CN111327052B - Method and device for accelerating and optimizing combination of power system units - Google Patents

Method and device for accelerating and optimizing combination of power system units Download PDF

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CN111327052B
CN111327052B CN202010172018.5A CN202010172018A CN111327052B CN 111327052 B CN111327052 B CN 111327052B CN 202010172018 A CN202010172018 A CN 202010172018A CN 111327052 B CN111327052 B CN 111327052B
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钟海旺
马子明
夏清
康重庆
王强
曹欣
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State Grid Corp of China SGCC
State Grid Hebei Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention provides a method and a device for accelerating and optimizing combination of units of an electric power system, and belongs to the technical field of electric power systems. The method comprises the steps of firstly obtaining basic data from a power system dispatching department, constructing a power system unit combination optimization model, relaxing 0-1 variable in the model into continuous variable with the value range of 0-1, then solving to obtain the optimal relaxation solution of the model, constructing a relaxation neighborhood search constraint and a symmetric induction function, then adding the relaxation neighborhood search constraint into the constraint condition of the original optimization model, adding the symmetric induction function into the target function of the original optimization model, constructing a power system unit combination optimization substitution model, and solving the substitution model to obtain a power system unit combination optimization result. The method greatly improves the combination optimization efficiency of the power system unit, improves the safety and stability of the operation of the power system, and can be applied to scheduling operation, risk evaluation and the like of the power system.

Description

Method and device for accelerating and optimizing combination of power system units
Technical Field
The invention belongs to the technical field of electric power systems, and particularly relates to the field of acceleration optimization of unit combination of an electric power system.
Background
The optimization of the power system unit combination is one of key technologies in the scheduling operation of the power system, and is used for obtaining a power system unit startup and shutdown scheme and a planned output curve, providing a scheme for the safe and stable operation of the power system, carrying out advanced arrangement on a power system production plan according to the scheme, and reserving sufficient time for the startup and adjustment of each device of the power system so as to ensure the safe and stable operation of the power system.
The core of the day-ahead plan is how to combine and optimize the units of the power system, and the work flow of the dispatching operation of the power system requires that the day-ahead plan must be completed within a certain time, otherwise, the work of making a unit start-up and shut-down scheme and a planned output curve cannot be completed, the advance arrangement of the production plan of the power system on the second day cannot be completed, and the safety and stability of the power system are seriously threatened.
With the development of electric power market construction, the day-ahead plan in the traditional planning mode is replaced by the day-ahead market, and the core of the clearing of the day-ahead market is still to optimize the combination of the electric power system units. The time for leaving the market in the day-ahead is very limited in the market flow in the day-ahead, and the requirement on the time for leaving the market is very strict. Because the generator set needs a long starting time and the unit combination optimization includes complex safety constraints, if the power system unit combination optimization result cannot be obtained within the set time, the day-ahead arrangement of the power system production plan of the second day is difficult to be stably and orderly completed, so that a great threat is caused to the safe and stable operation of the power system, and even a safe and stable power system operation mode may not be obtained.
The existing power system unit combination optimization model is shown as (1) - (12), and specifically comprises the following steps:
1) constructing an objective function of a power system unit combination optimization model, wherein the expression is as follows:
Figure GDA0002769399100000011
wherein, PktIs the output of the unit k in the time period t, f (-) is a varying cost function about the output of the unit, SUkIs the starting cost of unit k, yktIs a variable of 0-1 of the starting state of the unit k in the time period t, if the unit k is converted from the shutdown state to the starting state in the time period t, yktEqual to 1, otherwise 0, SDkFor the shutdown cost of unit k, zktIs the shutdown state 0-1 variable of the unit k in the time period t, if the unit k is converted from the startup state to the shutdown state in the time period t, z isktEqual to 1, otherwise 0;
2) the method comprises the following steps of constructing constraint conditions of a power system unit combination optimization model, specifically:
2-1) system load balancing constraints:
Figure GDA0002769399100000021
wherein D isbtThe load of the node b in the time period t, and the unit combination must meet the system load balance constraint of each time period;
2-2) technical constraint of the generator set:
Figure GDA0002769399100000022
Figure GDA0002769399100000023
Figure GDA0002769399100000024
Figure GDA0002769399100000025
Figure GDA0002769399100000026
Figure GDA0002769399100000027
Figure GDA0002769399100000028
Figure GDA0002769399100000029
Figure GDA00027693991000000210
wherein u isktIs a variable of 0-1 in the starting and stopping state of the unit k at the time t, and if the unit k is in the starting state at the time t, uktIs 1, if the unit k is in a shutdown state in a time period t, uktIs 0, Pk,minMinimum output of unit k, Pk,maxIs the maximum output of the unit k,
Figure GDA00027693991000000211
for the climbing capacity of unit k, Tk,onIs the minimum continuous start-up time, T, of unit kk,offMinimum continuous shutdown time, y, of unit kk,maxIs the maximum number of starts of unit k, zk,maxMaximum number of shutdowns of unit k, Ek,minIs the minimum generated electricity quantity of the unit k in all days, Ek,maxThe maximum generation electric quantity of the unit K in all days, KENumbering a set of generator sets with electric quantity constraint;
the constraint of the upper limit and the lower limit of the generating set is shown as a formula (3), the constraint of the upper limit and the lower limit of the climbing capability of the generating set is shown as a formula (4), and the constraint of the logical coupling of 0-1 integer variables is shown as a formula (5) and a formula (6), wherein the formula (5) shows that the difference between the startup state variable and the shutdown state variable of the generating set at the current time interval is the difference between the startup state variable and the startup state variable at the last time interval, the formula (6) shows that for a certain specific time interval of a certain generating set, the generating set is either opened or closed or maintained at the previous state, and is neither opened nor closed, the constraint of the minimum continuous startup time of the generating set is shown as a formula (7) and shows that once the generating set is opened, the startup state of the generating set must be maintained for a certain time and then closed, the constraint of the minimum continuous shutdown time of the generating set is shown, the maximum startup time constraint of the unit is shown as a formula (9), which indicates the maximum startup time of the unit in the whole day, the maximum shutdown time constraint of the unit is shown as a formula (10), which indicates the maximum shutdown time of the unit in the whole day, and the electric quantity constraint of the unit is shown as a formula (11);
2-3) constraint conditions of active transmission capacity of the line:
Figure GDA0002769399100000031
wherein, TPl,maxFor the maximum active transmission capacity of line l, the matrix G is the transfer distribution factor matrix for the node pair line, nkAnd numbering the nodes of the unit k.
However, the power system unit combination optimization is a large-scale mixed integer program, and in a modern power system, the scale of a power system unit combination optimization model is very large, and the solving efficiency is seriously reduced. In a provincial or regional power grid, a large number of units and a large number of line sections are provided, so that the combination state of unit combination is subjected to combination explosion, the constraint conditions are complicated, and the unit combination optimization efficiency is severely restricted. Taking a certain provincial power grid in China as an example, the provincial power grid comprises more than 200 direct-regulating power generating units and more than 1400 lines, and a unit combination model at 96 time intervals before day has more than 57000 0-1 variables, more than 20000 continuous variables and more than 38 ten thousand constraint conditions, so that the optimization model is very large in scale and low in combination optimization efficiency. Most of the current power system unit combination optimization directly calls a mixed integer programming solver to solve, and calculation is often required for hours.
Therefore, a new method for optimizing the combination of the units of the power system is urgently needed to improve the efficiency of optimizing the combination of the units of the power system, so that a high-quality feasible solution meeting the safety and stability constraints of the power system can be obtained within a specified time, and the safety and stability of the dispatching operation of the power system are improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method and a device for accelerating and optimizing the combination of a power system unit. The method greatly improves the optimization efficiency of the power system unit combination, can provide key technical support for the power system unit combination, solves the problems that the power system unit combination optimization model is complex in scale, too long in solving time, and high-quality feasible solutions or even feasible solutions cannot be obtained within a specified time, and improves the safety and stability of the power system operation.
The invention provides a combined acceleration optimization method for a power system unit, which is characterized by comprising the following steps of:
1) acquiring basic data from a power system dispatching department:
the basic data comprise unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data;
the unit cost data comprises a unit variation cost function, a unit startup cost and a unit shutdown cost;
the running characteristic data of the unit is output upper limit/lower limit data of the generator set, climbing capacity of the unit, minimum continuous startup time of the unit, minimum continuous shutdown time of the unit, maximum startup times of the unit and maximum shutdown times of the unit;
the unit electric quantity constraint data is the minimum generating electric quantity of the generator set all day and the maximum generating electric quantity of the generator set all day;
the day-ahead load prediction data is the power load demand condition of each node in each time interval on the second day;
the power grid topological data comprise the connection relation between nodes of a power network and power transmission lines, the maximum active transmission capacity of each line section and the line number contained in the maximum active transmission capacity, and generator output power transfer distribution factor matrix data of each power transmission line by each unit and node load;
2) constructing a power system unit combination optimization model:
2-1) constructing an objective function of the power system unit combination optimization model, wherein the expression is as follows:
Figure GDA0002769399100000041
wherein, PktIs the output of the unit k in the time period t, f (-) is a varying cost function about the output of the unit, SUkIs the starting cost of the unit k; y isktIs a variable of 0-1 of the starting state of the unit k in the time period t, if the unit k is converted from the shutdown state to the starting state in the time period t, yktEqual to 1, otherwise 0; SDkThe shutdown cost of the unit k; z is a radical ofktIs the shutdown state 0-1 variable of the unit k in the time period t, if the unit k is converted from the startup state to the shutdown state in the time period t, z isktEqual to 1, otherwise 0;
2-2) constructing constraint conditions of the power system unit combination optimization model, specifically as follows:
2-2-1) system load balancing constraints:
Figure GDA0002769399100000042
wherein D isbtIs the load of node b during time period t;
2-2-2) technical constraint of the generator set:
Figure GDA0002769399100000043
Figure GDA0002769399100000044
Figure GDA0002769399100000045
Figure GDA0002769399100000046
Figure GDA0002769399100000051
Figure GDA0002769399100000052
Figure GDA0002769399100000053
Figure GDA0002769399100000054
Figure GDA0002769399100000055
wherein u isktIs a variable of 0-1 in the starting and stopping state of the unit k at the time t, and if the unit k is in the starting state at the time t, uktIs 1, if the unit k is in a shutdown state in a time period t, uktIs 0; pk,minIs the minimum output of unit kForce, Pk,maxIs the maximum output of the unit k,
Figure GDA0002769399100000056
for the climbing capacity of unit k, Tk,onIs the minimum continuous start-up time, T, of unit kk,offMinimum continuous shutdown time, y, of unit kk,maxIs the maximum number of starts of unit k, zk,maxMaximum number of shutdowns of unit k, Ek,minIs the minimum generated electricity quantity of the unit k in all days, Ek,maxThe maximum generation electric quantity of the unit K in all days, KENumbering a set of generator sets with electric quantity constraint;
2-2-3) line active transmission capacity constraint:
Figure GDA0002769399100000057
wherein, TPl,maxFor the maximum active transmission capacity of line l, matrix G is the generator output power transfer distribution factor matrix for the node pair line, nkNumbering the nodes of the unit k;
3) solving a relaxation optimal solution of the power system unit combination optimization model established in the step 2); the method comprises the following specific steps:
3-1) relaxing 0-1 variable in the power system unit combination optimization model formed by the formulas (1) - (12) into continuous variable with the value range of 0-1 to form a relaxation model for power system unit combination optimization;
3-2) solving the relaxation model of the combination optimization of the power system unit to obtain the optimal relaxation solution x of the combination optimization of the power system unit*The method comprises the following steps: vector u of optimal solution of 0-1 variable relaxation in unit starting and stopping state*Vector y of optimal solution for 0-1 variable relaxation of starting state of unit*Vector z of the optimal solution for 0-1 variable relaxation of the shutdown state of a unit*Vector P of the optimal solution for the relaxation of the output variables of the unit*；
4) Constructing a relaxed neighborhood search constraint, which comprises the following specific steps:
4-1) constructing a relaxation distance expression according to the optimal relaxation solution of the power system unit combination optimization obtained in the step 3):
Figure GDA0002769399100000061
wherein RD (u, y, z, u)*,y*,z*) Representing the relaxation distance between any solution of the power system unit combination optimization model and the relaxation optimal solution, u is a vector of a unit startup and shutdown state variable 0-1, y is a vector of a unit startup state variable 0-1, z is a vector of a unit shutdown state variable 0-1, u is a vector of a unit shutdown state variable 0-1*Vector, y, of the optimal solution for the unit startup and shutdown state 0-1 variable relaxation*Vector, z, of the optimal solution for the unit startup state 0-1 variable relaxation*The vector of the optimal solution is relaxed for the unit shutdown state 0-1 variable,
Figure GDA0002769399100000062
for unit start-up and shut-down state 0-1 variable uktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000063
for the unit starting state 0-1 variable yktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000064
for a unit shutdown state 0-1 variable zktα (·) is a function for determining the weight coefficient, and the expression is shown as (14):
Figure GDA0002769399100000065
4-2) constructing search neighborhood search constraints, as shown in formula (15):
RD(u,y,z,u*,y*,z*)≤r (15)
wherein r is a neighborhood radius coefficient;
5) constructing a symmetric induction function, as shown in equation (16):
Figure GDA0002769399100000066
wherein, IF (u, y, z, u)*,y*,z*) Representing a symmetric induction function obtained based on a relaxation optimal solution, wherein W is a weight coefficient of the symmetric induction function;
6) adding an equation (15) serving as a constraint condition into the constraint condition of the power system unit combination optimization model in the step 2), adding an equation (16) into an objective function of the power system unit combination optimization model in the step 2), and constructing a power system unit combination optimization substitution model;
the objective function of the combined optimization substitution model of the power system unit is shown as the following formula (17):
Figure GDA0002769399100000071
7) solving the combined optimization substitution model of the power system unit to obtain a combined optimization result x' of the power system unit, comprising the following steps: the unit startup and shutdown state 0-1 variable optimization result vector u ', the unit startup state 0-1 variable optimization result vector y', the unit shutdown state 0-1 variable optimization result vector z ', and the unit output variable optimization result vector P'.
The invention has the technical characteristics and beneficial effects that:
the invention provides a method and a device for accelerating optimization of a power system unit combination, provides a relaxation neighborhood search constraint and a symmetry induction function capable of improving the efficiency of the power system unit combination optimization, and realizes accelerating solution of a power system unit combination optimization model by constructing a substitution model. The method greatly improves the optimization efficiency of the power system unit combination, can provide key technical support for the power system unit combination, solves the problems that the power system unit combination optimization model is complex in scale, too long in solving time, and high-quality feasible solutions or even feasible solutions cannot be obtained within a specified time, improves the safety and stability of the power system operation, and can be applied to scheduling operation, risk assessment and the like of the power system.
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FIG. 1 is an overall flow diagram of the method of the present invention.
Detailed Description
The invention provides a method and a device for accelerating and optimizing the combination of a power system unit, which are further described in detail with reference to the accompanying drawings and specific implementation modes; it should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a combined accelerated optimization method for a power system unit, the overall flow is shown as figure 1, and the method comprises the following specific steps:
1) acquiring basic data from a power system dispatching department:
the basic data comprise unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data;
the unit cost data comprises a unit variation cost function, a unit startup cost and a unit shutdown cost;
the running characteristic data of the unit is output upper limit/lower limit data of the generator set, climbing capacity of the unit, minimum continuous startup time of the unit, minimum continuous shutdown time of the unit, maximum startup times of the unit and maximum shutdown times of the unit;
the unit electric quantity constraint data is the minimum generating electric quantity of the generator set all day and the maximum generating electric quantity of the generator set all day;
the day-ahead load prediction data is the power load demand condition of each node in each time interval of the second day, which is obtained by the power dispatching mechanism according to a certain technical means;
the power grid topological data comprise the connection relation between nodes of a power network and power transmission lines, the maximum active transmission capacity of each line section and the line number contained in the maximum active transmission capacity, and generator output power transfer distribution factor matrix data of each power transmission line by each unit and node load;
2) constructing a power system unit combination optimization model:
2-1) constructing an objective function of the power system unit combination optimization model, wherein the expression is as follows:
Figure GDA0002769399100000081
wherein, PktIs the output of the unit k in the time period t, f (-) is a varying cost function about the output of the unit, SUkIs the starting cost of the unit k; y isktIs a variable of 0-1 of the starting state of the unit k in the time period t, if the unit k is converted from the shutdown state to the starting state in the time period t, yktEqual to 1, otherwise 0; SDkThe shutdown cost of the unit k; z is a radical ofktIs the shutdown state 0-1 variable of the unit k in the time period t, if the unit k is converted from the startup state to the shutdown state in the time period t, z isktEqual to 1, otherwise 0;
2-2) constructing constraint conditions of the power system unit combination optimization model, specifically as follows:
2-2-1) system load balancing constraints:
Figure GDA0002769399100000082
wherein D isbtThe load of the node b in the time period t, and the unit combination must meet the system load balance constraint of each time period;
2-2-2) technical constraint of the generator set:
Figure GDA0002769399100000083
Figure GDA0002769399100000084
Figure GDA0002769399100000085
Figure GDA0002769399100000086
Figure GDA0002769399100000087
Figure GDA0002769399100000088
Figure GDA0002769399100000089
Figure GDA0002769399100000091
Figure GDA0002769399100000092
wherein u isktIs a variable of 0-1 in the starting and stopping state of the unit k at the time t, and if the unit k is in the starting state at the time t, uktIs 1, if the unit k is in a shutdown state in a time period t, uktIs 0; pk,minMinimum output of unit k, Pk,maxIs the maximum output of the unit k,
Figure GDA0002769399100000094
for the climbing capacity of unit k, Tk,onIs the minimum continuous start-up time, T, of unit kk,offMinimum continuous shutdown time, y, of unit kk,maxIs the maximum number of starts of unit k, zk,maxMaximum number of shutdowns of unit k, Ek,minIs the minimum generated electricity quantity of the unit k in all days, Ek,maxThe maximum generation electric quantity of the unit K in all days, KENumbering a set of generator sets with electric quantity constraint;
the constraint of the upper limit and the lower limit of the generating set is shown as a formula (3), the constraint of the upper limit and the lower limit of the climbing capability of the generating set is shown as a formula (4), and the constraint of the logical coupling of 0-1 integer variables is shown as a formula (5) and a formula (6), wherein the formula (5) shows that the difference between the startup state variable and the shutdown state variable of the generating set at the current time interval is the difference between the startup state variable and the startup state variable at the last time interval, the formula (6) shows that for a certain specific time interval of a certain generating set, the generating set is either opened or closed or maintained at the previous state, and is neither opened nor closed, the constraint of the minimum continuous startup time of the generating set is shown as a formula (7) and shows that once the generating set is opened, the startup state of the generating set must be maintained for a certain time and then closed, the constraint of the minimum continuous shutdown time of the generating set is shown, the maximum startup time constraint of the unit is shown as a formula (9), which indicates the maximum startup time of the unit in the whole day, the maximum shutdown time constraint of the unit is shown as a formula (10), which indicates the maximum shutdown time of the unit in the whole day, and the electric quantity constraint of the unit is shown as a formula (11);
2-2-3) line active transmission capacity constraint:
Figure GDA0002769399100000093
wherein, TPl,maxFor the maximum active transmission capacity of line l, matrix G is the generator output power transfer distribution factor matrix for the node pair line, nkNumbering the nodes of the unit k;
3) solving a relaxation optimal solution of the power system unit combination optimization model established in the step 2); the method comprises the following specific steps:
3-1) relaxing 0-1 variable in the power system unit combination optimization model formed by the formulas (1) - (12) into continuous variable with the value range of 0-1 to form a relaxation model for power system unit combination optimization;
3-2) solving the relaxation model of the combination optimization of the power system unit by adopting a linear programming solver to obtain an optimal relaxation solution x of the combination optimization of the power system unit*，x*The method comprises the following steps: vector u of optimal solution of 0-1 variable relaxation in unit starting and stopping state*Vector y of optimal solution for 0-1 variable relaxation of starting state of unit*Vector z of the optimal solution for 0-1 variable relaxation of the shutdown state of a unit*Vector P of the optimal solution for the relaxation of the output variables of the unit*；
4) Constructing a relaxed neighborhood search constraint, which comprises the following specific steps:
4-1) constructing a relaxation distance expression according to the optimal relaxation solution of the power system unit combination optimization obtained in the step 3):
Figure GDA0002769399100000101
wherein RD (u, y, z, u)*,y*,z*) Representing the relaxation distance between any solution of the power system unit combination optimization model and the relaxation optimal solution, u is a vector of a unit startup and shutdown state variable 0-1, y is a vector of a unit startup state variable 0-1, z is a vector of a unit shutdown state variable 0-1, u is a vector of a unit shutdown state variable 0-1*Vector, y, of the optimal solution for the unit startup and shutdown state 0-1 variable relaxation*Vector, z, of the optimal solution for the unit startup state 0-1 variable relaxation*The vector of the optimal solution is relaxed for the unit shutdown state 0-1 variable,
Figure GDA0002769399100000102
for unit start-up and shut-down state 0-1 variable uktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000103
for the unit starting state 0-1 variable yktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000104
for a unit shutdown state 0-1 variable zktα (·) is a function for determining a weight coefficient for describing the degree to which the relaxed optimal solution tends to its tendency, and is expressed as (14):
Figure GDA0002769399100000105
4-2) constructing search neighborhood search constraints, as shown in formula (15):
RD(u,y,z,u*,y*,z*)≤r (15)
wherein r is a neighborhood radius coefficient, the value range of r is a certain proportion of the number of 0-1 variables of the model in principle, and 5% -15% of the number of 0-1 variables of the model can be selected;
5) constructing a symmetric induction function, as shown in equation (16):
Figure GDA0002769399100000106
wherein, IF (u, y, z, u)*,y*,z*) Representing a symmetric induction function obtained based on a relaxed optimal solution, W is a weight coefficient of the symmetric induction function, and the value range of the weight coefficient is calculated according to the formula (13) to obtain a relaxed distance RD (u) corresponding to the relaxed optimal solution*,y*,z*,u*,y*,z*) And calculating to obtain a target function value obj (u) of the combined optimization model of the power system unit corresponding to the relaxation optimal solution according to the formula (1)*,y*,z*) Assuming that the interval tolerance (i.e., the calculation precision) set by the mixed integer linear programming solver is epsilon when the power system unit combination optimization model is solved, the value of W should be such that W · RD (u · RD)*,y*,z*,u*,y*,z*) To epsilon.obj (u)*,y*,z*) 0.2-0.4 times of;
6) adding an equation (15) serving as a constraint condition into the constraint condition of the power system unit combination optimization model in the step 2), adding an equation (16) into an objective function of the power system unit combination optimization model in the step 2), and constructing a power system unit combination optimization substitution model;
the objective function of the combined optimization substitution model of the power system unit is shown as the following formula (17):
Figure GDA0002769399100000111
7) solving the power system unit combination optimization substitution model by using a mixed integer linear programming solver to obtain a power system unit combination optimization result x ', x' comprising: the unit startup and shutdown state 0-1 variable optimization result vector u ', the unit startup state 0-1 variable optimization result vector y', the unit shutdown state 0-1 variable optimization result vector z ', and the unit output variable optimization result vector P'.
The invention also provides a combined accelerating device of the power system unit based on the method, which is characterized by comprising a data acquisition module, a model construction module, a relaxation solving module, a relaxation neighborhood search constraint and symmetry induction function module, a substitution model construction module and a calculation solving module which are sequentially connected;
the data acquisition module is used for acquiring basic data from a power system dispatching department and sending the acquired basic data to the model construction module; the basic data comprises unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data.
The model construction module is used for constructing a power system unit combination optimization model according to the basic data obtained from the data acquisition module and sending the model to the relaxation solving module;
the relaxation solving module is used for relaxing 0-1 variable in the combined optimization model of the power system unit into continuous variable with the value range of 0 to 1 to form a relaxation model for the combined optimization of the power system unit, solving a relaxation optimal solution of the combined optimization model of the power system unit and sending the relaxation optimal solution to the relaxation neighborhood search constraint and symmetric induction function module;
the relaxation neighborhood search constraint and symmetry induction function module comprises a relaxation neighborhood search constraint submodule and a symmetry induction function submodule;
the relaxation neighborhood search constraint submodule constructs a relaxation distance expression and a relaxation neighborhood search constraint by using a relaxation optimal solution, and then sends the relaxation neighborhood search constraint to the surrogate model construction module; (ii) a
The symmetric induction function submodule constructs a symmetric induction function by using the relaxed optimal solution structure and sends the symmetric induction function to the surrogate model constructing module;
the surrogate model building module is used for adding relaxed neighborhood search constraints into constraint conditions of the power system unit combination optimization model, adding a symmetric induction function into a target function of the power system unit combination optimization model, and building the power system unit combination optimization surrogate model;
and the calculation solving module is used for solving the combined optimization substitution model of the power system unit to obtain a combined optimization result of the power system unit.
The process according to the invention is further explained below with reference to a specific example:
in this embodiment, an IEEE-300 node power system is taken as an example to describe the method for accelerating and optimizing the combination of power system units proposed in the present invention, and verify the effect achieved by the present invention.
The embodiment provides a combined acceleration optimization method for a power system unit, which comprises the following steps:
1) acquiring basic data from a power system dispatching department:
the basic data comprise unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data;
the unit cost data comprises a unit variation cost function, a unit startup cost and a unit shutdown cost;
the running characteristic data of the unit is output upper limit/lower limit data of the generator set, climbing capacity of the unit, minimum continuous startup time of the unit, minimum continuous shutdown time of the unit, maximum startup times of the unit and maximum shutdown times of the unit;
the unit electric quantity constraint data is the minimum generating electric quantity of the generator set all day and the maximum generating electric quantity of the generator set all day;
the day-ahead load prediction data is the power load demand condition of each node in each time interval of the second day, which is obtained by the power dispatching mechanism according to a certain technical means;
the power grid topological data comprise the connection relation between nodes of a power network and power transmission lines, the maximum active transmission capacity of each line section and the line number contained in the maximum active transmission capacity, and generator output power transfer distribution factor matrix data of each power transmission line by each unit and node load;
the IEEE 300 node standard test system used in this embodiment has 300 nodes, 69 units of units and 411 transmission lines, the power system unit combination of this embodiment has 96 periods, and the basic data includes unit cost data, unit operating characteristic data, unit electric quantity constraint data, day-ahead load prediction data, and grid topology data of each period;
2) constructing a power system unit combination optimization model:
2-1) constructing an objective function of the power system unit combination optimization model, wherein the expression is as follows:
Figure GDA0002769399100000131
wherein, PktIs the output of the unit k in the time period t, f (-) is a varying cost function about the output of the unit, SUkIs the starting cost of unit k, yktIs a variable of 0-1 of the starting state of the unit k in the time period t, if the unit k is converted from the shutdown state to the starting state in the time period t, yktEqual to 1, otherwise 0, SDkFor the shutdown cost of unit k, zktIs the shutdown state 0-1 variable of the unit k in the time period t, if the unit k is converted from the startup state to the shutdown state in the time period t, z isktEqual to 1, otherwise 0;
2-2) constructing constraint conditions of the power system unit combination optimization model, specifically as follows:
2-2-1) system load balancing constraints:
Figure GDA0002769399100000132
wherein D isbtIs node b during time period tThe unit combination must satisfy the system load balance constraint of each time interval;
2-2-2) technical constraint of the generator set:
Figure GDA0002769399100000133
Figure GDA0002769399100000134
Figure GDA0002769399100000135
Figure GDA0002769399100000136
Figure GDA0002769399100000137
Figure GDA0002769399100000138
Figure GDA0002769399100000139
Figure GDA00027693991000001310
Figure GDA00027693991000001311
wherein u isktIs a variable of 0-1 in the starting and stopping state of the unit k at the time t, and if the unit k is in the starting state at the time t, uktIs 1 if the unit k is in time slott is in shutdown state, then uktIs 0; pk,minMinimum output of unit k, Pk,maxIs the maximum output of the unit k,
Figure GDA0002769399100000141
for the climbing capacity of unit k, Tk,onIs the minimum continuous start-up time, T, of unit kk,offMinimum continuous shutdown time, y, of unit kk,maxIs the maximum number of starts of unit k, zk,maxMaximum number of shutdowns of unit k, Ek,minIs the minimum generated electricity quantity of the unit k in all days, Ek,maxThe maximum generation electric quantity of the unit K in all days, KENumbering a set of generator sets with electric quantity constraint;
the restriction of the upper limit and the lower limit of the generating set is shown as a formula (3), the restriction of the upper limit and the lower limit of the climbing capability of the generating set is shown as a formula (4), and the restriction of the logical coupling of 0-1 integer variables is shown as a formula (5) and a formula (6), wherein the formula (5) shows that the difference between the starting state variable and the stopping state variable of the generating set at the current time interval is the difference between the starting state variable and the stopping state variable of the generating set at the last time interval, the formula (6) shows that the generating set is either opened or closed or maintained at the previous state and is neither opened nor closed for a certain specific time interval of a certain generating set, the restriction of the minimum continuous starting time of the generating set is shown as a formula (7), the generating set is required to be maintained at the starting state for a certain time to be closed once the generating set is opened, the restriction of the minimum continuous shutdown time of the generating set is, the maximum startup time constraint of the unit is shown as a formula (9), which indicates the maximum startup time of the unit in the whole day, the maximum shutdown time constraint of the unit is shown as a formula (10), which indicates the maximum shutdown time of the unit in the whole day, and the electric quantity constraint of the unit is shown as a formula (11);
2-2-3) line active transmission capacity constraint:
Figure GDA0002769399100000142
wherein, TPl,maxFor the maximum active transmission capacity of line l, matrix G is the generator output power transfer distribution factor matrix for the node pair line, nkNumbering the nodes of the unit k;
3) solving a relaxation optimal solution of the power system unit combination optimization model established in the step 2); the method comprises the following specific steps:
3-1) relaxing 0-1 variable in the power system unit combination optimization model formed by the formulas (1) - (12) into continuous variable with the value range of 0-1 to form a relaxation model for power system unit combination optimization;
3-2) solving the relaxation model of the combination optimization of the power system unit by adopting a linear programming solver to obtain an optimal relaxation solution x of the combination optimization of the power system unit*，x*The method comprises the following steps: vector u of optimal solution of 0-1 variable relaxation in unit starting and stopping state*Vector y of optimal solution for 0-1 variable relaxation of starting state of unit*Vector z of the optimal solution for 0-1 variable relaxation of the shutdown state of a unit*Vector P of the optimal solution for the relaxation of the output variables of the unit*；
4) Constructing a relaxed neighborhood search constraint:
4-1) constructing a relaxation distance expression according to the optimal relaxation solution of the power system unit combination optimization obtained in the step 3):
Figure GDA0002769399100000151
wherein RD (u, y, z, u)*,y*,z*) Representing the relaxation distance between any solution of the power system unit combination optimization model and the relaxation optimal solution, u is a vector of a unit startup and shutdown state variable 0-1, y is a vector of a unit startup state variable 0-1, z is a vector of a unit shutdown state variable 0-1, u is a vector of a unit shutdown state variable 0-1*Vector, y, of the optimal solution for the unit startup and shutdown state 0-1 variable relaxation*Vector, z, of the optimal solution for the unit startup state 0-1 variable relaxation*The vector of the optimal solution is relaxed for the unit shutdown state 0-1 variable,
Figure GDA0002769399100000152
for unit start-up and shut-down state 0-1 variable uktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000153
for the unit starting state 0-1 variable yktThe optimal solution of the relaxation of (a),
Figure GDA0002769399100000154
for a unit shutdown state 0-1 variable zktα (·) is a function for determining a weight coefficient for describing the degree to which the relaxed optimal solution tends to its tendency, and is expressed by the following equation (14):
Figure GDA0002769399100000155
4-2) constructing search neighborhood search constraints, as shown in formula (15):
RD(u,y,z,u*,y*,z*)≤r (15)
wherein r is a neighborhood radius coefficient, and in this embodiment, the value of r is 10% of the number of variables of the model 0-1, that is, r is 1987.2;
5) constructing a symmetric induction function, as shown in equation (16):
Figure GDA0002769399100000156
wherein, IF (u, y, z, u)*,y*,z*) Represents a symmetric induction function obtained based on a relaxation optimal solution, W is a weight coefficient of the symmetric induction function, and in the embodiment, W is 10000;
6) adding an equation (15) as a constraint condition into the constraint condition of the power system unit combination optimization model in the step 2), adding an equation (16) into an objective function of the power system unit combination optimization model in the step 2), and constructing a power system unit combination optimization substitution model;
the objective function of the combined optimization substitution model of the power system unit is shown as the following formula (17):
Figure GDA0002769399100000161
7) solving the power system unit combination optimization substitution model by using a mixed integer linear programming solver to obtain a power system unit combination optimization result x ', x' comprising: the unit startup and shutdown state 0-1 variable optimization result vector u ', the unit startup state 0-1 variable optimization result vector y', the unit shutdown state 0-1 variable optimization result vector z ', and the unit output variable optimization result vector P'.
In the embodiment, the solving platform is CPLEX 12.4, the server is ThinkPad T470(RAM:16GB, CPU: Intel (R) core (TM) i7-7500U CPU @2.70GHz 2.90GHz), the CPLEX 12.4 is directly adopted, the interval tolerance (namely, the calculation precision) of the solving of the mixed integer linear programming solver is set to be 1%, 13322 seconds (about 3.7 hours) are needed, and by adopting the accelerated optimization method for the power system unit combination, the 2322 seconds (about 30 minutes) are only required to be solved, the calculation time is reduced by 82.6%, the jump from hour level to minute level is realized, and the solving efficiency of the power system unit combination is greatly improved;
it is worth mentioning that in the method of the invention, the objective function of the power system unit combination optimization model can be flexibly selected and customized according to the needs, the constraint conditions of the power system unit combination optimization model can be added and deleted according to the actual needs, and the expandability is strong; therefore, the above implementation steps are only used for illustrating and not limiting the technical solution of the present invention; any modification or partial replacement without departing from the spirit and scope of the present invention should be covered in the claims of the present invention.

Claims (2)

1. A combined acceleration optimization method for a power system unit is characterized by comprising the following steps:
1) acquiring basic data from a power system dispatching department:
the basic data comprise unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data;
the unit cost data comprises a unit variation cost function, a unit startup cost and a unit shutdown cost;
the running characteristic data of the unit is output upper limit/lower limit data of the generator set, climbing capacity of the unit, minimum continuous startup time of the unit, minimum continuous shutdown time of the unit, maximum startup times of the unit and maximum shutdown times of the unit;
the unit electric quantity constraint data is the minimum generating electric quantity of the generator set all day and the maximum generating electric quantity of the generator set all day;
the day-ahead load prediction data is the power load demand condition of each node in each time interval on the second day;
the power grid topological data comprise the connection relation between nodes of a power network and power transmission lines, the maximum active transmission capacity of each line section and the line number contained in the maximum active transmission capacity, and generator output power transfer distribution factor matrix data of each power transmission line by each unit and node load;
2) constructing a power system unit combination optimization model:
2-1) constructing an objective function of the power system unit combination optimization model, wherein the expression is as follows:
Figure FDA0002409505720000011
wherein, PktIs the output of the unit k in the time period t, f (-) is a varying cost function about the output of the unit, SUkIs the starting cost of the unit k; y isktIs a variable of 0-1 of the starting state of the unit k in the time period t, if the unit k is converted from the shutdown state to the starting state in the time period t, yktEqual to 1, otherwise 0; SDkThe shutdown cost of the unit k; z is a radical ofktIs the shutdown state 0-1 variable of the unit k in the time period t, if the unit k is converted from the startup state to the shutdown state in the time period t, z isktEqual to 1, otherwise 0;
2-2) constructing constraint conditions of the power system unit combination optimization model, specifically as follows:
2-2-1) system load balancing constraints:
Figure FDA0002409505720000012
wherein D isbtIs the load of node b during time period t;
2-2-2) technical constraint of the generator set:
Figure FDA0002409505720000013
Figure FDA0002409505720000021
Figure FDA0002409505720000022
Figure FDA0002409505720000023
Figure FDA0002409505720000024
Figure FDA0002409505720000025
Figure FDA0002409505720000026
Figure FDA0002409505720000027
Figure FDA0002409505720000028
wherein u isktIs a variable of 0-1 in the starting and stopping state of the unit k at the time t, and if the unit k is in the starting state at the time t, uktIs 1, if the unit k is in a shutdown state in a time period t, uktIs 0; pk,minMinimum output of unit k, Pk,maxMaximum output of unit k, Pk cFor the climbing capacity of unit k, Tk,onIs the minimum continuous start-up time, T, of unit kk,offMinimum continuous shutdown time, y, of unit kk,maxIs the maximum number of starts of unit k, zk,maxMaximum number of shutdowns of unit k, Ek,minIs the minimum generated electricity quantity of the unit k in all days, Ek,maxThe maximum generation electric quantity of the unit K in all days, KENumbering a set of generator sets with electric quantity constraint;
2-2-3) line active transmission capacity constraint:
Figure FDA0002409505720000029
wherein, TPl,maxFor the maximum active transmission capacity of line l, matrix G is the generator output power transfer distribution factor matrix for the node pair line, nkNumbering the nodes of the unit k;
3) solving a relaxation optimal solution of the power system unit combination optimization model established in the step 2); the method comprises the following specific steps:
3-1) relaxing 0-1 variable in the power system unit combination optimization model formed by the formulas (1) - (12) into continuous variable with the value range of 0-1 to form a relaxation model for power system unit combination optimization;
3-2) solving the relaxation model of the combination optimization of the power system unit to obtain the optimal relaxation solution x of the combination optimization of the power system unit*The method comprises the following steps: vector u of optimal solution of 0-1 variable relaxation in unit starting and stopping state*Vector y of optimal solution for 0-1 variable relaxation of starting state of unit*Vector z of the optimal solution for 0-1 variable relaxation of the shutdown state of a unit*Vector P of the optimal solution for the relaxation of the output variables of the unit*；
4) Constructing a relaxed neighborhood search constraint, which comprises the following specific steps:
4-1) constructing a relaxation distance expression according to the optimal relaxation solution of the power system unit combination optimization obtained in the step 3):
Figure FDA0002409505720000031
wherein RD (u, y, z, u)*,y*,z*) Representing the relaxation distance between any solution of the power system unit combination optimization model and the relaxation optimal solution, u is a vector of a unit startup and shutdown state variable 0-1, y is a vector of a unit startup state variable 0-1, z is a vector of a unit shutdown state variable 0-1, u is a vector of a unit shutdown state variable 0-1*Vector, y, of the optimal solution for the unit startup and shutdown state 0-1 variable relaxation*Vector, z, of the optimal solution for the unit startup state 0-1 variable relaxation*The vector of the optimal solution is relaxed for the unit shutdown state 0-1 variable,
Figure FDA0002409505720000032
for unit start-up and shut-down state 0-1 variable uktThe optimal solution of the relaxation of (a),
Figure FDA0002409505720000033
for the unit starting state 0-1 variable yktThe optimal solution of the relaxation of (a),
Figure FDA0002409505720000034
for a unit shutdown state 0-1 variable zktα (·) is a function for determining the weight coefficient, and the expression is shown as (14):
Figure FDA0002409505720000035
4-2) constructing search neighborhood search constraints, as shown in formula (15):
RD(u,y,z,u*,y*,z*)≤r (15)
wherein r is a neighborhood radius coefficient;
5) constructing a symmetric induction function, as shown in equation (16):
Figure FDA0002409505720000036
wherein, IF (u, y, z, u)*,y*,z*) Representing a symmetric induction function obtained based on a relaxation optimal solution, wherein W is a weight coefficient of the symmetric induction function;
6) adding an equation (15) serving as a constraint condition into the constraint condition of the power system unit combination optimization model in the step 2), adding an equation (16) into an objective function of the power system unit combination optimization model in the step 2), and constructing a power system unit combination optimization substitution model;
the objective function of the combined optimization substitution model of the power system unit is shown as the following formula (17):
Figure FDA0002409505720000041
7) solving the combined optimization substitution model of the power system unit to obtain a combined optimization result x' of the power system unit, comprising the following steps: the unit startup and shutdown state 0-1 variable optimization result vector u ', the unit startup state 0-1 variable optimization result vector y', the unit shutdown state 0-1 variable optimization result vector z ', and the unit output variable optimization result vector P'.
2. An electric power system unit combination acceleration optimization device based on the method of claim 1 is characterized by comprising a data acquisition module, a model construction module, a relaxation solving module, a relaxation neighborhood search constraint and symmetry induction function module, a substitution model construction module and a calculation solving module which are connected in sequence;
the data acquisition module is used for acquiring basic data from a power system dispatching department and sending the acquired basic data to the model construction module; the basic data comprise unit cost data, unit operation characteristic data, unit electric quantity constraint data, day-ahead load prediction data and power grid topological data;
the model construction module is used for constructing a power system unit combination optimization model according to the basic data obtained from the data acquisition module and sending the model to the relaxation solving module;
the relaxation solving module is used for relaxing 0-1 variable in the combined optimization model of the power system unit into continuous variable with the value range of 0 to 1 to form a relaxation model for the combined optimization of the power system unit, solving a relaxation optimal solution of the combined optimization model of the power system unit and sending the relaxation optimal solution to the relaxation neighborhood search constraint and symmetric induction function module;
the relaxation neighborhood search constraint and symmetry induction function module comprises a relaxation neighborhood search constraint submodule and a symmetry induction function submodule;
the relaxation neighborhood search constraint submodule constructs a relaxation distance expression and a relaxation neighborhood search constraint by using a relaxation optimal solution, and then sends the relaxation neighborhood search constraint to the surrogate model construction module;
the symmetric induction function submodule constructs a symmetric induction function by using the relaxed optimal solution structure and sends the symmetric induction function to the surrogate model constructing module;
the surrogate model building module is used for adding relaxed neighborhood search constraints into constraint conditions of the power system unit combination optimization model, adding a symmetric induction function into a target function of the power system unit combination optimization model, and building the power system unit combination optimization surrogate model;
and the calculation solving module is used for solving the combined optimization substitution model of the power system unit to obtain a combined optimization result of the power system unit.
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