CN115438847A - Information gap robust optimization scheduling model of random electrothermal coupling system - Google Patents

Information gap robust optimization scheduling model of random electrothermal coupling system Download PDF

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CN115438847A
CN115438847A CN202211037824.7A CN202211037824A CN115438847A CN 115438847 A CN115438847 A CN 115438847A CN 202211037824 A CN202211037824 A CN 202211037824A CN 115438847 A CN115438847 A CN 115438847A
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张磊
叶婧
马宇飞
李振华
张涛
黄悦华
薛田良
杨楠
刘颂凯
程江洲
肖繁
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Abstract

The random electric heating coupling system information gap robust optimization scheduling model comprises an upper layer optimization scheduling model and a lower layer optimization scheduling model; the upper-layer optimized scheduling model comprises the following steps: an objective function of the upper-layer optimized scheduling model and a constraint condition of the upper-layer optimized scheduling model. The lower layer optimized scheduling model comprises: an objective function of the lower-layer optimized scheduling model and a constraint condition of the lower-layer optimized scheduling model. The stochastic electric heating coupling system information gap robust optimization scheduling model has the characteristic of double-layer optimization, the original optimization scheduling model needs to be reasonably loosened before the model is solved, and the KKT condition of the lower-layer optimization scheduling model is equivalently replaced by the KKT condition. The method adopts an information gap robust optimization method to solve, can be suitable for the current situation of wind power uncertainty of a random electric heating coupling system, and fully ensures the safety and stability of system operation.

Description

Information gap robust optimization scheduling model of random electric heating coupling system
Technical Field
The invention relates to the technical field of operation control of an integrated energy system, in particular to a robust optimization scheduling model for information gaps of a random electric heating coupling system.
Background
During the winter period of the three north region, the central heating demand and the wind power consumption demand are mutually overlapped, and the receiving capacity of renewable energy sources of a power grid is seriously reduced. From a physical point of view, electrical energy is relatively easy to transfer but difficult to store, thermal energy is relatively easy to store but difficult to transfer, and there is a natural complementarity between electrical and thermal systems. The electric power system and the thermodynamic system are integrated to be further dispatched in a unified mode, and coordination flexibility spaces among the electric power network, the thermodynamic network, thermal power generating units, cogeneration units, boilers and other equipment are fully excavated, so that the method becomes one of important ways for solving large-scale renewable energy consumption at present.
The electric heating coupling system is scheduled to operate on a small-scale time scale, the temperature of a heat supply network pipeline can change along with heat loss, the change is much slower than the electromagnetic transient and electromechanical transient processes of the power system, at the moment, the power system can describe the power flow process by an algebraic equation, and the thermodynamic system still needs to take account of the dynamic process of heat transfer of the heat supply network. However, in practical engineering applications, the water return pipe and the water supply pipe of the heat supply network are embedded in the same insulating sleeve for laying, and the heat loss of the heat supply network is influenced not only by the environment but also by the heat loss between the water supply/return pipes. In the dispatching of the electric heating coupling system, flexibility of equipment such as a cogeneration unit and the like is released, so that the fluctuation frequency and amplitude of the inlet temperature of a heat source pipeline are increased, the non-uniform distribution of the pipeline temperature is severe, and the heat loss of a water supply/return pipeline of the pipeline is increased. In fact, the heat loss is the main operation cost of the thermodynamic system for supporting the flexibility of the power grid, and therefore, the heat loss influence in the heat transfer dynamic process must be accurately considered to improve the economy of the electric-thermal coupling scheduling result in the actual engineering application.
In addition, wind power uncertainty is also one of the important factors influencing the electric-heat coupling scheduling result. At present, two solving methods of random optimization and robust optimization are mainly adopted to deal with wind power uncertainty existing in the system. However, the probability distribution of wind power in practical engineering application has uncertainty, and the effectiveness of the random optimization result is difficult to ensure. Also, while robust optimization can be represented by its uncertain boundary parameters, the final results are often too conservative. Therefore, how to greatly mine the fluctuation resistance of the system while ensuring the economic benefit of the system is a technical problem which needs to be solved urgently in the optimization scheduling of the random electric heating coupling system at the present stage.
Disclosure of Invention
In order to further exert the comprehensive benefits of the random electrothermal coupling system, the invention provides a random electrothermal coupling system optimization scheduling method considering heat asymmetric heat loss, and aims to fully utilize the heat migration dynamic process of a thermodynamic system so as to improve the wind power consumption level and the economic benefits of the random electrothermal coupling system, and effectively resist the wind power uncertainty existing in the electric power system while ensuring the economy of the random electrothermal coupling system through an information gap robust optimization method.
The technical scheme adopted by the invention is as follows:
the random electric heating coupling system optimal scheduling method considering the asymmetric heat loss of heat comprises the following steps of:
step 1: establishing a thermodynamic system model considering asymmetric heat loss based on a heat transfer process of a heat supply network pipeline considering actual heat loss;
step 2: the thermodynamic system model which is established in the step 1 and takes the asymmetric heat loss into account is adopted, the influence of wind power uncertainty is considered in the structure of the traditional electric heating coupling system, and a random electric heating coupling system optimization scheduling model is established;
and step 3: based on the random electric heating coupling system optimized scheduling model established in the step 2, modeling the wind power uncertainty of the model by adopting an information gap robust optimization method and solving model relaxation;
by the steps, the optimized scheduling of the random electrothermal coupling system is realized.
The invention relates to a random electric heating coupling system optimal scheduling method considering heat asymmetric heat loss, which has the advantages that:
and establishing constraint conditions for the operation of the power system and the thermodynamic system by taking the minimum total scheduling cost of the random electrothermal coupling system as an objective function, wherein the heat transfer process considering the heat asymmetric loss is taken into account in the constraint conditions for the operation of the thermodynamic system. Meanwhile, modeling is carried out on wind power uncertainty existing in the power system by using an information gap robust optimization method, an original optimization scheduling model is further converted into a random electric heating coupling system information gap robust optimization scheduling model, and the optimal result of the random electric heating coupling system optimization scheduling method considering heat asymmetric loss is obtained by relaxation of the model and solution of commercial software.
The method of the invention considers the heat asymmetric loss process of the heat supply network pipeline, and fully exerts the heat transfer dynamic characteristic of the thermodynamic system so as to improve the wind power consumption level and the economic benefit of the random electric heating coupling system. And an information gap robust optimization method is adopted for solving, so that the method is suitable for the current situation of wind power uncertainty of a random electric heating coupling system, and the safety and the stability of the system operation are fully ensured.
Drawings
FIG. 1 is a diagram of an actual random electro-thermal coupling system for a region;
FIG. 2 is a graph of the actual electric heating load demand and its wind power predicted maximum power output for a certain area;
FIG. 3 is a graph of inlet and outlet temperatures of a water supply line for thermodynamic system 67;
FIG. 4 is a graph of inlet and outlet temperatures of the No. 67 return line of the thermodynamic system;
FIG. 5 is a scheduling plan diagram of heat output of the cogeneration unit;
FIG. 6 is a plan view of electric power dispatching for cogeneration units, thermal power units and wind power units;
FIG. 7 is a diagram of the air abandon rate of the random electro-thermal coupling system;
fig. 8 is a graph of the total scheduling cost of the system and the uncertainty radius variation trend thereof.
Detailed Description
The random electric heating coupling system optimization scheduling method considering the heat asymmetric heat loss comprises the following steps:
step 1: establishing a thermodynamic system model considering heat asymmetric loss based on a heat transfer process of a heat supply network pipeline considering actual heat loss;
step 2: the thermodynamic system model which is established in the step 1 and takes the asymmetric heat loss into account is adopted, the influence of wind power uncertainty is considered in the structure of the traditional electric heating coupling system, and a random electric heating coupling system optimization scheduling model is established;
and 3, step 3: based on the random electric heating coupling system optimized scheduling model established in the step 2, modeling the wind power uncertainty of the model by adopting an information gap robust optimization method and solving model relaxation;
by the steps, the optimized scheduling of the random electrothermal coupling system is realized.
In the step 1, the heat transfer process of the heat supply network pipeline is represented by a steady-state temperature model, as shown in formula (1):
Figure BDA0003819039080000031
in the formula, m and c respectively represent the mass flow and the specific heat capacity of pipeline hot water; t represents the average temperature of the pipe in space; q represents the heat loss corresponding to the length dx of the pipe.
In the step 1, in the heat transfer process of the heat supply network pipeline, the actual heat loss includes: symmetric heat loss process and asymmetric heat loss process;
the symmetrical heat loss process is caused by heat exchange between the water supply pipeline and the external environment through the pipe wall insulating layer and the water return pipeline respectively, and the heat loss in the process is calculated as shown in the formula (2) and the formula (3):
Figure BDA0003819039080000032
Figure BDA0003819039080000033
in the above formula, v represents a water supply pipe network; r represents a return water pipe network; s represents a symmetric heat loss process;
Figure BDA0003819039080000034
and
Figure BDA0003819039080000035
respectively representing the symmetrical heat loss of the water supply/return pipeline; t is a unit of v And T r Respectively representing the average temperature of the water supply/return pipes; t is b Represents the average temperature of the external environment; r s Representing the thermal resistivity of the symmetric heat loss process.
The asymmetric heat loss process is caused by heat transfer from a water supply pipeline to a water return pipeline through an insulating layer in the pipeline, and the heat loss in the process is calculated as shown in a formula (4):
Figure BDA0003819039080000036
in the formula, q a Representing the asymmetric heat loss of the water supply/return pipeline; r a Represents the thermal resistivity of the asymmetric heat loss process;
the heat transfer process of the heat supply network pipeline after the asymmetrical heat loss is considered is shown in formulas (5) to (6):
Figure BDA0003819039080000041
in the formula, m v Representing the mass flow of hot water in the water supply pipeline; c represents the specific heat capacity of the pipeline hot water; t is v And T r Respectively represent the average temperature on the water supply/return piping space; t is b Represents the average temperature of the external environment;
Figure BDA0003819039080000042
representing the symmetric heat loss of the water supply pipeline; q. q of a Representing the asymmetrical heat loss amount of the water supply/return pipe; r is s And R a Representing the thermal resistivity of symmetric and asymmetric heat loss processes, respectively.
Figure BDA0003819039080000043
In the formula, m r Representing the mass flow of the hot water in the return pipeline; c represents the specific heat capacity of the pipeline hot water; t is a unit of v And T r Respectively represents the average temperature of the water supply/return pipe space; t is b Represents the average temperature of the external environment;
Figure BDA0003819039080000044
representing the symmetrical heat loss of the water return pipeline; q. q.s a Representing the asymmetrical heat loss amount of the water supply/return pipe; r is s And R a Representing the thermal resistivity of symmetric and asymmetric heat loss processes, respectively. Wherein in the formula (6) — m r The negative sign of (a) indicates that the opposite flow of the return pipe is explained by the negative sign on the premise that the flow direction of the hot water of the water supply pipe is positive.
The operation adjusting mode of the thermodynamic system model is a quality adjusting mode, namely the mass flow of hot water in a heat supply network pipeline is not changed, and the temperature of the heat supply network pipeline is only adjusted. Meanwhile, the structure of the thermodynamic system network is a universal node structure, subscripts e and n are adopted to respectively number the heat supply network pipelines and the network nodes,
Figure BDA0003819039080000045
and
Figure BDA0003819039080000046
respectively representing the front and back side sets of thermal network channels connected to the network node n.
In step 1, after considering the asymmetric heat loss, the thermodynamic system model includes: network node part and heat supply network pipe part:
the network node part represents the mass flow balance and the heat balance of the pipeline hot water at the network node, and the balance equation comprises: heat balance equations (7) - (8) of the cogeneration unit and the network node at the user heat load:
Figure BDA0003819039080000047
in the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000048
representing the heat output of the cogeneration unit g at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000051
indicating cogeneration at network node n at time tThe mass flow of pipeline hot water of the unit g;
Figure BDA0003819039080000052
and
Figure BDA0003819039080000053
respectively representing the inlet and outlet temperatures of the pipeline of the combined heat and power generation unit g at the network node n at the time t.
Figure BDA0003819039080000054
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000055
representing the heat demand of the user heat load d at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000056
representing the mass flow of hot water in a pipeline of a user heat load d at a network node n at the time t;
Figure BDA0003819039080000057
and
Figure BDA0003819039080000058
respectively representing the inlet and outlet temperatures of the customer heat load dduct at network node n at time t.
Heat balance equations (9) - (10) for network nodes:
Figure BDA0003819039080000059
wherein e represents the number of the heat supply network pipeline,
Figure BDA00038190390800000510
and
Figure BDA00038190390800000511
respectively representing phases n with the network nodeThe serial front side and back side heat network channel number sets;
Figure BDA00038190390800000512
showing the mass flow of the hot water in the water supply pipeline e at the time t;
Figure BDA00038190390800000513
and
Figure BDA00038190390800000514
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800000515
represents the outlet temperature of the water supply pipeline e at the time t;
Figure BDA00038190390800000516
representing the outlet temperature of a pipeline of the cogeneration unit g at a network node n at the time t;
Figure BDA00038190390800000517
representing the temperature at the network node n of the water supply pipe at time t.
Figure BDA00038190390800000518
Wherein e represents the number of the heat supply network pipeline,
Figure BDA00038190390800000519
and
Figure BDA00038190390800000520
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800000521
the mass flow of the hot water in the water return pipeline e at the time t is shown;
Figure BDA00038190390800000522
and
Figure BDA00038190390800000523
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800000524
respectively representing the outlet temperature of the water return pipeline e at the moment t;
Figure BDA00038190390800000525
representing the outlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure BDA00038190390800000526
and the temperature of the return water pipeline network node n at the time t is shown.
Mass flow balancing equations (11) - (12) for the network nodes:
Figure BDA00038190390800000527
wherein e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000061
and
Figure BDA0003819039080000062
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA0003819039080000063
and
Figure BDA0003819039080000064
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA0003819039080000065
indicating the mass flow of hot water in the water supply line e at time t.
Figure BDA0003819039080000066
Wherein e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000067
and
Figure BDA0003819039080000068
respectively representing front side and back side heat network channel number sets connected with the network node n;
Figure BDA0003819039080000069
and
Figure BDA00038190390800000610
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800000611
indicating the mass flow of hot water in the return line e at time t.
The balance of the network node front side pipe outlet temperature and the back side pipe inlet temperature assumes equations (13) - (14):
Figure BDA00038190390800000612
in the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800000613
a set of back-end thermal network pipe numbers representing connections to the network node n;
Figure BDA00038190390800000614
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA00038190390800000615
representing the inlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure BDA00038190390800000616
representing the temperature at the network node n of the water supply pipe at time t.
Figure BDA00038190390800000617
Wherein e represents the number of the heat supply network pipeline,
Figure BDA00038190390800000618
a front-side hot network pipe number set which is connected with the network node n is represented;
Figure BDA00038190390800000619
representing the inlet temperature of the water return pipeline e at the moment t;
Figure BDA00038190390800000620
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure BDA00038190390800000621
and the temperature of the return water pipeline network node n at the time t is shown.
The heat network pipe section represents the pipe temperature variation connecting the network nodes. Taking a water supply pipeline as an example, the temperature of the pipeline is not only determined by the heat transfer process of the pipeline, but also influenced by the temperature from the external environment and the temperature of a water return pipeline, and the water return pipeline is the same. The inlet and outlet temperature relationships of the water supply/return pipe e are as shown in equations (15) to (18):
Figure BDA0003819039080000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000072
and
Figure BDA0003819039080000073
respectively representing the inlet temperature of the water supply/return pipeline e at the time t;
Figure BDA0003819039080000074
represents the outlet temperature of the water supply pipeline e at the time t; t is a unit of b Represents the average temperature of the external environment; r s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi shape e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA0003819039080000075
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000076
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA0003819039080000077
and
Figure BDA0003819039080000078
respectively representing the outlet temperature of the water supply/return pipeline e at the time t; t is b Represents the average temperature of the external environment; r s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA0003819039080000079
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; r s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; c represents the specific heat capacity of the pipeline hot water; l e Indicates the length of the water supply/return pipe e; m is a unit of e,t Indicating hot water in supply/return line eMass flow rate.
Figure BDA00038190390800000710
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; m is a unit of e,t Representing the mass flow of the hot water of the water supply/return pipeline e; l. the e Indicates the length of the water supply/return pipe e; r represents a thermal resistivity without physical significance, and in the process of actually solving the equations (5) - (6) of the differential equation set and obtaining the equations (15) - (16) of the differential equation set, the step and the difficulty of the calculation process are simplified by setting the thermal resistivity R.
In step 2, the structure of the conventional electric-thermal coupling system includes: large-scale wind power generation units, thermal power generation units, cogeneration units, power system line networks and thermodynamic system pipeline networks. And (3) establishing a random electric heating coupling system optimization scheduling model considering heat asymmetric loss by adopting the thermodynamic system model in the step 1 and considering the influence of wind power uncertainty factors on the wind power generator set under the structure of the traditional electric heating coupling system.
The optimized scheduling model of the random electrothermal coupling system comprises an objective function of the optimized scheduling model and a constraint condition of the optimized scheduling model.
And (3) optimizing an objective function of the scheduling model by taking the minimum total scheduling cost of the scheduling model as an optimization objective, and adding the abandoned wind power into the objective function in the form of a penalty term, as shown in formula (19):
min F total ＝F chp +F con +F wind (19)；
in the formula, F total Representing the total scheduling cost of the random electric heating coupling system; f chp And F con Respectively representing the scheduling cost of a cogeneration unit and a thermal power unit in the random electric heating coupling system; f wind And (4) representing the wind abandon punishment cost of the wind generating set in the random electric heating coupling system.
F chp 、F con And F wind As shown in equations (20) to (22):
Figure BDA0003819039080000081
in the formula, F chp The dispatching cost of the thermoelectric cogeneration unit and the thermal power unit in the random electric-thermal coupling system is represented; t represents the current scheduling time; t represents a set formed by all scheduling time instants; g represents the number of the cogeneration unit in the random electric heating coupling system; psi chp Represents the set of all cogeneration units; f. of g,p And f g,q Respectively representing the electricity/heat output cost of the cogeneration unit g; p g,t And Q g,t Respectively representing the electric/thermal output of the cogeneration unit g at the time t.
Figure BDA0003819039080000082
In the formula, F con Representing the dispatching cost of a thermoelectric generator set in the random electric heating coupling system; t represents the current scheduling time; t represents a set formed by all scheduling time instants; k represents the number of the fire-electricity generator set in the random electric heating coupling system; psi con Representing a set of all thermal power generating units; f. of k Representing the electricity output cost of the thermal power generating unit k; p k,t And (4) representing the electric output of the thermal power generating unit k at the moment t.
Figure BDA0003819039080000083
In the formula, F wind Representing the wind abandoning punishment cost of a wind generating set in the random electric heating coupling system; t represents the current scheduling time; t represents a set formed by all scheduling time; i represents the serial number of a wind turbine generator set in the random electric heating coupling system; psi wind Representing a set of all wind turbines; delta i Representing a wind abandon penalty item coefficient of the wind turbine generator i; p i,t,max Representing the actual maximum electric output of the wind turbine generator i at the moment t; p is i,t And the electric output of the wind turbine generator i at the moment t is shown.
The constraint condition of the optimization scheduling model comprises a constraint condition of the operation of the power system and a constraint condition of the operation of the thermal system,
1): the constraint condition of the operation of the power system is composed of the constraint condition of the balance of the power output of the generator set, the constraint condition of the operation of the thermal power generating set, the constraint condition of the operation of the wind power generating set, the constraint condition of the operation of the cogeneration set and the constraint condition of the power of the line of the connecting line,
the constraint condition of the unit power output balance is as shown in formula (23):
Figure BDA0003819039080000091
in the formula, g, k, i and j represent the numbers of a thermoelectric cogeneration unit, a thermal power unit, a wind power unit and a user electric load in the random electric-heat coupling system; psi chp 、ψ con 、ψ wind And psi d Representing a set formed by all cogeneration units, thermal power units, wind power units and user electric loads; p is g,t Representing the power output of the cogeneration unit g at the moment t; p is k,t Representing the electric output of the thermal power generating unit k at the moment t; p is i,t Representing the electric output of the wind turbine generator i at the time t; p is j,t Representing the electrical demand of the consumer electrical load j at time t.
The constraint condition of the operation of the thermal power generating unit is shown as the formula (24):
P k,t,min ≤P k,t ≤P k,t,max (24)；
in the formula, P k,t Representing the electric output of the thermal power generating unit k at the moment t; p is k,t,min And P k,t,max And respectively representing the minimum and maximum electric output of the thermal power generating unit k at the moment t.
The constraint condition of the operation of the wind turbine generator is shown as the formula (25):
0≤P i,t ≤P i,t,max (25)；
in the formula, P i,t,max Representing the actual maximum electric output of the wind turbine generator i at the time t; p i,t And the electric output of the wind turbine generator i at the moment t is shown.
The constraint conditions of the operation of the cogeneration unit are shown in formulas (26) to (28):
P g,t ≥r g Q g,t (26)；
in the formula, P g,t And Q g,t Respectively representing the electricity/heat output of the cogeneration unit g at the moment t; r is g The electric/thermal output coupling coefficient of the cogeneration unit g is expressed.
F g,t,min ≤ρ g,p P g,t +ρ g,q Q g,t ≤F g,t,max (27)；
In the formula, F g,t,min And F g,t,max Respectively representing the minimum and maximum fuel intakes of the cogeneration unit g at the time t; rho g,p And ρ g,q Respectively representing the electricity/heat output fuel consumption rate of the cogeneration unit g; p g,t And Q g,t Respectively representing the electric/thermal output of the cogeneration unit g at the time t.
0≤Q g,t ≤Q g,t,max (28)；
In the formula, Q g,t The heat output of the combined heat and power generation unit g at the moment t is represented; q g,t,max Representing the maximum thermal output of the cogeneration unit g at time t.
The constraint conditions of the tie line power are shown in equations (29) to (30):
L l,t,min ≤L l,t ≤L l,t,max (29)；
in the formula, L l,t Represents the power of the tie line l at time t; l is l,t,min And L l,t,max Respectively representing the minimum and maximum power values of the link line l at time t.
Figure BDA0003819039080000101
In the formula, L l,t Represents the power of the link line l at time t; l, g, k, i and j represent the numbers of a line, a cogeneration unit, a thermal power unit, a wind power unit and a user electric load in the random electric heating coupling system; psi chp 、ψ con 、ψ wind And psi d Representing all cogeneration units, thermal power units, wind power units and consumer electricity terminalsA set of loads; g l-g Representing a power distribution coefficient of the cogeneration unit; g l-i Representing the power distribution coefficient of the wind turbine generator; g l-k Representing the power distribution coefficient of the thermal power generating unit; g l-j A power distribution coefficient representing a consumer electrical load; p g,t Representing the power output of the cogeneration unit g at the moment t; p k,t Representing the electric output of the thermal power generating unit k at the moment t; p i,t Representing the electric output of the wind turbine generator i at the time t; p j,t Representing the electrical demand of the consumer electrical load j at time t.
2): the constraint condition of the operation of the thermodynamic system is formed by the constraint condition of the network node and the constraint condition of the heat supply network pipeline.
The constraints of the network node are as shown in equations (31) to (38):
Figure BDA0003819039080000102
in the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000103
representing the heat output of the cogeneration unit g at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000104
representing the mass flow of the hot water in the g pipeline of the cogeneration unit at the n network node at the time t;
Figure BDA0003819039080000105
and
Figure BDA0003819039080000106
respectively representing the inlet temperature and the outlet temperature of the pipeline of the cogeneration unit g at the network node n at the time t.
Figure BDA0003819039080000111
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000112
representing the thermal demand of a user thermal load d at a network node n at time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000113
representing the mass flow of hot water in a pipeline of a user heat load d at a network node n at the time t;
Figure BDA0003819039080000114
and
Figure BDA0003819039080000115
respectively representing the inlet and outlet temperatures of the customer heat load dduct at network node n at time t.
Figure BDA0003819039080000116
Wherein e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000117
and
Figure BDA0003819039080000118
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA0003819039080000119
representing the mass flow of hot water in the water supply pipeline e at the time t;
Figure BDA00038190390800001110
and
Figure BDA00038190390800001111
respectively representing the mass flow of pipeline hot water of a combined heat and power generation unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800001112
indicating water supply line e at time tAn outlet temperature;
Figure BDA00038190390800001113
representing the outlet temperature of a pipeline of the cogeneration unit g at a network node n at the time t;
Figure BDA00038190390800001114
representing the temperature at time t at the water supply pipe network node n.
Figure BDA00038190390800001115
Wherein e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001116
and
Figure BDA00038190390800001117
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800001118
representing the mass flow of the hot water in the water return pipeline e at the moment t;
Figure BDA00038190390800001119
and
Figure BDA00038190390800001120
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800001121
respectively representing the outlet temperature of the water return pipeline e at the moment t;
Figure BDA00038190390800001122
the outlet temperature of a pipeline of a user heat load d at a network node n at the time t is represented;
Figure BDA00038190390800001123
and the temperature of the return water pipeline network node n at the time t is shown.
Figure BDA00038190390800001124
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001125
and
Figure BDA00038190390800001126
respectively representing front side and back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800001127
and
Figure BDA00038190390800001128
respectively representing the mass flow of pipeline hot water of a combined heat and power generation unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800001129
representing the mass flow of hot water in the water supply line e at time t.
Figure BDA00038190390800001130
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000121
and
Figure BDA0003819039080000122
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA0003819039080000123
and
Figure BDA0003819039080000124
respectively representing the mass flow of pipeline hot water of a combined heat and power generation unit g and a user heat load d at a network node n at the time t;
Figure BDA0003819039080000125
representing the mass flow of hot water in the return line e at time t.
Figure BDA0003819039080000126
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000127
a set of back-end thermal network pipe numbers representing connections to the network node n;
Figure BDA0003819039080000128
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA0003819039080000129
representing the inlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure BDA00038190390800001210
representing the temperature at the network node n of the water supply pipe at time t.
Figure BDA00038190390800001211
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001212
a set of front-side thermal network pipe numbers representing connections to the network node n;
Figure BDA00038190390800001213
the inlet temperature of the water return pipeline e at the time t is shown;
Figure BDA00038190390800001214
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure BDA00038190390800001215
and the temperature of the return water pipeline network node n at the time t is shown.
The constraints of the heat supply network pipes are as shown in formulas (39) to (42):
Figure BDA00038190390800001216
in the formula (I), the compound is shown in the specification,
Figure BDA00038190390800001217
and
Figure BDA00038190390800001218
respectively representing the inlet temperature of the water supply/return pipeline e at the time t;
Figure BDA00038190390800001219
represents the outlet temperature of the water supply pipeline e at the time t; t is a unit of b Represents the average temperature of the external environment; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA0003819039080000131
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000132
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA0003819039080000133
and
Figure BDA0003819039080000134
respectively representing the outlet temperature of the water supply/return pipeline e at the time t; t is a unit of b Represents the average temperature of the external environment; r s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA0003819039080000135
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; c represents the specific heat capacity of the pipeline hot water; l e Indicates the length of the water supply/return pipe e; m is a unit of e,t Indicating the mass flow of hot water in the supply/return line e.
Figure BDA0003819039080000136
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; m is a unit of e,t Representing the mass flow of the hot water of the water supply/return pipeline e; l. the e Indicates the length of the water supply/return pipe e; r represents a thermal resistance coefficient without physical significance, and in the process of actually solving equations (5) - (6) of a differential equation set and obtaining the equations (15) - (16) of the differential equation set, the steps and the difficulty of the calculation process are simplified by setting the thermal resistance coefficient R.
In the step 3, based on the stochastic electric heating coupled system optimization scheduling model in the step 2, an information gap robust optimization method is adopted to model wind power uncertainty existing in the system, as shown in the formula (43):
U(α,P′ i,t,max )＝{|P′ i,t,max -P i,t,max |≤α|P′ i,t,max |} (43)；
in the formula (II), U (alpha, P' i,t,max ) Representing the fluctuation range of the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius; p' i,t,max And the predicted maximum power output of the wind turbine generator i at the time t is shown.
When wind power uncertainty is accounted in the random electric heating coupling system optimization scheduling model, the model target is difficult to achieve the optimal result. To ensure the optimization effect, the expected scheduling cost F of the model is also set ro As shown in equation (44):
F ro ＝(1+β)F 0 (44)；
in the formula, F 0 Representing the determined scheduling cost, i.e. the scheduling cost calculated when the wind uncertainty (α = 0) is not considered in the optimized scheduling model; beta represents a scheduling cost deviation coefficient, namely a deviation degree between the expected scheduling cost and the determined scheduling cost, and the larger the deviation degree is, the larger the risk avoiding capability of the system is.
At this time, the optimization objective of the stochastic electric heating coupling system optimization scheduling model in the step 2 is changed into that when the total scheduling cost is not higher than the expected scheduling cost, the corresponding maximum wind power uncertainty radius is sought, and the stochastic electric heating coupling system information gap robust optimization scheduling model is established according to the maximum wind power uncertainty radius.
In step 3, the stochastic electrothermal coupling system information gap robust optimization scheduling model includes: an upper layer optimized scheduling model and a lower layer optimized scheduling model:
(1) the method comprises the following steps The upper-layer optimized scheduling model comprises the following steps: an objective function of the upper-layer optimization scheduling model and a constraint condition of the upper-layer optimization scheduling model are as follows:
1) The objective function of the upper-layer optimization scheduling model is as shown in equation (45):
maxα (45)；
in the formula, α represents the fluctuation range of the actual maximum electrical output, i.e., the uncertainty radius.
2) The constraints of the upper-layer optimization scheduling model are as shown in equations (46) - (65):
Figure BDA0003819039080000141
in the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000142
representing the heat output of the cogeneration unit g at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000143
representing the mass flow of the hot water in the g pipeline of the cogeneration unit at the n network node at the time t;
Figure BDA0003819039080000144
and
Figure BDA0003819039080000145
respectively representing the inlet and outlet temperatures of the pipeline of the combined heat and power generation unit g at the network node n at the time t.
Figure BDA0003819039080000146
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000147
representing the heat demand of the user heat load d at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure BDA0003819039080000148
representing the mass flow of hot water in a pipeline of a user heat load d at a network node n at the time t;
Figure BDA0003819039080000149
and
Figure BDA00038190390800001410
respectively representing the inlet and outlet temperatures of the customer heat load dduct at network node n at time t.
Figure BDA00038190390800001411
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001412
and
Figure BDA00038190390800001413
respectively representing front side and back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800001414
showing the mass flow of the hot water in the water supply pipeline e at the time t;
Figure BDA00038190390800001415
and
Figure BDA00038190390800001416
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA0003819039080000151
represents the outlet temperature of the water supply pipeline e at the time t;
Figure BDA0003819039080000152
representing the outlet temperature of the pipeline of the cogeneration unit g at the network node n at the time t;
Figure BDA0003819039080000153
representing the temperature at the network node n of the water supply pipe at time t.
Figure BDA0003819039080000154
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA0003819039080000155
a set of front-side thermal network pipe numbers representing connections to the network node n;
Figure BDA0003819039080000156
representing return line e at time tAn inlet temperature;
Figure BDA0003819039080000157
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure BDA0003819039080000158
and the temperature of the return water pipeline network node n at the moment t is shown.
Figure BDA0003819039080000159
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001510
and
Figure BDA00038190390800001511
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800001512
and
Figure BDA00038190390800001513
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800001514
indicating the mass flow of hot water in the water supply line e at time t.
Figure BDA00038190390800001515
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001516
and
Figure BDA00038190390800001517
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure BDA00038190390800001518
and
Figure BDA00038190390800001519
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure BDA00038190390800001520
indicating the mass flow of hot water in the return line e at time t.
Figure BDA00038190390800001521
Wherein e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001522
a set of back-end thermal network pipe numbers representing connections to the network node n;
Figure BDA00038190390800001523
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA00038190390800001524
representing the inlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure BDA00038190390800001525
representing the temperature at time t at the water supply pipe network node n.
Figure BDA00038190390800001526
In the formula, e represents the number of the heat supply network pipeline,
Figure BDA00038190390800001527
a front-side hot network pipe number set which is connected with the network node n is represented;
Figure BDA0003819039080000161
representing the inlet temperature of the water return pipeline e at the moment t;
Figure BDA0003819039080000162
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure BDA0003819039080000163
and the temperature of the return water pipeline network node n at the moment t is shown.
Figure BDA0003819039080000164
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000165
and
Figure BDA0003819039080000166
respectively representing the inlet temperature of the water supply/return pipeline e at the time t;
Figure BDA0003819039080000167
represents the outlet temperature of the water supply pipeline e at the time t; t is b Represents the average temperature of the external environment; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA0003819039080000168
In the formula (I), the compound is shown in the specification,
Figure BDA0003819039080000169
represents the inlet temperature of the water supply pipeline e at the time t;
Figure BDA00038190390800001610
and
Figure BDA00038190390800001611
respectively representing the outlet temperature of the water supply/return pipeline e at the time t; t is b Represents the average temperature of the external environment; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi shape e,t Representing the heat loss coefficient of the heat network pipe e at time t.
Figure BDA00038190390800001612
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; c represents the specific heat capacity of the pipeline hot water; l e Indicates the length of the water supply/return pipe e; m is e,t Representing the mass flow of hot water in the supply/return line e.
Figure BDA00038190390800001613
In the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; m is e,t Representing the mass flow of the hot water of the water supply/return pipeline e; l e Indicates the length of the water supply/return pipe e; r represents a thermal resistance coefficient without physical significance, and in the process of actually solving equations (5) - (6) of a differential equation set and obtaining the equations (15) - (16) of the differential equation set, the steps and the difficulty of the calculation process are simplified by setting the thermal resistance coefficient R.
Figure BDA0003819039080000171
In the formula, g, k, i and j represent the numbers of a thermoelectric cogeneration unit, a thermal power unit, a wind power unit and a user electric load in the random electric-heat coupling system; psi chp 、ψ con 、ψ wind And psi d Representing a set formed by all cogeneration units, thermal power units, wind power units and user electric loads; p is g,t Representing the power output of the combined heat and power unit g at the time t; p k,t Representing the electric output of the thermal power generating unit k at the moment t; p is i,t Representing the electric output of the wind turbine generator i at the time t; p j,t Representing the electrical demand of the consumer electrical load j at time t.
P k,t,min ≤P k,t ≤P k,t,max (59)；
In the formula, P k,t Representing the electric output of the thermal power generating unit k at the moment t; p k,t,min And P k,t,max And respectively representing the minimum and maximum electric output of the thermal power generating unit k at the moment t.
0≤P i,t ≤P i,t,max (60)；
In the formula, P i,t,max Representing the actual maximum electric output of the wind turbine generator i at the moment t; p i,t And the electric output of the wind turbine generator i at the moment t is shown.
P g,t ≥r g Q g,t (61)；
In the formula, P g,t And Q g,t Respectively representing the electric/thermal output of the cogeneration unit g at the moment t; r is g The electric/thermal output coupling coefficient of the cogeneration unit g is expressed.
F g,t,min ≤ρ g,p P g,t +ρ g,q Q g,t ≤F g,t,max (62)；
In the formula, F g,t,min And F g,t,max Respectively representing the minimum and maximum fuel intake of the cogeneration unit g at the time t; rho g,p And ρ g,q Respectively representing the electricity/heat output fuel consumption rate of the cogeneration unit g; p g,t And Q g,t Respectively representing the electric/thermal output of the cogeneration unit g at the time t.
0≤Q g,t ≤Q g,t,max (63)；
In the formula, Q g,t The heat output of the combined heat and power generation unit g at the moment t is represented; q g,t,max Representing the maximum thermal output of the cogeneration unit g at time t.
L l,t,min ≤L l,t ≤L l,t,max (64)；
In the formula, L l,t Represents the power of the link line l at time t; l is l,t,min And L l,t,max Respectively representing the minimum and maximum power values of the link line l at time t.
Figure BDA0003819039080000181
In the formula, L l,t Represents the power of the tie line l at time t; l, g, k, i and j represent the numbers of lines, cogeneration units, thermal power units, wind power units and user electric loads in the random electric-heating coupling system; psi chp 、ψ con 、ψ wind And psi d Representing a set formed by all cogeneration units, thermal power units, wind power units and user electric loads; g l-g Representing a power distribution coefficient of the cogeneration unit; g l-i Representing the power distribution coefficient of the wind turbine; g l-k Representing a power distribution coefficient of the thermal power generating unit; g l-j A power distribution coefficient representing a consumer electrical load; p is g,t Representing the power output of the combined heat and power unit g at the time t; p is k,t Representing the electric output of the thermal power generating unit k at the moment t; p i,t Representing the electric output of the wind turbine generator i at the time t; p is j,t Representing the electrical demand of the consumer electrical load j at time t.
(2) The method comprises the following steps The lower layer optimized scheduling model comprises: an objective function of the lower-layer optimized scheduling model and a constraint condition of the lower-layer optimized scheduling model.
1) The objective function of the lower-layer optimized scheduling model is as shown in equation (66):
max F total ≤F ro (66)
in the formula, F ro Representing the expected scheduling cost of the decision maker; f total And the total scheduling cost of the random electrothermal coupling system information gap optimization scheduling model is represented.
2) The constraint condition of the lower-layer optimization scheduling model is as shown in formula (67):
U(α,P′ i,t,max )＝{|P′ i,t,max -P i,t,max |≤α|P′ i,t,max |} (67)
in the formula (II), U (alpha, P' i,t,max ) Representing the fluctuation range of the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius; p' i,t,max And representing the predicted maximum power output of the wind turbine generator i at the moment t.
In view of the fact that the random electric heating coupling system information gap robust optimization scheduling model has the characteristic of double-layer optimization, the original optimization scheduling model needs to be reasonably loosened before the model is solved, and the lower-layer optimization scheduling model is equivalently replaced by the KKT condition, as shown in formulas (68) to (73):
-μ 1 +μ 2 ＝δ i (68)；
in the formula, mu 1 And mu 2 Respectively, the complementary relaxation coefficients for the KKT conditions; delta i And representing a wind curtailment penalty coefficient of the wind turbine generator i.
μ 1 ((1-α)P′ i,t,max -P i,t,max )＝0 (69)；
In the formula, mu 1 A complementary relaxation coefficient representing a KKT condition; p' i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p i,t,max Representing the actual maximum electric output of the wind turbine generator i at the time t; α represents the fluctuation amplitude of the actual maximum electrical output, i.e., the uncertainty radius.
μ 2 ((1+α)P′ i,t,max -P i,t,max )＝0 (70)；
In the formula, mu 2 A complementary relaxation coefficient representing a KKT condition; p' i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p i,t,max Representing the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electrical output, i.e. the uncertainty radius.
μ 1 ≥0 (71)；
In the formula, mu 1 Representing the complementary relaxation coefficients of the KKT condition.
μ 2 ≥0 (72)；
In the formula, mu 2 Representing the complementary relaxation coefficients of the KKT condition.
(1-α)P′ i,t,max ≤P i,t,max ≤(1+α)P′ i,t,max (73)；
P′ i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p is i,t,max Representing the actual maximum electric output of the wind turbine generator i at the moment t; alpha represents the fluctuation amplitude of the actual maximum electrical output, i.e. the uncertainty radius.
Aiming at the relaxed robust optimization scheduling model of the random electrothermal coupling system information gap, a solving tool CPLEX can be called in commercial software Matlab to solve the model.
Example (b):
an actual random electric heating coupling system model in a certain area is adopted, a model structure diagram is shown in detail in figure 1, a system electric heating load demand and wind power prediction maximum power are shown in figure 2, and other parameters are as follows:
1. parameters of the power system:
in this embodiment, the power system line network parameters are all derived from IEEE standard 39 node model parameters, the power output cost of the cogeneration unit is 0.2 (kW) × h, the heat output cost of the cogeneration unit is 0.3 (kW) × h, the power output cost of the thermal power unit is 0.4 (kW) × h, the wind power cost penalty coefficient is 0.7 (kW) × h, the minimum power output of the thermal power unit is 0MW, the maximum power output of the thermal power unit is 100MW, the electric heat coupling system of the cogeneration unit is 0.6, the maximum fuel intake of the cogeneration unit is 365kg, the minimum fuel intake of the cogeneration unit is 200kg, the power output fuel consumption of the cogeneration unit is 1.2kg/MW, the heat output fuel consumption of the cogeneration unit is 0.8kg/MW, and the maximum heat output of the cogeneration unit is 240MW.
2. Thermodynamic system parameters:
in this embodiment, the pipeline network parameters of the thermodynamic system are all obtained from actual parameters in a certain area.
And finally, establishing a corresponding mathematical simulation model in the commercial software Matlab, and calculating the effectiveness of the asymmetric heat loss on the aspect of improving the comprehensive benefit of the asymmetric heat loss in a random electric heating coupling system and the reasonability and superiority of an information gap robust optimization method on the aspect of processing the wind power uncertainty problem through simulation verification.
Fig. 3-7 are graphs showing simulation results of verifying effectiveness of asymmetric heat loss in improving comprehensive benefits of the stochastic electrothermal coupling system. Two operation conditions are set during simulation: under the working condition 1, only the random electrothermal coupling system optimization scheduling of the heat symmetrical loss is taken into consideration, and the thermal resistance coefficient in the symmetrical heat loss process is 3.448 (mK)/W; and under the working condition 2, the random electric heating coupling system optimization scheduling considering the asymmetric heat loss is realized, the thermal resistance coefficient of the symmetric heat loss process is 3.992 (mK)/W, and the thermal resistance coefficient of the asymmetric heat loss process is 12.605 (mK)/W.
Looking at the inlet and outlet temperatures of the No. 67 water supply/return line shown in FIGS. 3 and 4, it can be calculated from the data shown that the average heat losses of the water supply/return line were 0.6836MW and 0.5741MW during operation in condition 1 and 0.6217MW and 0.4710MW during operation in condition 2. Contrast operating mode 1 can know with operating mode 2, and the heat loss of water supply/return water pipe all reduces on a par among the operating mode 2. The average reduction amount of the heat loss of the water supply pipeline accounts for about 8.57% of the original heat loss, and the average reduction amount of the heat loss of the water return pipeline is far larger than that of the water supply pipeline and accounts for about 19.31% of the original heat loss. The reason is that after the asymmetric heat loss process is taken into account in the heat supply network pipeline, part of the heat loss caused by heat exchange between the water supply pipeline and the external environment originally is supplemented to the water return pipeline in a heat transfer mode through the inner insulating layer with larger heat resistance. In this way, not only is the heat loss of the water supply pipeline reduced due to the increased thermal resistance of the loss process, but also the heat loss of the water return pipeline is further reduced due to the heat supplement from the water supply pipeline.
Observing the unit thermal/electrical output scheduling plans shown in fig. 5 and 6, it can be known by comparing the working condition 1 and the working condition 2 that the thermal output variation trends of the cogeneration unit are basically the same. However, in condition 2, with the overall temperature rise of the heat supply network pipes, the heat output of the unit is constrained by the heat balance equation of the network nodes, and is reduced by 11.23MW on a same scale (the reduction amount is about 4.89% of the original heat output). Similarly, with the reduction of the heat output of the cogeneration unit, the electricity output cost of the cogeneration unit is lower than that of the thermal power unit in the heat load valley period (9-15 hours), and the output of the cogeneration unit is increased and the output of the thermal power unit is reduced under the condition that the wind power unit fully generates the output, so that the scheduling has better economy in the 9-15 periods.
Observing the condition of the wind curtailment rate shown in fig. 7, comparing the working condition 1 with the working condition 2, it can be known that, for the peak time (0-6 hours) of the predicted maximum power of the wind power, the power of the cogeneration unit can be adjusted under the constraint of the electric-thermal coupling relationship of the cogeneration unit along with the reduction of the power of the cogeneration unit, so that the wind power has a larger grid-connected space. The wind abandon rate situation chart more intuitively shows that the wind abandon rate situation in the working condition 2 is obviously better than that in the working condition 1, and the reduced wind abandon rate can reach 9.13 percent at most. The wind power consumption of the system can be effectively relieved, and the economy of dispatching in the time interval is further improved.
Simulation results of the two working conditions show that when the working condition 1 operates, the total system cost is 266.7704747 ten thousand yuan, the electricity cost of a cogeneration unit is 77.6416273 ten thousand yuan, the heat cost of the cogeneration is 150.4988149 ten thousand yuan, the cost of a thermal power unit is 28.4183713 ten thousand yuan, and the wind power abandoned cost is 10.2116612 ten thousand yuan; when the system operates in the working condition 2, the total system cost is 252.5551305 ten thousand yuan, the electricity cost of the cogeneration unit is 79.3413844 ten thousand yuan, the cogeneration heat cost is 142.2849972 ten thousand yuan, the cost of the thermal power unit is 23.4552688 ten thousand yuan, and the wind power abandoned wind cost is 7.4734801 ten thousand yuan. Comparing the working condition 1 with the working condition 2, the heat output of the cogeneration unit is reduced after the asymmetrical loss process of the heat supply network is accounted in the working condition 2; because the air volume is reduced, the wind power output is increased, and the system electric load born by the cogeneration unit and the thermal power unit is reduced; meanwhile, in the low-ebb period of the heat load, the cogeneration unit with lower cost shares part of the electric output of the thermal power unit. Under the comprehensive influence of the three conditions, the electricity cost of the cogeneration unit in the working condition 2 is increased, and the total system cost, the heat cost of the cogeneration unit, the cost of the thermal power unit and the cost of wind power waste wind are all reduced relative to the working condition 1.
FIG. 8 is a simulation result of verifying the rationality of the information gap robust optimization method in handling wind power uncertaintyDrawing. It can be known from observation of the scheduling cost and the uncertainty radius variation trend shown in fig. 8 that in the information gap robust optimization method, as the cost deviation coefficient formulated by the decision maker increases, the uncertainty radius increases, and the scheduling cost increases, because in the information gap robust optimization, the decision maker considers that uncertainty negatively affects reduction of the scheduling cost, the larger the uncertainty radius is, the smaller the risk brought by uncertainty of the actual maximum wind power is, and therefore the scheduling cost is smaller, and the output is [ (1- α) P' i,t,max ,(1+α)P′ i,t,max ]When the range is changed, the scheduling cost can be ensured to be lower than the expected scheduling cost of a decision maker.
Meanwhile, the advantage of the information gap robust optimization method in the aspect of processing the wind power uncertainty problem is verified. Two operation conditions are set during simulation: under a working condition 3, solving an optimized scheduling model of the random electrothermal coupling system by adopting a traditional min-max (maximum and minimum extreme scene) robust optimization method; and under the working condition 4, solving an optimized scheduling model of the random electrothermal coupling system by adopting an information gap robust optimization method. Setting the current uncertainty radiuses to be 0.012, 0.035 and 0.057, wherein the simulation results of the two working conditions show that when the working condition 3 runs, the scheduling cost corresponding to the uncertainty radius of 0.012 is 256.2127417 ten thousand yuan, the scheduling cost corresponding to the uncertainty radius of 0.035 is 263.2423923 ten thousand yuan, and the scheduling cost corresponding to the uncertainty radius of 0.057 is 270.0066608 ten thousand yuan; when the operating condition 4 operates, the scheduling cost corresponding to the uncertainty radius 0.012 is 252.8076856 ten thousand yuan, the scheduling cost corresponding to the uncertainty radius 0.035 is 253.3127959 ten thousand yuan, and the scheduling cost corresponding to the uncertainty radius 0.057 is 253.8179062 ten thousand yuan. Comparing the working condition 3 with the working condition 4, it can be known that the scheduling cost results obtained by optimization have little difference under the condition that the wind power uncertainty radius of the information gap robust optimization method is far larger than that of the traditional robust optimization method. Obviously, compared with the traditional robust optimization, the information gap robust optimization method can be more suitable for wind power uncertainty existing in a random electric heating coupling system. Similarly, under the condition that the wind power uncertainty radius of the information gap robust optimization method is equal to that of the traditional robust optimization method, the cost obtained by the information gap robust optimization method is far lower than that of the traditional robust optimization method, and the economic advantage of the information gap robust optimization method relative to the traditional robust optimization method can be proved again.

Claims (2)

1. The robust optimization scheduling model of the information gap of the random electric heating coupling system is characterized in that: the method comprises an upper-layer optimized scheduling model and a lower-layer optimized scheduling model:
(1) the method comprises the following steps The upper-layer optimized scheduling model comprises the following steps: an objective function of the upper-layer optimized scheduling model and a constraint condition of the upper-layer optimized scheduling model are as follows:
1) The objective function of the upper-layer optimization scheduling model is as shown in equation (45):
maxα (45)；
in the formula, alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius;
2) The constraints of the upper-layer optimization scheduling model are as shown in equations (46) - (65):
Figure FDA0003819039070000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003819039070000012
representing the heat output of the cogeneration unit g at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure FDA0003819039070000013
representing the mass flow of the hot water in the g pipeline of the cogeneration unit at the n network node at the time t;
Figure FDA0003819039070000014
and
Figure FDA0003819039070000015
respectively representing the inlet temperature and the outlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure FDA0003819039070000016
in the formula (I), the compound is shown in the specification,
Figure FDA0003819039070000017
representing the heat demand of the user heat load d at the network node n at the time t; c represents the specific heat capacity of the pipeline hot water;
Figure FDA0003819039070000018
representing the mass flow of hot water in a pipeline of a user heat load d at a network node n at the time t;
Figure FDA0003819039070000019
and
Figure FDA00038190390700000110
respectively representing the inlet temperature and the outlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure FDA00038190390700000111
wherein e represents the number of the heat supply network pipeline,
Figure FDA00038190390700000112
and
Figure FDA00038190390700000113
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure FDA00038190390700000114
showing the mass flow of the hot water in the water supply pipeline e at the time t;
Figure FDA00038190390700000115
and
Figure FDA00038190390700000116
respectively representing the mass flow of pipeline hot water of a combined heat and power generation unit g and a user heat load d at a network node n at the time t;
Figure FDA00038190390700000117
represents the outlet temperature of the water supply pipeline e at the time t;
Figure FDA00038190390700000118
representing the outlet temperature of the pipeline of the cogeneration unit g at the network node n at the time t;
Figure FDA00038190390700000119
representing the temperature of a water supply pipeline network node n at the time t;
Figure FDA00038190390700000120
wherein e represents the number of the heat supply network pipeline,
Figure FDA0003819039070000021
a set of front-side thermal network pipe numbers representing connections to the network node n;
Figure FDA0003819039070000022
the inlet temperature of the water return pipeline e at the time t is shown;
Figure FDA0003819039070000023
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure FDA0003819039070000024
the temperature of a return water pipeline network node n at the moment t is represented;
Figure FDA0003819039070000025
wherein e represents the number of the heat supply network pipeline,
Figure FDA0003819039070000026
and
Figure FDA0003819039070000027
respectively representing front side and back side heat network channel number sets connected with the network node n;
Figure FDA0003819039070000028
and
Figure FDA0003819039070000029
respectively representing the mass flow of pipeline hot water of a cogeneration unit g and a user heat load d at a network node n at the time t;
Figure FDA00038190390700000210
showing the mass flow of the hot water in the water supply pipeline e at the time t;
Figure FDA00038190390700000211
in the formula, e represents the number of the heat supply network pipeline,
Figure FDA00038190390700000212
and
Figure FDA00038190390700000213
respectively representing the front side and the back side heat network channel number sets connected with the network node n;
Figure FDA00038190390700000214
and
Figure FDA00038190390700000215
respectively representing the mass flow of pipeline hot water of a combined heat and power generation unit g and a user heat load d at a network node n at the time t;
Figure FDA00038190390700000216
the mass flow of the hot water in the water return pipeline e at the time t is shown;
Figure FDA00038190390700000217
wherein e represents the number of the heat supply network pipeline,
Figure FDA00038190390700000218
a set of back-end thermal network pipe numbers representing connections to the network node n;
Figure FDA00038190390700000219
represents the inlet temperature of the water supply pipeline e at the time t;
Figure FDA00038190390700000220
representing the inlet temperature of a user heat load d pipeline at a network node n at the time t;
Figure FDA00038190390700000221
representing the temperature of a water supply pipeline network node n at the time t;
Figure FDA00038190390700000222
wherein e represents the number of the heat supply network pipeline,
Figure FDA00038190390700000223
a set of front-side thermal network pipe numbers representing connections to the network node n;
Figure FDA00038190390700000224
return pipe for indicating t timeThe inlet temperature of lane e;
Figure FDA00038190390700000225
representing the inlet temperature of a pipeline of a combined heat and power generation unit g at a network node n at the time t;
Figure FDA00038190390700000226
the temperature of a return water pipeline network node n at the moment t is represented;
Figure FDA0003819039070000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003819039070000032
and
Figure FDA0003819039070000033
respectively representing the inlet temperature of the water supply/return pipeline e at the time t;
Figure FDA0003819039070000034
represents the outlet temperature of the water supply pipeline e at the time t; t is a unit of b Represents the average temperature of the external environment; r is s And R a Respectively representing the thermal resistivity of symmetrical and asymmetrical heat loss processes; xi shape e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t;
Figure FDA0003819039070000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003819039070000036
represents the inlet temperature of the water supply pipeline e at the time t;
Figure FDA0003819039070000037
and
Figure FDA0003819039070000038
respectively representing the outlet temperature of the water supply/return pipeline e at the time t; t is b Represents the average temperature of the external environment; r s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t;
Figure FDA0003819039070000039
in the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; r is s And R a Respectively representing the thermal resistance coefficients of symmetrical and asymmetrical heat loss processes; c represents the specific heat capacity of the pipeline hot water; l e Indicates the length of the water supply/return pipe e; m is e,t Representing the mass flow of the hot water of the water supply/return pipeline e;
Figure FDA00038190390700000310
in the formula, xi e,t Representing the heat loss coefficient of the heat supply network pipeline e at the moment t; m is e,t Represents the mass flow of the hot water of the water supply/return pipeline e; l e Indicates the length of the water supply/return pipe e;
Figure FDA0003819039070000041
in the formula, g, k, i and j represent the numbers of a thermoelectric cogeneration unit, a thermal power unit, a wind power unit and a user electric load in the random electric-heat coupling system; psi chp 、ψ con 、ψ wind And psi d Representing a set formed by all the cogeneration sets, the thermal power generating sets, the wind power generating sets and the user electric loads; p g,t Representing the power output of the cogeneration unit g at the moment t; p k,t Representing the electric output of the thermal power generating unit k at the moment t; p i,t Representing wind power at time tThe electric output of the unit i; p j,t Representing the electrical demand of the user electrical load j at time t;
P k,t,min ≤P k,t ≤P k,t,max (59)；
in the formula, P k,t Representing the electric output of the thermal power generating unit k at the moment t; p k,t,min And P k,t,max Respectively representing the minimum and maximum electric output of the thermal power generating unit k at the moment t;
0≤P i,t ≤P i,t,max (60)；
in the formula, P i,t,max Representing the actual maximum electric output of the wind turbine generator i at the moment t; p i,t Representing the electric output of the wind turbine generator i at the time t;
P g,t ≥r g Q g,t (61)；
in the formula, P g,t And Q g,t Respectively representing the electricity/heat output of the cogeneration unit g at the moment t; r is g Representing the electricity/heat output coupling coefficient of the cogeneration unit g;
F g,t,min ≤ρ g,p P g,t +ρ g,q Q g,t ≤F g,t,max (62)；
in the formula, F g,t,min And F g,t,max Respectively representing the minimum and maximum fuel intakes of the cogeneration unit g at the time t; ρ is a unit of a gradient g,p And ρ g,q Respectively representing the electricity/heat output fuel consumption rate of the cogeneration unit g; p g,t And Q g,t Respectively representing the electricity/heat output of the cogeneration unit g at the moment t;
0≤Q g,t ≤Q g,t,max (63)；
in the formula, Q g,t Representing the heat output of the cogeneration unit g at the moment t; q g,t,max The maximum thermal output of the combined heat and power generation unit g at the moment t is represented;
L l,t,min ≤L l,t ≤L l,t,max (64)；
in the formula, L l,t Represents the power of the link line l at time t; l is l,t,min And L l,t,max Respectively representing the minimum value and the maximum value of the power of a tie line l at the moment t;
Figure FDA0003819039070000051
in the formula, L l,t Represents the power of the tie line l at time t; l, g, k, i and j represent the numbers of lines, cogeneration units, thermal power units, wind power units and user electric loads in the random electric-heating coupling system; psi chp 、ψ con 、ψ wind And psi d Representing a set formed by all the cogeneration sets, the thermal power generating sets, the wind power generating sets and the user electric loads; g l-g Representing a power distribution coefficient of the cogeneration unit; g l-i Representing the power distribution coefficient of the wind turbine; g l-k Representing a power distribution coefficient of the thermal power generating unit; g l-j A power distribution coefficient representing a consumer electrical load; p g,t Representing the power output of the combined heat and power unit g at the time t; p k,t Representing the electric output of the thermal power generating unit k at the moment t; p i,t Representing the electric output of the wind turbine generator i at the time t; p j,t Representing the electrical demand of the user electrical load j at time t;
(2) the method comprises the following steps The lower layer optimized scheduling model comprises: an objective function of the lower-layer optimized scheduling model and a constraint condition of the lower-layer optimized scheduling model;
1) The objective function of the lower-layer optimized scheduling model is as shown in equation (66):
maxF total ≤F ro (66)；
in the formula, F ro Representing the expected scheduling cost of the decision maker; f total Representing the total scheduling cost of the random electrothermal coupling system information gap optimization scheduling model;
2) The constraint condition of the lower-layer optimization scheduling model is as shown in formula (67):
U(α,P′ i,t,max )＝{|P′ i,t,max -P i,t,max |≤α|P′ i,t,max |} (67)；
in the formula (II), U (alpha, P' i,t,max ) Representing the fluctuation range of the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius; p' i,t,max And the predicted maximum power output of the wind turbine generator i at the time t is shown.
2. The robust optimized scheduling model for information gaps of the stochastic electrothermal coupling system according to claim 1, wherein: performing reasonable relaxation on the optimized scheduling model before the model is solved, and equivalently replacing a lower optimized scheduling model with a KKT condition of the optimized scheduling model, wherein the KKT condition is shown in formulas (68) to (73):
-μ 1 +μ 2 ＝δ i (68)；
in the formula, mu 1 And mu 2 Respectively, the complementary relaxation coefficients for the KKT condition; delta i Representing a wind abandonment penalty coefficient of the wind turbine generator i;
μ 1 ((1-α)P′ i,t,max -P i,t,max )＝0 (69)；
in the formula, mu 1 A complementary relaxation coefficient representing the KKT condition; p' i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p is i,t,max Representing the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius;
μ 2 ((1+α)P′ i,t,max -P i,t,max )＝0 (70)；
in the formula, mu 2 A complementary relaxation coefficient representing a KKT condition; p' i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p is i,t,max Representing the actual maximum electric output of the wind turbine generator i at the time t; alpha represents the fluctuation amplitude of the actual maximum electric output, namely the uncertainty radius;
μ 1 ≥0 (71)；
in the formula, mu 1 A complementary relaxation coefficient representing the KKT condition;
μ 2 ≥0 (72)；
in the formula, mu 2 A complementary relaxation coefficient representing a KKT condition;
(1-α)P′ i,t,max ≤P i,t,max ≤(1+α)P′ i,t,max (73)；
of formula (II) to (III)' i,t,max Representing the predicted maximum power output of the wind turbine generator i at the time t; p i,t,max Representing the actual maximum electric output of the wind turbine generator i at the moment t; alpha represents the fluctuation amplitude of the actual maximum electrical output, i.e. the uncertainty radius.
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