferably, the optimization model of the backbone grid structure of the bottom-preserving power grid in the normal scene in the step 3 is as follows:
Fnormal＝max(f1,f2,f3)
in the formula, FnormalThe optimal solution under the normal energy supply scene is obtained; f. of1Is a power supply capacity index; f. of2Is a safety margin index; f. of3Is the index of smooth transmission.
And 3, optimally solving the fitness function values corresponding to the three indexes in the normal energy supply scene by using a discrete particle swarm algorithm, wherein the fitness function values are:
step 3.1: initializing particle group X ═ X1,X2,…,Xn) Each individual in the population of particlesPosition coordinate is Xi＝(xi1,xi2,…,xid) Dimension d is equal to the number of branches of the original net rack, and in the discrete particle swarm algorithm, x is one dimension of all particle position variablesikIs limited to 0 or 1;
step 3.2: the velocity and position of the particles are updated as follows:
Figure GDA0003339551890000035
Figure GDA0003339551890000036
in the formula, k is iteration times; flight velocity V of particle ii(vi1,…,vid)；
Particle i is currently found with the most preferred position Pi(pi1,pi2,…,pid)；Pg(pg1,pg2,…,pgd) The optimal position currently found by the particle group is obtained; w is an inertia coefficient, and the value range is more than 0.4 and less than 1.4; c. C1、c2For learning factors, the value is typically taken as c1＝c2When the value of the learning factor is too small, the particles are easy to be far away from the target area, and when the value of the learning factor is too large, the particles are likely to fly through the target area; r is1And r2Is [0,1 ]]Two random numbers over the interval;
step 3.3: and carrying out validity detection on the updated particles. Since this is a graph theory problem, the connectivity of the set of nodes and branches corresponding to the particle position must be determined. If the particles are communicated, the particles are effective particles, and the step 3.4 is carried out; if not, the particles are invalid, the step 3.2 is returned to modify the invalid particles and then the subsequent steps are carried out;
step 3.4: determining branches and node sets according to the particle positions so as to determine a grid structure, performing load flow calculation to obtain node voltage and load flow distribution, judging whether constraint conditions of safe and stable operation of the power system are met, and if the constraint conditions are met, entering the step 3.5; otherwise, returning to the step 3.2 to regenerate new particles;
step 3.5: according to the load flow calculation result and the basic data, the related index f-f of the optimization objective function under the normal energy supply scene1+f2+f3Depicting the fitness so as to update the optimal positions of the particles and the optimal positions of the particle swarms;
step 3.6: if the iteration times are reached, the iteration is terminated, and a Pareto non-dominated solution set X obtained by optimizing a network frame under a normal scene is output (X)1,X2,…,Xn) Solution centralization of each element Xi＝(xi1,xi2,…,xid) In xikWhen the value of (1) is corresponding to the circuit reservation, and when the value of (0) is not reserved, a corresponding grid structure is obtained, and the power supply capacity index, the safety margin index and the power transmission smoothness index are calculated according to the grid structure, and all X are calculatedi＝(xi1,xi2,…,xid) According to the power supply capacity index, the safety margin index and the power transmission smoothness index, establishing a three-dimensional coordinate to define a Pareto non-dominated solution set; if the iteration times are not reached, skipping to the step 3.2 to continuously execute the particle updating;
preferably, the considered index for optimizing the backbone network frame recovery in the step 4 comprises a recovery success rate and recovery consumption time;
and step 4, the recovery success rate is as follows:
Figure GDA0003339551890000037
in the formula (f)ableIn order to recover the success rate, since the plurality of units are respectively started through a plurality of paths, and the recovery success requires all the paths and the unit starting success, fableThe recovery success rate of the path which is the most difficult to recover in the path complete set phi is obtained; l isiAnd the ith generator set to be recovered is the optimal recovery path.
The line index WLi
Figure GDA0003339551890000041
In the formula, XCjIs a path LiThe equivalent capacitive reactance of the middle branch j can cause line overvoltage and self-excitation of a generator set when an air-load line is charged, and the voltage multiple and the self-excitation are mainly influenced by the line capacitive reactance; xCmaxThe maximum capacitive reactance value in all lines; l isiThe ith generator set to be recovered has the optimal recovery path; n is the number of branches included in the path.
The transformer index
Figure GDA0003339551890000042
Figure GDA0003339551890000043
In the formula, phisatk、φresk、φsskAre respectively a transformer TkSaturation flux, residual flux and steady state flux.
And step 4, the recovery time is as follows:
T＝T1+T2
in the formula, T1The time required for the first phase to resume; t is2Time required to restore the second stage;
T1the time required to restore the first phase is mainly determined by the time to start the unit. Because a plurality of machine sets are respectively started through a plurality of paths, the time consumed for recovering the longest time-consuming path in the path selection path set phi is T1The value of (c):
Figure GDA0003339551890000044
in the formula, LiStarting a path which is passed by other units by the black start unit; phi is a path L involved in starting all unitsiA set of (a);
Figure GDA0003339551890000045
is a path LiThe charging time of the j line;
Figure GDA0003339551890000046
is a path LiThe contained kth power station is time-consuming to start; t is tblackThe time consumed for starting the black start unit is shortened;
Figure GDA0003339551890000047
in the formula, T2The time required for recovering the second stage is mainly determined by the time for recovering the residual nodes; l ismaxConnecting the longest path for the unrecovered node and the restored node;
Figure GDA0003339551890000048
the gradient rate of the kth power generation node is set; m is the total number of all starting power generation nodes in the net rack;
Figure GDA0003339551890000049
is a path LiThe charging time of the j line;
Figure GDA00033395518900000410
the rated power generation amount of the kth power generation node in the net rack is obtained;
preferably, the comprehensive recovery index f in step 5recCan be expressed as:
frec＝fable-β3T
wherein T is recovery time; f. ofableTo restore success rate; beta is a3For the total recovery time Tweight, weight β3The value can be taken according to the operation experience;
step 5, under the power failure scene, the net rack construction re-optimization model based on the recovery capability is as follows:
setting the Pareto non-dominated solution set X under a normal scene as (X)1,X2,…,Xn) And optimizing under a power failure recovery scene by calculating the comprehensive recovery indexes of the grid structure corresponding to each solution, wherein the objective function is as follows:
Fblack＝minfrec
in the formula, FblackThe optimal solution is obtained in the power failure scene; f. ofrecIs a comprehensive recovery index.
And 5, optimizing and solving the recovery time by using a Dijkstra algorithm, wherein the recovery success rate indexes are as follows:
searching the path with the highest recovery success rate and the path with the longest recovery time by improving the Dijkstra algorithm, wherein the line length is selected as follows:
Figure GDA00033395518900000411
in the formula, qiIs the equivalent length of line i; xCjIs a path LiThe equivalent capacitive reactance of the middle branch j; xCmaxThe maximum capacitive reactance value among all lines. On the basis, the Dijkstra algorithm obtains that the farthest path between the node where the black start power supply is located and the unit node to be recovered is the path with the highest recovery success rate;
the flow of solving the optimal recovery scheme under the power failure scene by adopting the Dijkstra algorithm comprises the following steps:
step 5.1, extracting Pareto non-dominated solution set X ═ X (X) in normal scene1,X2,…,Xn) Any one of the elements Xi＝(xi1,xi2,…,xid) According to xikThe principle that the value of (1) is reserved corresponding to the line and is not reserved when the value of (0) is adopted to obtain a corresponding net rack network topological graph, and the transformer indexes W at the two ends of the line are usedTiLogarithm of (d) and the per unit capacitive reactance value of the line itself
Figure GDA0003339551890000051
Assigning the sum of logarithms as the line length:
Figure GDA0003339551890000052
then using Dijkstra algorithm to obtain shortest path, according to the path calculating fableAnd T1。fableFor the recovery success rate, T, of the most difficult path in the path corpus phi1The time required for the first stage to resume.
Step 5.2, confirming the nodes and lines related to the optimal path, equivalently setting the nodes and lines as initial nodes, assigning the sum of the recovery time of the lines and the equipment at the two ends of the lines as the line length, calculating the farthest path by using a Dijkstra algorithm, and calculating T2。T2The time required to restore the second stage is mainly determined by the time of restoring the remaining nodes.
Step 5.3, calculating the comprehensive recovery index f of the net rackrecComparing the comprehensive recovery index with the net rack comprehensive recovery index which is searched and calculated, and if the comprehensive recovery index f of the net rack is the net rack comprehensive recovery index frecIf the optimal solution is larger than the optimal solution, the optimal solution is updated to X corresponding to the current net racki＝(xi1,xi2,…,xid) And smaller, no update. Judging whether all net racks in the Pareto non-dominated solution set are analyzed, and if so, outputting an optimal net rack structure; otherwise, jumping to step 5.1 and continuing searching.
In summary, the construction method of the bottom-preserving grid backbone network frame considering the restoration capability of the invention constructs an optimization model under a three-target normal scene with power supply capability, safety margin and smoothness of power transmission based on electrical parameters reflecting the guarantee capability of the network frame to important loads, analyzes factors influencing the network frame restoration under a power failure scene, quantificationally obtains restoration indexes and optimizes the restoration indexes, forms the construction method of the bottom-preserving grid backbone network frame considering the restoration capability, can be used for a core backbone network frame construction strategy of the bottom-preserving grid, optimizes a network frame unit and a load node restoration path, enables the comprehensive effect of the network frame considering the restoration time and the restoration success rate to be the best and effectively adjusts the optimal scheme, and has strong practicability.
Drawings
Fig. 1 is a framework for constructing a backbone grid of a guaranteed-base power grid with recovery capability taken into consideration.
Fig. 2 shows different scenario consideration indicators.
Fig. 3 is a process of an algorithm for optimizing the backbone network frame of the bottom-protected power grid in a normal power supply scene.
Fig. 4 is a multipath schematic of a unit to be started and a black start power supply.
FIG. 5 is an equivalent node of a recovered node and line set.
FIG. 6 is a Pareto solution set by the conventional method.
Fig. 7 is a backbone grid structure corresponding to Pareto solution set.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. In addition, the technical features mentioned in the embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
The following is a preferred embodiment of the present invention and further illustrates the specific application of the present invention in conjunction with fig. 1-7.
The specific implementation mode of the invention is a construction method of a bottom-preserving grid backbone grid structure considering recovery capacity, which specifically comprises the following steps:
step 1: dividing a normal energy supply scene and a power failure recovery scene, and setting initial conditions in the normal energy supply scene and the power failure recovery scene;
1, under the normal energy supply scene, the initial condition is that each line and equipment in the net rack work normally, and under the power failure recovery scene, the initial condition is that the net rack is completely black;
step 2: respectively defining a power supply capacity index, a safety margin index and a power transmission smoothness index in a normal power supply scene;
step 2, the power supply capacity indexes comprise important load storage rate and power supply storage rate in a backbone network frame of a bottom-preserving power grid, which are reflected in that the backbone network frame ensures important load requirements, so that the network frame selects an accessed load according to the load capacity and the important grade of a user, and meanwhile, enough energy supply of a unit is required to be reserved for ensuring the balance of electric power and electric quantity;
the power supply capacity index f1Can be expressed as:
f1＝a1+β1a2
in the formula, a1The power conservation rate; a is2Important load retention rate; beta is a1To a significant load retention rate a2And (4) weighting.
a1、a2Standardized processing is carried out, and the standard processing is in the same order of magnitude; when beta is1When the load is more than 1, the important load is reserved by the grid frame in preference to the reserved power supply when the grid frame is selected; otherwise, the power source node is reserved preferentially. From the power balance, take beta here11 corresponds to the actual operating situation.
The power conservation rate is as follows:
Figure GDA0003339551890000061
in the formula, bgThe total number of the power generation nodes in the net rack;
Figure GDA0003339551890000062
the rated power generation amount of the kth power generation node in the net rack is obtained; n isgThe total number of the nodes of the power generation group in the net rack before reconstruction;
Figure GDA0003339551890000063
the rated power generation amount of the ith power generation node in the reconstructed front net rack is obtained;
the important load retention rate is as follows:
Figure GDA0003339551890000064
in the formula, blThe total number of the load nodes in the net rack;
Figure GDA0003339551890000065
the power consumption of the kth load node in the net rack; alpha is alphakSelecting the weight of the load node in the net rack based on the power consumer grade, thereby distinguishing the user importance grade; n islThe total number of load nodes in the net rack before reconstruction;
Figure GDA0003339551890000066
the rated power generation amount of the ith power generation node in the reconstructed front net rack is obtained;
2, the safety margin indexes comprise the average electric energy transmission distance and the transmission power margin of a line, reflect the reliability of the backbone network frame of the bottom-protection power grid during operation, quantize the reliability into the relative margin between the electric quantity and the limit operation state, which meets the requirement that the backbone network frame can stably operate for a period of time, and when the active power in the network frame is sufficient and the reactive power is sufficient, the system has stronger capability of dealing with sudden small disturbance, so the safety margin is quantized into the margin between the electric quantity and the limit operation state;
safety margin index f2Comprises the following steps:
f2＝s1+β2s2
in the formula, s1Is the node voltage margin; s2Is the power margin of the power generation node; beta is a2For the power margin s of the power generation node2And (4) weighting.
At the calculation node voltage margin s1Power margin s of power generation node2Then, a standardization process is performed, s1And s2Are all in the same order of magnitude; when beta is2When the voltage is more than 1, the power margin of the node is ensured more importantly than the voltage margin of the node; otherwise, the voltage margin is more emphasized, beta2The selection can be carried out between 0.5 and 1.5 according to actual requirements;
the node voltage margin s1Comprises the following steps:
Figure GDA0003339551890000067
Figure GDA0003339551890000068
in the formula, b is the total number of nodes in the net rack;
Figure GDA0003339551890000069
is a netThe weight of the kth node in the rack is determined by the active power injected into the node;
Figure GDA00033395518900000610
is the voltage margin of the kth node; u shapemax,kIs the allowable upper voltage limit of the kth node; u shapemin,kIs the allowable lower voltage limit of the kth node; u shapekNIs the rated voltage value of the kth node.
The power margin s of the power generation node2Comprises the following steps:
Figure GDA0003339551890000071
in the formula (I), the compound is shown in the specification,
Figure GDA0003339551890000072
the maximum active output of the ith power generation node in the net rack is obtained;
Figure GDA0003339551890000073
the rated power generation amount of the ith power generation node in the net rack is obtained; bgThe total number of the power generation nodes in the net rack.
And 2, the transmission smoothness index comprises power supply generation standby and grid node voltage, the margin between the backbone grid line and the transmission power upper limit is reflected, a large amount of loads in the grid are reserved, the backbone grid line is reversely and greatly reduced, the line burden is increased, and the tidal current is out of limit and transmission is blocked under extreme conditions. The transmission smoothness index reflects the margin of transmission active power on each transmission path when the backbone network frame operates, and the calculation formula is as follows:
Figure GDA0003339551890000074
wherein:
Figure GDA0003339551890000075
in the formula, npathReserving the number of lines in the net rack;
Figure GDA0003339551890000076
the weight occupied by the kth line in the net rack is calculated;
Figure GDA0003339551890000077
the active transmission limit of the kth line in the net rack is set;
Figure GDA0003339551890000078
and transmitting active power for the kth line in the net rack in a normal power supply scene.
And step 3: according to the power supply capacity index, the safety margin index and the power transmission smoothness index, a multi-target optimization model of the backbone grid frame of the bottom-protected power grid under a normal scene is established, a discrete particle swarm algorithm is used for carrying out optimization solving on the fitness function values corresponding to the three indexes under the normal energy supply scene, and a Pareto non-dominated solution set under the normal scene of comprehensively considering the power supply capacity index, the safety margin index and the power transmission smoothness index is obtained;
and 3, the bottom-preserving power grid backbone grid frame optimization model in the normal scene is as follows:
Fnormal＝max(f1,f2,f3)
in the formula, FnormalThe optimal solution under the normal energy supply scene is obtained; f. of1Is a power supply capacity index; f. of2Is a safety margin index; f. of3Is the index of smooth transmission.
The method comprises the following steps that (1) bottom-guaranteed power grid backbone network frame optimization in a normal energy supply scene is a multi-objective optimization problem, and a discrete particle swarm algorithm with strong global convergence capacity and good robustness is adopted to solve a model in a normal scene;
and 3, optimally solving the fitness function values corresponding to the three indexes in the normal energy supply scene by using a discrete particle swarm algorithm, wherein the fitness function values are:
step 3.1: initializing particle group X ═ X1,X2,…,Xn) Each individual position in the particle swarm having a coordinate of Xi＝(xi1,xi2,…,xid) Dimension d is equal to the number of branches of the original net rack, and in the discrete particle swarm algorithm, x is one dimension of all particle position variablesikIs limited to 0 or 1;
step 3.2: the velocity and position of the particles are updated as follows:
Figure GDA0003339551890000079
Figure GDA00033395518900000710
in the formula, k is iteration times; flight velocity V of particle ii(vi1,…,vid)；
Particle i is currently found with the most preferred position Pi(pi1,pi2,…,pid)；Pg(pg1,pg2,…,pgd) The optimal position currently found by the particle group is obtained; w is an inertia coefficient, and the value range is more than 0.4 and less than 1.4; c. C1、c2For learning factors, the value is typically taken as c1＝c2When the value of the learning factor is too small, the particles are easy to be far away from the target area, and when the value of the learning factor is too large, the particles are likely to fly through the target area; r is1And r2Is [0,1 ]]Two random numbers over the interval;
step 3.3: and carrying out validity detection on the updated particles. Since this is a graph theory problem, the connectivity of the set of nodes and branches corresponding to the particle position must be determined. If the particles are communicated, the particles are effective particles, and the step 3.4 is carried out; if not, the particles are invalid, the step 3.2 is returned to modify the invalid particles and then the subsequent steps are carried out;
step 3.4: determining branches and node sets according to the particle positions so as to determine a grid structure, performing load flow calculation to obtain node voltage and load flow distribution, judging whether constraint conditions of safe and stable operation of the power system are met, and if the constraint conditions are met, entering the step 3.5; otherwise, returning to the step 3.2 to regenerate new particles;
step 3.5: according to the load flow calculation result and the basic data, the related index f-f of the optimization objective function under the normal energy supply scene1+f2+f3Depicting the fitness so as to update the optimal positions of the particles and the optimal positions of the particle swarms;
step 3.6: if the iteration times are reached, the iteration is terminated, and a Pareto non-dominated solution set X obtained by optimizing a network frame under a normal scene is output (X)1,X2,…,Xn) Solution centralization of each element Xi＝(xi1,xi2,…,xid) In xikWhen the value of (1) is corresponding to the circuit reservation, and when the value of (0) is not reserved, a corresponding grid structure is obtained, and the power supply capacity index, the safety margin index and the power transmission smoothness index are calculated according to the grid structure, and all X are calculatedi＝(xi1,xi2,…,xid) According to the power supply capacity index, the safety margin index and the power transmission smoothness index, establishing a three-dimensional coordinate to define a Pareto non-dominated solution set; if the iteration times are not reached, skipping to the step 3.2 to continuously execute the particle updating;
and 4, step 4: and under the power failure recovery scene, defining the recovery success rate and the recovery time.
The considered index for optimizing the recovery of the backbone network frame in the step 4 comprises a recovery success rate and recovery consumption time, namely: under the power failure scene, the reliability and the recovery time of the backbone network frame are essentially determined by the network frame topology structure and the positions of all units in the network frame topology, and the appropriate core backbone network frame structure can enable the black start power supply to recover the station power of a power plant through fewer lines and equipment, so that the recovery success rate is higher under the condition that the start success rate of each piece of equipment is not much different;
and step 4, the recovery success rate is as follows:
Figure GDA0003339551890000081
in the formula (f)ableIn order to recover the success rate, all paths and machines are needed for the successful recovery because a plurality of machine sets are respectively started through a plurality of pathsSuccessful set start-up, soableThe recovery success rate of the path which is the most difficult to recover in the path complete set phi is obtained; l isiAnd the ith generator set to be recovered is the optimal recovery path.
The line index WLi
Figure GDA0003339551890000082
In the formula, XCjIs a path LiThe equivalent capacitive reactance of the middle branch j can cause line overvoltage and self-excitation of a generator set when an air-load line is charged, and the voltage multiple and the self-excitation are mainly influenced by the line capacitive reactance; xCmaxThe maximum capacitive reactance value in all lines; l isiThe ith generator set to be recovered has the optimal recovery path; n is the number of branches included in the path.
The transformer index
Figure GDA0003339551890000087
Figure GDA0003339551890000083
In the formula, phisatk、φresk、φsskAre respectively a transformer TkSaturation flux, residual flux and steady state flux.
And step 4, the recovery time is as follows:
T＝T1+T2
in the formula, T1The time required for the first phase to resume; t is2Time required to restore the second stage;
T1the time required to restore the first phase is mainly determined by the time to start the unit. Because a plurality of machine sets are respectively started through a plurality of paths, the time consumed for recovering the longest time-consuming path in the path selection path set phi is T1The value of (c):
Figure GDA0003339551890000084
in the formula, LiStarting a path which is passed by other units by the black start unit; phi is a path L involved in starting all unitsiA set of (a);
Figure GDA0003339551890000085
is a path LiThe charging time of the j line;
Figure GDA0003339551890000086
is a path LiThe contained kth power station is time-consuming to start; t is tblackThe time consumed for starting the black start unit is shortened;
Figure GDA0003339551890000091
in the formula, T2The time required for recovering the second stage is mainly determined by the time for recovering the residual nodes; l ismaxConnecting the longest path for the unrecovered node and the restored node;
Figure GDA0003339551890000092
the gradient rate of the kth power generation node is set; m is the total number of all starting power generation nodes in the net rack;
Figure GDA0003339551890000093
is a path LiThe charging time of the j line;
Figure GDA0003339551890000094
the rated power generation amount of the kth power generation node in the net rack is obtained;
and 5: establishing a comprehensive recovery index according to the recovery success rate and the recovery time, establishing a grid construction re-optimization model based on the recovery capacity in the power failure scene, and selecting an optimal bottom-preserving backbone grid in the power failure scene from a Pareto non-dominated solution set in the normal scene based on the comprehensive recovery index;
step 5 the comprehensive recovery index frecCan be expressed as：
frec＝fable-β3T
Wherein T is recovery time; f. ofableTo restore success rate; beta is a3For the total recovery time Tweight, weight β3The value can be taken according to the operation experience;
step 5, under the power failure scene, the net rack construction re-optimization model based on the recovery capability is as follows:
setting the Pareto non-dominated solution set X under a normal scene as (X)1,X2,…,Xn) And optimizing under a power failure recovery scene by calculating the comprehensive recovery indexes of the grid structure corresponding to each solution, wherein the objective function is as follows:
Fblack＝minfrec
in the formula, FblackThe optimal solution is obtained in the power failure scene; f. ofrecIs a comprehensive recovery index.
And 5, optimizing and solving the recovery time by using a Dijkstra algorithm, wherein the recovery success rate indexes are as follows:
under the condition that the positions of the black start unit and the started unit in the net racks are determined, a plurality of paths may be connected, so that when an objective function under a power failure scene is calculated, except for searching the path with the longest recovery time, each net rack searching unit in a Pareto non-dominated solution set under a normal scene recovers the path with the highest success rate;
searching a path with the highest recovery success rate and a path with the longest recovery time through an improved Dijkstra algorithm; when searching for the path with the highest recovery success rate, the Dijkstra algorithm adds the lengths of the lines between the line nodes when calculating the distance, and the recovery success rate index is multiplied, so that a logarithm method is adopted to multiply the lengths into a sum, namely the line lengths are selected as:
Figure GDA0003339551890000095
in the formula, qiIs the equivalent length of line i; xCjIs a path LiThe equivalent capacitive reactance of the middle branch j; xCmaxThe maximum capacitive reactance value among all lines. On the basis, the Dijkstra algorithm obtains that the farthest path between the node where the black start power supply is located and the unit node to be recovered is the path with the highest recovery success rate;
the flow of solving the optimal recovery scheme under the power failure scene by adopting the Dijkstra algorithm comprises the following steps:
step 5.1, extracting Pareto non-dominated solution set X ═ X (X) in normal scene1,X2,…,Xn) Any one of the elements Xi＝(xi1,xi2,…,xid) According to xikThe principle that the value of (1) is reserved corresponding to the line and is not reserved when the value of (0) is adopted to obtain a corresponding net rack network topological graph, and the transformer indexes W at the two ends of the line are usedTiLogarithm of (d) and the per unit capacitive reactance value of the line itself
Figure GDA0003339551890000096
Assigning the sum of logarithms as the line length:
Figure GDA0003339551890000097
then using Dijkstra algorithm to obtain shortest path, according to the path calculating fableAnd T1。fableFor the recovery success rate, T, of the most difficult path in the path corpus phi1The time required for the first stage to resume.
Step 5.2, confirming the nodes and lines related to the optimal path, equivalently setting the nodes and lines as initial nodes, assigning the sum of the recovery time of the lines and the equipment at the two ends of the lines as the line length, calculating the farthest path by using a Dijkstra algorithm, and calculating T2。T2The time required to restore the second stage is mainly determined by the time of restoring the remaining nodes.
Step 5.3, calculating the comprehensive recovery index f of the net rackrecComparing the comprehensive recovery index with the net rack comprehensive recovery index which is searched and calculated, and if the comprehensive recovery index f of the net rack is the net rack comprehensive recovery index frecIf the optimal solution is larger than the optimal solution, the optimal solution is updated to X corresponding to the current net racki＝(xi1,xi2,…,xid) And smaller, no update. Judging whether all net racks in the Pareto non-dominated solution set are analyzed, and if so, outputting an optimal net rack structure; otherwise, jumping to step 5.1 and continuing searching.
Setting parameters of a discrete particle swarm algorithm as follows: the number of particles 20, the number of iterations 100, the inertia coefficient and the learning factor are respectively set as w to 1.2, c1＝2，c2And (2) nesting the load flow calculation in a loop by adopting a PQ method, and obtaining three optimal schemes of the multi-target optimization model after simulation calculation for 328.4s, namely about 5 minutes, wherein the timeliness is basically guaranteed when the method is applied to small node system reconstruction. The non-dominated solution set is shown in fig. 6, and the grid structure is shown in fig. 7.
In the three schemes, the power supply capacity of the first scheme is the highest, and the corresponding safety margin and smooth power transmission are relatively low; the safety margin of the second scheme is the highest, the power transmission is smooth, and the power supply capacity is relatively low; the third scheme has the highest smooth transmission, and the corresponding power supply capacity and safety margin are relatively low; only considering power supply capacity, power transmission smoothness and safety margin under normal conditions, the scheme I, the scheme II and the scheme III are not mutually independent, the optimal scheme cannot be determined, and the recovery capacity of the backbone network frame of the bottom-guaranteed power grid is not reflected and considered.
And searching and optimizing the solution set again by using Dijkstra algorithm on the basis of the pareto non-dominated net rack set obtained by searching in the normal scene in the power failure scene. Recovery time weight value beta3And (4) calculating the recovery index of each alternative scheme, wherein the highest recovery index is the optimal scheme, and comparing the optimal scheme with the optimization method only considering the normal scene.
The optimal scheme obtained by the construction method of the bottom-preserving grid backbone network frame considering the recovery capacity is scheme 2, and the method is analyzed and known as follows: f of scheme 1ableThe time is 0.315, T is 116 minutes, the net rack recovery success rate is relatively low, and meanwhile, the recovery time is long; the reason is that the power supply capacity is outstanding, more load nodes and units are reserved, so that the 22 # unit needs to be recovered through a long path such as 1-3-4-12-16-17-10-20-19-18-15-23-24-22, more lines and transformers are involved, and the starting caused by the occurrence of excitation inrush current and line overvoltage is increasedAnd the risk of failure and excessive nodes to be recovered require a plurality of lines to recover the node 21, so that the recovery speed is greatly delayed. The inverse scheme 2 reduces part of generator sets, load nodes and power supply capacity f1Compared with the scheme 1, the method reduces the rate by 15.5 percent, but no unit can be started by excessive lines and equipment, and the success rate f of recovery is increasedableThe improvement is 24.4%.
In summary, considering the power failure scene compared with only considering the normal scene, the recovery capability difference between different grid structures is reflected quantitatively, and meanwhile, the loads and the units reserved in the grid can be recovered by the black-start power supply through a path with higher reliability and shorter time consumption, so that the constructed bottom-protection power grid backbone network has good recovery capability on the basis of smooth power supply capability, safety margin and power transmission.
The embodiment verifies the effectiveness of the provided construction method of the backbone grid structure of the bottom-preserving power grid considering the recovery capability.
The present invention has been described in terms of specific examples, which are provided to aid understanding of the invention and are not intended to be limiting. For a person skilled in the art to which the invention pertains, several simple deductions, modifications or substitutions may be made according to the idea of the invention. It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of this invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of this invention should be included within the scope of protection of this invention.

Claims (1)

1. A construction method of a bottom-preserving grid backbone net rack considering recovery capacity is characterized by comprising the following steps:
step 1: dividing a normal energy supply scene and a power failure recovery scene, and setting initial conditions in the normal energy supply scene and the power failure recovery scene;
step 2: respectively defining a power supply capacity index, a safety margin index and a power transmission smoothness index in a normal power supply scene;
and step 3: according to the power supply capacity index, the safety margin index and the smooth power transmission index, a multi-target optimization model of the backbone network frame of the bottom-preserving power grid under a normal power supply scene is established, a discrete particle swarm algorithm is used for carrying out optimization solution on the fitness function values corresponding to the three indexes under the normal power supply scene, and a Pareto non-dominated solution set under the normal power supply scene is obtained, wherein the power supply capacity index, the safety margin index and the smooth power transmission index are comprehensively considered;
and 4, step 4: under the power failure recovery scene, defining the recovery success rate and the recovery time, and constructing a consideration index for optimizing the recovery of the backbone network frame;
and 5: building a comprehensive recovery index according to the recovery success rate and the recovery time, building a grid construction re-optimization model based on recovery capacity in a power failure recovery scene, and selecting an optimal bottom-preserving power grid backbone grid under the power failure recovery scene from a Pareto non-dominated solution set under a normal energy supply scene based on the comprehensive recovery index;
1, under the normal energy supply scene, the initial condition is that each line and equipment in the net rack work normally, and under the power failure recovery scene, the initial condition is that the net rack is completely black;
step 2, the power supply capacity indexes comprise important load storage rate and power supply storage rate in the backbone network frame of the bottom-protected power grid;
the power supply capacity index f1Can be expressed as:
f1＝a1+β1a2
in the formula, a1The power conservation rate; a is2Important load retention rate; beta is a1To a significant load retention rate a2A weight;
a1、a2standardized processing is carried out, and the standard processing is in the same order of magnitude; when beta is1When the load is more than 1, the important load is reserved by the grid frame in preference to the reserved power supply when the grid frame is selected; otherwise, the power supply node is reserved preferentially; from the power balance, take beta here11 conforms to the actual operation condition;
the power conservation rate is as follows:
Figure FDA0003487008680000011
in the formula, bgThe total number of the power generation nodes in the net rack;
Figure FDA0003487008680000012
the rated power generation amount of the kth power generation node in the net rack is obtained; n isgThe total number of the power generation nodes in the net rack before reconstruction;
Figure FDA0003487008680000013
the rated power generation amount of the ith power generation node in the reconstructed front net rack is obtained;
the important load retention rate is as follows:
Figure FDA0003487008680000014
in the formula, blThe total number of the load nodes in the net rack;
Figure FDA0003487008680000015
the power consumption of the kth load node in the net rack; alpha is alphakSelecting the weight of the load node in the net rack based on the power consumer grade, thereby distinguishing the user importance grade; n islThe total number of load nodes in the net rack before reconstruction;
Figure FDA0003487008680000016
the power consumption of the ith load node in the pre-reconstructed net rack is used;
step 2, the safety margin indexes comprise a node voltage margin and a power generation node power margin;
safety margin index f2Comprises the following steps:
f2＝s1+β2s2
in the formula, s1Is the node voltage margin; s2Is the power margin of the power generation node; beta is a2For the power margin s of the power generation node2A weight;
in the calculation ofNode voltage margin s1Power margin s of power generation node2Then, a standardization process is performed, s1And s2Are all in the same order of magnitude; when beta is2When the voltage is more than 1, the power margin of the power generation node is ensured more importantly than the voltage margin of the node; otherwise, the node voltage margin is ensured more importantly2Selecting between 0.5 and 1.5 according to actual requirements;
the node voltage margin s1Comprises the following steps:
Figure FDA0003487008680000017
Figure FDA0003487008680000021
in the formula, b is the total number of nodes in the net rack;
Figure FDA0003487008680000022
the weight of the kth node in the net rack is determined by the active power injected into the node
Figure FDA0003487008680000023
Is the voltage margin of the kth node; u shapekIs the voltage value of the kth node; u shapemax,kIs the allowable upper voltage limit of the kth node; u shapemin,kIs the allowable lower voltage limit of the kth node; u shapekNIs the rated voltage value of the kth node;
the power margin s of the power generation node2Comprises the following steps:
Figure FDA0003487008680000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003487008680000025
the maximum active output of the ith power generation node in the net rack is obtained;
Figure FDA0003487008680000026
the rated power generation amount of the ith power generation node in the net rack is obtained; bgThe total number of the power generation nodes in the net rack;
step 2 the transmission smoothness index f3Comprises the following steps:
Figure FDA0003487008680000027
wherein:
Figure FDA0003487008680000028
in the formula, npathReserving the number of lines in the net rack;
Figure FDA0003487008680000029
the weight occupied by the kth line in the net rack is calculated;
Figure FDA00034870086800000210
the active transmission limit of the kth line in the net rack is set;
Figure FDA00034870086800000211
active power is transmitted to the kth line in the net rack under the normal energy supply scene;
and 3, under the normal energy supply scene, the multi-objective optimization model of the backbone network frame of the bottom-preserving power grid is as follows:
Fnormal＝max(f1,f2,f3)
in the formula, FnormalThe optimal solution under the normal energy supply scene is obtained; f. of1Is a power supply capacity index; f. of2Is a safety margin index; f. of3Is the smooth index of power transmission;
and 3, optimally solving the fitness function values corresponding to the three indexes in the normal energy supply scene by using a discrete particle swarm algorithm, wherein the fitness function values are:
step 3.1: initializing particle group X ═ X1,X2,…,Xn) Each individual position in the particle swarm having a coordinate of Xi＝(xi1,xi2,…,xid) Dimension d is equal to the number of branches of the original net rack, and in the discrete particle swarm algorithm, x is one dimension of all particle position variablesikIs limited to 0 or 1;
step 3.2: defining the flight velocity V of a particle ii＝(vi1，...，vid)；
The current individual historical optimal position of the particle i is Pi＝(pi1，...pid)；
Pg＝(pg1，..，pgd) The historical optimal position of the currently found population of the particle population is obtained;
the velocity and position of the particles are updated as follows:
Figure FDA00034870086800000212
Figure FDA00034870086800000213
in the formula, k is iteration times; w is an inertia coefficient, w is more than 0.4 and less than 1.4; c. C1、c2C, taking c, wherein if the value of the learning factor is too small, the particles are easy to be far away from the target area, if the value of the learning factor is too large, the particles are likely to fly through the target area1＝c2＝2.0；r1And r2Is [0,1 ]]Two random numbers over the interval;
step 3.3: carrying out validity detection on the updated particles; because this is a graph theory problem, the connectivity of the branch and node set corresponding to the particle position must be judged; if the particles are communicated, the particles are effective particles, and the step 3.4 is carried out; if not, the particles are invalid, the step 3.2 is returned to modify the invalid particles and then the subsequent steps are carried out;
step 3.4: determining branches and node sets according to the particle positions so as to determine a grid structure, performing load flow calculation to obtain node voltage and load flow distribution, judging whether constraint conditions of safe and stable operation of the power system are met, and entering step 3.5 if the constraint conditions are met; otherwise, returning to the step 3.2 to regenerate new particles;
step 3.5: according to the load flow calculation result and the basic data, the related index f-f of the optimization objective function under the normal energy supply scene1+f2+f3Depicting the fitness so as to update the optimal positions of the particles and the optimal positions of the particle swarms;
wherein f is1As a power supply capability index, f2As an index of safety margin, f3Is the smooth index of power transmission;
step 3.6: if the iteration times are reached, the iteration is terminated, and a Pareto non-dominated solution set X (X) obtained by optimizing a network frame under a normal energy supply scene is output1,X2,…,Xn) Solution centralization of each element Xi＝(xi1,xi2,…,xid) In xikWhen the value of (1) is corresponding to the circuit reservation, and when the value of (0) is not reserved, a corresponding grid structure is obtained, and the power supply capacity index, the safety margin index and the power transmission smoothness index are calculated according to the grid structure, and all X are calculatedi＝(xi1,xi2,…,xid) According to the power supply capacity index, the safety margin index and the power transmission smoothness index, establishing a three-dimensional coordinate to define a Pareto non-dominated solution set; if the iteration times are not reached, skipping to the step 3.2 to continuously execute the particle updating;
4, optimizing the considered indexes of the backbone network frame recovery, wherein the considered indexes comprise recovery success rate and recovery time;
and step 4, the recovery success rate is as follows:
Figure FDA0003487008680000031
in the formula (f)ableIn order to recover the success rate, since the plurality of units are respectively started through a plurality of paths, and the recovery success requires all the paths and the unit starting success, fableThe recovery success rate of the path which is the most difficult to recover in the path complete set phi is obtained; l isiThe optimal recovery path of the ith generator set to be recovered is determined; t iskIs path LiA transformer contained;
Figure FDA0003487008680000032
is the transformer index;
the line index is:
Figure FDA0003487008680000033
in the formula, XCjIs a path LiThe equivalent capacitive reactance of the middle branch j can cause line overvoltage and self-excitation of a generator set when an air-load line is charged, and the voltage multiple and the self-excitation are mainly influenced by the line capacitive reactance; xCmaxThe maximum capacitive reactance value in all lines; l isiThe optimal recovery path of the ith generator set to be recovered is determined; n is the number of branches included in the path;
the transformer index
Figure FDA0003487008680000034
Figure FDA0003487008680000035
In the formula, phisatk、φresk、φsskAre respectively a transformer TkSaturation flux, residual flux and steady state flux;
and step 4, the recovery time is as follows:
T＝T1+T2
in the formula, T1The time required for the first phase to resume; t is2Time required to restore the second stage;
T1the time required for recovering the first stage is mainly determined by the time for starting the unit; since multiple units are respectively started through multiple paths, path selection setThe time spent on recovering the longest time-consuming path in phi is T1The value of (c):
Figure FDA0003487008680000036
in the formula, LiStarting a path which is passed by other units by the black start unit; phi is a path L involved in starting all unitsiA set of (a);
Figure FDA0003487008680000041
is a path LiThe charging time of the j line;
Figure FDA0003487008680000042
is a path LiThe contained kth power station is time-consuming to start; t is tblackThe time consumed for starting the black start unit is shortened;
Figure FDA0003487008680000043
in the formula, T2The time required for recovering the second stage is mainly determined by the time for recovering the residual nodes; l ismaxConnecting the longest path for the unrecovered node and the restored node; pk GThe gradient rate of the kth power generation node is set; m is the total number of all starting power generation nodes in the net rack;
Figure FDA0003487008680000044
is a path LiThe charging time of the j line;
Figure FDA0003487008680000045
the rated power generation amount of the kth power generation node in the net rack is obtained;
step 5 the comprehensive recovery index frecCan be expressed as:
frec＝fable-β3T
in the formula (I), the compound is shown in the specification,t is recovery time; f. ofableTo restore success rate; beta is a3For recovering the time Tweight, weight β3The value can be taken according to the operation experience;
step 5, under the power failure recovery scene, the net rack construction re-optimization model based on the recovery capability is as follows:
setting a Pareto non-dominated solution set X (X) under a normal energy supply scene1,X2,…,Xn) And optimizing under a power failure recovery scene by calculating the comprehensive recovery indexes of the grid structure corresponding to each solution, wherein the objective function is as follows:
Fblack＝min frec
in the formula, FblackRecovering an optimal solution under a scene for power failure; f. ofrecIs a comprehensive recovery index;
adopting Dijkstra algorithm to optimize and solve the recovery time and recovery success rate indexes:
searching the path with the highest recovery success rate and the path with the longest recovery time by improving the Dijkstra algorithm, wherein the line length is selected as follows:
Figure FDA0003487008680000046
in the formula, qiIs the equivalent length of line i; xCjIs a path LiThe equivalent capacitive reactance of the middle branch j; xCmaxThe maximum capacitive reactance value in all lines; on the basis, the Dijkstra algorithm obtains that the farthest path between the node where the black start power supply is located and the unit node to be recovered is the path with the highest recovery success rate;
the method for solving the optimal recovery scheme under the power failure recovery scene by adopting the Dijkstra algorithm comprises the following steps:
step 5.1, extracting Pareto non-dominated solution set X ═ X (X) in normal scene1,X2,…,Xn) Any one of the elements Xi＝(xi1,xi2,…,xid) According to xim，m∈[1,d]If the value is 1, the corresponding line is reserved, and if the value is 0, the corresponding net rack network topological graph is obtained, and the corresponding net rack network topological graph is obtainedTransformer index W at both ends of the lineTiLogarithm of (d) and the per unit capacitive reactance value of the line itself
Figure FDA0003487008680000047
Assigning the sum of logarithms as the line length:
Figure FDA0003487008680000048
then using Dijkstra algorithm to obtain shortest path, according to the path calculating fableAnd T1；fableFor the recovery success rate, T, of the most difficult path in the path corpus phi1The time required for the first phase to resume;
step 5.2, confirming the nodes and lines related to the optimal path, equivalently setting the nodes and lines as initial nodes, assigning the sum of the recovery time of the lines and the equipment at the two ends of the lines as the line length, solving the farthest path by the Dijkstra algorithm, and calculating T2；T2The time required for recovering the second stage is mainly determined by the time for recovering the residual nodes;
step 5.3, calculating the comprehensive recovery index f of the net rackrecComparing the comprehensive recovery index with the net rack comprehensive recovery index which is searched and calculated, and if the comprehensive recovery index f of the net rack is the net rack comprehensive recovery index frecIf the optimal solution is larger than the optimal solution, the optimal solution is updated to X corresponding to the current net racki＝(xi1,xi2,…,xid) And if smaller, the updating is not carried out; judging whether all net racks in the Pareto non-dominated solution set are analyzed, and if so, outputting an optimal net rack structure; otherwise, jumping to step 5.1 and continuing searching.
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