CN112051762A - Closed-loop management method and system for micro-grid and comprehensive energy - Google Patents
Closed-loop management method and system for micro-grid and comprehensive energy Download PDFInfo
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- 238000007726 management method Methods 0.000 title claims abstract description 37
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- 238000003491 array Methods 0.000 claims description 5
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- WKBOTKDWSSQWDR-UHFFFAOYSA-N Bromine atom Chemical compound [Br] WKBOTKDWSSQWDR-UHFFFAOYSA-N 0.000 description 5
- GDTBXPJZTBHREO-UHFFFAOYSA-N bromine Substances BrBr GDTBXPJZTBHREO-UHFFFAOYSA-N 0.000 description 5
- 229910052794 bromium Inorganic materials 0.000 description 5
- UGFAIRIUMAVXCW-UHFFFAOYSA-N Carbon monoxide Chemical compound [O+]#[C-] UGFAIRIUMAVXCW-UHFFFAOYSA-N 0.000 description 3
- 238000009825 accumulation Methods 0.000 description 3
- 239000003546 flue gas Substances 0.000 description 3
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- 230000004048 modification Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000004146 energy storage Methods 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- AMXOYNBUYSYVKV-UHFFFAOYSA-M lithium bromide Chemical group [Li+].[Br-] AMXOYNBUYSYVKV-UHFFFAOYSA-M 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 239000002918 waste heat Substances 0.000 description 1
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Abstract
The invention provides a closed-loop management method and a closed-loop management system for a micro-grid and comprehensive energy, which comprise the following steps: step S1: acquiring parameter array initialization result information; step S2: establishing an objective function and a constraint condition; step S3: acquiring equipment running state information and equipment power value information; step S4: sending data to a central controller; step S5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller; step S6: the unit controller issues instructions to each device to execute; step S7: the equipment transmits data required by the algorithm to the unit controller; step S8: data are collected through a unit controller; step S9: the central controller transmits the data to the database; step S10: carrying out summary analysis; step S11: calling the standby operation data information in the database; step S12: and acquiring closed-loop management result information of the micro-grid and the comprehensive energy. The invention can realize the method of the scheduling strategy for energy closed-loop management.
Description
Technical Field
The invention relates to the technical field of distributed energy management, in particular to a closed-loop management method and system for a micro-grid and comprehensive energy.
Background
The existing micro-grid and comprehensive energy system control strategy operates according to rated power or automatically adjusts power operation according to load, and also adopts construction constraint conditions and optimization targets, and establishes a multi-micro-grid optimization model according to the constraint conditions and the optimization targets, but the optimization operation only considers single influence factors, and global closed-loop management is not formed. The optimized operation control of the comprehensive energy system comprising a gas internal combustion engine triple co-generation system, electric refrigeration, an electric boiler, a gas boiler, cold accumulation, heat accumulation, a power grid and the like needs to correspondingly adjust the change control strategies of electricity price, gas price, operation and maintenance cost and other constraint conditions.
Patent document CN108510404A discloses a method, a device and a system for orderly grid-connected optimal scheduling of multiple micro-grids, which includes: constructing a constraint condition and an optimization target, and establishing a multi-microgrid optimization model according to the constraint condition and the optimization target; decomposing the multi-microgrid optimization model into a main problem and a sub problem according to the discreteness and continuity of variables; and solving the main problem and the sub-problem according to the parameters of each microgrid and the electricity price information to obtain a scheduling plan. The method is mainly used for a centralized multi-microgrid energy management system to coordinate multi-microgrid energy transactions, overcome disturbance of uncertain factors, improve operation economy and energy utilization efficiency and help system operators to make optimal operation decisions. However, the optimization operation only considers a single influence factor, and global closed-loop management is not formed.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a closed-loop management method and a closed-loop management system for a microgrid and comprehensive energy.
The invention provides a closed-loop management method for a micro-grid and comprehensive energy, which comprises the following steps:
step S1: setting control information according to the initialized parameter array, initializing the parameter array, and acquiring initialized result information of the parameter array;
step S2: establishing an objective function and constraint conditions according to the objective function establishing information and the constraint condition establishing information;
step S3: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
step S4: sending data to a central controller through an MQQT protocol;
step S5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller;
step S6: the unit controller issues instructions to each device to execute;
step S7: the equipment transmits data required by the algorithm to the unit controller;
step S8: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
step S9: the central controller transmits the data to the database;
step S10: the database summarizes and analyzes data required by the algorithm, and COP information is obtained through the power consumption and refrigeration number of electric refrigeration;
acquiring efficiency information of the electric boiler according to power consumption and heating data of the electric boiler;
acquiring the sectional efficiency of the gas internal combustion engine through the gas consumption and the electric power;
acquiring segmented thermoelectric ratio data through data of electric power and flue gas heat;
step S11: step S12, invoking the spare operation data information in the database, updating the data information, and calculating the value as the parameter array: and forming closed-loop system execution to obtain closed-loop management result information of the micro-grid and the comprehensive energy.
Preferably, the method further comprises the following steps: the step S3 includes: step S3.1: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
preferably, the method further comprises the following steps: the step S4 includes: step S4.1: sending data to a central controller through an MQQT protocol;
preferably, the method further comprises the following steps: the step S8 includes:
step S8.1: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
preferably, the method further comprises the following steps: the step S11 includes: and S11.1, calling equipment operation data information, electricity price updating data, gas price updating data and operation and maintenance cost updating data in the database by an algorithm to calculate the values serving as parameter arrays.
According to the invention, the closed-loop management system for the micro-grid and the comprehensive energy comprises:
module M1: setting control information according to the initialized parameter array, initializing the parameter array, and acquiring initialized result information of the parameter array;
module M2: establishing an objective function and constraint conditions according to the objective function establishing information and the constraint condition establishing information;
module M3: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
module M4: sending data to a central controller through an MQQT protocol;
module M5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller;
module M6: the unit controller issues instructions to each device to execute;
module M7: the equipment transmits data required by the algorithm to the unit controller;
module M8: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
module M9: the central controller transmits the data to the database;
module M10: the database summarizes and analyzes data required by the algorithm, and COP information is obtained through the power consumption and refrigeration number of electric refrigeration;
acquiring efficiency information of the electric boiler according to power consumption and heating data of the electric boiler;
acquiring the sectional efficiency of the gas internal combustion engine through the gas consumption and the electric power;
acquiring segmented thermoelectric ratio data through data of electric power and flue gas heat;
module M11: calling the standby operation data information in the database, updating the data information and calculating the value as the parameter array
Module M12: and forming closed-loop system execution to obtain closed-loop management result information of the micro-grid and the comprehensive energy.
Preferably, the method further comprises the following steps: the module M3 includes: module M3.1: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
preferably, the method further comprises the following steps: the module M4 includes: module M4.1: sending data to a central controller through an MQQT protocol;
preferably, the method further comprises the following steps: the module M8 includes:
module M8.1: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
preferably, the method further comprises the following steps: the module M11 includes: and a module M11.1, calculating the values of the parameter arrays by calling equipment operation data information, electricity price updating data, gas price updating data and operation and maintenance cost updating data in the database through an algorithm.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention establishes a closed-loop management system consisting of a database, an upper-layer algorithm and a bottom-layer controller, and can modify a target function and a constraint condition according to the running state of the system and automatically optimize the running system;
2. the invention can overcome the defects of the prior art, can comprehensively consider the influence factors and form global closed-loop management;
3. the invention can realize the method of the scheduling strategy for energy closed-loop management.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a schematic structural diagram of a closed-loop management system in an embodiment of the present invention.
Fig. 2 is a schematic flow chart of a closed-loop management system according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
The invention provides a closed-loop management method for a micro-grid and comprehensive energy, which comprises the following steps:
step S1: setting control information according to the initialized parameter array, initializing the parameter array, and acquiring initialized result information of the parameter array;
step S2: establishing an objective function and constraint conditions according to the objective function establishing information and the constraint condition establishing information;
step S3: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
step S4: sending data to a central controller through an MQQT protocol;
step S5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller;
step S6: the unit controller issues instructions to each device to execute;
step S7: the equipment transmits data required by the algorithm to the unit controller;
step S8: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
specifically, in one embodiment, the integrated energy closed-loop management algorithm transmits an instruction to the central controller through an MQQT or 104 protocol, the central controller issues an instruction of a specific device to the unit controller, the central controller includes a combustion engine controller, a boiler controller, an electric refrigeration controller and the like, the unit controller issues a control instruction to the device, the device transmits data required by the algorithm to the unit controller, the unit controller transmits the data to the central controller, the central controller transmits the data to the database, the database summarizes and analyzes the required data, and the integrated energy closed-loop management algorithm extracts the data in the database as input of the algorithm according to the requirement to form a closed-loop management system, so that the optimized operation control of the unit is realized.
Step S9: the central controller transmits the data to the database;
step S10: the database summarizes and analyzes data required by the algorithm, and COP information is obtained through the power consumption and refrigeration number of electric refrigeration;
acquiring efficiency information of the electric boiler according to power consumption and heating data of the electric boiler;
acquiring the sectional efficiency of the gas internal combustion engine through the gas consumption and the electric power;
acquiring segmented thermoelectric ratio data through data of electric power and flue gas heat;
step S11: calling the standby operation data information in the database, updating the data information and calculating the value as the parameter array
Step S12: and forming closed-loop system execution to obtain closed-loop management result information of the micro-grid and the comprehensive energy.
Preferably, the method further comprises the following steps: the step S3 includes: step S3.1: solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
preferably, the method further comprises the following steps: the step S4 includes: step S4.1: sending data to a central controller through an MQQT protocol;
preferably, the method further comprises the following steps: the step S8 includes:
step S8.1: data are collected by the group controller and transmitted to the group controller through MQQT and 104 protocols, and the data are transmitted to the central controller;
preferably, the method further comprises the following steps: the step S11 includes: and S11.1, calling equipment operation data information, electricity price updating data, gas price updating data and operation and maintenance cost updating data in the database by an algorithm to calculate the values serving as parameter arrays.
Specifically, in one embodiment, a micro-grid and a closed-loop management method for integrated energy are used for establishing an optimized scheduling strategy of an integrated energy system with the aim of minimizing operation cost
The optimization target is that the annual total running cost is the lowest, and the annual total cost comprises running maintenance cost, gas internal combustion engine starting and stopping cost, fuel cost, energy purchasing cost and energy selling benefit.
Wherein, CtotalThe annual total operating cost;
the operation and maintenance cost of the bromine refrigerator;
the maintenance cost for electric refrigeration;
the operation and maintenance cost of the electric boiler;
for the operation and maintenance cost of the gas internal combustion engine,
the annual fuel purchase cost is set to be,
the electricity charge per year is obtained by the electricity-purchasing system,
annual electricity sales income;
annual start-stop costs.
Wherein the content of the first and second substances,
is the rated capacity of the combustion engine;
the rated capacity of the bromine refrigerator;
is the rated capacity of the point boiler;
rated power for electrical refrigeration; pchpIs the output of the combustion engine; cAbscThe refrigeration power of the bromine refrigerator; hebThe heat power of the electric boiler; cecPower for electrical refrigeration;
to purchase electrical power;
to sell electric power.
a1 a2 a3a4 is the operation and maintenance coefficient of each device; b1 is the coefficient of gas cost; e1 is the price of electricity bought; e2 is the price of electricity sold; v1 is the annual start stop cost coefficient.
in the objective function
Based on a gas internal combustion engine, a lithium bromide unit, gas boiler equipment, electric refrigeration and an electric boiler, the method establishes the constraint conditions of the gas combined cooling heating and power system equation and the inequality:
H(i)＝0,i＝1,2,3···,k (7)
g(i)≤0,j＝1,2,3···,m (8)
x＝(x1,x2,···,xn)∈En (9)
wherein, h (i) ≦ 0 is an equality constraint, and g (i) ≦ 0 is an inequality constraint, wherein the equality constraint is a power balance constraint, i.e., the generated power is equal to the load power;
heating power equal to heat load, Hchp+Heb＝HloadThe refrigeration capacity is equal to the refrigeration load, Cchp+Cec+CAbsc＝Cload(ii) a Gas internal combustion engine, electric boiler and electric refrigeration equality relation Qchp*ηchp＝Pchp，
The power of the waste heat utilization of the gas internal combustion engine and the power of the generator have the equation constraint of thermoelectric ratio, Pchp*βchp＝Hchp. And
Pchp＝x2W2+x3W3+x4W4+x5W5+x6W6 (11)
Hchp＝C2W2+C3W3+C4W4+C5W5+C6W6 (12)
Qchp＝C7W2+C8W3+C9W4+C10W5+C11W6 (13)
W1+W2+W3+W4+W5+W6＝1 (14)
Z1+Z2+Z3+Z4+Z5＝1 (15)
wherein, PloadIs an electrical load;
power consumption for electrical refrigeration;
the power consumption of the electric boiler; etachpFor the generating efficiency of gas internal combustion engine set, etaebFor electric boiler efficiency, betachpHot spot ratio, Cop, of gas internal combustion engineecIs the energy efficiency ratio of electric refrigeration.
Indicating CHP Start-stop status, Xchp(i) Indicating the operating state of the CHP at time i. x1, x2, x3, x4 and x5 are values of 5 segments of the electric power output of the combustion engine; values of 5 segments of thermal power output of C1, C2, C3, C4 and C5 combustion engines; the values of 5 subsections of the gas energy output of the C6, C7, C8, C9 and C10 combustion engines are shown.
Wk、ZkSolving variables for the intermediate of the solution; bkIs the kth cut point of the piecewise function segment; f (x) is a function based on x.
The inequality constraint comprises a constraint equation that the energy storage battery, the gas internal combustion engine, the bromine refrigerator and the gas boiler cannot exceed rated power:
and a constraint comprising 0 ≦ M (i) + N (i) ≦ 1.
And adding inequality constraints for piecewise-linearized models
W1≤Z1，W2≤Z1+Z2，W3≤Z2+Z3，W4≤Z3+Z4，W5≤Z4。 (17)
Solving by adopting mixed linear integer programming: and modeling the target function and the constraint condition by adopting mixed linear integer programming, and solving by adopting a CPLEX algorithm.
The parameters in the objective function and the constraints are set to empirical values or, for example, the electricity price and the gas price may change. The corresponding policy should be changed accordingly.
Parameters that vary with policy and time: the price of electricity purchase e 1; electricity selling price e 2; coefficient of gas cost b 1.
Parameters updated according to data accumulation: generating efficiency eta of gas internal combustion engine setchpEfficiency η of electric boilereb, hot spot ratio beta of gas internal combustion enginechpIs the energy efficiency ratio Cop of electric refrigerationec. The method comprises the following steps that values x1, x2, x3, x4 and x5 of 5 segments of electric power output of the combustion engine, values C1, C2, C3, C4 and C5 of 5 segments of thermal power output of the combustion engine, values C6, C7, C8, C9 and C10 of 5 segments of gas energy output of the combustion engine, operation and maintenance coefficients a1 a2 a3a4 of each device and annual start-stop cost coefficients v1 of each device are changed differently as equipment time goes on or after overhaul.
Specifically, in one embodiment, a closed-loop management method for a microgrid and integrated energy source is characterized in that coefficients x2, x3, x4, x5 and x6 are set to be 51.1, 61.1, 71.5, 81.8, 92, C2, C3, C4, C5, C6, C7, C8, C9, C10 and C11 to be 136.5, 160.1, 184.4, 207.9, 222.9, 51.9, 57.2, 62.7, 68.9 and 76.0 respectively, and C1C 2C 3C 4 is set to be 0.6; a1 a2 a3a4 is 0.05, which is the operation and maintenance coefficient of each device; b1 is the coefficient of gas cost is 58.4; e1 is the price of electricity bought;
[ 10.910.99.59.532.7505550424349.553.369.151.941.839.740.965.8123.1100.367.6483020.4 ]; e2 is the electricity price 0.4;
electrical loading: [0.3450.3450.3450.3450.3450.3450.7080.708001.1590.7080.7080.7080.7080.7080.7080000.708]
Heat load: [10.910.99.59.532.7505550424349.553.369.151.941.839.740.965.8123.1100.367.6483020.4]
Cold load: [10.910.99.59.532.7505550424349.553.369.151.941.839.740.965.8123.1100.367.6483020.4]
ηchpIs 0.4, etaebIs 0.9, betachp0.85, CopecIs 3.
An objective function based on the annual average cost optimization is established as follows:
the optimization objective is to minimize the total annual cost, which includes investment costs, operational maintenance costs, fuel costs, energy purchase costs, and energy sales revenue.
The constraint relationship is established as follows:
and (3) constraint of an equation:
Hchp+Heb＝Hload (20)
Cchp+Cec+CAbsc＝Cload (21)
Qchp*ηchp＝Pchp
(22)
Pchp*βchp＝Hchp (25)
Pchp＝x2W2+x3W3+x4W4+x5W5+x6W6 (26)
Hchp＝C2W2+C3W3+C4W4+C5W5+C6W6 (27)
Qchp＝C7W2+C8W3+C9W4+C10W5+C11W6 (28)
W1+W2+W3+W4+W5+W6＝1 (29)
Z1+Z2+Z3+Z4+Z5＝1 (30)
the inequality constrains:
W1≤Z1，W2≤Z1+Z2，W3≤Z2+Z3，W4≤Z3+Z4，W5≤Z4+Z5，W6≤Z5 (33)
0≤M(i)+N(i)≤1 (34)
based on the capacity configuration result of the improved segmented linearization gas internal combustion engine combined cooling heating and power supply, the capacity of the gas combustion engine is 110kW, the power of an electric boiler is 69.1332kW, the power of electric refrigeration is 217.6804kW, the power of a bromine refrigerator is 53.3602kW, and the power of a power grid is 176.52 kW. And good electric, hot and cold running curves.
In the description of the present application, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience in describing the present application and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present application.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. A closed-loop management method for a micro-grid and comprehensive energy is characterized by comprising the following steps:
step S1: setting control information according to the initialized parameter array, initializing the parameter array, and acquiring initialized result information of the parameter array;
step S2: establishing an objective function and constraint conditions according to the objective function establishing information and the constraint condition establishing information;
step S3: solving to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
step S4: sending data to a central controller;
step S5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller;
step S6: the unit controller issues instructions to each device to execute;
step S7: the equipment transmits data required by the algorithm to the unit controller;
step S8: the data is collected by the unit controller and transmitted to the unit controller to be transmitted to the central controller;
step S9: the central controller transmits the data to the database;
step S10: the database collects and analyzes data required by the algorithm to obtain COP information;
acquiring any one or more of:
-electric boiler efficiency information;
-gas engine segment efficiency;
-segmented thermoelectric ratio data;
step S11: calling spare operation data information in a database, updating data information and calculating the data information to be used as a value of a parameter array;
step S12: and forming closed-loop system execution to obtain closed-loop management result information of the micro-grid and the comprehensive energy.
2. The method of claim 1, further comprising: the step S3 includes:
step S3.1: and solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring the running state information and the power value information of the devices.
3. The method of claim 1, further comprising: the step S4 includes:
step S4.1: and sending the data to the central controller through an MQQT protocol.
4. The method of claim 1, further comprising: the step S8 includes:
step S8.1: data are collected by the group controller, transmitted to the group controller through MQQT and 104 protocols and transmitted to the central controller.
5. The method of claim 1, further comprising: the step S11 includes:
and S11.1, calling equipment operation data information, electricity price updating data, gas price updating data and operation and maintenance cost updating data in the database by an algorithm to calculate the values serving as parameter arrays.
6. A closed-loop management system for micro-grids and comprehensive energy sources is characterized by comprising:
module M1: setting control information according to the initialized parameter array, initializing the parameter array, and acquiring initialized result information of the parameter array;
module M2: establishing an objective function and constraint conditions according to the objective function establishing information and the constraint condition establishing information;
module M3: solving to obtain the running state and power value of each device, and acquiring running state information and power value information of the devices;
module M4: sending data to a central controller;
module M5: the central controller acquires data and analyzes the data and then sends the data to the generating set controller;
module M6: the unit controller issues instructions to each device to execute;
module M7: the equipment transmits data required by the algorithm to the unit controller;
module M8: the data is collected by the unit controller and transmitted to the unit controller to be transmitted to the central controller;
module M9: the central controller transmits the data to the database;
module M10: the database collects and analyzes data required by the algorithm to obtain COP information;
acquiring any one or more of:
-electric boiler efficiency information;
-gas engine segment efficiency;
-segmented thermoelectric ratio data;
module M11: calling spare operation data information in a database, updating data information and calculating the data information to be used as a value of a parameter array;
module M12: and forming closed-loop system execution to obtain closed-loop management result information of the micro-grid and the comprehensive energy.
7. The microgrid and integrated energy closed-loop management system of claim 6, further comprising: the module M3 includes:
module M3.1: and solving by adopting an MILP algorithm and CPLEX to obtain the running state and power value of each device, and acquiring the running state information and the power value information of the devices.
8. The microgrid and integrated energy closed-loop management system of claim 1, further comprising: the module M4 includes:
module M4.1: and sending the data to the central controller through an MQQT protocol.
9. The microgrid and integrated energy closed-loop management system of claim 6, further comprising: the module M8 includes:
module M8.1: data are collected by the group controller, transmitted to the group controller through MQQT and 104 protocols and transmitted to the central controller.
10. The microgrid and integrated energy closed-loop management system of claim 6, further comprising: the module M11 includes:
and a module M11.1, calculating the values of the parameter arrays by calling equipment operation data information, electricity price updating data, gas price updating data and operation and maintenance cost updating data in the database through an algorithm.
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