CN109286204B - power distribution network black start reconstruction method based on minimum expected power failure loss - Google Patents
power distribution network black start reconstruction method based on minimum expected power failure loss Download PDFInfo
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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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
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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
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Abstract
the invention relates to the technical field of power distribution network reconstruction, in particular to a power distribution network black start reconstruction method based on minimized expected power failure loss; the method has the advantages that the advantages and disadvantages of the black start reconstruction method of the power distribution network are measured by adopting an economic means, the inconsistent unified relation between the distributed power sources and the load recovery is effectively balanced, the recovery sequence of the power-losing nodes is determined and the recovery path is optimized by the black start reconstruction of the power distribution network through linear programming optimization, and the important load recovery time and the power failure loss are shortened.
Description
Technical Field
the invention relates to the technical field of power distribution network reconstruction, in particular to a power distribution network black start reconstruction method based on minimum expected power failure loss.
Background
the reconstruction of the distribution network is an important means for the self-healing control of the distribution network. The conventional power distribution network reconstruction can be divided into two conditions of optimization reconstruction and fault recovery reconstruction according to whether a fault occurs or not, and the functions of optimizing the operation structure of the power distribution network and guaranteeing the power supply reliability are achieved.
with the gradual increase of the permeability and the admission power of the distributed power sources, the operation and control method of the intelligent power distribution network has more operable space to improve. After the micro-grid is connected to the power distribution network, the micro-grid can operate in an island mode and is disconnected from the power distribution network; the micro-grid in isolated island operation has the capability of guaranteeing the continuous power supply of key load and adjacent areas. The method is characterized in that a power distribution system with a planned island needs to ensure the power supply of key loads under the condition of large-area power failure, namely, a micro-grid or a distributed power supply is utilized to divide a power distribution network into a plurality of islands, the key loads are divided into the islands as much as possible, the continuous power supply of the islands is ensured, and the key loads are merged into the power distribution network after fault recovery.
disclosure of Invention
The invention aims to overcome at least one defect in the prior art, provides a black start reconstruction method of a power distribution network based on minimized expected power failure loss, converts the black start reconstruction problem of the power distribution network into a mixed integer linear programming problem, adopts linear programming optimization to solve the black start reconstruction method of the power distribution network with the minimized power failure loss, and effectively balances the contradiction unified relationship between a distributed power supply and load recovery.
in order to solve the technical problems, the invention adopts the technical scheme that: a black start reconstruction method for a power distribution network based on minimization of expected power outage loss comprises the following steps:
s1, inputting original data including DG, load and line parameters of a power distribution network to be optimized, and providing load types and unit power failure loss for the load;
s2, determining relevant parameters of an optimization model according to engineering experience and actual needs, wherein the relevant parameters comprise a time period for restoring reconstruction, the number of lines allowed to be simultaneously input, a system standby rate, a load fluctuation coefficient and the maximum frequency deviation allowed by a system;
s3, calling the Yalmip to establish a black-start reconstruction model of the power distribution network based on the minimized expected power failure loss in the MATLAB environment;
S4, solving a power distribution network black start reconstruction model based on the minimized expected power failure loss by calling a CPLEX branch-and-bound method under an MATLAB environment to obtain a solution to be determined, wherein the solution to be determined corresponds to the recovery action of each moment in the power distribution network;
s5, carrying out power flow verification on the recovery action corresponding to the solution to be determined, if the safety constraint is not met, adding a constraint condition in a black start reconstruction model of the power distribution network established by Yalmip, setting the solution to be determined as an infeasible solution, namely, enabling a new optimized solution not to be equal to the original solution to be determined, so as to eliminate the solution to be determined which does not pass the power flow verification, turning to the step S4, and carrying out optimization again;
And S6, outputting a recovery action corresponding to the undetermined solution passing through the power flow verification, namely a power distribution network black start reconstruction scheme for minimizing expected power failure loss.
It should be noted that safety constraints such as power balance constraint, system standby constraint, frequency constraint and the like are considered in the model, and the reconstruction scheme corresponding to the obtained optimization solution can generally meet the power flow constraint, so that the power flow verification is performed after the optimization solution is finished, so that the consideration of a large amount of complex power flow constraints in the model solution can be avoided, and the model solution efficiency is greatly improved.
further, the step S3 specifically includes:
s31, defining a black start reconstruction model of the power distribution network: supposing that the power distribution network is completely powered off, the external input power is 0, namely the system is in an island state; assume that the recovery time of the load charging is 0; it is assumed that the line restoration operation can be completed within one period;
s32, establishing a target function: the goal of power system restoration is to minimize the loss of an accident, where the proportion of the loss of a user's power outage is large; the method is characterized in that an economic means is adopted to quantify the accident loss, the power failure loss of users in the black starting process of the power distribution network is used for measuring the advantages and disadvantages of a network reconstruction scheme, and an objective function for minimizing the expected power failure loss of power users is established and expressed as follows:
Where NL is the number of loads to be restored, PL, k is the power consumed by load k (kW); fk (tL, k) is the unit outage loss (yuan/kW) of the load k, and is related to the outage time tL, k and the load type of the load k;
and S33, setting constraint conditions, including unit power failure loss constraint, unit recovery constraint, line recovery constraint, bus recovery constraint, load recovery constraint, power balance constraint, system standby constraint and system frequency constraint.
further, the unit blackout loss constraint is expressed by a relation between blackout time and load state:
the method comprises the steps of carrying out piecewise linearization processing on a load unit power failure loss curve, selecting NH sampling points (Xh, Fi, h), introducing continuous variables lambdai, h (lambdai, h is more than or equal to 0) and NH-1 variables (0-1) yh, and enabling
wherein tL and k are the power failure duration time of the load k; NH is the number of sampling points; xh and Fk, h are respectively the abscissa and the ordinate of the h sampling point; λ k,1, λ k, h, the 1 st, h th and NH th continuous variables introduced for the load k, respectively; yk,1, yk, h-1, yk, h and the 1 st, h-1 th, h and NH-1 th 0-1 variables introduced for the load k, respectively;
Thus, fk (tL, k) can be represented linearly as:
further, the setting of the unit recovery constraint mainly comprises the following steps:
s3311, the maximum output power of the unit is represented as:
in the formula: PG, j, t is the maximum output power of the unit j at the moment t; PGmax, j is the rated output power of the unit j; PGstart, j is the rated starting power of the unit j; TC, j is the time required by the unit j from starting to synchronously outputting power; rj is the load-lifting rate of the unit j; j is 0 for the black start power supply PGstart; tGstart, j is the starting time of the jth DG; t is the considered black start period;
the unit startup power is expressed as:
s3312, setting the state constraint of the unit as follows: during black start, the unit, once started, is no longer stopped, and is represented as:
u≥u
wherein t is a time index; uj, t is a variable from 0 to 1 and represents the running state of the unit j at the time t, uj, t is 1 and represents the unit running, uj, t is 0 and represents the unit not running;
s3313, introducing a 0-1 variable u' j, t to represent the starting state of the unit j at the moment t:
S3314, in the black start process, the started unit cannot be stopped, so the unit can be started at most once, and then:
Uj, t can be expressed as:
wherein t1 is a time index;
S3315, introduce a 0-1 variable v ' j, t representing the state of the unit j supplying power to the system at time t, v ' j, t ═ 1 represents that the unit supplies power to the system, v ' j, t ═ 0 represents that the unit does not supply power to the system, then:
s3316, introducing an integer variable vj, t, representing the accumulated time of the unit j supplying power to the system at the moment t:
S3317. the maximum output power constraint of the unit is expressed as:
P＝min(vR,P)
the starting power constraint of the unit is expressed as:
P＝uP；
s3318, for the non-black starting unit node, after the bus is recovered, the unit can be started, namely:
in the formula, Nb is the number of buses; BGb, j indicates the relationship between the unit j and the bus b, BGb, j equals 1 indicates that the unit j is connected with the bus b, BGb, j equals 0 indicates not connected; busb, t represents the state of the bus b at the time t, busb, t-1 represents that the bus b is recovered, and busb, t-0 represents that the bus b is not recovered.
Further, the setting of the line restoration constraint mainly includes the following steps:
s3321, only when the bus at one end of the line is charged, the line can be restored, namely:
brx, t is the state of the line x at the time t, brx, t is 1 and brx, and t is 0 and does not input; BBx, b represents the relation between the bus b and the line x, BBx, b-1 represents that the bus b is connected with the line x, BBx, and b-0 represents that the bus b is not connected with the line x;
s3322, limiting the number of lines recovered at the same time:
in the formula, Nbr is the number of lines; br 'x, t is the putting state of the line x at the time t, if and only if the line is put into operation at the time t, br' x, t is 1, and the rest of the time is 0; kbr is the maximum number of lines allowed to be recovered at the same time;
s3323. once the line is restored, it is not cut off, that is:
br≥br
Further, the setting of the bus recovery constraint mainly comprises the following steps:
s3331, bus recovery can be realized in two modes of starting by a black-start unit or connecting a line, namely:
in the formula, the influence of the black start unit on the state of the bus is shown, the bus b can be recovered in a mode of starting the black start unit at the time t, and the bus b cannot be started; the bus state recovery method comprises the steps of showing the influence of a line on the state of a bus, showing that the bus b can be recovered in a line connection mode at the time t, and showing that the bus b cannot be recovered;
the above formula can be expressed as:
S3332, after the black start unit is started, the bus where the black start unit is located can be recovered, namely:
in the formula, BGbj, b represents the relationship between the black start unit j and the bus b, BGbj, b ═ 1 represents that the black start unit j is connected with the bus b, and BGbj, b ═ 0 represents that the black start unit j is not connected;
if the line to which the bus bar is connected has been restored, the bus bar can be restored, i.e.:
once the bus bar is restored, it is no longer de-energized, i.e.:
bus≥bus。
further, the setting of the load recovery constraint mainly comprises the following steps:
s3341. according to the assumption, the load charge recovery time is 0, which is expressed as:
P＝cP
In the formula, PL, k and t are power consumed by the load k at the time t; PL, k is the power of load k; ck, t is a variable from 0 to 1 and represents the state of the load k at the time t, wherein ck, t-1 represents recovery, and ck, t-0 represents non-recovery;
S3342, in the black start process, once the load is recovered, the load is not cut off, namely:
c≥c
S3343, introducing a 0-1 variable c' k, t, which represents the recovery of the load k at time t and is expressed as:
in the formula, tL and k are the time when the load k obtains the recovery power;
the load node state may be represented as:
s3344, for all load nodes, after the bus is recovered, the load can be recovered, namely:
Where NL is the number of loads; BLb, k denotes the relationship between load k and bus b, BLb, k ═ 1 denotes that load k is connected to bus b, and BLb, k ═ 0 denotes that it is not connected.
further, the system power balance constraint is expressed as:
in the formula, P 'G, j, t is the actual output power of the unit j at the moment t, and P' G, j, t is more than or equal to 0 and less than or equal to PG, j, t; NG is the number of units;
the system standby constraint is expressed as:
Wherein, alpha is the system standby rate.
further, considering that the frequency deviation caused when the recovered load varies within a certain range does not exceed the maximum frequency deviation allowed by the system, it is expressed as:
wherein, beta is the load fluctuation coefficient; Δ f is the maximum frequency deviation allowed by the system; KG, j is the unit adjusting power of the unit j; KL, k is the unit regulated power of load k.
Further, before listing the specific steps of solving the power distribution network reconstruction model that minimizes the expected power outage loss by using the branch-and-bound method, some symbols are defined: recording as (P0) a power distribution network reconfiguration problem that minimizes expected blackout losses; fu is an upper bound of an optimal value of an integer programming (P0), which represents the load power failure loss corresponding to the optimal power distribution network reconstruction scheme which can be found currently, and the initial setting can be positive infinity, and the load power failure loss is continuously updated along with the solution process; s (P0) is a feasible set of integer programming (P0) and corresponds to different power distribution network reconstruction schemes; (P1),. and (Pk) are the sub-problems resulting from the decomposition of (P0), whose feasible sets are S (P1),. and S (Pk), respectively; the relaxation linear plan of the sub-problem (Pi) is marked as a distribution network reconstruction scheme corresponding to the relaxation problem in a feasible set; NF is a subscript set of the problem (Pi) to be detected, is initially 0, and represents that the solution is started from (P0), and elements are deleted in the set NF along with the decomposition of the subproblem (Pi); a feasible solution of S (P0) represents decision variables for determining an optimal power distribution network reconstruction scheme, such as load outage duration tL, k, unit/load/line recovery actions u ' j at time t, t/c ' k, t/brx ', t;
the specific solving step of the step S4 includes:
s41, setting NF as {0}, Fu as + ∞;
s42, selecting a subscript k belonging to NF, solving the relaxation problem of the distribution network reconstruction problem (Pk) which minimizes expected power failure loss by using a simple method, and setting the reconstruction scheme with the minimum power failure loss as x (k), wherein the power failure loss is fk which is the lower bound of the optimal value of the subproblem (Pk); if no feasible solution exists, setting fk to be + ∞;
s43, if fk is ∞, and the subproblem has no feasible solution, then NF is NF \ k (i.e. k element in NF is deleted), go to step S47; otherwise, executing step S44;
s44, if fk is larger than or equal to Fu, namely the power failure loss of the sub-problem is larger, and no better recovery scheme exists, setting NF as NF \ k }, and turning to the step S47; otherwise, executing step S44;
S45, if fk < Fu, x (k) belongs to S (P0), namely the power failure loss of the subproblem is smaller and the power failure time belongs to a feasible solution, updating the upper bound Fu of the minimum power failure loss and a decision variable set Fu ═ fk and NF ═ NF \ { k }, and turning to the step S47; otherwise, executing step S46;
s46, if fk < Fu, that is, the power outage loss of the subproblem is smaller but the power outage time does not belong to a feasible solution, then decomposing S (pk) into two subsets and placing NF ═ ({ k }) -u { k1, k2}, and going to step S42;
s47, if yes, turning to the step S42; if so, the optimal solution of the problem (P0) is obtained, namely the power distribution network reconstruction scheme Fu with the minimum power outage loss is the minimum power outage loss, and if the problem (P0) has no feasible solution.
compared with the prior art, the beneficial effects are: the black start reconstruction method for the power distribution network based on the minimized expected power failure loss adopts an economic means to measure the advantages and disadvantages of the black start reconstruction method for the power distribution network, effectively balances the inconsistent unified relationship between the distributed power supply and the load recovery, determines the recovery sequence of power failure nodes and optimizes the recovery path through the black start reconstruction of the power distribution network by linear programming optimization, and shortens the important load recovery time and the power failure loss.
Drawings
fig. 1 is a flow chart of a power distribution network black start reconstruction solving method of the invention.
Fig. 2 is a schematic diagram of the power outage loss piecewise linearization of the invention.
FIG. 3 is a schematic diagram of the power output and start-up curves of the present invention.
FIG. 4 is a flowchart of the method for solving the black start reconstruction model.
fig. 5 is an IEEE33 node power distribution system including a DG in an embodiment of the present invention.
fig. 6 to 10 are schematic diagrams of black start reconfiguration processes of an IEEE33 node power distribution system according to an embodiment of the present invention.
Detailed Description
the drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.
as shown in fig. 1, a black start reconstruction method for a power distribution network based on minimizing expected blackout loss includes the following steps:
S1, inputting original data including DG, load and line parameters of a power distribution network to be optimized, and providing load types and unit power failure loss for the load;
s2, determining relevant parameters of an optimization model according to engineering experience and actual needs, wherein the relevant parameters comprise a time period for restoring reconstruction, the number of lines allowed to be simultaneously input, a system standby rate, a load fluctuation coefficient and the maximum frequency deviation allowed by a system;
s3, calling the Yalmip to establish a black-start reconstruction model of the power distribution network based on the minimized expected power failure loss in the MATLAB environment;
s4, solving a power distribution network black start reconstruction model based on the minimized expected power failure loss by calling a CPLEX branch-and-bound method under an MATLAB environment to obtain a solution to be determined, wherein the solution to be determined corresponds to the recovery action of each moment in the power distribution network;
s5, carrying out power flow verification on the recovery action corresponding to the solution to be determined, if the safety constraint is not met, adding a constraint condition in a black start reconstruction model of the power distribution network established by Yalmip, setting the solution to be determined as an infeasible solution, namely, enabling a new optimized solution not to be equal to the original solution to be determined, so as to eliminate the solution to be determined which does not pass the power flow verification, turning to the step S4, and carrying out optimization again;
and S6, outputting a recovery action corresponding to the undetermined solution passing through the power flow verification, namely a power distribution network black start reconstruction scheme for minimizing expected power failure loss.
it should be noted that safety constraints such as power balance constraint, system standby constraint, frequency constraint and the like are considered in the model, and the reconstruction scheme corresponding to the obtained optimization solution can generally meet the power flow constraint, so that the power flow verification is performed after the optimization solution is finished, so that the consideration of a large amount of complex power flow constraints in the model solution can be avoided, and the model solution efficiency is greatly improved.
specifically, the step S3 specifically includes:
S31, defining a black start reconstruction model of the power distribution network: supposing that the power distribution network is completely powered off, the external input power is 0, namely the system is in an island state; assume that the recovery time of the load charging is 0; it is assumed that the line restoration operation can be completed within one period;
s32, establishing a target function: the goal of power system restoration is to minimize the loss of an accident, where the proportion of the loss of a user's power outage is large; the method is characterized in that an economic means is adopted to quantify the accident loss, the power failure loss of users in the black starting process of the power distribution network is used for measuring the advantages and disadvantages of a network reconstruction scheme, and an objective function for minimizing the expected power failure loss of power users is established and expressed as follows:
where NL is the number of loads to be restored, PL, k is the power consumed by load k (kW); fk (tL, k) is the unit outage loss (yuan/kW) of the load k, and is related to the outage time tL, k and the load type of the load k;
And S33, setting constraint conditions, including unit power failure loss constraint, unit recovery constraint, line recovery constraint, bus recovery constraint, load recovery constraint, power balance constraint, system standby constraint and system frequency constraint.
(1) Unit blackout loss constraint:
the unit blackout loss constraint is expressed by the relationship between blackout time and load state:
the method comprises the steps of carrying out piecewise linearization processing on a load unit power failure loss curve, selecting NH sampling points (Xh, Fi, h), introducing continuous variables lambdai, h (lambdai, h is more than or equal to 0) and 0-1 variable yh, and enabling
thus, fk (tL, k) can be represented linearly as:
(2) unit recovery constraint
After the unit is started, the unit can be raised from an idle state to a full load state according to a certain curve, the process is carried out in stages, and as shown by a thick solid line in fig. 3, the actual output power of the unit at any time cannot be larger than the curve. The unit startup power curve is shown as a thin solid line in fig. 3, and j is 0 for the black start power supply PGstart.
in the figure, PG, j, t is the maximum output power of the unit j at the time t; PGmax, j is the rated output power of the unit j; PGstart, j is the rated starting power of the unit j; TC, j is the time required by the unit j from starting to synchronously outputting power; rj is the load-lifting rate of the unit j;
the maximum output power of the unit is expressed as:
the unit startup power is expressed as:
the set state constraint is set as follows: during black start, the unit, once started, is no longer stopped, and is represented as:
u≥u
Wherein t is a time index; uj, t is a variable from 0 to 1 and represents the running state of the unit j at the time t, uj, t is 1 and represents the unit running, uj, t is 0 and represents the unit not running;
introducing a 0-1 variable u' j, t to represent the starting state of the unit j at the moment t:
in the black start process, the started unit is not stopped, so the unit can be started at most only once, and then:
uj, t can be expressed as:
Wherein t1 is a time index;
introducing a 0-1 variable v ' j, wherein t represents the state that the unit j supplies power to the system at the time t, v ' j, t is 1 and represents that the unit supplies power to the system, and v ' j, t is 0 and represents that the unit does not supply power to the system, then:
introducing an integer variable vj, t to represent the accumulated time for the unit j to supply power to the system at the moment t:
The maximum output power constraint of the unit is expressed as:
P＝min(vR,P)
the starting power constraint of the unit is expressed as:
P＝uP；
for the non-black starting unit node, after the bus is recovered, the unit can be started, namely:
In the formula, Nb is the number of buses; BGb, j indicates the relationship between the unit j and the bus b, BGb, j equals 1 indicates that the unit j is connected with the bus b, BGb, j equals 0 indicates not connected; busb, t represents the state of the bus b at the time t, busb, t-1 represents that the bus b is recovered, and busb, t-0 represents that the bus b is not recovered.
(3) line restoration constraints
only when the bus at one end of the line has been charged, the line can be restored, namely:
brx, t is the state of the line x at the time t, brx, t is 1 and brx, and t is 0 and does not input; BBx, b represents the relation between the bus b and the line x, BBx, b-1 represents that the bus b is connected with the line x, BBx, and b-0 represents that the bus b is not connected with the line x;
limiting the number of lines recovered at the same time:
in the formula, Nbr is the number of lines; br 'x, t is the putting state of the line x at the time t, if and only if the line is put into operation at the time t, br' x, t is 1, and the rest of the time is 0; kbr is the maximum number of lines allowed to be recovered at the same time;
Once the line is restored, it is no longer cut, i.e.:
br≥br
(4) bus recovery constraints
The bus recovery can be realized by two modes of starting the black start unit or connecting the line, namely:
in the formula, the influence of the black start unit on the state of the bus is shown, the bus b can be recovered in a mode of starting the black start unit at the time t, and the bus b cannot be started; the bus state recovery method comprises the steps of showing the influence of a line on the state of a bus, showing that the bus b can be recovered in a line connection mode at the time t, and showing that the bus b cannot be recovered;
the above formula can be expressed as:
After the black start unit starts, its generating line that is located can resume, promptly:
in the formula, BGbj, b represents the relationship between the black start unit j and the bus b, BGbj, b ═ 1 represents that the black start unit j is connected with the bus b, and BGbj, b ═ 0 represents that the black start unit j is not connected;
if the line to which the bus bar is connected has been restored, the bus bar can be restored, i.e.:
Once the bus bar is restored, it is no longer de-energized, i.e.:
bus≥bus。
(5) load recovery constraints
according to the assumption, the load charge recovery time is 0, expressed as:
P＝cP
in the formula, PL, k and t are power consumed by the load k at the time t; PL, k is the power of load k; ck, t is a variable from 0 to 1 and represents the state of the load k at the time t, wherein ck, t-1 represents recovery, and ck, t-0 represents non-recovery;
during black start, once the load is restored, it is not disconnected, i.e.:
c≥c
introducing a 0-1 variable c' k, t, representing the recovery of the load k at time t, expressed as:
in the formula, tL and k are the time when the load k obtains the recovery power;
the load node state may be represented as:
for all load nodes, after the bus is recovered, the load can be recovered, that is:
where NL is the number of loads; BLb, k denotes the relationship between load k and bus b, BLb, k ═ 1 denotes that load k is connected to bus b, and BLb, k ═ 0 denotes that it is not connected.
(6) Power balance constraint
the system power balance constraint is expressed as:
In the formula, P 'G, j, t is the actual output power of the unit j at the moment t, and P' G, j, t is more than or equal to 0 and less than or equal to PG, j, t; NG is the number of units;
(7) system backup constraints
Sufficient spare capacity must be left during black start, expressed as:
wherein, alpha is the system standby rate.
(8) system frequency constraint
In order to ensure the safe and stable recovery of the power distribution network, the variation range of the system frequency needs to be strictly controlled within a reasonable range. Considering that the frequency deviation caused when the recovered load is changed within a certain range does not exceed the maximum frequency deviation allowed by the system, it is expressed as:
wherein, beta is the load fluctuation coefficient; Δ f is the maximum frequency deviation allowed by the system; KG, j is the unit adjusting power of the unit j; KL, k is the unit regulated power of load k.
before listing the concrete steps of solving the power distribution network reconstruction model for minimizing the expected power failure loss by adopting a branch-and-bound method, a plurality of symbols are defined: recording as (P0) a power distribution network reconfiguration problem that minimizes expected blackout losses; fu is an upper bound of an optimal value of an integer programming (P0), which represents the load power failure loss corresponding to the optimal power distribution network reconstruction scheme which can be found currently, and the initial setting can be positive infinity, and the load power failure loss is continuously updated along with the solution process; s (P0) is a feasible set of integer programming (P0) and corresponds to different power distribution network reconstruction schemes; (P1),. and (Pk) are the sub-problems resulting from the decomposition of (P0), whose feasible sets are S (P1),. and S (Pk), respectively; the relaxation linear plan of the sub-problem (Pi) is marked as a distribution network reconstruction scheme corresponding to the relaxation problem in a feasible set; NF is a subscript set of the problem (Pi) to be detected, is initially 0, and represents that the solution is started from (P0), and elements are deleted in the set NF along with the decomposition of the subproblem (Pi); a feasible solution of S (P0) represents decision variables used to determine an optimal power distribution network reconfiguration scheme, such as load outage duration tL, k, unit/load/line recovery actions u ' j, t/c ' k, t/br ' x, t at time t;
as shown in fig. 4, the specific solving step of the step S4 includes:
s41, setting NF as {0}, Fu as + ∞;
s42, selecting a subscript k belonging to NF, solving the relaxation problem of the distribution network reconstruction problem (Pk) which minimizes expected power failure loss by using a simple method, and setting the reconstruction scheme with the minimum power failure loss as x (k), wherein the power failure loss is fk which is the lower bound of the optimal value of the subproblem (Pk); if no feasible solution exists, setting fk to be + ∞;
S43, if fk is ∞, and the subproblem has no feasible solution, then NF is NF \ k (i.e. k element in NF is deleted), go to step S47; otherwise, executing step S44;
S44, if fk is larger than or equal to Fu, namely the power failure loss of the sub-problem is larger, and no better recovery scheme exists, setting NF as NF \ k }, and turning to the step S47; otherwise, executing step S44;
s45, if fk < Fu, x (k) belongs to S (P0), namely the power failure loss of the subproblem is smaller and the power failure time belongs to a feasible solution, updating the upper bound Fu of the minimum power failure loss and a decision variable set Fu ═ fk and NF ═ NF \ { k }, and turning to the step S47; otherwise, executing step S46;
s46, if fk < Fu, that is, the power outage loss of the subproblem is smaller but the power outage time does not belong to a feasible solution, then decomposing S (pk) into two subsets and placing NF ═ ({ k }) -u { k1, k2}, and going to step S42;
s47, if yes, turning to the step S42; if so, the optimal solution of the problem (P0) is obtained, namely the power distribution network reconstruction scheme Fu with the minimum power outage loss is the minimum power outage loss, and if the problem (P0) has no feasible solution.
power distribution network black start reconstruction method model simulation example based on minimized power failure loss
The proposed method of reconfiguration of a distribution network to minimize expected blackout losses is validated by the present example. The example carries out modeling in an MATLAB environment, and calls a CPLEX solver to realize efficient solving, the CPU main frequency of the simulation computer of the example is 4.3GHz, and the memory is 12 GB.
the calculation example is based on an IEEE33 node power distribution system, and is improved, as shown in FIG. 5, distributed power supplies are added at nodes 1, 7, 12, 17, 20 and 32, and sequentially include DG1, DG2, DG3, DG4, DG5 and DG6, unit parameters are shown in table 1, and load and line parameters are shown in table 2, wherein loads at nodes j corresponding to load types TL 1-5 are respectively residential, government, commercial, small industry and industrial important loads. In this example, DG1 is used as a black start unit, the system availability factor α is 0.2, the load fluctuation coefficient β is 0.1, the maximum allowable frequency deviation of the system is 0.5Hz, the upper limit Kbr of the number of recovery lines at the same time is 2, and the discrete time step is 1 minute in consideration of the recovery operation within 60 minutes. Assuming that the system is partitioned, the optimal recovery sequence and recovery path of the unit and the load are solved by adopting the provided power distribution network reconstruction algorithm for minimizing the expected power failure loss, and the result is shown in table 3.
table 1 IEEE33 node distribution system unit parameters including DG
table 2IEEE33 node distribution system load and line parameters
TABLE 3IEEE33 node distribution system load and line parameters
in this example, DG1 is a black start power supply with self-start capability and stable output power, and is scheduled to start first at time 0; at 4 minutes, the output power of the DG1 can meet the requirement of the DG5 for starting, and the restoration path between the DG1 and the DG5 is charged, and the DG5 is restored; similarly, DG3, DG2, DG6, and DG4 obtain starting power at 7 minutes, 8 minutes, 10 minutes, and 11 minutes, respectively, to recover sequentially. The DG start sequence follows the black start principle of high capacity priority start, high load capacity priority start, and short start time priority start. On the premise of meeting system constraints, load recovery and DG starting are carried out simultaneously, for example, loads L12, L20, L29 and DG5 with large power failure loss are recovered simultaneously in 10 minutes, the load recovery efficiency is improved, and the total power failure loss of a power user is reduced. When the other loads have the recovery condition, the other loads are sequentially recovered according to the principle of priority recovery with large power failure loss. At 29 minutes, the black start reconfiguration of the distribution network is completed, and since the output power of DG in the system is less than the power demand of all loads, and considering that sufficient spare capacity should be left in the black start process, the loads L3, L7, L9, L10, L11, L25, L26, and L28 are not recovered. Through power flow verification, the voltage of each node and the line power are within an allowable range in the recovery process, and the recovery scheme does not need to be adjusted.
the black start reconstruction process schematic diagram of the IEEE33 node power distribution system is shown in fig. 6 to 10, and the bold black color represents the recovery action;
the power failure loss of the system in a 1-hour recovery period is 82.7125 ten thousand yuan and the calculation time is 288.82 seconds, which is obtained by solving the power distribution network reconstruction method for minimizing the expected power failure loss, and the method shows that the proposed black start optimization method can quickly obtain a high-precision optimized solution and can meet the requirement of making a power distribution network black start reconstruction strategy for minimizing the expected power failure loss.
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (9)
1. a black start reconstruction method for a power distribution network based on minimizing expected power outage loss is characterized by comprising the following steps:
s1, inputting original data including DG, load and line parameters of a power distribution network to be optimized, and providing load types and unit power failure loss for the load;
s2, determining relevant parameters of an optimization model according to engineering experience and actual needs, wherein the relevant parameters comprise a time period for restoring reconstruction, the number of lines allowed to be simultaneously input, a system standby rate, a load fluctuation coefficient and the maximum frequency deviation allowed by a system;
S3, calling the Yalmip to establish a black-start reconstruction model of the power distribution network based on the minimized expected power failure loss in the MATLAB environment;
S4, solving a power distribution network black start reconstruction model based on the minimized expected power failure loss by calling a CPLEX branch-and-bound method under an MATLAB environment to obtain a solution to be determined, wherein the solution to be determined corresponds to the recovery action of each moment in the power distribution network; firstly, before listing the concrete steps of solving the power distribution network reconstruction model for minimizing the expected power failure loss by adopting a branch-and-bound method, a plurality of symbols are defined: recording as (P0) a power distribution network reconfiguration problem that minimizes expected blackout losses; fu is an upper bound of an optimal value of an integer programming (P0), which represents the load power failure loss corresponding to the optimal power distribution network reconstruction scheme which can be found currently, and the initial setting can be positive infinity, and the load power failure loss is continuously updated along with the solution process; s (P0) is a feasible set of integer programming (P0) and corresponds to different power distribution network reconstruction schemes; (P1),. and (Pk) are the sub-problems resulting from the decomposition of (P0), whose feasible sets are S (P1),. and S (Pk), respectively; the relaxation linear plan of the sub-problem (Pi) is marked as a distribution network reconstruction scheme corresponding to the relaxation problem in a feasible set; NF is a subscript set of the problem (Pi) to be detected, is initially 0, and represents that the solution is started from (P0), and elements are deleted in the set NF along with the decomposition of the subproblem (Pi); a feasible solution of S (P0) represents decision variables used to determine an optimal power distribution network reconfiguration scheme, such as load outage duration tL, k, unit/load/line recovery actions u ' j, t/c ' k, t/br ' x, t at time t;
wherein, the specific solving step of the step of S4 includes:
S41, setting NF as {0}, Fu as + ∞;
S42, selecting a subscript k belonging to NF, solving the relaxation problem of the distribution network reconstruction problem (Pk) which minimizes expected power failure loss by using a simple method, and setting the reconstruction scheme with the minimum power failure loss as x (k), wherein the power failure loss is fk which is the lower bound of the optimal value of the subproblem (Pk); if no feasible solution exists, setting fk to be + ∞;
s43, if fk is + ∞, and the subproblem has no feasible solution, NF is NF \ k, and the step S47 is switched to; otherwise, executing step S44;
s44, if fk is larger than or equal to Fu, namely the power failure loss of the sub-problem is larger, and no better recovery scheme exists, setting NF as NF \ k }, and turning to the step S47; otherwise, executing step S44;
s45, if fk < Fu, x (k) belongs to S (P0), namely the power failure loss of the subproblem is smaller and the power failure time belongs to a feasible solution, updating the upper bound Fu of the minimum power failure loss and a decision variable set Fu ═ fk and NF ═ NF \ { k }, and turning to the step S47; otherwise, executing step S46;
S46, if fk < Fu, that is, the power outage loss of the subproblem is smaller but the power outage time does not belong to a feasible solution, then decomposing S (pk) into two subsets and placing NF ═ ({ k }) -u { k1, k2}, and going to step S42;
s47, if yes, turning to the step S42; if so, ending, namely, currently, obtaining the optimal solution of the problem (P0), namely, the power distribution network reconstruction scheme Fu with the minimum power outage loss is the minimum power outage loss, and if so, the problem (P0) has no feasible solution;
s5, carrying out power flow verification on the recovery action corresponding to the solution to be determined, if the safety constraint is not met, adding a constraint condition in a black start reconstruction model of the power distribution network established by Yalmip, setting the solution to be determined as an infeasible solution, namely, enabling a new optimized solution not to be equal to the original solution to be determined, so as to eliminate the solution to be determined which does not pass the power flow verification, turning to the step S4, and carrying out optimization again;
and S6, outputting a recovery action corresponding to the undetermined solution passing through the power flow verification, namely a power distribution network black start reconstruction scheme for minimizing expected power failure loss.
2. the method according to claim 1, wherein the step S3 specifically includes:
s31, defining a black start reconstruction model of the power distribution network: supposing that the power distribution network is completely powered off, the external input power is 0, namely the system is in an island state; assume that the recovery time of the load charging is 0; it is assumed that the line restoration operation can be completed within one period;
S32, establishing a target function: the method is characterized in that an economic means is adopted to quantify the accident loss, the power failure loss of users in the black starting process of the power distribution network is used for measuring the advantages and disadvantages of a network reconstruction scheme, and an objective function for minimizing the expected power failure loss of power users is established and expressed as follows:
in the formula, NL is the number of loads to be recovered, and PL and k are the power consumed by the load k; fk (tL, k) is the unit outage loss of the load k, and is related to the outage time tL, k of the load k and the load type;
and S33, setting constraint conditions, including unit power failure loss constraint, unit recovery constraint, line recovery constraint, bus recovery constraint, load recovery constraint, power balance constraint, system standby constraint and system frequency constraint.
3. A power distribution network black start reconfiguration method based on minimizing expected blackout loss according to claim 2, wherein said unit blackout loss constraint is expressed by a relationship of blackout time to load conditions:
the method comprises the steps of carrying out piecewise linearization processing on a load unit power failure loss curve, selecting NH sampling points (Xh, Fi, h), introducing continuous variables lambdai, h, lambdai, h is not less than 0 and NH-1 variables yh of 0-1, and enabling
Wherein tL and k are the power failure duration time of the load k; NH is the number of sampling points; xh and Fk, h are respectively the abscissa and the ordinate of the h sampling point; λ k,1, λ k, h, the 1 st, h th and NH th continuous variables introduced for the load k, respectively; yk,1, yk, h-1, yk, h and the 1 st, h-1 th, h and NH-1 th 0-1 variables introduced for the load k, respectively;
thus, fk (tL, k) can be represented linearly as:
4. a power distribution network black start reconfiguration method based on minimizing expected blackout losses according to claim 3, characterized in that said setting of unit restoration constraints mainly comprises the following steps:
s3311, the maximum output power of the unit is represented as:
in the formula: PG, j, t is the maximum output power of the unit j at the moment t; PGmax, j is the rated output power of the unit j; PGstart, j is the rated starting power of the unit j; TC, j is the time required by the unit j from starting to synchronously outputting power; rj is the load-lifting rate of the unit j; j is 0 for the black start power supply PGstart; tGstart, j is the starting time of the jth DG; t is the considered black start period;
the unit startup power is expressed as:
s3312, setting the state constraint of the unit as follows: during black start, the unit, once started, is no longer stopped, and is represented as:
u≥u
wherein t is a time index; uj, t is a variable from 0 to 1 and represents the running state of the unit j at the time t, uj, t is 1 and represents the unit running, uj, t is 0 and represents the unit not running;
s3313, introducing a 0-1 variable u' j, t to represent the starting state of the unit j at the moment t:
s3314, in the black start process, the started unit cannot be stopped, so the unit can be started at most once, and then:
uj, t can be expressed as:
Wherein t1 is a time index;
s3315, introduce a 0-1 variable v ' j, t representing the state of the unit j supplying power to the system at time t, v ' j, t ═ 1 represents that the unit supplies power to the system, v ' j, t ═ 0 represents that the unit does not supply power to the system, then:
S3316, introducing an integer variable vj, t, representing the accumulated time of the unit j supplying power to the system at the moment t:
s3317. the maximum output power constraint of the unit is expressed as:
P＝min(vR,P)
the starting power constraint of the unit is expressed as:
P＝uP；
s3318, for the non-black starting unit node, after the bus is recovered, the unit can be started, namely:
in the formula, Nb is the number of buses; BGb, j indicates the relationship between the unit j and the bus b, BGb, j equals 1 indicates that the unit j is connected with the bus b, BGb, j equals 0 indicates not connected; busb, t represents the state of the bus b at the time t, busb, t-1 represents that the bus b is recovered, and busb, t-0 represents that the bus b is not recovered.
5. the method of claim 4, wherein the step of setting the line restoration constraints comprises the steps of:
s3321, only when the bus at one end of the line is charged, the line can be restored, namely:
brx, t is the state of the line x at the time t, brx, t is 1 and brx, and t is 0 and does not input; BBx, b represents the relation between the bus b and the line x, BBx, b-1 represents that the bus b is connected with the line x, BBx, and b-0 represents that the bus b is not connected with the line x;
s3322, limiting the number of lines recovered at the same time:
in the formula, Nbr is the number of lines; br 'x, t is the putting state of the line x at the time t, if and only if the line is put into operation at the time t, br' x, t is 1, and the rest of the time is 0; kbr is the maximum number of lines allowed to be recovered at the same time;
s3323. once the line is restored, it is not cut off, that is:
br≥br
6. a distribution network black start reconfiguration method based on minimizing expected blackout losses according to claim 5, wherein said setting of bus recovery constraints essentially comprises the steps of:
s3331, bus recovery can be realized in two modes of starting by a black-start unit or connecting a line, namely:
in the formula, the influence of the black start unit on the state of the bus is shown, the bus b can be recovered in a mode of starting the black start unit at the time t, and the bus b cannot be started; the bus state recovery method comprises the steps of showing the influence of a line on the state of a bus, showing that the bus b can be recovered in a line connection mode at the time t, and showing that the bus b cannot be recovered;
the above formula can be expressed as:
s3332, after the black start unit is started, the bus where the black start unit is located can be recovered, namely:
in the formula, BGbj, b represents the relationship between the black start unit j and the bus b, BGbj, b ═ 1 represents that the black start unit j is connected with the bus b, and BGbj, b ═ 0 represents that the black start unit j is not connected;
If the line to which the bus bar is connected has been restored, the bus bar can be restored, i.e.:
in the formula, BBx, b represents the relationship between the bus b and the line x, BBx, b-1 represents that the bus b is connected with the line x, BBx, and b-0 represents that the bus b is not connected with the line x;
Once the bus bar is restored, it is no longer de-energized, i.e.:
bus≥bus。
7. the method of claim 6, wherein the setting of the load restoration constraints comprises the steps of:
S3341. according to the assumption, the load charge recovery time is 0, which is expressed as:
P＝cP
in the formula, PL, k and t are power consumed by the load k at the time t; PL, k is the power of load k; ck, t is a variable from 0 to 1 and represents the state of the load k at the time t, wherein ck, t-1 represents recovery, and ck, t-0 represents non-recovery;
s3342, in the black start process, once the load is recovered, the load is not cut off, namely:
c≥c
S3343, introducing a 0-1 variable c' k, t, which represents the recovery of the load k at time t and is expressed as:
in the formula, tL and k are the time when the load k obtains the recovery power;
the load node state may be represented as:
s3344, for all load nodes, after the bus is recovered, the load can be recovered, namely:
where NL is the number of loads; BLb, k denotes the relationship between load k and bus b, BLb, k ═ 1 denotes that load k is connected to bus b, and BLb, k ═ 0 denotes that it is not connected.
8. The method of claim 7, wherein the system power balance constraint is expressed as:
in the formula, P 'G, j, t is the actual output power of the unit j at the moment t, and P' G, j, t is more than or equal to 0 and less than or equal to PG, j, t; NG is the number of units;
the system standby constraint is expressed as:
wherein, alpha is the system standby rate.
9. the black start reconstruction method for power distribution network based on minimizing expected blackout loss according to claim 8, wherein the frequency deviation caused by the change of the recovered load within a certain range is considered not to exceed the maximum frequency deviation allowed by the system, and is represented as:
Wherein, beta is the load fluctuation coefficient; Δ f is the maximum frequency deviation allowed by the system; KG, j is the unit adjusting power of the unit j; KL, k is the unit regulated power of load k.
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