CN107294101B - Multi-target unit combination model based on security domain target and constraint and solving method - Google Patents

Multi-target unit combination model based on security domain target and constraint and solving method Download PDF

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CN107294101B
CN107294101B CN201710534523.8A CN201710534523A CN107294101B CN 107294101 B CN107294101 B CN 107294101B CN 201710534523 A CN201710534523 A CN 201710534523A CN 107294101 B CN107294101 B CN 107294101B
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CN107294101A (en
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林涛
叶婧
陈汝斯
毕如玉
陈宝平
盛逸标
杨明臻
李勇
徐友平
徐遐龄
崔晓丹
李碧君
石渠
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STATE GRID CENTER CHINA GRID Co Ltd
State Grid Corp of China SGCC
Wuhan University WHU
State Grid Ningxia Electric Power Co Ltd
Nanjing NARI Group Corp
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STATE GRID CENTER CHINA GRID Co Ltd
State Grid Corp of China SGCC
Wuhan University WHU
State Grid Ningxia Electric Power Co Ltd
Nanjing NARI Group Corp
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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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention relates to a security domain target and constraint-based multi-target unit combination model and a solving method, and provides an improved unit combination method aiming at the problem that the existing unit combination method possibly causes that the active static security domain constraint is not satisfied. According to the method, the model conforms to the standard type of the mixed integer linear optimization problem by introducing the intermediate variable, and the multi-objective problem is solved by using an extended epsilon constraint method and optimization software CPLEX, so that a Pareto optimal solution set is obtained. The invention can coordinate economy and safety and better meet the actual power grid requirements.

Description

Multi-target unit combination model based on security domain target and constraint and solving method
Technical Field
The invention relates to the field of operation, analysis and scheduling of an electric power system, in particular to a multi-target unit combination model based on security domain targets and constraints and a solving method.
Background
The unit combination is the core part of the power generation plan, determines the start, stop and output of the units, and can be used for improving the economy and safety of the system. The traditional unit combination only considers the operation constraint and does not contain the network security constraint. In this case, the optimization results may violate network security constraints. With the access of high-permeability new energy, the randomness and the volatility of the new energy bring more serious challenges to the safety and stability problems of the system.
At present, direct current power flow, alternating current power flow or active static security domain constraints are considered in part of research. Compared with the AC and DC power flow constraint, the safety domain can give the distance between the current operating point and the safety boundary, and the safety margin can be quantitatively evaluated. And the single target of the lowest power generation cost or the largest safety margin is taken separately, so that the problems of small safety margin or poor economical efficiency of a scheduling scheme are easy to occur. And the multi-objective optimization can effectively consider the influence of a plurality of objectives and provide effective reference for operators. The conventional multi-objective optimization problem processing method is an artificial intelligence algorithm or a single-objective problem solving method by conversion. The artificial intelligence algorithm has the defects of dependence on an initial total group, unstable convergence, easy precocity and the like. The multi-target conversion single comprehensive target problem is solved, the essence of the method is that the single target optimization problem is solved, and a Pareto optimal solution set cannot be obtained. The method for expanding the epsilon constraint has the characteristics of high calculation efficiency, capability of ensuring the effectiveness of Pareto solution and capability of being effectively combined with commercial software CPLEX, GUROBI and the like for solving the mixed integer optimization problem. However, the application of the extended epsilon constraint method in the optimization problem of the power system is not reported. In addition, optimization solving software such as CPLEX, GUROBI and the like can quickly and efficiently obtain the optimal solution of the mixed integer linear optimization problem, so that the mode of converting the established model into the mixed integer linear optimization problem is also the key of model establishment and solving.
Disclosure of Invention
The invention provides a multi-target unit combination model based on security domain targets and constraints. Because the target function expression of the security domain contains absolute values and does not meet the standard form of mixed integer optimization, the invention provides a method for leading a model to conform to the standard form of the mixed integer linear optimization problem by introducing intermediate variables SP1 and SP2, and solving the multi-target problem by utilizing an extended epsilon constraint method and optimization software CPLEX. Therefore, the unit combination method which has both safety and economy is provided.
A multi-target unit combination model and a solving method based on security domain targets and constraints are characterized in that the model is based on the following target functions and constraint conditions:
the objective function is in a multi-objective form:
in the formula: fl(X) is the l-th objective function; x is a decision vector; gj(X)、hk(X) is an equality or inequality constraint functionCounting; n is1、n2The number of equality constraints and inequality constraints;
one of the objective functions is defined as the lowest cost of system power generation based on:
Figure BDA0001340274150000022
in the formula PitOutputting active power for the conventional unit i in a time period t; f. ofit(Pit) The running cost of the conventional unit i is reduced; u shapeitFor starting and stopping state of conventional unit i in time period t, Uit1 denotes operation, UitA stop is indicated by a value of 0,
Figure BDA0001340274150000023
ai、bi、cia coefficient that is a cost function; sitStarting cost for the unit i in a time period t;
the second objective function is defined as the maximum total margin of the active static security domain of the system, and is based on:
Figure BDA0001340274150000031
Figure BDA0001340274150000032
Figure BDA0001340274150000033
in the formula: alpha is alphakiThe active static security domain coefficient is determined by the system structure parameter;the load and the active upper limit value of the branch k determine;
Figure BDA00013402741500000317
the load and the active lower limit value of the branch k determine;
Figure BDA00013402741500000316
is the transmission capacity margin scheduled for branch k in time period t; etatIn a time period t, the branch transmission capacity margin of the scheduling scheme is obtained; eta is the active static safety margin measure in the whole scheduling period; b is the set of all branches in the system;
the constraint conditions are as follows:
and (3) power generation and load power balance constraint of a conventional unit:
Figure BDA0001340274150000035
a formula seven; system rotation reserve capacity
Figure BDA0001340274150000036
A eighth formula;
Figure BDA0001340274150000037
nine is shown; constraint of upper and lower limits of active output of unit
Figure BDA0001340274150000038
Formula ten; unit active power ramp rate constraint Di≤Pit-Pi(t-1)≤LiEleven; minimum on-off time constraint
Figure BDA0001340274150000039
Twelve formulas,
Figure BDA00013402741500000310
Thirteen of the formula; branch active static safety constraint
Figure BDA00013402741500000311
Fourteen of the formula; in the formula PLtThe predicted value of the load in the t-th time interval is obtained;
Figure BDA00013402741500000312
the upper limit and the lower limit of the output of the unit i are respectively set; l isi、DiThe upper limit and the lower limit of the climbing slope of the ith unit;
Figure BDA00013402741500000314
the time of the ith unit is continuously started and stopped in the time period t respectively; UT (unified device)i、DTiRespectively the minimum starting time and the minimum stopping time of the ith unit; pdmax、PdminThe upper limit and the lower limit of the active power flow of the branch d are respectively; c. CdtThe load power of each node is related to the time period t;
the optimization method specifically comprises the following steps:
step 1: acquiring unit characteristic data of each generator set of the power system, wherein the unit characteristic data comprises an active power output upper limit, an active power output lower limit, a climbing rate, minimum start-stop time and minimum start-stop time; the load predicted value of each time interval in 24 time intervals; network structure parameters including node and branch connection conditions, and branch active power flow upper and lower limits; and calculating formula III according to load prediction data and network structure parameters
Figure BDA0001340274150000041
Step 2: will be in the model
Figure BDA0001340274150000042
Conversion to max (SP)1,SP2) In the form of (a);
and step 3: considering only the objective function F1Obtaining an optimal value F of the first objective function1'; optimizing a second objective function and adding F1＝F1' As a constraint, take F2To optimize the objective, obtain F at this time2Of (2) an optimal solution F2'; similar to the calculation method of the first row of data, only with F2As the objective function, the optimum value of the second objective function at that time is obtainedThen only the first objective function is considered and
Figure BDA0001340274150000044
as a constraint, take F1To optimize the objective, obtain F at this time1Optimum value of (2)
Figure BDA0001340274150000045
The payment table is obtained as shown in table 1;
table 1 Payment Table
And 4, step 4: by maximum value of corresponding objective function l in column l of payment table
Figure BDA0001340274150000047
Minimum value
Figure BDA0001340274150000048
Calculating to obtain a span value of the objective function l, wherein the calculation method comprises the following steps:
Figure BDA0001340274150000049
and 5: the multi-objective optimization problem is finally converted into a group of single-objective optimization problems and solved, and the method comprises the following steps:
Figure BDA00013402741500000410
s.t.F2-s2＝e2sixteen formula
Figure BDA00013402741500000411
In the formula q2The number of intervals taken in the calculation; s2A relaxation variable introduced for newly added constraint conditions;
step 6: calculating a group of single-target optimization problems in the step 5 through CPLEX, and calculating an optimal compromise solution by adopting a fuzzy set theory; the satisfaction degree corresponding to each objective function in each Pareto optimal solution can be represented by a fuzzy membership function, and finally the Pareto optimal solution with the maximum mu value is determined as an optimal compromise solution; the calculation method is as follows:
Figure BDA0001340274150000051
in the multi-target unit combination model and the solving method based on the security domain target and the constraint, the formula III
Figure BDA0001340274150000054
Conversion to the following form:
Figure BDA0001340274150000055
Figure BDA0001340274150000056
compared with the prior art, the invention has the following advantages and effects: the invention establishes a multi-target unit combination model based on the security domain target and the constraint, and overcomes the problem that the optimization result of the traditional unit combination may not meet the security domain constraint. And the multi-objective optimization model is converted into a group of single-objective optimization problems by an extended epsilon constraint method, and the problems are converted into an MILP form, so that the problems can be solved through MILP commercial software, and the method has good popularization and application values and prospects.
Drawings
FIG. 1 is a computational flow diagram of the method of the present invention.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and data analysis.
Example (b):
firstly, the specific method steps of the invention are introduced:
the model of the invention is based on the following objective functions and constraints:
the objective function is in a multi-objective form:
Figure BDA0001340274150000061
in the formula: fl(X) is the l-th objective function; x is a decision vector; gj(X)、hk(X) is an equality and inequality constraint function; n is1、n2The number of equality constraints and inequality constraints.
One of the objective functions is defined as the lowest cost of system power generation based on:
in the formula PitOutputting active power for the conventional unit i in a time period t; f. ofit(Pit) The running cost of the conventional unit i is reduced; u shapeitFor starting and stopping state of conventional unit i in time period t, Uit1 denotes operation, UitA stop is indicated by a value of 0,
Figure BDA0001340274150000063
ai、bi、cia coefficient that is a cost function; sitAnd starting cost for the unit i in the time period t.
The second objective function is defined as the maximum measure index of the active static security domain of the system, and is based on:
Figure BDA0001340274150000065
Figure BDA0001340274150000066
Figure BDA0001340274150000067
in the formula: alpha is alphakiThe active static security domain coefficient is determined by the system structure parameter;the load and the active upper limit value of the branch k determine;
Figure BDA0001340274150000072
the load and the active lower limit value of the branch k determine;
Figure BDA0001340274150000073
is the transmission capacity margin scheduled for branch k in time period t; etatIn a time period t, the branch transmission capacity margin of the scheduling scheme is obtained; eta is the active static safety margin measure in the whole scheduling period; and B is the set of all branches in the system.
The constraint conditions are as follows:
and (3) power generation and load power balance constraint of a conventional unit:a formula seven; system rotation reserve capacity
Figure BDA0001340274150000075
A eighth formula;
Figure BDA0001340274150000076
nine is shown; constraint of upper and lower limits of active output of unit
Figure BDA0001340274150000077
Formula ten; unit active power ramp rate constraint Di≤Pit-Pi(t-1)≤LiEleven; minimum on-off time constraint
Figure BDA0001340274150000078
Twelve formulas,
Figure BDA0001340274150000079
Thirteen of the formula; branch active static safety constraint
Figure BDA00013402741500000710
And fourteen in formula. In the formula PLtThe predicted value of the load in the t-th time interval is obtained;
Figure BDA00013402741500000711
Figure BDA00013402741500000712
the upper limit and the lower limit of the output of the unit i are respectively set; l isi、DiThe upper limit and the lower limit of the climbing slope of the ith unit;the time of the ith unit is continuously started and stopped in the time period t respectively; UT (unified device)i、DTiRespectively the minimum starting time and the minimum stopping time of the ith unit; pdmax、PdminThe upper limit and the lower limit of the active power flow of the branch d are respectively; c. CdtIn relation to the load power of the respective node for time period t.
The specific treatment comprises the following steps:
step 1: acquiring unit characteristic data, load prediction data and network structure parameters of each generator set of the power system, and calculating the parameters according to the load prediction data and the network structure parameters;
step 2: establishing a multi-target unit combination model based on security domain targets and constraints, and describing a target function and constraint conditions;
and step 3: target function F in established model2The expression contains absolute values and does not meet the standard form of mixed integer optimization, and the model is converted into a multi-objective mixed integer linear programming problem by introducing intermediate variables; the formula III in the step 3 contains absolute value calculation, optimization software CPLEX cannot perform optimization calculation on the objective function in the form, and the formula III
Figure BDA0001340274150000081
Conversion to the following form:
Figure BDA0001340274150000082
Figure BDA0001340274150000084
and 4, step 4: optimizing each sub-target according to the dictionary sequence to obtain a payment table; the method for optimizing each sub-target according to the dictionary sequence in the step 4 to obtain the payment table is as follows:
considering only the objective function F1Obtaining an optimal value F of the first objective function1'. Optimizing a second objective function and adding F1＝F1' As a constraint, take F2To optimize the objective, obtain F at this time2Of (2) an optimal solution F2'. Similar to the calculation method of the first row of data, only with F2As the objective function, the optimum value of the second objective function at that time is obtained
Figure BDA0001340274150000085
Then only the first objective function is considered and
Figure BDA0001340274150000086
as a constraint, take F1To optimize the objective, obtain F at this time1Optimum value of (2)
Figure BDA0001340274150000087
Table 1 Payment Table
Figure BDA0001340274150000088
And 5: the span value of the objective function l can be calculated through the maximum value and the minimum value of the objective function l corresponding to the ith column of the payment table, and the calculation method is as follows:
Figure BDA0001340274150000089
step 6: with (q)2-1) mesh points to the objective function F2Is divided into q2Are equally spaced. Taking into account the minimum and maximum values of the span, for F2Is shown by (q)2+1) grid points. The multiobjective optimization problem is thus finally transformed into (q)2+1) single-target optimization problems; in step 6, the multi-objective optimization problem is finally converted into a group of single-objective optimization problems and solved, and the method comprises the following steps:
Figure BDA00013402741500000810
s.t.F2-s2＝e2nineteen-form
Figure BDA0001340274150000091
In the formula
Figure BDA0001340274150000092
Representing an objective function F in a pay table2Maximum and minimum values of; r isiIs the span value of the objective function; q. q.s2The number of intervals of the 2 nd target; s2And (4) introducing relaxation variables for newly added constraint conditions.
And 7: using CPLEX pairs (q)2+1) single-target optimization problems are solved to obtain a final Pareto optimal solution set. Go toAnd step (3) solving the optimal compromise solution by adopting a fuzzy set theory.
In step 7, the optimal compromise solution needs to be calculated by adopting fuzzy set theory. And finally, determining the Pareto optimal solution with the maximum mu value as the optimal compromise solution. The calculation method is as follows:
second, the following is a specific example using the above method.
The method provided by the application is verified under a plurality of example models, is limited to space, and is used for analyzing and verifying the feasibility and effectiveness of the method provided by the application by taking a three-machine six-node system example as an example. The specific situation is as follows:
three schemes are designed to verify the effectiveness and superiority of the model provided by the text. Scheme I: conventional UC, target F1Irrespective of security domain constraints and target F2. Scheme II: the object is F2The security domain constraints are not considered. Scheme III: the multi-objective optimization model is provided.
Schemes II and III take into account SR constraints, so the results of schemes II and III fully satisfy the power flow constraints. Table 1 gives the active power flow of branch L2-3 for 24 periods under scheme I, with branch L2-3 allowing a maximum of 100MW of power to pass. The results of table 1 show that the active power flow of branch L2-3 is greater than the limit value for some time period, which means that the optimal scheduling scheme I does not meet the power flow constraint.
TABLE 1 active power flow of Branch L2-3
Figure BDA0001340274150000101
The cost of power generation and the security domain size for the three schemes are compared in table 2. Since scheme I does not consider security domain constraints or objectives, the scheme I optimization results do not satisfy the security domain constraints. The goal of scheme II is to maximize SR with the highest operating cost, 10.87% higher than the cost of power generation for scheme I. The pareto optimal compromise solution of solution III follows the trend constraints and has a lower operating cost than solution II.
TABLE 2 active power flow of Branch L2-3
Figure BDA0001340274150000102
According to the simulation experiment results, the method can comprehensively consider the goals of minimum power generation cost and maximum security domain in the unit combination, can effectively obtain a Pareto optimal solution set, can convert a model into a mixed integer linear optimization form, and is combined with commercial optimization software to quickly obtain an optimal compromise solution. The optimization result shows that the method has safety and economy, avoids the problem that the unit combination scheme does not meet the active static security domain, and shows that the method can meet the actual requirements of a power grid company and has important practical significance and good application prospect.

Claims (2)

1. A multi-target unit combination model and a solving method based on security domain targets and constraints are characterized in that the model is based on the following target functions and constraint conditions:
the objective function is in a multi-objective form:
Figure FDA0002237126910000011
in the formula: fl(X) is the l-th objective function; x is a decision vector; gj(X)、hk(X) is an equality and inequality constraint function; n is1、n2The number of equality constraints and inequality constraints;
one of the objective functions is defined as the lowest cost of system power generation based on:
Figure FDA0002237126910000012
in the formula PitOutputting active power for the conventional unit i in a time period t; f. ofit(Pit) The running cost of the conventional unit i is reduced; u shapeitFor starting and stopping state of conventional unit i in time period t, Uit1 denotes operation, UitA stop is indicated by a value of 0,
Figure FDA0002237126910000013
ai、bi、cia coefficient that is a cost function; sitStarting cost for the unit i in a time period t;
the second objective function is defined as the maximum total margin of the active static security domain of the system, and is based on:
Figure FDA0002237126910000014
Figure FDA0002237126910000015
Figure FDA0002237126910000016
Figure FDA0002237126910000017
in the formula: alpha is alphakiThe active static security domain coefficient is determined by the system structure parameter;
Figure FDA0002237126910000018
the load and the active upper limit value of the branch k determine;
Figure FDA0002237126910000021
the load and the active lower limit value of the branch k determine;
Figure FDA0002237126910000022
is the transmission capacity margin scheduled for branch k in time period t; etatIn a time period t, the branch transmission capacity margin of the scheduling scheme is obtained; eta is the active static safety margin measure in the whole scheduling period; b is the set of all branches in the system;
the constraint conditions are as follows:
and (3) power generation and load power balance constraint of a conventional unit:
Figure FDA0002237126910000023
system rotation reserve capacity
Figure FDA0002237126910000024
Unit active output upper and lower limit restraint Pi min≤Pit≤Pi maxFormula ten; unit active power ramp rate constraint Di≤Pit-Pi(t-1)≤LiEleven; minimum on-off time constraint
Figure FDA0002237126910000025
Branch active static safety constraint
Figure FDA0002237126910000026
In the formula PLtThe predicted value of the load in the t-th time interval is obtained; pi max、Pi minThe upper limit and the lower limit of the output of the unit i are respectively set; l isi、DiThe upper limit and the lower limit of the climbing slope of the ith unit;
Figure FDA0002237126910000027
the time of the ith unit is continuously started and stopped in the time period t respectively; UT (unified device)i、DTiAre respectively the firsti, the minimum starting and stopping time of the unit; pdmax、PdminThe upper limit and the lower limit of the active power flow of the branch d are respectively; c. CdtThe load power of each node is related to the time period t;
the optimization method specifically comprises the following steps:
step 1: acquiring unit characteristic data of each generator set of the power system, wherein the unit characteristic data comprises an active power output upper limit, an active power output lower limit, a climbing rate, minimum start-stop time and minimum start-stop time; the load predicted value of each time interval in 24 time intervals; network structure parameters including node and branch connection conditions, and branch active power flow upper and lower limits; and calculating formula III according to load prediction data and network structure parameters
Figure FDA0002237126910000028
Step 2: will be in the model
Figure FDA0002237126910000029
Conversion to max (SP)1,SP2) In the form of (a);
and step 3: considering only the objective function F1Obtaining an optimal value F of the first objective function1'; optimizing a second objective function and adding F1＝F1' As a constraint, take F2To optimize the objective, obtain F at this time2Of (2) an optimal solution F2'; similar to the calculation method of the first row of data, only with F2As the objective function, the optimum value of the second objective function at that time is obtained
Figure FDA0002237126910000031
Considering only the first objective function and dividing F2＝F2 *As a constraint, take F1To optimize the objective, obtain F at this time1Optimum value of F1 *(ii) a Obtaining a payment table;
and 4, step 4: by maximum value of corresponding objective function l in column l of payment table
Figure FDA0002237126910000032
Minimum value
Figure FDA0002237126910000033
Calculating to obtain a span value of the objective function l, wherein the calculation method comprises the following steps: r isl＝Fl max-Fl min；
And 5: the multi-objective optimization problem is finally converted into a group of single-objective optimization problems and solved, and the method comprises the following steps:
Figure FDA0002237126910000034
s.t.F2-s2＝e2sixteen formula
Figure FDA0002237126910000035
In the formula q2The number of intervals taken in the calculation; s2A relaxation variable introduced for newly added constraint conditions;
step 6: calculating a group of single-target optimization problems in the step 5 through CPLEX, and calculating an optimal compromise solution by adopting a fuzzy set theory; the satisfaction degree corresponding to each objective function in each Pareto optimal solution can be represented by a fuzzy membership function, and finally the Pareto optimal solution with the maximum mu value is determined as an optimal compromise solution; the calculation method is as follows:
Figure FDA0002237126910000036
Figure FDA0002237126910000037
Figure FDA0002237126910000038
2. the multi-objective unit combination model and solving method based on security domain objectives and constraints as claimed in claim 1, wherein the equation IIIConversion to the following form:
Figure FDA0002237126910000042
Figure FDA0002237126910000043
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