CN109767078B - Multi-type power supply maintenance arrangement method based on mixed integer programming - Google Patents

Multi-type power supply maintenance arrangement method based on mixed integer programming Download PDF

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CN109767078B
CN109767078B CN201811559271.5A CN201811559271A CN109767078B CN 109767078 B CN109767078 B CN 109767078B CN 201811559271 A CN201811559271 A CN 201811559271A CN 109767078 B CN109767078 B CN 109767078B
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邵成成
王雅楠
冯陈佳
王锡凡
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Xian Jiaotong University
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Abstract

A multi-type power supply maintenance arrangement method based on mixed integer programming comprises the steps of collecting system data such as power supplies and loads, wherein the power supply data comprise output characteristics, coal consumption curves and maintenance duration of various units, and hydropower unit data need to be collected; the load data comprises data such as annual maximum load, total electric quantity, typical daily load characteristics and monthly load characteristics; the time sequence load curve is simplified into a segmented continuous load curve: establishing a long-term generator set maintenance planning model with economy as a target, and taking the lowest system operation cost as a target function, wherein the minimum system operation cost mainly comprises fuel cost of a thermal power generating unit, electricity abandonment cost of new energy and the like; establishing an overhaul model of each type of unit: establishing an operation constraint model of each type of unit: establishing a system operation constraint model: and solving, the method is not only suitable for maintenance arrangement of the conventional unit, but also has strong expandability.

Description

Multi-type power supply maintenance arrangement method based on mixed integer programming
Technical Field
The invention relates to the field of power system planning, in particular to a multi-type power supply maintenance arrangement method based on mixed integer planning.
Background
The generator set maintenance is an important content of the arrangement of the operation mode of the power grid, is an important link in the operation planning of the power system, and directly influences the starting mode of the power system. Because the production and consumption of electric energy are carried out simultaneously, the system operation has higher requirements on the reliability of electric equipment, particularly a generator set. The reasonable arrangement of the generator set maintenance can effectively reduce the failure rate of equipment, prolong the normal working time of the equipment and effectively improve the economical efficiency and reliability of the system operation. In the actual operation of the power system, generally, a year or a plurality of years are taken as a time period, and a month or a ten-day is taken as a basic time unit to arrange the overhaul type and the overhaul sequence of the unit; similar or simplified processing is also performed to simulate and analyze the operation of the system during system planning and design.
The arrangement and execution of the maintenance can cause part of the units to be in a planned shutdown state, thereby causing the reduction of the available generating capacity of the system and the shortage of the actual spare capacity, and affecting the reliability of the power supply. Meanwhile, when the high-efficiency generator set is in a maintenance state, the generator set with lower efficiency is used for replacing the generator set to generate electricity, so that the operation cost of the system is increased. The maintenance strategy of the unit can have a significant influence on the reliability and the economy of the operation of the power system.
The solving method of the existing generator set maintenance planning problem can be divided into mathematical optimization and heuristic algorithm. The method comprises the steps of considering system operation and unit maintenance constraints and carrying out necessary simplification, establishing a deterministic optimization model, and solving by methods such as integer programming and linear programming; the latter mainly refers to an equal-standby method and an equal-risk method, random shutdown factors of the unit are considered, and a more reasonable solution is obtained with less calculation amount from the aspect of reliability.
In the actual operation of the power system, multiple maintenance types are usually involved, the starting time and the duration of various types of maintenance need to be considered, and the interaction influence among different types of maintenance also needs to be considered, so that a maintenance arrangement model is very complex, and an optimal solution is difficult to obtain. Meanwhile, with the increase of the types of power supplies, the maintenance arrangement of the unit is closely related to the problems of water and electricity distribution, renewable energy power consumption, fuel storage plan and the like, and the range which can be processed by the traditional heuristic maintenance arrangement method is greatly exceeded.
Disclosure of Invention
In order to overcome the technical problems, the invention aims to provide a multi-type power supply maintenance scheduling method based on mixed integer programming, a multi-type power supply maintenance model based on mixed integer programming can meet different time scales, the lowest production cost of a system is taken as an objective function, the influence of multiple maintenance types of a unit and the output characteristics of the maintenance types on maintenance scheduling and system operation is considered while maintenance constraint is considered, and therefore multi-type power supply maintenance scheduling is completed.
In order to achieve the purpose, the invention adopts the technical scheme that:
the method comprises the following steps: collecting system data including a power supply and a load, wherein the power supply data comprises output characteristics, coal consumption curves and maintenance duration of various units, and hydroelectric power quantity data is collected for a hydroelectric generating set; the load data comprises annual maximum load, total electric quantity, typical daily load characteristic and monthly load characteristic data;
step two: the time sequence load curve is simplified into a segmented continuous load curve:
simplifying the time sequence load curve into a segmented continuous load curve for modeling: firstly, sequencing time sequence load curves from big to small in sequence to form an accurate continuous load curve; secondly, selecting reasonable number of sections and load level according to the requirement of precision, and carrying out approximation on the continuous curve by counting corresponding duration; finally, adjusting the duration time of each load level to ensure that the total electric quantity of the system is unchanged, and obtaining an approximate continuous load curve for calculation;
step three: establishing a long-term generator set maintenance planning model with economy as a target, and taking the lowest system operation cost as a target function, wherein the model mainly comprises fuel cost of a thermal power generating unit and electricity abandoning cost of new energy;
Figure BDA0001912815060000031
where T represents a time period, T is a calculation cycle, for example, when the total calculation time is 6 years, and 1 week is taken as a 1 time period, T is 312; j represents the segment of the approximate continuous load curve, and B is the number of segments; NS represents the number of scenes, and s represents a scene label; subscripts k and g are labels of the thermal power generating units and the thermal power plants, and k belongs to g of the thermal power generating unit set belonging to the thermal power plant; f. ofkThe power generation cost p of the thermal power generating unit kk,j,t,sRepresenting the output of the unit k in the j load section of the t time period; dj,tIs the duration of the jth load level in the tth period in hours; lambda [ alpha ]RRepresenting the punishment of the electric quantity abandoned by the new energy; RC (resistor-capacitor) capacitorj,t,sRepresenting the electric quantity abandoned by the new energy;
step four: establishing an overhaul model of each type of unit:
a reasonable system operation planning arrangement should consider multiple service types, where the number of times of each service type is considered to be one, and only one of the service types is taken as an example to write constraints, and the remaining service type constraints are the same as the form:
(1) maintenance frequency constraint
Figure BDA0001912815060000032
Figure BDA0001912815060000033
Figure BDA0001912815060000034
In the formula, subscripts h and p are the labels of the hydroelectric generating set and the pumped storage unit; z is a radical ofk,t、zh,tAnd zp,tThe variable is a 0-1 variable representing that the unit starts to be overhauled, when the unit starts to be overhauled at the moment t, the value of the variable is 1, otherwise, the value is 0; MN (Mobile node)k、MNhAnd MNpThe required maintenance times of each unit in T periods are shown, and in the research period, the maintenance times of the units in the types of thermal power, hydropower, pumping storage and the like meet the requirements. When a plurality of overhaul types (such as major overhaul and minor overhaul) need to be considered, different overhaul starting variables z are set for different types of overhaul for distinguishing;
(2) time constraints for maintenance
Namely, each overhaul of the unit should meet the corresponding duration requirement.
Figure BDA0001912815060000035
Figure BDA0001912815060000041
Figure BDA0001912815060000042
In the formula, mk,t、mh,tAnd mp,tThe variable is a 0-1 variable which indicates whether the unit is in a maintenance state, the value of the variable is 1 when the unit is in the maintenance state, and otherwise, the value is 0; MT (multiple terminal)k、MThAnd MTpTaking an integer value for the duration of each overhaul of each type of unit;
(3) maintenance continuity constraints
One unit must be completed within a continuous interval after beginning to overhaul, i.e.
Figure BDA0001912815060000043
Figure BDA0001912815060000044
Figure BDA0001912815060000045
In the formula, the superscript a represents the type of overhaul; subscripts k, h and p respectively represent the labels of the thermal power generating unit, the hydroelectric generating unit and the pumped storage unit; taking the class a maintenance as an example,
Figure BDA0001912815060000046
and
Figure BDA0001912815060000047
the maintenance starting time interval for various units generally takes week as unit;
Figure BDA0001912815060000048
and
Figure BDA0001912815060000049
the maintenance duration of various units is generally in weeks; m isk,t、mh,tAnd mp,tThe variable is in the maintenance state of various units, the value of the variable is 1 when the unit is in the maintenance state, and otherwise, the value of the variable is 0;
(4) minimum overhaul time interval constraint
The minimum time interval between the two overhauls of the unit k is limited:
Figure BDA00019128150600000410
Figure BDA00019128150600000411
Figure BDA00019128150600000412
in the formula, Bk、BhAnd BpThe maintenance interval time of various units is long;
(5) constraint of maintenance capability
The generating set number that same power plant overhauld in same moment receives the influence of its maintenance ability, and only allow a unit to overhaul under the general condition, promptly:
Figure BDA0001912815060000051
Figure BDA0001912815060000052
Figure BDA0001912815060000053
in the formula, Cg、ChgAnd CpgRepresenting the number of overhaulable power plants at the same time;
step five: establishing an operation constraint model of each type of unit:
the operation of various units is restricted by the maintenance work, and the restrictions such as the output range of the units, the relationship between the starting state and the maintenance state of the units and the like need to be considered;
(1) unit output range constraint
The output of the thermal power generating unit, the hydroelectric power generating unit and the pumped storage unit is limited by the minimum technical output and the installed capacity, namely the output range of the units in each scene is between the minimum technical output and the installed capacity;
(2) unit start-up constraint
The unit in the maintenance state cannot be started to operate, namely the sum of the operation state and the starting state of the unit is less than or equal to 1. When the unit is in a starting state, the operation variable is taken as 1, and the shutdown state is taken as 0; when the pumping storage unit is in a power generation or water pumping state, the corresponding state variable value is 1, and the shutdown state is 0;
(3) hydro-electric operation constraints
The total output of the hydropower station is limited by its forced output and the predicted output.
Figure BDA0001912815060000054
Figure BDA0001912815060000055
In the formula, HPhg,min,tAnd HPhg,max,tRespectively representing the forced output and the predicted output of the hg of the hydroelectric power plant; HEhs,tRepresenting the power generation capacity of the hydropower plant hg in the period t; sigmasRepresenting the probability of scene s;
(4) pumped storage power station operation constraints
Figure BDA0001912815060000061
In the formula (I), the compound is shown in the specification,
Figure BDA0001912815060000062
and
Figure BDA0001912815060000063
respectively showing the efficiency of the pumping storage unit p for generating electricity and pumping water.
Step six: establishing a system operation constraint model:
on the basis of the operation constraint aiming at each type of unit, the power system also needs to meet the constraints of power balance, standby and the like during operation;
(1) power balance constraint
Figure BDA0001912815060000064
(2) Standby restraint
In order to cope with random conditions such as unit failure shutdown and load fluctuation, the system needs to reserve sufficient spare capacity.
Figure BDA0001912815060000065
Wherein r represents a spare coefficient;
step seven: solving:
as the objective function and the constraint condition are mostly linear (including some integer variables), the target function and the constraint condition only have some nonlinear characteristics on the fuel consumption characteristic of the thermal power generating unit, and are described and approximated by a linear or piecewise linear curve, a mixed integer programming method is utilized to solve to obtain the result of the multi-type power supply maintenance arrangement method.
The invention has the beneficial effects that:
the large-scale grid connection of power supplies such as wind power and photovoltaic power generation brings challenges to the operation of a power system, and the existing power system maintenance plan mainly depends on manual arrangement. The method utilizes a mixed integer programming method, considers various maintenance types of the unit, considers the seasonal characteristics of new energy power and hydropower output while considering maintenance constraints, efficiently and accurately completes modeling calculation of conventional power supplies such as thermal power, hydropower, pumped storage and the like, improves the calculation accuracy degree, and improves the calculation efficiency as far as possible. The method has universal applicability to various different types of power supplies such as wind power, photovoltaic power, hydroelectric power, thermal power and nuclear power, can fully reflect different characteristics of the different types of power supplies, and adopts an MILP method to give indexes such as wind abandonment, light abandonment and water abandonment through calculation, thereby realizing efficient solution of the model. Compared with the maintenance scheduling method of the power system, the method has obvious advantages.
Drawings
Fig. 1 maximum load and service capacity.
FIG. 2 is an overall process of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Adopting an adapted IEEE-RTS79 system to carry out example analysis, wherein the example period is 6 years, the unit maintenance modes are 3 types, wherein the a type maintenance is carried out for 1 time, and the duration of each time is 5 weeks; class b overhaul 2 times, each time lasting 4 weeks; class c was examined 3 times for 3 weeks each.
26 thermal power (nuclear power) units are shared in the system of the embodiment, and the installed capacity is 3105 MW. The total annual electric quantity of the system is 1.1 hundred million degrees, and the maximum load is 2800MW.
The system load is arranged from large to small according to the requirement, and the maintenance plan arrangement is carried out on the power supply in the system according to the principle that the total electric quantity is unchanged and divided into four sections, namely, a full load section, a flat load section 1, a flat load section 2 and a valley load section.
The overhaul arrangement method is high in applicability, the overhaul result is only shown by taking the thermal power generating unit as an example, and the overhaul method can be expanded to various types of units including water, electricity, pumping storage, new energy and the like.
A maintenance schedule of a typical thermal power generating unit is selected to display the calculation results, as shown in Table 1, wherein '0' indicates an overhauled state, and '1' indicates an overhauled state.
TABLE 1 thermal power generating unit maintenance week arrangement
Figure BDA0001912815060000071
Figure BDA0001912815060000081
As shown in fig. 1, which is a graph of the overhaul capacity of each unit and the maximum load of the system, it can be seen that the overhaul of the thermoelectric units in the system is usually arranged in summer and autumn. Analysis shows that the load level during this period is relatively low, so that sufficient reserve power can be reserved for the system while scheduling maintenance.

Claims (3)

1. A multi-type power supply maintenance arrangement method based on mixed integer programming is characterized by comprising the following steps;
the method comprises the following steps: collecting system data including a power supply and a load, wherein the power supply data comprises output characteristics, coal consumption curves and maintenance duration of various units, and hydroelectric power quantity data is collected for a hydroelectric generating set; the load data comprises annual maximum load, total electric quantity, typical daily load characteristic and monthly load characteristic data;
step two: the time sequence load curve is simplified into a segmented continuous load curve:
simplifying the time sequence load curve into a segmented continuous load curve for modeling: firstly, sequencing time sequence load curves from big to small in sequence to form an accurate continuous load curve; secondly, selecting reasonable number of sections and load level according to the requirement of precision, and carrying out approximation on the continuous curve by counting corresponding duration; finally, adjusting the duration time of each load level to ensure that the total electric quantity of the system is unchanged, and obtaining an approximate continuous load curve for calculation;
step three: establishing a long-term generator set maintenance planning model with economy as a target, and taking the lowest system operation cost as a target function, wherein the model mainly comprises fuel cost of a thermal power generating unit and electricity abandoning cost of new energy;
step four: establishing an overhaul model of each type of unit:
the reasonable system operation planning arrangement needs to consider a plurality of maintenance types, wherein the times of each maintenance type are considered to be once, only one maintenance type is taken as an example to write constraints, and the constraints of the other maintenance types are the same as the constraints of the maintenance types;
step five: establishing an operation constraint model of each type of unit:
the operation of various units is restricted by the maintenance work, and the output range of the units and the relation restriction of the starting state and the maintenance state of the units need to be considered;
step six: establishing a system operation constraint model:
on the basis of the operation constraint aiming at each type of unit, the power balance and the standby constraint should be met in the operation of the power system;
step seven: solving:
because the target function and the constraint condition are mostly linear, the target function and the constraint condition only have some nonlinear characteristics on the fuel consumption characteristic of the thermal power generating unit, and the nonlinear characteristics are described and approximated by a linear or piecewise linear curve, a mixed integer programming method is utilized to solve and obtain the result of the multi-type power supply maintenance arrangement method;
the third step is specifically as follows:
Figure FDA0003093341160000021
wherein T represents a time period, T represents a calculation cycle, j represents a segment of an approximate continuous load curve, and B is the number of segments; NS represents the number of scenes, and s represents a scene label; subscripts k and g are labels of the thermal power generating units and the thermal power plants, and k belongs to g of the thermal power generating unit set belonging to the thermal power plant; f. ofkThe power generation cost p of the thermal power generating unit kk,j,t,sRepresenting the output of the unit k in the j load section of the t time period; dj,tIs the duration of the jth load level in the tth period in hours; lambda [ alpha ]RRepresenting the punishment of the electric quantity abandoned by the new energy; RC (resistor-capacitor) capacitorj,t,sRepresenting the electric quantity abandoned by the new energy;
the fifth step is specifically as follows:
(1) unit output range constraint
The output of the thermal power generating unit, the hydroelectric power generating unit and the pumped storage unit is limited by the minimum technical output and the installed capacity, namely the output range of the units in each scene is between the minimum technical output and the installed capacity;
(2) unit start-up constraint
The unit in the maintenance state cannot be started to operate, namely the sum of the operation state and the starting state of the unit is less than or equal to 1, the operation variable is 1 when the unit is in the starting state, and the shutdown state is 0; when the pumping storage unit is in a power generation or water pumping state, the corresponding state variable value is 1, and the shutdown state is 0;
(3) hydro-electric operation constraints
The total output of the hydropower station is limited by the forced output and the expected output;
Figure FDA0003093341160000031
Figure FDA0003093341160000032
in the formula, HPhg,min,tAnd HPhg,max,tRespectively representing the forced output and the predicted output of the hg of the hydroelectric power plant; HEhg，tRepresenting the power generation capacity of the hydropower plant hg in the t period; sigmasRepresenting the probability of scene s;
(4) pumped storage power station operation constraints
Figure FDA0003093341160000033
In the formula (I), the compound is shown in the specification,
Figure FDA0003093341160000034
and
Figure FDA0003093341160000035
respectively showing the efficiency of the pumping storage unit p for generating electricity and pumping water.
2. The mixed integer programming-based multi-type power supply overhaul scheduling method according to claim 1, wherein the fourth step is specifically:
(1) maintenance frequency constraint
Figure FDA0003093341160000036
Figure FDA0003093341160000037
Figure FDA0003093341160000038
In the formula, subscripts h and p are the labels of the hydroelectric generating set and the pumped storage unit; z is a radical ofk,t、zh,tAnd zp,tThe variable is a 0-1 variable representing that the unit starts to be overhauled, when the unit starts to be overhauled at the moment t, the value of the variable is 1, otherwise, the value is 0; MN (Mobile node)k、MNhAnd MNpThe method comprises the steps that the required overhaul times of each unit in T time periods are represented, in a research period, the overhaul times of the units in the thermal power type, the hydroelectric type and the storage type meet requirements, multiple overhaul types need to be considered, the overhaul types comprise major overhaul and minor overhaul, and different overhaul starting variables z are set for different types of overhaul for distinguishing;
(2) time constraints for maintenance
Namely, each overhaul of the unit needs to meet the corresponding requirement of duration;
Figure FDA0003093341160000041
Figure FDA0003093341160000042
Figure FDA0003093341160000043
in the formula, mk,t、mh,tAnd mp,tThe variable is a 0-1 variable which indicates whether the unit is in a maintenance state, the value of the variable is 1 when the unit is in the maintenance state, and otherwise, the value is 0; MT (multiple terminal)k、MThAnd MTpTaking an integer value for the duration of each overhaul of each type of unit;
(3) maintenance continuity constraints
One unit must be completed within a continuous interval after beginning to overhaul, i.e.
Figure FDA0003093341160000044
Figure FDA0003093341160000045
Figure FDA0003093341160000046
In the formula, the superscript a represents the type of overhaul; subscripts k, h and p respectively represent the labels of the thermal power generating unit, the hydroelectric generating unit and the pumped storage unit; taking the class a maintenance as an example,
Figure FDA0003093341160000047
and
Figure FDA0003093341160000048
taking weeks as units for the beginning period of maintenance of various units;
Figure FDA0003093341160000049
and
Figure FDA00030933411600000410
the maintenance duration of various units is in weeks; m isk,t、mh,tAnd mp,tThe variable is in the maintenance state of various units, the value of the variable is 1 when the unit is in the maintenance state, and otherwise, the value of the variable is 0;
(4) minimum overhaul time interval constraint
The minimum time interval between the two overhauls of the unit k, h and p is limited:
Figure FDA0003093341160000051
Figure FDA0003093341160000052
Figure FDA0003093341160000053
in the formula, Bk、BhAnd BpThe maintenance interval time of various units is long;
(5) constraint of maintenance capability
The generating set number that same power plant overhauld in same moment receives the influence of its maintenance ability, only allows a unit to overhaul simultaneously, promptly:
Figure FDA0003093341160000054
Figure FDA0003093341160000055
Figure FDA0003093341160000056
in the formula, Cg、ChgAnd CpgRepresenting the number of overhaulable units of various power plants at the same time.
3. The mixed integer programming-based multi-type power supply overhaul scheduling method according to claim 1, wherein the sixth step is specifically:
(1) power balance constraint
Figure FDA0003093341160000057
(2) Standby restraint
In order to deal with the conditions of unit failure shutdown and random load fluctuation, the system needs to reserve sufficient spare capacity;
Figure FDA0003093341160000058
in the formula, r represents a spare coefficient.
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