CN111092427A - Path optimization method for parallel recovery of power system - Google Patents

Path optimization method for parallel recovery of power system Download PDF

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CN111092427A
CN111092427A CN201911261330.5A CN201911261330A CN111092427A CN 111092427 A CN111092427 A CN 111092427A CN 201911261330 A CN201911261330 A CN 201911261330A CN 111092427 A CN111092427 A CN 111092427A
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time
power
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CN111092427B (en
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谢云云
李德正
蔡胜
杨正婷
吴昊
刘琳
谷志强
黄祥琪
郭伟清
严欣腾
张俊芳
殷明慧
卜京
邹云
姚娟
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Nanjing University of Science and Technology
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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 discloses a path optimization method for parallel recovery of an electric power system, which constructs active power constraint according to rated power, climbing rate, starting power, starting time and 0-1 variable of each unit; establishing a recovery time constraint of the power transmission line according to a system topological structure; establishing cold and hot start time limit constraint of the non-black start unit according to the maximum hot start time limit and the minimum cold start time limit; establishing a recovery target function according to the maximum target of the generated energy in the system recovery process; and solving a recovery path optimization model formed by the constraint conditions and the objective function, and determining the starting time and the recovery path of each unit. The invention greatly reduces the calculated amount, increases the application range of the model and better meets the requirement of the actual situation on the recovery scheme.

Description

Path optimization method for parallel recovery of power system
Technical Field
The invention belongs to the technical field of power grids, and particularly relates to a path optimization method for parallel recovery of a power system.
Background
With the development of power systems, the connection between regional power grids is becoming more and more intimate, and once a blackout accident caused by equipment failure, misoperation and severe weather occurs, huge economic loss and severe social influence can be caused. The recovery path optimization is important work in the recovery process of the power system after a blackout, and has important influence on improving the recovery efficiency of the power system and reducing economic and social losses. The existing restoration path optimization method mainly comprises two types: firstly, a nonlinear recovery path optimization model is established, and a meta-heuristic intelligent algorithm is used for solving, so that the solving efficiency is low, and the local optimal solution is easy to converge; secondly, the system topology structure is added into the recovery path optimization model in a connectivity constraint verification mode, the influence of the system topology structure on the recovery path optimization is weakened, and the optimality of the recovery scheme is reduced.
The method linearizes the topological structure of the system by utilizing the recovery time of the power transmission line, and establishes a recovery path optimization hybrid integer programming linear model which can simultaneously take the unit attribute and the topological structure of the power system into account.
Disclosure of Invention
The invention aims to provide a path optimization method for parallel recovery of a power system.
The technical solution for realizing the purpose of the invention is as follows: a path optimization method for parallel recovery of a power system comprises the following steps:
step 1, constructing active power constraint according to rated power, climbing rate, starting power, starting time and 0-1 variable of each unit;
step 2, establishing a power transmission line recovery time constraint according to a system topological structure;
step 3, establishing cold and hot start time limit constraint of the non-black start unit according to the maximum hot start time limit and the minimum cold start time limit;
step 4, establishing a recovery target function by taking the maximum generated energy in the system recovery process as a target;
and 5, solving a recovery path optimization model formed by the constraint conditions and the objective function, and determining the starting time and the recovery path of each unit.
Compared with the prior art, the invention has the following remarkable advantages: 1) the active power constraint is established by utilizing the rated power, the climbing rate, the starting power, the starting time and the 0-1 variable of each unit, so that the calculated amount is greatly reduced, the optimized model can be used for a larger-scale system, and the application range of the model is enlarged; 2) the influence of a system topological structure on the recovery path optimization is considered, and the scheduling requirement can be better adapted; 3) the maximum hot start time limit and the minimum cold start time limit of the unit can be considered at the same time, and the actual scheduling requirement is better met.
Drawings
Fig. 1 is a modeling flow chart of a parallel restoration path optimization model of an electric power system based on mixed integer programming.
Fig. 2 is a topology diagram of an IEEE standard 10 machine 39 node system according to the present invention.
FIG. 3 is a schematic diagram of a recovery area according to the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings.
The invention discloses a path optimization method for parallel recovery of a power system, which comprises the following steps:
step 1, constructing active power constraint by using rated power, climbing rate, starting power, starting time and 0-1 variable of each unit;
in the recovery process after the power system blackout, the active power of the system should be always non-negative, that is:
Figure BDA0002311675720000021
in the formula I, a unit set;
i-unit serial number;
pi(t) -the output power of the crew i at time t, which is a linear expression function of the crew properties:
Figure BDA0002311675720000022
wherein t is the current time;
xi-set i start-up time;
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
ri-the set i ramp rate;
ti rthe time required for the unit i to climb from 0 to rated power;
pi-rated power of unit i;
pi(t) -the output power of the unit i at time t;
t is the total time required by system recovery;
in order to linearly represent the active power constraint, p needs to be expressedi(t) linear expression function is rewritten asAs follows:
Figure BDA0002311675720000031
in the formula
Figure BDA0002311675720000032
A variable of 0 to 1, which indicates whether the unit i is between 0 and x at the time tiA stage;
Figure BDA0002311675720000033
a variable 0-1 representing whether the unit i is at x at time ti～xi+ti cA stage;
Figure BDA0002311675720000034
a variable 0-1 representing whether the unit i is at x at time ti+ti c～xi+ti c+ti rA stage;
Figure BDA0002311675720000035
a variable 0-1 representing whether the unit i is at x at time ti+ti c+ti r-T phase. When in use
Figure BDA0002311675720000036
Time, the unit i is between 0 and x at time tiA stage;
Figure BDA0002311675720000037
Figure BDA0002311675720000038
the same is true.
Substituting equation (3) for equation (1) may rewrite the active power constraint to the form:
Figure BDA0002311675720000039
through the analysis of the linear expression function of the unit attribute in the formula (2), the sum of the active power of the system is reduced only when each non-black start unit is started, so that the sum of the active power of the system is not negative only when each non-black start unit is started, and the sum of the active power of the system in the whole recovery process can be ensured to be not negative. Therefore, the active power constraint equation (4) can be further modified to the following form:
Figure BDA00023116757200000310
in the formula
Figure BDA00023116757200000311
A variable of-0 to 1, which indicates whether the unit i is between 0 and x when the unit m is startediA stage;
Figure BDA00023116757200000312
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi～xi+ti cA stage;
Figure BDA00023116757200000313
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi+ti c～xi+ti c+ti rA stage;
Figure BDA00023116757200000314
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi+ti c+ti r-T phase. When in use
Figure BDA00023116757200000315
When the time, the unit i is between 0 and x when the unit m is startediA stage;
Figure BDA00023116757200000316
the same is true.
The form of multiplication of variables appears in the active power constraint formula (5) —
Figure BDA00023116757200000317
Now, in the formula (5) by using the formula (6) -formula (9)
Figure BDA00023116757200000318
And carrying out linearization treatment.
Figure BDA00023116757200000319
Figure BDA00023116757200000320
Figure BDA00023116757200000321
Figure BDA00023116757200000322
In the formula wimA variable of-0 to 1
Figure BDA00023116757200000323
When wim0; when in use
Figure BDA00023116757200000324
When wim＝xi；
vimA variable of-0 to 1
Figure BDA00023116757200000325
When, vim0; when in use
Figure BDA00023116757200000326
When, vim＝xm；
Will assist variable wimAnd vimAfter equation (4) is substituted, the linear expression of the active power constraint is rewritten as:
Figure BDA0002311675720000041
according to the linear expression function formula (2) of the unit attributes, the output of the unit i is sequentially in 1 of 4 stages, namely:
Figure BDA0002311675720000042
for determining the state of the unit i when the unit m is started, a variable of 0-1 is set
Figure BDA0002311675720000043
The following constraints are constructed:
Figure BDA0002311675720000044
Figure BDA0002311675720000045
Figure BDA0002311675720000046
Figure BDA0002311675720000047
in the formula xm-start-up time of unit m;
xi-start-up time of unit i;
ε -a sufficiently small number close to 0, e.g. 10-4；
Maximum of M-big M algorithm, e.g. 107；
Step 2, establishing a power transmission line recovery time constraint according to a system topological structure;
firstly, partitioning a power failure system according to the number of black start units under the condition that the capacity-load basic balance of a subsystem unit is met, and ensuring that only one black start unit exists in each partition; then, each transmission line in each subarea is set according to the scheduling requirement or the actual situationThe recovery time of the way; and finally, calculating the recovery time T between the non-black start unit i and the black start unit in each partition by using a Floyd algorithmiAnd then the power transmission line recovery time constraint is as follows:
xi≥Ti(16)
step 3, establishing cold and hot start time limit constraint of the non-black start unit according to the maximum hot start time limit and the minimum cold start time limit;
Figure BDA0002311675720000048
Figure BDA0002311675720000049
Figure BDA00023116757200000410
in the formula hi-is the maximum warm start time limit for unit i;
ci-is the minimum cold start time limit for unit i;
Figure BDA0002311675720000051
a variable of-0 to 1
Figure BDA0002311675720000052
In time, the unit i is started before the maximum hot start time limit; when in use
Figure BDA0002311675720000053
When, the constraint fails;
Figure BDA0002311675720000054
a variable of-0 to 1
Figure BDA0002311675720000055
Then, the unit i is started after the minimum cold start time limit; when in use
Figure BDA0002311675720000056
When, the constraint fails;
and 4, establishing a recovery objective function according to the maximum target of the generated energy in the system recovery process.
The final aim of the recovery of the power system is to finish the starting and load recovery of all non-black start units of the system as soon as possible and reduce load loss. In order to improve the system recovery efficiency and reduce the load loss, the invention takes the maximum generating capacity of the unit in the system recovery process as a target function:
Figure BDA0002311675720000057
in the formula EsysThe total power generation of all the units in the system recovery process;
Eigen-the total force output value of the unit i in the recovery process;
Eicrankand the total power consumption of the unit i in the starting process.
In order to build a unit restoration path model based on mixed integer linear programming, the objective function described in the formula (20) is required to be simplified.
Because the total power generation amount of the system in the recovery process is equal to the integral of the output values of all the units to the recovery time of the system:
Figure BDA0002311675720000058
in the formula Eigen-the total force output value of the unit i in the recovery process;
pi(t) -the output power of the unit i at time t;
t is the current time;
pi-rated power of unit i;
ti rthe time required for the unit i to climb from 0 to rated power;
t is the total time required by system recovery;
xi-the unit i is openedThe moving time;
ti cthe time required by the unit i from starting to grid connection is shortened;
the total power consumption of the system in the recovery process is equal to the integral of the starting power of all the units to the recovery time of the system:
Figure BDA0002311675720000061
in the formula EicrankAnd the total power consumption of the unit i in the starting process.
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
substituting formulae (21) and (22) for formula (20) yields:
Figure BDA0002311675720000062
in the formula EsysThe total power generation of all the units in the system recovery process;
Eigen-the total force output value of the unit i in the recovery process;
Eicrankand the total power consumption of the unit i in the starting process.
pi-rated power of unit i;
ti rthe time required for the unit i to climb from 0 to rated power;
t is the total time required by system recovery;
xi-set i start-up time;
ti cthe time required by the unit i from starting to grid connection is shortened;
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
wherein the content of the first and second substances,
Figure BDA0002311675720000063
and therefore equation (20) reduces to:
Figure BDA0002311675720000064
in the formula EsysThe total power generation of all the units in the system recovery process;
pi-rated power of unit i;
xi-set i start-up time;
and 5, solving a restoration path optimization model formed by the constraint conditions and the objective function by using CPLEX.
Constraint conditions are as follows: formula (6) -formula (19);
an objective function: formula (24);
firstly, a recovery path optimization model based on mixed integer linear programming is established according to the formula (6) -formula (19), and p in the formula (9) is respectively set according to the rated power, the climbing rate, the starting power and the starting time of each unit in the power failure systemi、ri、ci、ti c(ii) a H in the formula (16) is respectively set according to the maximum hot start time limit and the minimum cold start time limit of each unitiAnd c in formula (17)i。
Then, setting the recovery time of each section of power transmission line according to the scheduling requirement or the actual condition, and establishing a matrix representing the communication relation of each node of the system according to the system structure and the Floyd algorithm requirement:
① if node i is directly connected to node j, then (i, j) and (j, i) in the matrix are set as the recovery time of the line;
② if node i is not directly connected to node j, then (i, j) and (j, i) in the matrix are set to ∞.
Calling Floyd algorithm to obtain the shortest time between the black start unit 30 and all the non-black start units i, and the shortest time is T in the formula (16)iThe value is assigned to the value to be assigned,
and finally, calling and utilizing CPLEX to solve the recovery path optimization model, and obtaining the starting time and the recovery path of each unit.
Examples
In order to verify the effectiveness of the scheme of the invention, the following simulation experiment is performed by taking an IEEE10 machine 39 node system as an example. The power grid topology is shown in fig. 2, wherein the number 30 unit is a hydroelectric generating unit and has self-starting capability, and the rest are thermal generating units and do not have self-starting capability. All unit attribute data are shown in table 1.
TABLE 1 Unit Attribute
Figure BDA0002311675720000071
A restoration path optimization model based on mixed integer programming is established in MATLAB according to equations (6) -19.
The values of the relevant parameters in the equations (10), (17), (18) are assigned according to table 1:
① substituting rated power, ramp rate, start power and start time for p in formula (10)i、ri、ci、ti c；
② substituting the maximum warm boot time limit for h in equation (17)iC in formula (18) is substituted for minimum cold start time limiti。
Assuming that the recovery time of each section of power transmission line is 4 minutes, establishing a matrix representing the communication relation of each node of the system according to the system structure and the Floyd algorithm requirement:
① if node i is directly connected to node j, then (i, j) and (j, i) in the matrix are set to 4;
② if node i is not directly connected to node j, then (i, j) and (j, i) in the matrix are set to ∞.
Calling Floyd algorithm to obtain the shortest time between the black start unit 30 and all the non-black start units i, and the shortest time is T in the formula (16)iAnd (5) assigning values, wherein specific numerical values are shown in a table 2. According to scheduling requirements and actual conditions, the recovery time of each line can be flexibly set, if the line is in permanent failure or cannot be recovered due to other reasons, the recovery time can be set to be infinity in a node communication matrix, and then the Floyd algorithm is utilized to recalculate the unit recoveryTime constraints are sufficient.
TABLE 2 Transmission line recovery time constraints
Figure BDA0002311675720000081
And solving the recovery path optimization model by using a CPLEX solver to obtain the recovery time of each unit, wherein the recovery scheme is shown in a table 3.
TABLE 3 recovery scheme
Figure BDA0002311675720000091
Fig. 3 is a schematic diagram of a system recovered area, in which a solid line part represents a system recovered area at the current time, and a parallel recovery path of the power system can be obtained by the method of the present invention, which takes into account both the topology of the system and the properties of the unit.

Claims (6)

1. A path optimization method for parallel recovery of a power system is characterized by comprising the following steps:
step 1, constructing active power constraint according to rated power, climbing rate, starting power, starting time and 0-1 variable of each unit;
step 2, establishing a power transmission line recovery time constraint according to a system topological structure;
step 3, establishing cold and hot start time limit constraint of the non-black start unit according to the maximum hot start time limit and the minimum cold start time limit;
step 4, establishing a recovery target function by taking the maximum generated energy in the system recovery process as a target;
and 5, solving a recovery path optimization model formed by the constraint conditions and the objective function, and determining the starting time and the recovery path of each unit.
2. The method for optimizing paths for parallel restoration of an electric power system according to claim 1, wherein in step 1, the active power constraint specifically includes:
Figure FDA0002311675710000011
in the formula I, a unit set;
i-unit serial number;
pi(t) -the output power of the crew i at time t, which is a linear expression function of the crew properties:
Figure FDA0002311675710000012
wherein t is the current time;
xi-set i start-up time;
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
ri-the set i ramp rate;
ti rthe time required for the unit i to climb from 0 to rated power;
pi-rated power of unit i;
pi(t) -the output power of the unit i at time t;
t is the total time required by system recovery;
in order to linearly represent the active power constraint, p needs to be expressediThe linear expression function of (t) is rewritten as follows:
Figure FDA0002311675710000021
in the formula
Figure FDA0002311675710000022
A variable of 0 to 1, which indicates whether the unit i is between 0 and x at the time tiA stage;
Figure FDA0002311675710000023
a variable 0-1 representing whether the unit i is at x at time ti～xi+ti cA stage;
Figure FDA0002311675710000024
a variable 0-1 representing whether the unit i is at x at time ti+ti c～xi+ti c+ti rA stage;
Figure FDA0002311675710000025
a variable 0-1 representing whether the unit i is at x at time ti+ti c+ti r-T phase. When in use
Figure FDA0002311675710000026
Time, the unit i is between 0 and x at time tiA stage;
Figure FDA0002311675710000027
Figure FDA0002311675710000028
the same process is carried out;
substituting equation (3) for equation (1), the active power constraint is rewritten as follows:
Figure FDA0002311675710000029
through the analysis of the linear expression function of the unit attribute of the formula (2), the sum of the active power of the system is only reduced when each non-black start unit is started, so that the sum of the active power of the system is not negative only when each non-black start unit is started, that is, the sum of the active power of the system in the whole recovery process is not negative, therefore, the active power constraint formula (4) can be further rewritten into the following form:
Figure FDA00023116757100000210
in the formula
Figure FDA00023116757100000211
A variable of-0 to 1, which indicates whether the unit i is between 0 and x when the unit m is startediA stage;
Figure FDA00023116757100000212
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi～xi+ti cA stage;
Figure FDA00023116757100000213
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi+ti c～xi+ti c+ti rA stage;
Figure FDA00023116757100000214
a variable of 0 to 1 representing whether the unit i is at x or not when the unit m is startedi+ti c+ti r-T phase. When in use
Figure FDA00023116757100000215
When the time, the unit i is between 0 and x when the unit m is startediA stage;
Figure FDA00023116757100000216
the same is true.
The form of multiplication of variables appears in the active power constraint formula (5) —
Figure FDA00023116757100000217
Now, in the formula (5) by using the formula (6) -formula (9)
Figure FDA00023116757100000218
Carrying out linearization treatment;
Figure FDA00023116757100000219
Figure FDA00023116757100000220
Figure FDA00023116757100000221
Figure FDA00023116757100000222
in the formula wimA variable of-0 to 1
Figure FDA00023116757100000223
When wim0; when in use
Figure FDA00023116757100000224
When wim＝xi；
vimA variable of-0 to 1
Figure FDA00023116757100000225
When, vim0; when in use
Figure FDA00023116757100000226
When, vim＝xm；
Will assist variable wimAnd vimAfter equation (4) is substituted, the linear expression of the active power constraint is rewritten as:
Figure FDA0002311675710000031
according to the linear expression function formula (2) of the unit attributes, the output of the unit i is sequentially in 1 of 4 stages, namely:
Figure FDA0002311675710000032
for determining the state of the unit i when the unit m is started, a variable of 0-1 is set
Figure FDA0002311675710000033
The following constraints are constructed:
Figure FDA0002311675710000034
Figure FDA0002311675710000035
Figure FDA0002311675710000036
Figure FDA0002311675710000037
in the formula xm-start-up time of unit m;
xi-start-up time of unit i;
ε -a sufficiently small number close to 0;
m-maximum of the big M algorithm.
3. The method for optimizing the paths for the parallel restoration of the power system according to claim 1, wherein in the step 2, the specific method for establishing the power transmission line restoration time constraint is as follows:
firstly, partitioning a power failure system according to the number of black start units under the condition that the capacity-load basic balance of a subsystem unit is met, and ensuring that only one black start unit exists in each partition; then, setting the recovery time of each transmission line in each partition according to the scheduling requirement or the actual condition; and finally, calculating the recovery time T between the non-black start unit i and the black start unit in each partition by using a Floyd algorithmiAnd then the power transmission line recovery time constraint is as follows:
xi≥Ti(16)
in the formula xi-set i start time.
4. The method for optimizing the paths for the parallel recovery of the power system according to claim 1, wherein in step 3, the cold and hot start time limit of the non-black start unit is constrained as follows:
Figure FDA0002311675710000038
Figure FDA0002311675710000039
Figure FDA00023116757100000310
in the formula xi-set i start-up time;
hi-is the maximum warm start time limit for unit i;
ci-is the minimum cold start time limit for unit i;
Figure FDA0002311675710000041
a variable of-0 to 1
Figure FDA0002311675710000042
In time, the unit i is started before the maximum hot start time limit; when in use
Figure FDA0002311675710000043
When, the constraint fails;
Figure FDA0002311675710000044
a variable of-0 to 1
Figure FDA0002311675710000045
Then, the unit i is started after the minimum cold start time limit; when in use
Figure FDA0002311675710000046
When, the constraint fails;
m-maximum of the big M algorithm.
5. The method for optimizing paths for parallel restoration of a power system according to claim 1, wherein in step 4, the objective function is specifically:
Figure FDA0002311675710000047
in the formula EsysThe total power generation of all the units in the system recovery process;
Eigen-the total force output value of the unit i in the recovery process;
Eicrankand the total power consumption of the unit i in the starting process.
In order to establish a unit recovery path model based on mixed integer linear programming, the objective function described by the formula (20) is required to be simplified;
because the total power generation amount of the system in the recovery process is equal to the integral of the output values of all the units to the recovery time of the system:
Figure FDA0002311675710000048
in the formula Eigen-the total force output value of the unit i in the recovery process;
pi(t) -the output power of the unit i at time t;
t is the current time;
pi-rated power of unit i;
ti rthe time required for the unit i to climb from 0 to rated power;
t is the total time required by system recovery;
xi-set i start-up time;
ti cthe time required by the unit i from starting to grid connection is shortened;
the total power consumption of the system in the recovery process is equal to the integral of the starting power of all the units to the recovery time of the system:
Figure FDA0002311675710000051
in the formula EicrankAnd the total power consumption of the unit i in the starting process.
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
substituting formulae (21) and (22) for formula (20) yields:
Figure FDA0002311675710000052
in the formula EsysThe total power generation of all the units in the system recovery process;
Eigen-the total force output value of the unit i in the recovery process;
Eicrankand the total power consumption of the unit i in the starting process.
pi-rated power of unit i;
ti rthe time required for the unit i to climb from 0 to rated power;
t is the total time required by system recovery;
xi-set i start-up time;
ti cthe time required by the unit i from starting to grid connection is shortened;
ci-the power required for starting the unit i;
ti cthe time required by the unit i from starting to grid connection is shortened;
wherein the content of the first and second substances,
Figure FDA0002311675710000053
and therefore equation (20) reduces to:
Figure FDA0002311675710000054
in the formula EsysThe total power generation of all the units in the system recovery process;
pi-rated power of unit i;
xi-set i start time.
6. The method for optimizing paths for parallel restoration of a power system according to claim 1, wherein in step 5, the restoration path optimization model is solved by CPLEX.
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