CN111817302A - Load operation optimization method considering flexibility potential - Google Patents

Load operation optimization method considering flexibility potential Download PDF

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Publication number
CN111817302A
CN111817302A CN202010762828.6A CN202010762828A CN111817302A CN 111817302 A CN111817302 A CN 111817302A CN 202010762828 A CN202010762828 A CN 202010762828A CN 111817302 A CN111817302 A CN 111817302A
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water heater
electric water
load
time
optimal
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王灿
张高瑞
应宇辰
陈思睿
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China Three Gorges University CTGU
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China Three Gorges University CTGU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
    • H02J3/144—Demand-response operation of the power transmission or distribution network
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
    • Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
    • Y04S20/20—End-user application control systems
    • Y04S20/222—Demand response systems, e.g. load shedding, peak shaving

Abstract

A load operation optimization method considering flexibility potential, comprising the steps of: (1) establishing a mathematical model of adjustable load; (2) establishing a load optimization model based on the flexibility potential; (3) and obtaining the optimal operation time period of each load. In the step 1), aiming at various loads, establishing a mathematical model capable of regulating and controlling the loads; in step 2), a load optimization model based on the flexibility potential is established, and the load optimization model aims to reduce the electricity utilization cost of the user to the minimum. The invention aims to solve the technical problems that the load type considered in the prior art is single, the applicable scene has great limitation, and the flexibility potential of the demand side needs to be further improved.

Description

Load operation optimization method considering flexibility potential
Technical Field
The invention belongs to the technical field of power systems, particularly relates to a load operation optimization method, and particularly relates to a load operation optimization method considering the flexibility potential of various loads.
Background
With the continuous expansion of the micro-grid scale, the response of the power demand side is increasingly paid more attention by people. The load with the flexibility potential is used as an important resource for the response of the load demand side, and has important significance for improving the safe and stable operation level of the power grid. Because a large amount of adjustable loads exist in the micro-grid, and the adjustable loads are various, the stable operation of the micro-grid is influenced. Therefore, optimizing load requirements is the focus of current research.
In the prior art documents: a data driven model is built for simulating a building group, and the model utilizes the thermal load flexibility potential to deal with the renewable output fluctuation of Energy generation, thereby achieving supply and demand balance. The Economic dispatch plan of multiple micro-grid periods under different power fluctuation constraints is proposed by the Economic operation of micro-grid-grouping regulation of interactive power (M.Zang, J.Chen, Z.Du, S.Wang, and H.Sun.Economic operation of micro-grid-grouping regulation of interactive power [ J ]. Proceedings of the CSEE, 34, 7, pp.1013-1023, Mar.5, 2014). The scheme can be used for stabilizing the fluctuation of the interactive power by controlling the electric automobile and dispatching interruptible loads. From demand response in smart Grid aware demand response in smart Grid real-time pricing schemes are proposed (Shahab Bahrami, ArasSheikhi. From demand response in smart Grid aware integrated demand response hub [ J ]. IEEE Transactions on Smart Grid, vol.7, No.2, Mar.2016.). According to the scheme, on the premise that the load electricity consumption of the user is not influenced, the load requirement at the peak of the power grid can be greatly reduced, and the economic benefit of the user is increased. Although the research considers the flexibility potential of the demand side, the load type is single, and the application scene of the load type is greatly limited.
Aiming at the defects, the invention provides a load operation optimization method considering flexibility potential. The method considers the flexibility potential of various loads, quantifies the flexibility potential into demand response based on time-of-use electricity price, and optimizes various schedulable loads according to the electricity prices in different time periods so as to achieve the purpose of reducing the electricity consumption cost of users.
Disclosure of Invention
The invention aims to solve the technical problems that the load type considered in the prior art is single, the applicable scene has great limitation, and the flexibility potential of the demand side needs to be further improved.
A load operation optimization method considering flexibility potential, comprising the steps of:
(1) establishing a mathematical model of adjustable load;
(2) establishing a load optimization model based on the flexibility potential;
(3) and obtaining the optimal operation time period of each load.
In the step 1), aiming at various loads, establishing a mathematical model capable of regulating and controlling the loads;
in step 2), a load optimization model based on the flexibility potential is established, and the load optimization model aims to reduce the electricity utilization cost of the user to the minimum.
The objective function of the load optimization model is as follows:
Figure BDA0002613555500000021
wherein t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure BDA0002613555500000022
the output power of the washing machine at the moment t;
the indoor temperature constraint and hot water temperature constraint expressions of the load optimization model are as follows:
1) indoor temperature restraint
Figure BDA0002613555500000023
Wherein the content of the first and second substances,
Figure BDA0002613555500000024
and
Figure BDA0002613555500000025
the upper and lower limits of the indoor temperature.
2) Hot water temperature restraint
Figure BDA0002613555500000026
Wherein the content of the first and second substances,
Figure BDA0002613555500000027
and
Figure BDA0002613555500000028
the upper and lower limits of the hot water temperature.
In step 1), the plurality of loads include an air conditioning system;
the model of the air conditioning system is as follows:
Figure BDA0002613555500000031
wherein, Tin(t) is the indoor temperature at time t; t isout(t +1) is the outdoor temperature at time t + 1; eta is the energy efficiency ratio of the air conditioner; pAC(t) is the output power of the air conditioner at the time t; r is the equivalent resistance of the air conditioner; c is the equivalent capacitance of the air conditioner; Δ t is the time interval.
The plurality of loads further comprises an electric water heater;
the electric water heater comprises the following models:
Figure BDA0002613555500000032
in the formula
Figure BDA0002613555500000033
Wherein, TWater(t) the temperature of the water in the electric water heater at time tDegree; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
The plurality of loads include a washing machine;
the washing machine model is as follows:
Figure BDA0002613555500000034
in the formula
Figure BDA0002613555500000035
Wherein, PLD(t) is the load power after translation at time t, tqThe original service time of the washing machine is set; t is thThe use time of the washing machine after optimization; pload(t) power required by the load of the washing machine at the moment t;
Figure BDA0002613555500000036
is a translatable power; pWMAnd (t) is the rated power of the washing machine.
And solving the load optimization model by using a Lagrange relaxation algorithm to obtain the optimal operation time period of each load.
Integrating a mathematical model of the electric water heater into a target function formula (4), and introducing a Lagrange multiplier lambda to form the following relaxation problem:
Figure BDA0002613555500000041
forming a dual problem of the Lagrange relaxation algorithm according to the relaxation problem of the Lagrange relaxation algorithm, which is specifically as follows:
Figure BDA0002613555500000042
in the formula
Figure BDA0002613555500000043
Wherein, the constraint conditions of the relaxation problem are formulas (1), (3), (5) and (6); dual problem constraints are expressed as formulas (1), (3), (5) and (6); t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure BDA0002613555500000044
the output power of the washing machine at the moment t; λ is lagrange multiplier; t isWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
When solving the relaxation problem, the following steps are adopted:
1) solving an objective function value of the relaxation problem;
2) and judging whether the current dual target value is smaller than the optimal dual target value. If the current dual target value is smaller than the optimal dual target value, updating the optimal dual target value, otherwise, turning to the step 5);
3) performing feasible processing on the relaxation solution, solving an optimal feasible solution objective function value of the original problem, and updating an optimal feasible solution objective value and an optimal relaxation scheduling sequence of the original problem;
4) and judging the difference value between the optimal dual target value and the optimal feasible solution target value. If the difference value between the optimal dual target value and the optimal feasible solution target value is smaller than the dual gap threshold, stopping iteration and outputting the optimal solution, otherwise, executing the next step;
5) calculating a secondary gradient and updating a Lagrange multiplier;
6) if the maximum iteration number is reached, outputting the optimal solution, otherwise, repeating the step 1).
A method for solving a load optimization model by utilizing a Lagrange relaxation algorithm integrates a mathematical model of an electric water heater into an objective function, introduces a Lagrange multiplier lambda to form a relaxation problem, and solves the load optimization model to obtain the optimal operation time period of each load, and specifically comprises the following steps:
1) solving an objective function value of the relaxation problem;
2) and judging whether the current dual target value is smaller than the optimal dual target value. If the current dual target value is smaller than the optimal dual target value, updating the optimal dual target value, otherwise, turning to the step 5);
3) performing feasible processing on the relaxation solution, solving an optimal feasible solution objective function value of the original problem, and updating an optimal feasible solution objective value and an optimal relaxation scheduling sequence of the original problem;
4) and judging the difference value between the optimal dual target value and the optimal feasible solution target value. If the difference value between the optimal dual target value and the optimal feasible solution target value is smaller than the dual gap threshold, stopping iteration and outputting the optimal solution, otherwise, executing the next step;
5) calculating a secondary gradient and updating a Lagrange multiplier;
6) if the maximum iteration number is reached, outputting the optimal solution, otherwise, repeating the step 1).
The relaxation problem that forms is as follows:
Figure BDA0002613555500000051
forming a dual problem of the Lagrange relaxation algorithm according to the relaxation problem of the Lagrange relaxation algorithm, which is specifically as follows:
Figure BDA0002613555500000052
in the formula
Figure BDA0002613555500000061
The constraint conditions of the relaxation problem are expressions (1), (3), (5) and (6), the constraint conditions of the dual problem are expressions (1), (3), (5) and (6), and t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure BDA0002613555500000062
the output power of the washing machine at the moment t; λ is lagrange multiplier; t isWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
Compared with the prior art, the invention has the following technical effects:
1) the invention considers the flexibility potential of various loads, quantifies the flexibility potential into demand response based on time-of-use electricity price, and optimizes various schedulable loads according to the electricity prices in different time periods so as to achieve the purpose of reducing the electricity consumption cost of users;
2) the method can enable a user to actively respond according to the electricity price and change the working state or time of the load, thereby maintaining the balance of the supply and demand of the power grid.
Drawings
FIG. 1 is a flow chart of a method of load operation optimization taking into account flexibility potential;
FIG. 2 is a graph of load optimization results considering flexibility potential;
FIG. 3 is a graph comparing the electricity charges of users according to different optimization methods.
Detailed Description
As shown in fig. 1, a load operation optimization method considering flexibility potential includes the following steps:
1. and establishing a mathematical model of the adjustable load.
The mathematical model expressions of the air conditioner, the electric water heater and the washing machine are as follows:
1) an air conditioning system: the air conditioning system adjusts the indoor temperature according to the deviation of the indoor temperature and the adjusted temperature.
Figure BDA0002613555500000071
Wherein, Tin(t) is the indoor temperature at time t; t isout(t +1) is the outdoor temperature at time t + 1; eta is the energy efficiency ratio of the air conditioner; pAC(t) is the output power of the air conditioner at the time t; r is the equivalent resistance of the air conditioner; c is the equivalent capacitance of the air conditioner; Δ t is the time interval.
2) Electric water heater: the temperature of the hot water of the electric water heater is related to the rated power and the water inlet temperature of the electric water heater.
Figure BDA0002613555500000072
In the formula
Figure BDA0002613555500000073
Wherein, TWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area to the thermal resistance of the electric water heater at the moment tA value; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
3) Washing machine: the operation time of the washing machine can be shifted from a high-price period to other periods, and the power of the washing machine during operation is rated power.
Figure BDA0002613555500000074
In the formula
Figure BDA0002613555500000075
Wherein, PLD(t) is the load power after translation at time t, tqThe original service time of the washing machine is set; t is thThe use time of the washing machine after optimization; pload(t) power required by the load of the washing machine at the moment t;
Figure BDA0002613555500000076
is a translatable power; pWMAnd (t) is the rated power of the washing machine.
2. And establishing a load optimization model based on the flexibility potential.
The load optimization model aims to reduce the electricity consumption cost of a user to the minimum, and the target function expression of the load optimization model is as follows:
Figure BDA0002613555500000081
wherein t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure BDA0002613555500000082
for washing at time tOutput power of the machine.
The indoor temperature constraint and hot water temperature constraint expressions of the load optimization model are as follows:
1) indoor temperature restraint
Figure BDA0002613555500000083
Wherein the content of the first and second substances,
Figure BDA0002613555500000084
and
Figure BDA0002613555500000085
the upper and lower limits of the indoor temperature.
2) Hot water temperature restraint
Figure BDA0002613555500000086
Wherein the content of the first and second substances,
Figure BDA0002613555500000087
and
Figure BDA0002613555500000088
the upper and lower limits of the hot water temperature.
3. And solving the load optimization model by using a Lagrange relaxation algorithm to obtain the optimal operation time period of each load. Since the mathematical model of the electric water heater is much more complex than the other load models, the mathematical model of the electric water heater is integrated into the objective function formula (4). Introducing the lagrange multiplier λ creates the following relaxation problem:
Figure BDA0002613555500000089
forming a dual problem of the Lagrange relaxation algorithm according to the relaxation problem of the Lagrange relaxation algorithm, which is specifically as follows:
Figure BDA00026135555000000810
in the formula
Figure BDA00026135555000000811
Wherein, the constraint conditions of the relaxation problem are formulas (1), (3), (5) and (6). The dual problem constraints are equations (1), (3), (5) and (6). t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure BDA0002613555500000091
the output power of the washing machine at the moment t; λ is lagrange multiplier; t isWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t; b is the water flow speed of the electric water heater.
The specific calculation steps are as follows:
1) the objective function value of the relaxation problem is solved.
2) And judging whether the current dual target value is smaller than the optimal dual target value. And if the current dual target value is smaller than the optimal dual target value, updating the optimal dual target value, and otherwise, turning to the step 5).
3) And performing feasible treatment on the relaxation solution, solving an optimal feasible solution objective function value of the original problem, and updating an optimal feasible solution target value and an optimal relaxation scheduling sequence of the original problem.
4) And judging the difference value between the optimal dual target value and the optimal feasible solution target value. And if the difference value between the optimal dual target value and the optimal feasible solution target value is smaller than the dual gap threshold, stopping iteration and outputting the optimal solution. Otherwise, executing the next step.
5) And calculating a secondary gradient and updating a Lagrange multiplier.
6) If the maximum iteration number is reached, outputting the optimal solution, otherwise, repeating the step 1).
Fig. 2 is a graph of load optimization results considering flexibility potential. It can be seen in the figure that there is a large variation in the load power curve after taking into account the various load flexibility potentials. In the following step 7: 00-15: the 00 period, the load power demand considering the flexibility potential is smaller than the load power demand not considering the flexibility potential, and the reason for this change is that the user reduces unnecessary power consumption according to the time-of-use electricity price. At a temperature of 0: 00-6: 00 and 16: 00-17: the load demand based on the proposed optimization method is increased compared to the load demand without considering the flexibility potential during the 00 period. The reason for this change is that the user shifts the load with the potential for flexibility to the time slot to use, avoiding peak electricity usage periods.
FIG. 3 is a graph comparing the electricity charges of users according to different optimization methods. The user can adjust and control the load to be used from the high electricity price to the low electricity price according to the time-of-use electricity price and the characteristics of different types of loads. In the following step 7: 00-15: 00 and 18: 00-23: and in the 00 period, the electricity purchasing expense per hour of the load optimization method is less than the electricity purchasing expense per hour of the load optimization method without considering the flexibility potential. At a temperature of 0: 00-6: 00 and 16: 00-17: and in the 00 period, the time is influenced by the time-of-use electricity price, and the electricity charge per hour of the load optimization method is larger than that of the load optimization method without considering the flexibility potential. However, the total electricity consumption of the load optimization method provided by the invention is obviously less than that of the load optimization method without considering the flexibility potential in terms of total time.

Claims (10)

1. A method for optimizing load operation in consideration of flexibility potential, comprising the steps of:
(1) establishing a mathematical model of adjustable load;
(2) establishing a load optimization model based on the flexibility potential;
(3) obtaining the optimal operation time period of each load;
in the step 1), aiming at various loads, establishing a mathematical model capable of regulating and controlling the loads;
in step 2), a load optimization model based on the flexibility potential is established, and the load optimization model aims to reduce the electricity utilization cost of the user to the minimum.
2. The method for load operation optimization considering flexibility potential according to claim 1, wherein the objective function of the load optimization model is:
Figure FDA0002613555490000011
wherein t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure FDA0002613555490000012
the output power of the washing machine at the moment t;
the indoor temperature constraint and hot water temperature constraint expressions of the load optimization model are as follows:
1) indoor temperature restraint
Figure FDA0002613555490000013
Wherein the content of the first and second substances,
Figure FDA0002613555490000014
and
Figure FDA0002613555490000015
the upper and lower limits of the indoor temperature;
2) hot water temperature restraint
Figure FDA0002613555490000016
Wherein the content of the first and second substances,
Figure FDA0002613555490000017
and
Figure FDA0002613555490000018
the upper and lower limits of the hot water temperature.
3. A load operation optimization method considering flexibility potential according to claim 1 or 2, wherein in step 1), the plurality of loads include an air conditioning system;
the model of the air conditioning system is as follows:
Figure FDA0002613555490000019
wherein, Tin(t) is the indoor temperature at time t; t isout(t +1) is the outdoor temperature at time t + 1; eta is the energy efficiency ratio of the air conditioner; pAC(t) is the output power of the air conditioner at the time t; r is the equivalent resistance of the air conditioner; c is the equivalent capacitance of the air conditioner; Δ t is the time interval.
4. A load operation optimization method considering flexibility potential according to claim 3, characterized by: the various loads also include electric water heaters;
the electric water heater comprises the following models:
Figure FDA0002613555490000021
in the formula
Figure FDA0002613555490000022
Wherein, TWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
5. A load operation optimization method considering flexibility potential according to claim 3, wherein the plurality of loads includes a washing machine;
the washing machine model is as follows:
Figure FDA0002613555490000023
in the formula
Figure FDA0002613555490000024
Wherein, PLD(t) is the load power after translation at time t, tqThe original service time of the washing machine is set; t is thThe use time of the washing machine after optimization; pload(t) power required by the load of the washing machine at the moment t;
Figure FDA0002613555490000025
is a translatable power; pWMAnd (t) is the rated power of the washing machine.
6. A load operation optimization method considering flexibility potential according to claim 4 or 5, characterized by: and solving the load optimization model by using a Lagrange relaxation algorithm to obtain the optimal operation time period of each load.
7. The load operation optimization method considering flexibility potential according to claim 6, wherein: integrating a mathematical model of the electric water heater into a target function formula (4), and introducing a Lagrange multiplier lambda to form the following relaxation problem:
Figure FDA0002613555490000031
forming a dual problem of the Lagrange relaxation algorithm according to the relaxation problem of the Lagrange relaxation algorithm, which is specifically as follows:
Figure FDA0002613555490000032
in the formula
Figure FDA0002613555490000033
Wherein, the constraint conditions of the relaxation problem are formulas (1), (3), (5) and (6); dual problem constraints are expressed as formulas (1), (3), (5) and (6); t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure FDA0002613555490000034
the output power of the washing machine at the moment t; λ is lagrange multiplier; t isWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) the water inlet temperature of the electric water heater at the moment t; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
8. The method for optimizing load operation in consideration of flexibility potential according to claim 7, characterized in that, when solving the relaxation problem, the following steps are adopted:
1) solving an objective function value of the relaxation problem;
2) judging whether the current dual target value is smaller than the optimal dual target value, if so, updating the optimal dual target value, otherwise, turning to the step 5);
3) performing feasible processing on the relaxation solution, solving an optimal feasible solution objective function value of the original problem, and updating an optimal feasible solution objective value and an optimal relaxation scheduling sequence of the original problem;
4) judging the difference value between the optimal dual target value and the optimal feasible solution target value, if the difference value between the optimal dual target value and the optimal feasible solution target value is smaller than a dual gap threshold value, stopping iteration, outputting the optimal solution, and if not, executing the next step;
5) calculating a secondary gradient and updating a Lagrange multiplier;
6) if the maximum iteration number is reached, outputting the optimal solution, otherwise, repeating the step 1).
9. A method for solving a load optimization model by using a Lagrange relaxation algorithm is characterized in that a mathematical model of an electric water heater is integrated into an objective function, a Lagrange multiplier lambda is introduced to form a relaxation problem, the load optimization model is solved to obtain the optimal operation time period of each load, and the method specifically comprises the following steps:
1) solving an objective function value of the relaxation problem;
2) judging whether the current dual target value is smaller than the optimal dual target value, if so, updating the optimal dual target value, otherwise, turning to the step 5);
3) performing feasible processing on the relaxation solution, solving an optimal feasible solution objective function value of the original problem, and updating an optimal feasible solution objective value and an optimal relaxation scheduling sequence of the original problem;
4) judging the difference value between the optimal dual target value and the optimal feasible solution target value, if the difference value between the optimal dual target value and the optimal feasible solution target value is smaller than a dual gap threshold value, stopping iteration, outputting the optimal solution, and if not, executing the next step;
5) calculating a secondary gradient and updating a Lagrange multiplier;
6) if the maximum iteration number is reached, outputting the optimal solution, otherwise, repeating the step 1).
10. The method for solving a load optimization model using a lagrangian relaxation algorithm as claimed in claim 9, wherein the relaxation problem is formed as follows:
Figure FDA0002613555490000041
forming a dual problem of the Lagrange relaxation algorithm according to the relaxation problem of the Lagrange relaxation algorithm, which is specifically as follows:
Figure FDA0002613555490000051
in the formula
Figure FDA0002613555490000052
The constraint conditions of the relaxation problem are expressions (1), (3), (5) and (6), the constraint conditions of the dual problem are expressions (1), (3), (5) and (6), and t is a scheduling time period; t is the total time segment number in the scheduling period; rhoL,tThe time-of-use electricity price is obtained; p0,tIs a fixed load; pEWH,tThe output power of the electric water heater at the moment t; pAC,tThe output power of the air conditioner at the moment t;
Figure FDA0002613555490000053
the output power of the washing machine at the moment t; λ is lagrange multiplier; t isWater(t) is the temperature of the water in the electric water heater at time t; t isout(t) the ambient temperature of the electric water heater at the moment t; t isin(t) electric Water heater at time tWater temperature; pEWH(t) the power consumption of the electric water heater at the moment t; g is the ratio of the surface area of the electric water heater to the thermal resistance at the moment t; SA and R are the surface area and the heat resistance of the electric water heater respectively; c is equivalent heat capacity of the electric water heater at the time t; ρ and CPDensity and specific heat capacity of water, respectively; v is the volume of the electric water heater at the time t; f (t) is the hot water flow; etaEWHThe electric energy input rate coefficient of the electric water heater at the time t.
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