CN115455726A - Rolling optimization method for two-stage first-aid repair and recovery of power distribution network under extreme disasters - Google Patents

Rolling optimization method for two-stage first-aid repair and recovery of power distribution network under extreme disasters Download PDF

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CN115455726A
CN115455726A CN202211199161.9A CN202211199161A CN115455726A CN 115455726 A CN115455726 A CN 115455726A CN 202211199161 A CN202211199161 A CN 202211199161A CN 115455726 A CN115455726 A CN 115455726A
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谢云云
吴昊
蔡胜
时涵
卜京
殷明慧
邹云
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Nanjing University of Science and Technology
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Abstract

The invention discloses a rolling optimization method for two-stage emergency repair and recovery of a power distribution network under extreme disasters. The technical scheme of the invention can realize the cooperative optimization of emergency resources with different response times, and meanwhile, the decision scheme rolling optimization is used for considering the influence of subsequent faults in the emergency repair process, thereby realizing the aim of maximum load recovery amount in the distribution network recovery process and having certain theoretical value and engineering value.

Description

Rolling optimization method for two-stage first-aid repair and recovery of power distribution network under extreme disasters
Technical Field
The invention belongs to the technical field of power grids, and particularly relates to a rolling optimization method for two-stage first-aid repair and recovery of a power distribution network under an extreme disaster.
Background
The power distribution network is used as an important junction between a power transmission system and users and is used for guaranteeing normal operation of social economy and people's life. But because the design standard of the power distribution network is low, and with frequent occurrence of extreme disasters, large-scale faults of the power distribution network can cause large-area power failure. Therefore, in order to reduce the load loss caused by the distribution network fault, a reasonable optimization method of the emergency repair recovery strategy of the distribution network needs to be formulated.
In current power distribution network emergency repair restoration strategy research, a traditional method generally couples fault emergency repair and load restoration together. However, in the actual distribution network emergency repair process, the response time of emergency repair resource vehicle scheduling and power grid operation adjustment is greatly different, and the problems of fault emergency repair and load recovery under different time scales are difficult to effectively coordinate and optimize by the traditional method. In addition, in consideration of subsequent faults caused by continuous influence of extreme weather on distribution network equipment, the conventional emergency repair recovery method is difficult to dynamically adjust a distribution network recovery scheme, so that the problems of increased load loss, reduced emergency repair efficiency and the like are caused.
Therefore, a two-stage first-aid repair recovery rolling optimization method for the power distribution network under a cooperative long-time scale needs to be invented, so that the first-aid repair efficiency of the power distribution network is improved, and the power failure time of the power distribution network is reduced.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a rolling optimization method for the two-stage repair and restoration of the power distribution network under an extreme disaster in the post-disaster restoration process of the power distribution network.
The specific technical scheme for realizing the purpose of the invention is as follows:
a rolling optimization method for two-stage first-aid repair and recovery of a power distribution network under an extreme disaster comprises the following steps:
step 1, collecting information of a traffic network and a power distribution network, and mapping road networks, construction teams and mobile power supply positions, different road node moving paths and time, disaster elements and mobile power supply access nodes in the power distribution network and the like in the traffic network to construct a traffic network-power distribution network coupling network;
step 2, constructing a construction team and mobile energy storage scheduling optimization model considering the uncertainty of renewable energy output and load demand under a long-time scale;
step 3, according to the initial fault information of the power grid, constructing an uncertainty set of the output of the renewable energy sources and the load demand, and based on the scheduling optimization model in the step 2, solving by using a column and constraint generation algorithm according to the set long-time scale period delta T to obtain a scheduling strategy of construction teams and mobile energy storage in the long-time scale period delta T;
step 4, a power output and switching action optimization model under a short time scale is built, a deterministic model of distribution network load recovery under the short time scale is built, the optimization model is solved based on a short time scale period delta t, and a power output and switching action strategy within the short time scale period delta t is obtained;
and 5, performing rolling optimization on the power distribution network based on the optimization models in the step 3 and the step 4 until the power distribution network is restored to a normal operation state.
Compared with the prior art, the invention has the remarkable advantages that:
(1) Compared with the traditional post-disaster distribution network emergency repair method, the technical scheme of the invention fully considers the response time difference of emergency resource scheduling and power grid operation adjustment of construction teams, mobile power vehicles and the like in the distribution network emergency repair recovery process, and establishes a distribution network emergency repair recovery decision optimization model coordinating long and short time scales;
(2) According to the technical scheme, prediction errors of renewable energy output and load requirements are fully considered under a long-time scale, an uncertainty set interval is generated, a two-stage robust optimization model of a construction team and a mobile energy storage vehicle is constructed, and a scheduling scheme is obtained by utilizing a CCG algorithm;
(3) According to the technical scheme, the predicted values of the output of the renewable energy sources and the load demand are used as determined values in a short time scale, a deterministic power grid load recovery optimization model is constructed, and the optimal power output, switching action and other schemes are decided to be used for recovering the power failure load to the maximum extent based on the known construction team and mobile energy storage scheduling scheme;
(4) The technical scheme of the invention fully considers the follow-up faults caused by the continuous influence of extreme weather on the distribution network equipment, and establishes a power distribution network emergency repair recovery rolling optimization model for coordinating long and short time scales based on the real-time updated power grid fault information to obtain a dynamically adjusted distribution network emergency repair decision scheme.
The present invention is described in further detail below with reference to the attached drawing figures.
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FIG. 1 is a flow chart of the method steps of the present invention.
Fig. 2 is a schematic diagram of an IEEE 69 node system topology employed in an embodiment of the present invention.
Fig. 3 is a schematic diagram of a coupling network of a traffic network and a power distribution network in an embodiment of the invention.
Fig. 4 is a schematic diagram of a rolling optimization path of a construction team and a mobile energy storage in an embodiment of the invention.
Fig. 5 is a diagram illustrating a comparison between the method and other methods according to the embodiment of the present invention.
Detailed Description
With reference to fig. 1, a rolling optimization method for two-stage first-aid repair and recovery of a power distribution network in an extreme disaster includes the following steps:
step 1, collecting information of a traffic network and a power distribution network, and mapping road networks, construction teams and mobile power supply positions in the traffic network, different road node moving paths and time, disaster elements in the power distribution network, mobile power supply access nodes and the like to each other to construct a traffic network-power distribution network coupling network;
step 2, constructing a construction team and mobile energy storage scheduling optimization model considering the uncertainty of renewable energy output and load demand under a long-time scale, and specifically comprising the following steps:
due to the fact that errors exist in renewable energy output and load demand prediction under a long-time scale, uncertainty of renewable energy output and load demand is considered, and a two-stage robust decision model objective function is established:
Figure BDA0003871776620000031
Figure BDA0003871776620000032
Figure BDA0003871776620000033
wherein x represents a first-stage construction team and a mobile energy storage scheduling scheme, u represents a renewable energy output and load demand uncertainty set, y represents a second-stage power output and line switch action scheme, and C L The cost of the loss of the load is expressed,
Figure BDA0003871776620000034
at the cost of load loss, ρ i As a weight of the load, the load weight,
Figure BDA0003871776620000035
representing the fluctuation value of the load i at the time step t,
Figure BDA0003871776620000036
is the recovery value of the load i at time step T, Δ T is the unit time of each time step, C M In order to reduce the generating cost of the unit,
Figure BDA0003871776620000037
the cost of generating electricity by unit of the unit,
Figure BDA0003871776620000038
representing the output value of the unit i in the time step t;
wherein, the construction team of the distribution network emergency repair decision-making model under the long-time scale salvages restraint, removes energy storage restraint, distribution network operation restraint, specifically is:
(1) And (4) mobile energy storage restraint:
access state of mobile energy storage:
Figure BDA0003871776620000039
wherein,
Figure BDA00038717766200000310
indicating a mobile energy storage scheduling state, equal to 1 indicates that the mobile energy storage m accesses the node i at time t,
Figure BDA00038717766200000311
representing the access state of the mobile energy storage, and if the mobile energy storage m is in the commissioning state at the moment t, being equal to 1;
each mobile energy storage can be simultaneously accessed into one node at most:
Figure BDA00038717766200000312
vehicle movement time limit for mobile energy storage from the warehouse point to the first access point:
Figure BDA0003871776620000041
wherein,
Figure BDA0003871776620000042
representing the motion time of the mobile energy storage from the warehouse point to each access point;
vehicle motion time limit of mobile energy storage from access point i to access point j:
Figure BDA0003871776620000043
wherein, tr i,j Representing the motion time of the mobile energy storage from the access point i to the access point j;
charging and discharging power limitation and charge state constraint of mobile energy storage:
Figure BDA0003871776620000044
Figure BDA0003871776620000045
Figure BDA0003871776620000046
Figure BDA0003871776620000047
Figure BDA0003871776620000048
wherein,
Figure BDA0003871776620000049
and
Figure BDA00038717766200000410
the mobile energy storage node is a binary variable and represents the discharge and charge states of the mobile energy storage, and the charge and discharge operation can be carried out only when the mobile energy storage is connected to the node;
Figure BDA00038717766200000411
the output is scheduled for the mobile energy storage,
Figure BDA00038717766200000412
and
Figure BDA00038717766200000413
maximum power for discharging and charging mobile energy storage; soC (system on chip) m,t For moving the energy storage state of charge, ES m In order to move the energy storage capacity,
Figure BDA00038717766200000414
and
Figure BDA00038717766200000415
the upper and lower bounds of the energy storage state of charge;
(2) Construction team scheduling constraint conditions:
each construction team can repair at most one fault point at the same time:
Figure BDA00038717766200000416
wherein,
Figure BDA00038717766200000417
representing the scheduling state of a construction team, and if the scheduling state is equal to 1, representing that the construction team c repairs the fault point i at the time t; vehicle movement time limit for construction crew from warehouse point to first failure point:
Figure BDA00038717766200000418
and (3) the movement time constraint of the construction team from the fault point i to the fault point j:
Figure BDA00038717766200000419
wherein, tr i,j Representing the movement time of the construction team from a fault point i to a fault point j, wherein T is the time step of the construction team in the scheduling time scale of the construction team, and T is the total number of the time steps in the long time scale；
Limitation of repair time required by a construction team to repair a fault point:
Figure BDA0003871776620000051
wherein r is i,c Represents the repair time required for the construction team c to repair the failure point i,
Figure BDA0003871776620000052
indicating a repair completion status of the failed point; for example, when a fault requires two time steps to complete the repair, let x = [0, 1,0]Z = [0, 1 ] can be obtained]。
And (3) state constraint after the construction team repairs the fault point:
Figure BDA0003871776620000053
the constraint that a fault point can be repaired by only one construction team at most:
Figure BDA0003871776620000054
state constraint of the repair of the fault point:
Figure BDA0003871776620000055
wherein s is i,t The restoration state of the fault point i at the moment t is shown, and if the restoration state is finished, the value is 1;
(3) The power grid dispatching constraint conditions are as follows:
line restoration path constraint:
Figure BDA0003871776620000056
Figure BDA0003871776620000057
Figure BDA0003871776620000058
Figure BDA0003871776620000059
Figure BDA00038717766200000510
wherein Z is i,j,t Indicating that the restoration path goes from node i to node j at time t,
Figure BDA00038717766200000511
indicating the availability of the faulty line ij at time t,
Figure BDA00038717766200000512
representing the availability of the tie-line ij at time t; the restoration path direction constraint and the open loop operation constraint of the normal line, the fault line and the tie line are respectively represented.
And (3) line tidal current capacity constraint:
Figure BDA00038717766200000513
in the formula, P i,j,t Representing the magnitude of the power flow from node i to node j at time t,
Figure BDA00038717766200000514
for the size of the tidal current capacity of the line, when the line ij has a recovery path, the current line can have tidal current, otherwise, the current line is 0;
power output and load recovery constraints:
Figure BDA0003871776620000061
Figure BDA0003871776620000062
Figure BDA0003871776620000063
Figure BDA0003871776620000064
Figure BDA0003871776620000065
Figure BDA0003871776620000066
in the formula,
Figure BDA0003871776620000067
representing the mobile power supply power level of the node i at the time step t,
Figure BDA0003871776620000068
and
Figure BDA0003871776620000069
for the active and reactive power of the distributed power source i at time t,
Figure BDA00038717766200000610
and
Figure BDA00038717766200000611
for maximum active and reactive power of distributed power supply, RU i And RD i The active power output climbing limits of the power supply are respectively;
power balance and voltage safety constraints:
Figure BDA00038717766200000612
Figure BDA00038717766200000613
Figure BDA00038717766200000614
Figure BDA00038717766200000615
Figure BDA00038717766200000616
in the formula of U i,t Represents the voltage magnitude of the node i at the time step t, R i,j And X i,j Is the impedance value, U, of line ij i And
Figure BDA00038717766200000617
the upper and lower limits of the node voltage.
Step 3, according to the initial fault information of the power grid, constructing an uncertainty set of the output of the renewable energy and the load demand, based on the scheduling optimization model in the step 2, according to the set long-time scale period delta T, solving by using a column and constraint generation algorithm (CCG), and obtaining a scheduling strategy of construction teams and mobile energy storage in the long-time scale period delta T, wherein the scheduling strategy specifically comprises the following steps:
step 3-1, constructing a renewable energy output and load demand uncertainty set:
Figure BDA00038717766200000618
wherein u represents the uncertain renewable energy output and load demand value, u E A predicted value representing the amount of uncertainty is determined,
Figure BDA00038717766200000619
and
Figure BDA00038717766200000620
representing the upper and lower bounds of the prediction error of the uncertainty quantity;
3-2, solving a construction team and mobile energy storage scheduling optimization model under a long-time scale based on the constructed renewable energy output and load demand uncertainty set, specifically comprising the following steps:
the general formula of the two-stage robust decision model under the long time scale can be expressed as follows:
Figure BDA0003871776620000071
s.t.Ax≥g
Gy+Ex+Ku≥s
Hy+Ix+Nu＝d
Figure BDA0003871776620000072
in the formula, x represents variables of a first-stage construction team and a mobile energy storage scheduling variable, u represents an uncertainty set of output of renewable energy sources and load requirements, and y represents variables of output of a second-stage power source and line switching actions.
Solving a construction team and mobile energy storage scheduling optimization model under a long-time scale by using a CCG algorithm, decomposing the optimization model into a main problem and a sub-problem, and solving;
the main problem is to generate an optimal scheduling strategy for construction teams and mobile energy storage:
Figure BDA0003871776620000073
Figure BDA0003871776620000074
Ax≥g
Figure BDA0003871776620000075
Figure BDA0003871776620000076
where the uncertainty of the renewable energy output and the load demand is given in known conditions denoted u x.
The sub-problem is to search for the worst fluctuation scenario that maximizes the total cost under the given construction team and mobile energy storage scheduling strategy:
Figure BDA0003871776620000077
s.t.Gy+Ex * +Ku≥s
Hy+Ix * +Nu＝d
Figure BDA0003871776620000078
in the formula, the first stage construction team and the mobile energy storage scheduling variable are x ＊ The known conditions for the representation are given.
By strong dual theory, the two-layer sub-problem can be transformed into a single-layer maximum problem, and the dual problem can be expressed as:
obj f S ＝max[-Kλ 1 u+Nλ 2 u-λ 1 (Ex * -s)+λ 2 (Ix * -d)]
s.t.b T -λ 1 G+λ 2 H≥0
Figure BDA0003871776620000081
λ 1 ≥0，λ 2 ：free
however, the dual problem has a bilinear term λ 1 u and lambda 2 u, a linearization process is required. Since the worst case exists at the extreme points of the uncertainty set, the uncertainty variable can be described as:
Figure BDA0003871776620000082
in the formula u min Represents the minimum value of the uncertainty quantity, Δ u represents the fluctuation range of the uncertainty quantity, and the binary quantity α is used to represent whether the uncertainty quantity is at the maximum or minimum.
Bringing the set of uncertain variables into a dual problem can result in:
obj.f S ＝max[-K(λ 1 u min +λ 1 αΔu)+N(λ 2 u min +λ 2 αΔu)-λ 1 (Ex * -s)+λ 2 (Ix * -d)]
linearization of bilinear terms lambda by large M method 1 A and λ 2 Alpha, take omega 1 ＝λ 1 α、ω 2 ＝λ 2 α, one can obtain:
Figure BDA0003871776620000083
finally, the sub-problem can be expressed as:
obj f S ＝max[-Kλ 1 u min +Nλ 2 u min -Kω 1 Δu+Nω 2 Δu+λ 1 (Ex * -s)+λ 2 (Ix * -d)]
s.t.b T -λ 1 G+λ 2 H≥0
ω 1 ≤Mα，ω 1 ≤λ
ω 2 ≤Mα，ω 2 ≤λ 2
ω 1 ≥λ 1 -M(1-α)
ω 2 ≥λ 2 -M(1-α)
ω 1 ≥0，ω 2 ≥0，λ 1 ≥0，α∈{0，1}
and (3) iteratively solving the main problem model and the converted sub-problem model through a CCG algorithm until the deviation of the optimal results of the two problems is smaller than a predefined convergence tolerance, and obtaining the optimal strategy of the construction team and the mobile energy storage scheduling in a long-time scale.
Step 4, constructing a power output and switching action optimization model under a short time scale, constructing a deterministic model of distribution network load recovery under the short time scale, and solving the optimization model based on a short time scale period delta t to obtain a power output and switching action strategy within the short time scale period delta t, specifically comprising the following steps:
because the renewable energy output and load demand forecast is close to the true value in a short time scale, the uncertainty of the renewable energy output and load demand is not considered, and a deterministic load recovery decision model objective function is established:
Figure BDA0003871776620000091
Figure BDA0003871776620000092
Figure BDA0003871776620000093
wherein x represents a construction team rush-repair scheme and a mobile energy storage dispatching route obtained by a long-time scale decision model, y represents a power output and line switch action scheme needing decision making under a short-time scale, and C L The cost of the loss of the load is expressed,
Figure BDA0003871776620000094
at the cost of load loss, ρ i As a weight of the load, the load weight,
Figure BDA0003871776620000095
representing the fluctuation value of the load i at a time step t on a short time scale,
Figure BDA0003871776620000096
is the recovery value of the load i at a short timestep t, Δ t is the unit time of each short timestep, C M In order to reduce the generating cost of the unit,
Figure BDA0003871776620000097
the cost of generating electricity by unit of the unit,
Figure BDA0003871776620000098
and (4) representing the output value of the unit i at the time step t.
The constraint conditions of the optimization model are as follows:
(1) And (3) mobile energy storage output restraint:
since the scheduling path of mobile energy storage is optimized in the long time scale decision model, the access state of mobile energy storage in short time scale is known
Figure BDA0003871776620000099
And (4) showing. When the uncertainty variable is known at the short timescale, the output of the mobile energy store is adjusted to adjust the decision scheme used to modify the long timescale. Charge-discharge power limitation and charge state constraint of mobile energy storage in a short time scale:
Figure BDA00038717766200000910
Figure BDA00038717766200000911
Figure BDA00038717766200000912
Figure BDA00038717766200000913
Figure BDA00038717766200000914
wherein,
Figure BDA0003871776620000101
and
Figure BDA0003871776620000102
the mobile energy storage node is a binary variable and represents the discharge and charge states of the mobile energy storage, and the charge and discharge operation can be carried out only when the mobile energy storage is connected to the node;
Figure BDA0003871776620000103
the output is scheduled for the mobile energy storage,
Figure BDA0003871776620000104
and
Figure BDA0003871776620000105
maximum power for discharging and charging mobile energy storage; soC (system on chip) m,t For moving the energy storage state of charge, ES m In order to move the energy storage capacity,
Figure BDA0003871776620000106
and
Figure BDA0003871776620000107
the charge state of the mobile energy storage needs to be kept within a limited interval for the upper and lower bounds of the charge state of the energy storage.
(2) And (3) distribution network operation constraint:
the operation constraints of other distribution networks under the short time scale are consistent with the operation constraints of the distribution network under the long time scale:
Figure BDA0003871776620000108
Figure BDA0003871776620000109
Figure BDA00038717766200001010
Figure BDA00038717766200001011
Figure BDA00038717766200001012
Figure BDA00038717766200001013
Figure BDA00038717766200001014
Figure BDA00038717766200001015
Figure BDA00038717766200001016
Figure BDA00038717766200001017
Figure BDA00038717766200001018
Figure BDA00038717766200001019
Figure BDA00038717766200001020
Figure BDA00038717766200001021
Figure BDA00038717766200001022
Figure BDA00038717766200001023
Figure BDA00038717766200001024
wherein Z is i,j,t Indicating that the restoration path goes from node i to node j at time t,
Figure BDA00038717766200001025
indicating the availability of the faulty line ij at time t,
Figure BDA00038717766200001026
indicating the availability of the tie-line ij at time t, P i,j,t Representing the magnitude of the power flow from node i to node j at time t,
Figure BDA00038717766200001027
for the size of the power flow capacity of the line, when the line ij has a recovery path, the current line can have power flow, otherwise, the current line is 0,
Figure BDA0003871776620000111
representing the mobile power supply power level of the node i at the time step t,
Figure BDA0003871776620000112
and
Figure BDA0003871776620000113
for the active and reactive power of the distributed power source i at time t,
Figure BDA0003871776620000114
and
Figure BDA0003871776620000115
for maximum active and reactive power of a distributed power supply, RU i And RD i Is the power supply active power output climbing limit, U i,t Represents the voltage magnitude, R, of the node i in the time step t i,j And X i,j Is the value of the impedance of the line ij,U i and
Figure BDA0003871776620000116
the upper and lower limits of the node voltage.
The uncertainty of the short-time-scale power grid load recovery decision model is not considered, meanwhile, the model has no nonlinear item, the model can be constructed into a mixed integer linear programming model, and a load recovery decision scheme under the short-time scale is obtained by directly utilizing CPLEX commercial solving software.
Step 5, performing rolling optimization on the power distribution network based on the optimization models in the step 3 and the step 4 until the power distribution network is restored to a normal operation state, specifically:
and updating the power grid fault information in real time, judging whether the power distribution network recovers to a normal operation state or not when each long time scale period Delta T is finished, if not, updating and updating the power grid fault information, the construction team position and available state, the mobile energy storage position and charge level, the renewable energy output and load demand predicted value and the error range, returning to the step 3, and performing emergency repair recovery on the power distribution network of the next long time scale period Delta T again until the power distribution network recovers to the normal operation state.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the computer program implements the steps of:
step 1, collecting information of a traffic network and a power distribution network, and mapping road networks, construction teams and mobile power supply positions, different road node moving paths and time, disaster elements and mobile power supply access nodes in the power distribution network and the like in the traffic network to construct a traffic network-power distribution network coupling network;
step 2, constructing a construction team and mobile energy storage scheduling optimization model considering the uncertainty of renewable energy output and load demand under a long-time scale;
step 3, constructing an uncertainty set of renewable energy output and load demand according to the initial fault information of the power grid, and solving by using a column and constraint generation algorithm according to a set long-time scale period delta T on the basis of the scheduling optimization model in the step 2 to obtain a construction team and a mobile energy storage scheduling strategy in the long-time scale period delta T;
step 4, a power output and switching action optimization model under a short time scale is built, a deterministic model of distribution network load recovery under the short time scale is built, the optimization model is solved based on a short time scale period delta t, and a power output and switching action strategy within the short time scale period delta t is obtained;
and 5, performing rolling optimization on the power distribution network based on the optimization models in the step 3 and the step 4 until the power distribution network is restored to a normal operation state.
A computer-storable medium on which a computer program is stored which, when being executed by a processor, carries out the steps of:
step 1, collecting information of a traffic network and a power distribution network, and mapping road networks, construction teams and mobile power supply positions in the traffic network, different road node moving paths and time, disaster elements in the power distribution network, mobile power supply access nodes and the like to each other to construct a traffic network-power distribution network coupling network;
step 2, constructing a construction team and mobile energy storage scheduling optimization model considering the uncertainty of renewable energy output and load demand under a long-time scale;
step 3, according to the initial fault information of the power grid, constructing an uncertainty set of the output of the renewable energy sources and the load demand, and based on the scheduling optimization model in the step 2, solving by using a column and constraint generation algorithm according to the set long-time scale period delta T to obtain a scheduling strategy of construction teams and mobile energy storage in the long-time scale period delta T;
step 4, constructing a power output and switching action optimization model under a short time scale, constructing a distribution network load recovery deterministic model under the short time scale, and solving the optimization model based on a short time scale period delta t to obtain a power output and switching action strategy within the short time scale period delta t;
and 5, performing rolling optimization on the power distribution network based on the optimization models in the step 3 and the step 4 until the power distribution network is restored to a normal operation state.
The present invention will be further described with reference to the following examples.
Examples
The topology of the IEEE 69 node system in this embodiment is shown in fig. 2, and the coupling network of the traffic network and the distribution network is shown in fig. 3.
In order to reduce the power failure loss of the distribution network in extreme weather, a distributed power supply, a mobile energy storage and a construction team are considered for recovering the load. The distributed power supply is installed on nodes 24, 43 and 50 of the power distribution network, and specific output parameters are shown in table 1. The power limit and capacity of the mobile power supply is 400kW/1200kWh, initially located at node 48, with the interface of the mobile power supply to the distribution network being represented by the green node. In consideration of the moving process of typhoon, the initial fault and the subsequent fault of the power distribution network are considered, wherein F1-F7 are line faults occurring at the initial stage of the typhoon, F8-F9 are subsequent line faults caused by the continuous influence of the typhoon, and the occurrence time of the subsequent faults and the time for repairing each fault line by two construction teams are listed in table 2.
TABLE 1 distributed Power coefficients
Figure BDA0003871776620000131
TABLE 2 distribution network Fault parameters
Figure BDA0003871776620000132
The uncertainties of renewable energy output and load demand are set to ± 10% and ± 5%, respectively, taking into account the prediction error on the long time scale. And scheduling the construction team and the mobile power supply based on the uncertain worst condition by solving a two-stage robust decision model under a long-time scale for minimizing load loss. Meanwhile, the rolling optimization is used for dynamically updating the scheduling strategy in consideration of the follow-up faults of the distribution network. Fig. 4 is a schematic diagram of a rolling optimization path for construction team and mobile energy storage.
The construction team repairs the faults F1, F2, and F4 preferentially for restoring more load along the feeder. In addition, when the faults F4 and F2 are repaired, line switches 17-65 and 35-56 may be closed to restore nodes 60-65 and 30-35. When a subsequent fault F9 occurs in the time step 3, the construction team 1 is dispatched again to repair the fault F9, and the original dispatching to repair the fault F1 is shown by a dotted line; when a subsequent failure F8 occurs at time step 8, the construction team 2 is rescheduled to F8 and the failure F5 is delayed.
In order to show the advantages of the two-stage optimization method provided by the invention, the two-stage robust method is compared with other conventional methods, including a one-stage robust method, a two-stage random method and a two-stage deterministic method. In a one-stage robust model, robust optimization is carried out on a coordinated scheduling scheme based on an uncertainty set on a long time scale. In the two-stage deterministic model, uncertainty in wind speed and load demand is not taken into account. In the two-stage stochastic model, uncertainty over long time scales is handled using stochastic programming methods. The short time scale operation of the two-stage deterministic and stochastic models is the same as the proposed deterministic method. When the safety constraints cannot be met, the recovered load is set to zero. The results of the four methods are shown in figure 5.
Robust methods are lower than stochastic and deterministic methods in terms of the amount of load recovery, because robust strategies are optimized according to worst case scenarios. In terms of voltage out-of-limit, compared with random and deterministic methods, the robust method can always meet the safety constraint and maintain robustness to the uncertainty set. In addition, while ensuring safe and stable operation of the system, the performance of the two-stage robust method is superior to that of the single-stage robust method, because the second-stage decision can be adjusted to compensate for the first-stage strategy to reduce conservatism.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
The foregoing embodiments illustrate and describe the general principles and principal features of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.

Claims (10)

1. A rolling optimization method for two-stage first-aid repair and restoration of a power distribution network under extreme disasters is characterized by comprising the following steps:
step 1, collecting information of a traffic network and a power distribution network, and mapping road networks, construction teams and mobile power supply positions in the traffic network, different road node moving paths and time, disaster elements in the power distribution network, mobile power supply access nodes and the like to each other to construct a traffic network-power distribution network coupling network;
step 2, constructing a construction team and mobile energy storage scheduling optimization model considering the uncertainty of renewable energy output and load demand under a long-time scale;
step 3, according to the initial fault information of the power grid, constructing an uncertainty set of the output of the renewable energy sources and the load demand, and based on the scheduling optimization model in the step 2, solving by using a column and constraint generation algorithm according to the set long-time scale period delta T to obtain a scheduling strategy of construction teams and mobile energy storage in the long-time scale period delta T;
step 4, constructing a power output and switching action optimization model under a short time scale, constructing a distribution network load recovery deterministic model under the short time scale, and solving the optimization model based on a short time scale period delta t to obtain a power output and switching action strategy within the short time scale period delta t;
and 5, performing rolling optimization on the power distribution network based on the optimization models in the step 3 and the step 4 until the power distribution network is restored to a normal operation state.
2. The two-stage first-aid repair restoration rolling optimization method for the power distribution network under the extreme disaster condition as claimed in claim 1, wherein the step 2 of constructing a construction team and mobile energy storage scheduling optimization model under a long-time scale specifically comprises the following steps:
Figure FDA0003871776610000011
Figure FDA0003871776610000012
Figure FDA0003871776610000013
wherein x represents a first-stage construction team and a mobile energy storage scheduling scheme, u represents a renewable energy output and load demand uncertainty set, y represents a second-stage power output and line switch action scheme, and C L The cost of the loss of the load is expressed,
Figure FDA0003871776610000014
at the cost of load loss, ρ i Is a weight of the load, and is,
Figure FDA0003871776610000015
representing the fluctuation value of the load i at the time step t,
Figure FDA0003871776610000016
is the recovery value of the load i at time step T, Δ T is the unit time of each time step, C M In order to reduce the generating cost of the unit,
Figure FDA0003871776610000017
the cost of generating electricity by unit of the unit,
Figure FDA0003871776610000018
and (4) representing the output value of the unit i at the time step t.
3. The two-stage first-aid repair restoration rolling optimization method for the power distribution network under the extreme disaster condition as claimed in claim 2, wherein the constraint conditions of the construction team and the mobile energy storage scheduling optimization model are as follows:
(1) Mobile energy storage restraint:
access state of mobile energy storage:
Figure FDA0003871776610000021
wherein,
Figure FDA0003871776610000022
indicating a mobile energy storage scheduling state, equal to 1 indicates that the mobile energy storage m accesses the node i at time t,
Figure FDA0003871776610000023
representing the access state of the mobile energy storage, and if the mobile energy storage m is in the commissioning state at the moment t, being equal to 1;
each mobile energy storage can be simultaneously accessed into one node at most:
Figure FDA0003871776610000024
vehicle movement time limit for mobile energy storage from the warehouse point to the first access point:
Figure FDA0003871776610000025
wherein,
Figure FDA0003871776610000026
representing the motion time of the mobile energy storage from the warehouse point to each access point;
vehicle motion time limit of mobile energy storage from access point i to access point j:
Figure FDA0003871776610000027
wherein, tr i,j Representing the motion time of mobile energy storage from access point i to access point j;
charging and discharging power limitation and charge state constraint of mobile energy storage:
Figure FDA0003871776610000028
Figure FDA0003871776610000029
Figure FDA00038717766100000210
Figure FDA00038717766100000211
Figure FDA00038717766100000212
wherein,
Figure FDA00038717766100000213
and
Figure FDA00038717766100000214
the mobile energy storage node is a binary variable and represents the discharge and charge states of the mobile energy storage, and the charge and discharge operation can be carried out only when the mobile energy storage is connected to the node;
Figure FDA00038717766100000215
the output is scheduled for the mobile energy storage,
Figure FDA00038717766100000216
and
Figure FDA0003871776610000031
maximum power for discharging and charging mobile energy storage; soC (system on chip) m,t For moving the energy storage state of charge, ES m In order to move the energy storage capacity,
Figure FDA0003871776610000032
and
Figure FDA0003871776610000033
the upper and lower bounds of the energy storage state of charge;
(2) Construction team scheduling constraint conditions:
each construction team can repair at most one fault point at the same time:
Figure FDA0003871776610000034
wherein,
Figure FDA0003871776610000035
representing construction teamsThe scheduling state, which is equal to 1, represents that the construction team c repairs the fault point i at the time t;
vehicle movement time limit for construction crew from warehouse point to first failure point:
Figure FDA0003871776610000036
and (3) the movement time constraint of the construction team from the fault point i to the fault point j:
Figure FDA0003871776610000037
wherein, tr i,j Representing the movement time of a construction team from a fault point i to a fault point j, wherein T is a time step of the construction team in a scheduling time scale, and T is the total number of the time steps in the long time scale;
limitation of repair time required by a construction team to repair a fault point:
Figure FDA0003871776610000038
wherein r is i,c Represents the repair time required for the construction team c to repair the failure point i,
Figure FDA0003871776610000039
indicating a repair completion status of the failure point;
and (3) state constraint after the construction team repairs the fault point:
Figure FDA00038717766100000310
the constraint that a fault point can be repaired by only one construction team at most:
Figure FDA00038717766100000311
state constraint of the repair of the fault point:
Figure FDA00038717766100000312
wherein s is i,t Representing the repair state of the fault point i at the time t, and if the repair state is completed, the value is 1;
(3) The power grid dispatching constraint conditions are as follows:
line restoration path constraint:
Figure FDA0003871776610000041
Figure FDA0003871776610000042
Figure FDA0003871776610000043
Figure FDA0003871776610000044
Figure FDA0003871776610000045
wherein Z is i,j,t Indicating that the restoration path goes from node i to node j at time t,
Figure FDA0003871776610000046
indicating the availability of the faulty line ij at time t,
Figure FDA0003871776610000047
to representAvailability status of the tie-line ij at time t;
and (3) line tidal current capacity constraint:
Figure FDA0003871776610000048
in the formula, P i,j,t Representing the magnitude of the power flow from node i to node j at time t,
Figure FDA0003871776610000049
the power flow capacity of the line is set as the current capacity, when the line ij has a recovery path, the current line can have power flow, otherwise, the current line is set as 0;
power output and load recovery constraints:
Figure FDA00038717766100000410
Figure FDA00038717766100000411
Figure FDA00038717766100000412
Figure FDA00038717766100000413
Figure FDA00038717766100000414
Figure FDA00038717766100000415
in the formula,
Figure FDA00038717766100000416
representing the mobile power supply power level of node i at time step t,
Figure FDA00038717766100000417
and
Figure FDA00038717766100000418
for the active and reactive power of the distributed power supply i at t time steps,
Figure FDA00038717766100000419
and
Figure FDA00038717766100000420
for maximum active and reactive power of distributed power supply, RU i And RD i The active power output climbing limit of the power supply is respectively set;
power balance and voltage safety constraints:
Figure FDA00038717766100000421
Figure FDA00038717766100000422
Figure FDA00038717766100000423
Figure FDA00038717766100000424
Figure FDA00038717766100000425
in the formula of U i,t Represents the voltage magnitude, R, of the node i in the time step t i,j And X i,j For the value of the impedance of the line ij,U i and
Figure FDA0003871776610000051
the upper and lower limits of the node voltage.
4. The rolling optimization method for the two-stage first-aid repair and restoration of the power distribution network under the extreme disaster as claimed in claim 2, wherein the step 3 of constructing the uncertainty set of the output of the renewable energy source and the load demand and solving the optimization model specifically comprises the following steps:
step 3-1, constructing a renewable energy output and load demand uncertainty set:
Figure FDA0003871776610000052
where u represents the uncertainty renewable energy output and load demand value, u E A predicted value representing the amount of uncertainty,
Figure FDA0003871776610000053
and
Figure FDA0003871776610000054
representing the upper and lower bounds of the uncertainty prediction error;
and 3-2, solving a construction team and mobile energy storage scheduling optimization model under a long-time scale based on the constructed renewable energy output and load demand uncertainty set.
5. The rolling optimization method for the two-stage first-aid repair and restoration of the power distribution network under the extreme disaster as claimed in claim 4, wherein the solving optimization model in the step 3-2 is specifically as follows:
solving a construction team and a mobile energy storage scheduling optimization model under a long-time scale by using a CCG algorithm, decomposing the optimization model into a main problem and a sub-problem, and solving;
the main problem is to generate an optimal scheduling strategy for construction teams and mobile energy storage:
Figure FDA0003871776610000055
Figure FDA0003871776610000056
Ax≥g
Figure FDA0003871776610000057
Figure FDA0003871776610000058
the sub-problem is to search for the worst fluctuation scenario that maximizes the total cost under the given construction team and mobile energy storage scheduling strategy:
Figure FDA0003871776610000059
s.t.Gy+Ex * +Ku≥s
Hy+Ix * +Nu＝d
Figure FDA00038717766100000510
and (3) iteratively solving the main problem model and the converted sub-problem model through a CCG algorithm until the deviation of the optimal results of the two problems is smaller than a predefined convergence tolerance, and obtaining the optimal strategy of the construction team and the mobile energy storage scheduling in a long-time scale.
6. The rolling optimization method for two-stage first-aid repair and restoration of the power distribution network under the extreme disaster as claimed in claim 1, wherein the step 4 of constructing a power output and switching action optimization model under a short time scale and solving based on a short time scale period Δ t specifically comprises the following steps:
Figure FDA0003871776610000061
Figure FDA0003871776610000062
Figure FDA0003871776610000063
wherein x represents a construction team rush-repair scheme and a mobile energy storage dispatching route obtained by a long-time scale decision model, y represents a power output and line switch action scheme needing decision making under a short-time scale, and C L The cost of the loss of the load is expressed,
Figure FDA0003871776610000064
at the cost of load loss, ρ i As a weight of the load, the load weight,
Figure FDA0003871776610000065
representing the fluctuation value of the load i at a time step t on a short time scale,
Figure FDA0003871776610000066
is the recovery value of the load i at a short timestep t, Δ t is the unit time of each short timestep, C M In order to reduce the generating cost of the unit,
Figure FDA0003871776610000067
the cost of generating electricity by unit of the unit,
Figure FDA0003871776610000068
and (4) representing the output value of the unit i at the time step t.
7. The rolling optimization method for the two-stage first-aid repair and restoration of the power distribution network under the extreme disaster as claimed in claim 6, wherein the constraint conditions of the optimization model are as follows:
(1) And (3) mobile energy storage output restraint:
charge-discharge power limitation and charge state constraint of mobile energy storage in a short time scale:
Figure FDA0003871776610000069
Figure FDA00038717766100000610
Figure FDA00038717766100000611
Figure FDA00038717766100000612
Figure FDA00038717766100000613
wherein,
Figure FDA00038717766100000614
and
Figure FDA00038717766100000615
is a binary variable and represents the discharge and charge state of the mobile energy storage, and the mobile energy storage can be accessed to the node onlyCarrying out charging and discharging operations;
Figure FDA00038717766100000616
the output is scheduled for the mobile energy storage,
Figure FDA00038717766100000617
and
Figure FDA00038717766100000618
maximum power for discharging and charging mobile energy storage; soC (system on chip) m,t For moving the energy storage state of charge, ES m In order to move the energy storage capacity,
Figure FDA00038717766100000619
and
Figure FDA00038717766100000620
the upper and lower bounds of the energy storage state of charge;
(2) And (3) distribution network operation constraint:
Figure FDA0003871776610000071
Figure FDA0003871776610000072
Figure FDA0003871776610000073
Figure FDA0003871776610000074
Figure FDA0003871776610000075
Figure FDA0003871776610000076
Figure FDA0003871776610000077
Figure FDA0003871776610000078
Figure FDA0003871776610000079
Figure FDA00038717766100000710
Figure FDA00038717766100000711
Figure FDA00038717766100000712
Figure FDA00038717766100000713
Figure FDA00038717766100000714
Figure FDA00038717766100000715
Figure FDA00038717766100000716
Figure FDA00038717766100000717
wherein Z is i,j,t Indicating that the restoration path goes from node i to node j at time t,
Figure FDA00038717766100000718
indicating the availability of the faulty line ij at time t,
Figure FDA00038717766100000719
indicating the availability of the tie-line ij at time t, P i,j,t Representing the magnitude of the power flow from node i to node j at time t,
Figure FDA00038717766100000720
for the size of the power flow capacity of the line, when the line ij has a recovery path, the current line can have power flow, otherwise, the current line is 0,
Figure FDA00038717766100000721
representing the mobile power supply power level of node i at time step t,
Figure FDA00038717766100000722
and
Figure FDA00038717766100000723
for the active and reactive power of the distributed power source i at time t,
Figure FDA00038717766100000724
and
Figure FDA00038717766100000725
for maximum active and reactive power of distributed power supply, RU i And RD i Is the power supply active power output climbing limit, U i,t Represents the voltage magnitude of the node i at the time step t, R i,j And X i,j Is the value of the impedance of the line ij,U i and
Figure FDA00038717766100000726
the upper and lower limits of the node voltage.
8. The rolling optimization method for the two-stage first-aid repair and restoration of the power distribution network under the extreme disaster as claimed in claim 1, wherein the rolling optimization in the step 5 is performed until the power distribution network is restored, and specifically comprises the following steps:
and when each long time scale period delta T is finished, judging whether the power distribution network is recovered to a normal operation state, if not, updating and updating the power distribution network fault information, the construction team position and available state, the mobile energy storage position and charge level, the renewable energy output and load demand predicted value and the error range, returning to the step 3, and performing the rush repair recovery of the power distribution network of the next long time scale period delta T again until the power distribution network is recovered to the normal operation state.
9. A computer arrangement comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method according to any of claims 1-7 are implemented by the processor when executing the computer program.
10. A computer-storable medium having stored thereon a computer program, characterised in that the computer program, when being executed by a processor, carries out the steps of the method as set forth in claims 1-7.
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