CN113221299B - Operation optimization method for heat accumulating type electric boiler participating in peak shaving of electric power system - Google Patents

Operation optimization method for heat accumulating type electric boiler participating in peak shaving of electric power system Download PDF

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CN113221299B
CN113221299B CN202110465855.1A CN202110465855A CN113221299B CN 113221299 B CN113221299 B CN 113221299B CN 202110465855 A CN202110465855 A CN 202110465855A CN 113221299 B CN113221299 B CN 113221299B
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electric boiler
temperature
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胡泽春
刘礼恺
宁剑
文艺林
江长明
张哲�
张勇
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Tsinghua University
North China Grid Co Ltd
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North China Grid Co Ltd
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Abstract

The invention provides an operation optimization method for a heat accumulating type electric boiler to participate in peak shaving of an electric power system, and belongs to the field of operation optimization of flexible resources to participate in peak shaving. The method comprises the steps of firstly, converting historical data of an environment temperature predicted value and an environment temperature actual value through an empirical probability distribution function, constructing a joint probability distribution function of the converted environment temperature predicted value and the environment temperature actual value, and calculating to obtain empirical distribution of the next-day actual environment temperature; and then establishing an operation optimization model of the heat accumulating type electric boiler participating in peak shaving of the power system, which is composed of an objective function and constraint conditions, solving the model after carrying out distribution robust optimization on the objective function of the model to obtain an optimal solution of reported power when the heat accumulating type electric boiler participates in peak shaving at each time interval, and finally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, wherein the optimization is finished. The invention can reduce the influence of environment temperature uncertainty on the participation of the heat accumulating type electric boiler in peak shaving, and fully exert the peak shaving capacity of the heat accumulating type electric boiler.

Description

Operation optimization method for heat accumulating type electric boiler participating in peak shaving of electric power system
Technical Field
The invention belongs to the field of operation optimization of flexible resource participation peak shaving, and particularly relates to an operation optimization method of a heat accumulating type electric boiler participating in peak shaving of an electric power system.
Background
In recent years, renewable energy is developed vigorously, and the high-proportion renewable energy is accessed to bring great pressure to peak regulation of a power system. In northern areas of China, wind power often has higher output power at night in winter, and the peak regulation capacity of a thermal power generating unit is limited due to night heat supply. Because the power generation resources of the power system in northern China mainly comprise thermal power generating units, the insufficient night peak regulation capacity in the heat supply period becomes a key factor for restricting wind power consumption. Meanwhile, the heat accumulating type electric boiler in the north in winter has more load and also occupies a certain proportion in the whole load. Therefore, the heat accumulating type electric boiler is one of effective ways for improving wind power consumption in winter in the north by participating in peak shaving of the power system.
When the heat accumulating type electric boiler participates in peak shaving of the electric power system, peak shaving compensation and electricity consumption cost need to be considered at the same time, and the next day power curve is optimized in the day ahead. The outside air temperature is strongly correlated with the building indoor temperature, and therefore the energy required for heating is also significantly affected. However, currently, when optimizing the power curve of the heat accumulating type electric boiler, the temperature according to the weather forecast is often used as a deterministic input condition, and the temperature prediction error is not considered. In such a way, the actual power curve of the heat accumulating type electric boiler in the next day is possibly deviated from the reported power curve in the past day, and the peak regulation capacity of the heat accumulating type electric boiler cannot be fully exerted.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for optimizing the operation of a heat accumulating type electric boiler participating in peak shaving of an electric power system. The method can reduce the influence of the uncertainty of the ambient temperature on the participation of the heat accumulating type electric boiler in peak shaving, and fully exert the peak shaving capacity of the heat accumulating type electric boiler.
The invention provides an operation optimization method for a heat accumulating type electric boiler to participate in peak shaving of a power system, which is characterized in that the method comprises the steps of firstly, respectively constructing corresponding empirical probability distribution functions by utilizing historical data of an environment temperature predicted value and an environment temperature actual value, respectively transforming the historical data of the environment temperature predicted value and the environment temperature actual value by utilizing the functions, and then constructing a combined probability distribution function of the transformed environment temperature predicted value and the environment temperature actual value; calculating the empirical distribution of the next-day actual environment temperature by using the joint probability distribution function and the predicted value of the environment temperature at each time interval of the next day; and then establishing an operation optimization model of the heat accumulating type electric boiler participating in peak shaving of the power system, which is composed of an objective function and constraint conditions, solving the model after carrying out distribution robust optimization on the objective function of the model to obtain an optimal solution of reported power when the heat accumulating type electric boiler participates in peak shaving at each time interval, and finally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, wherein the optimization is finished. The method comprises the following steps:
1) calculating the empirical distribution of the actual environment temperature of the next day; the method comprises the following specific steps:
1-1) obtaining the predicted value of the environmental temperature
Figure GDA0003513993500000021
Historical samples and corresponding actual values of ambient temperature TenvHistorical samples respectively obtained by using statistical method
Figure GDA0003513993500000022
Empirical probability distribution function of
Figure GDA0003513993500000023
And TenvEmpirical probability distribution function of
Figure GDA0003513993500000024
The predicted value of the environmental temperature after the transformation by using the empirical probability distribution function
Figure GDA0003513993500000025
Is recorded as corresponding value
Figure GDA0003513993500000026
Will use the empirical probability distribution function to transform TenvIs recorded as corresponding value
Figure GDA0003513993500000027
Wherein will be
Figure GDA0003513993500000028
Recording the transformed value corresponding to the ith environmental temperature predicted value historical sample, and calculating the transformed value
Figure GDA0003513993500000029
Recording the history sample as a corresponding conversion value of the ith environmental temperature actual value history sample;
1-2) order
Figure GDA00035139935000000210
Combining any two history samples for the ith history sample combination formed by the transformation in the step 1-1)
Figure GDA00035139935000000211
And
Figure GDA00035139935000000212
forming a sample pair, wherein i ≠ j;
and (3) judging: if the sample pair satisfies
Figure GDA00035139935000000213
And is
Figure GDA00035139935000000214
Or satisfy
Figure GDA00035139935000000215
And is
Figure GDA00035139935000000216
The sample pair is an ordered pair, otherwise, the sample pair is an unordered pair;
combining all historical samplesAfter each formed sample pair is judged, calculation is carried out
Figure GDA00035139935000000217
And
Figure GDA00035139935000000218
the Kendall rank correlation coefficient tau is expressed as follows:
Figure GDA00035139935000000219
wherein N isGeneral pairRepresents the total number of sample pairs, NSame sequence pairAnd NPair of different ordersRespectively representing the log of the same sequence and the log of the different sequence;
1-3) construction Using Gaussiancopula function
Figure GDA00035139935000000220
And
Figure GDA00035139935000000221
the joint probability distribution function of (a):
Figure GDA00035139935000000222
wherein the content of the first and second substances,
Figure GDA00035139935000000227
represents a correlation matrix of
Figure GDA00035139935000000223
Of a standard multi-source normal distribution matrix of psi-1An inverse function representing a standard normal distribution; matrix array
Figure GDA00035139935000000224
The expression of (a) is as follows:
Figure GDA00035139935000000225
wherein, the calculation expression of the parameter rho is as follows:
Figure GDA00035139935000000226
1-4) evenly dividing the next day into Z time intervals, and executing the following operations for each time interval n: predicting the ambient temperature of the time interval n
Figure GDA0003513993500000031
Using empirical probability distribution functions
Figure GDA0003513993500000032
Convert it into corresponding
Figure GDA0003513993500000033
Will be provided with
Figure GDA0003513993500000034
Substituted joint probability distribution function and according to joint probability distribution function pair
Figure GDA0003513993500000035
Sampling J times to obtain Z X J samples, and recording the samples obtained by sampling
Figure GDA0003513993500000036
Using empirical probability distribution functions
Figure GDA0003513993500000037
Will be inverse function of
Figure GDA0003513993500000038
Transforming into corresponding actual value of the environmental temperature sample in the time period
Figure GDA0003513993500000039
After the operation is finished in all the time periods, obtaining the actual values of the environmental temperature samples in all the time periods;
1-5) calculating the empirical distribution of the next-day actual ambient temperature by adopting the following mode according to the actual values of the ambient temperature samples in all time periods obtained in the step 1-4)
Figure GDA00035139935000000310
Figure GDA00035139935000000311
The function I is an indication function, the value of the function is 1 when all comparison relations are satisfied, and the value of the function is 0 if not;
Figure GDA00035139935000000312
an actual value of ambient temperature representing time period n, n ═ 1,2, …, Z;
2) establishing an operation optimization model for the heat accumulating type electric boiler to participate in peak shaving of the electric power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
2-1) establishing an objective function of an operation optimization model, wherein the expression is as follows:
Figure GDA00035139935000000313
wherein the symbol E represents the mathematical expectation, PnRepresenting the actual power of the electric boiler in the time period n;
Figure GDA00035139935000000314
is the time-of-use electricity price of the time period n;
Figure GDA00035139935000000315
for unit capacity compensation of time period n, BnMaking a differential form determination for the baseline load for time period n; o isnIs the reported power of the time interval n when the heat accumulating electric cooker participates in peak regulation [ -sigma, sigma [ -]Bias bandwidth to avoid penalties;
Figure GDA00035139935000000316
a punishment factor of the deviation of the actual power of the electric boiler from the reported power in the period n;
Figure GDA00035139935000000317
wherein the content of the first and second substances,
Figure GDA00035139935000000318
represents the equivalent power of the boiler for storing heat to the heat storage tank of the heat storage type electric boiler in the time period n,
Figure GDA00035139935000000319
representing the equivalent power of the heat released by the heat storage tank in the time period n, eta represents the conversion efficiency of the electric boiler from electric energy to heat energy, and cbldIn order to obtain the equivalent specific heat capacity of the building,
Figure GDA00035139935000000320
for time period n the starting temperature of building m,
Figure GDA00035139935000000321
representing the coefficient of thermal conductivity between the building m and the environment,
Figure GDA00035139935000000322
is a collection of heating buildings;
by substituting equation (5) for equation (4), the objective function is expressed as follows:
Figure GDA0003513993500000041
wherein lk,nAnd hk,nIs represented by the formulae (7) and (8):
Figure GDA0003513993500000042
Figure GDA0003513993500000043
2-2) establishing constraint conditions of an operation optimization model; the method comprises the following specific steps:
2-2-1) operation restriction of the heat accumulating type electric boiler; the method comprises the following steps:
and (3) power balance constraint of the heat accumulating type electric boiler:
Figure GDA0003513993500000044
wherein D ism,nThe equivalent power of the heat accumulating type electric boiler for supplying heat to the heat supply building m in the time period n is shown;
range constraint of electric power for regenerative electric boilers:
Figure GDA0003513993500000045
wherein, PmaxAnd PminThe power of the heat accumulating type electric boiler is respectively an upper limit and a lower limit;
energy conservation constraint of the heat storage tank:
Figure GDA0003513993500000046
wherein HnRepresenting the initial heat energy of the heat storage tank in a time period n, and representing the heat storage efficiency coefficient of the heat storage tank upsilon;
and (3) heat storage capacity constraint:
Figure GDA0003513993500000047
in the formula, HmaxAnd HminThe upper limit and the lower limit of the heat storage capacity of the heat storage tank are respectively set;
2-2-2) heat sink related constraints; the method comprises the following steps:
the equivalent power constraint of the radiator:
equivalent power D of radiator of building m in time period nm,nFrom the flow of hot water
Figure GDA0003513993500000048
Specific heat capacity c of waterhotAnd the temperature of the water inlet and outlet of the radiator in the time period
Figure GDA0003513993500000051
And
Figure GDA0003513993500000052
expressed, the expression is as follows:
Figure GDA0003513993500000053
the temperature of inlet and outlet water of the radiator and the temperature of a building are restricted:
Figure GDA0003513993500000054
wherein theta ismTo reflect the coefficient of the overall heat dissipation effect of the radiator of the building m, the calculation expression is as follows:
Figure GDA0003513993500000055
wherein K is the heat dissipation coefficient of the radiator, and F is the heat dissipation area of the radiator;
restraint of temperature of inlet and outlet water of the radiator:
Figure GDA0003513993500000056
Figure GDA0003513993500000057
wherein the content of the first and second substances,
Figure GDA0003513993500000058
and
Figure GDA0003513993500000059
respectively an upper bound and a lower bound of the temperature of the water entering the radiator,
Figure GDA00035139935000000510
and
Figure GDA00035139935000000511
the upper bound and the lower bound of the water outlet temperature of the radiator are respectively set;
2-2-3) building related constraints; the method comprises the following steps:
and (3) restricting the building temperature change:
Figure GDA00035139935000000512
building temperature restraint:
Figure GDA00035139935000000513
wherein
Figure GDA00035139935000000514
And
Figure GDA00035139935000000515
upper and lower bounds for the temperature within the building, respectively;
3) converting the model established in the step 2) into a distributed robust optimization model;
and (3) converting the objective function formula (6) of the optimization model into the following form by adopting a distributed robust optimization technology:
Figure GDA00035139935000000516
wherein the ambient temperature of each time interval is recorded
Figure GDA00035139935000000517
The vector of composition is xi, and orderQ is the probability distribution function of the vector xi,
Figure GDA00035139935000000518
is a set of probability distributions Q;
uncertain set for constructing probability distribution Q based on Wasserstein distance
Figure GDA00035139935000000519
Figure GDA00035139935000000520
Wherein f represents any Lipschitz function which satisfies | f (xi) -f (xi ') | | < | xi-xi' |, xi is the value space of xi, and the expression is
Figure GDA0003513993500000061
Figure GDA0003513993500000062
And
Figure GDA0003513993500000063
is a coefficient matrix and a vector which limit the value range of the ambient temperature,
Figure GDA0003513993500000064
is the empirical distribution of the random vector xi obtained in the step 1), and epsilon is the construction of an uncertain set
Figure GDA0003513993500000065
Radius coefficient of time;
the objective function is converted to the following form:
Figure GDA0003513993500000066
wherein the variable gamman,k,j，sn,jAnd λnAre all the auxiliary variables introduced by the conversion,
Figure GDA0003513993500000067
the expression is as follows:
Figure GDA0003513993500000068
4) solving the optimization model transformed in the step 3) to obtain reported power O when the heat accumulating type electric cooker participates in peak load regulation at each time intervalnFinally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, and finishing the optimization.
The invention has the characteristics and beneficial effects that:
the method constructs a probability distribution model of the air temperature prediction error based on historical data, and considers the influence of the prediction error in the power curve formulation stage by combining distribution robust optimization to obtain a more accurate day-ahead reported power curve. The method can reduce the influence of the uncertainty of the ambient temperature on the participation of the heat accumulating type electric boiler in peak shaving, and fully exert the peak shaving capacity of the heat accumulating type electric boiler.
Detailed Description
The invention provides an operation optimization method for a heat accumulating type electric boiler to participate in peak shaving of an electric power system, which comprises the following steps:
1) calculating the empirical distribution of the actual environment temperature of the next day; the method comprises the following specific steps:
1-1) obtaining the predicted value of the environmental temperature recorded by the heat accumulating type electric boiler in the past period
Figure GDA0003513993500000069
Historical samples and corresponding actual values of ambient temperature TenvHistory samples (history data is usually history data of a month in which a date to be optimized is located, for example, in this embodiment, a month to which the day to be optimized belongs is 3 months, a history sample of an ambient temperature predicted value and a history sample of a corresponding ambient temperature actual value of 3 months in the last three years are selected from a database of a predicted value and an actual value of historical ambient temperature recorded by a heat storage type electric boiler), and the history samples are respectively obtained by using a statistical method
Figure GDA00035139935000000610
Empirical probability distribution function of
Figure GDA00035139935000000611
And TenvEmpirical probability distribution function of
Figure GDA00035139935000000612
And the predicted value of the environmental temperature after the transformation by using the empirical probability distribution function
Figure GDA0003513993500000071
Is recorded as corresponding value
Figure GDA0003513993500000072
Will use the empirical probability distribution function to transform TenvIs recorded as corresponding value
Figure GDA0003513993500000073
Wherein will be
Figure GDA0003513993500000074
Recording the transformed value corresponding to the ith environmental temperature predicted value historical sample, and calculating the transformed value
Figure GDA0003513993500000075
And recording the temperature as a conversion value corresponding to the ith history sample of the actual value of the environmental temperature.
1-2) order
Figure GDA0003513993500000076
Combining any two history samples for the ith history sample combination formed by the transformation in the step 1-1)
Figure GDA0003513993500000077
And
Figure GDA0003513993500000078
forming a sample pair, wherein i ≠ j (i, j are history sample numbers); if the sample is fullFoot
Figure GDA0003513993500000079
And is
Figure GDA00035139935000000710
Or satisfy
Figure GDA00035139935000000711
And is
Figure GDA00035139935000000712
The sample pair is an in-sequence pair, otherwise it is an out-of-sequence pair. Let NGeneral pairRepresents the total number of sample pairs, NSame sequence pairAnd NPair of different ordersThen the in-sequence and out-of-sequence pairs are indicated, respectively. Then calculate the variable
Figure GDA00035139935000000713
And
Figure GDA00035139935000000714
the expression of the Kendall rank correlation coefficient tau is as follows:
Figure GDA00035139935000000715
1-3) construction Using Gaussiancopula function
Figure GDA00035139935000000716
And
Figure GDA00035139935000000717
the joint probability distribution function of (a):
Figure GDA00035139935000000718
wherein the content of the first and second substances,
Figure GDA00035139935000000719
represents a correlation matrix of
Figure GDA00035139935000000720
Of a standard multi-source normal distribution matrix of psi-1An inverse function representing a standard normal distribution. Matrix array
Figure GDA00035139935000000721
The expression of (a) is as follows:
Figure GDA00035139935000000722
the calculation mode of the parameter rho is as follows:
Figure GDA00035139935000000723
1-4) the next day is evenly divided into Z periods (in this embodiment, Z is 24), and for each period n, the following operations are performed: predicting the ambient temperature of the time interval n
Figure GDA00035139935000000724
Using empirical probability distribution functions
Figure GDA00035139935000000725
Convert it into corresponding
Figure GDA00035139935000000726
Further will be
Figure GDA00035139935000000727
Substituting the joint probability distribution function shown in formula and according to the joint probability distribution function pair
Figure GDA00035139935000000728
Sampling for J times (the value of J ranges from 50 to 100), obtaining Z X J samples in total, and recording the samples obtained by sampling as
Figure GDA00035139935000000729
Figure GDA00035139935000000730
Using empirical probability distribution functions
Figure GDA00035139935000000731
Will be inverse function of
Figure GDA00035139935000000732
Transforming into corresponding actual value of the environmental temperature sample in the time period
Figure GDA00035139935000000733
1-5) obtaining the actual values of the environmental temperature samples in all time periods according to the step 1-4)
Figure GDA0003513993500000081
The empirical distribution of the actual ambient temperature of the next day is calculated as follows
Figure GDA0003513993500000082
Figure GDA0003513993500000083
The function I is an indication function, the value of the function is 1 when all comparison relations are satisfied, and the value of the function is 0 if not;
Figure GDA0003513993500000084
an actual value of ambient temperature representing time period n, n ═ 1,2, …, Z;
2) establishing an operation optimization model for the heat accumulating type electric boiler to participate in peak shaving of the electric power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
2-1) establishing an objective function of an operation optimization model;
the objective function of the heat accumulating type electric boiler participating in the peak regulation of the electric power system consists of electricity consumption, peak regulation income and default punishment: the electricity charge is time-of-use electricity price
Figure GDA0003513993500000085
Actual power P of electric boilernThe product of (a); compensation of peak regulation income of power grid according to regulation capacity and unit capacity
Figure GDA0003513993500000086
Calculated and the regulating capacity is a base line load B determined by the actual power consumption and the power gridnMaking a form determination of the difference; the default punishment is based on the actual power consumption of the heat accumulating type electric cooker and the reported power O when the heat accumulating type electric cooker participates in peak regulationnDetermining a deviation bandwidth free from penalties as [ - σ, σ [ ]]. In summary, the objective function of the regenerative electric boiler participating in the peak shaving market operation optimization can be expressed as:
Figure GDA0003513993500000087
wherein the symbol E represents the mathematical expectation, PnRepresenting the actual power of the electric boiler for a period n,
Figure GDA0003513993500000088
punishment factor for deviation of actual power of electric boiler from reported power in period n
Actual power P of upper-type medium electric boilernWill be subjected to the ambient temperature for that period
Figure GDA0003513993500000089
The relationship between them is as follows:
Figure GDA00035139935000000810
wherein the content of the first and second substances,
Figure GDA00035139935000000811
representing the equivalent power of the boiler for storing heat to the heat storage tank in the time period n,
Figure GDA00035139935000000812
representing the equivalent power of the heat release of the heat storage tank in the period n, eta representing the conversion efficiency of the heat storage tank during heat release, cbldIn order to obtain the equivalent specific heat capacity of the building,
Figure GDA00035139935000000813
for time period n the starting temperature of building m,
Figure GDA00035139935000000814
representing the coefficient of thermal conductivity between the building m and the environment,
Figure GDA00035139935000000815
is a collection of heating buildings.
By substituting equation (5) for equation (4), the objective function can be expressed as follows:
Figure GDA0003513993500000091
wherein lk,nAnd hk,nIs represented by the formulae (7) and (8):
Figure GDA0003513993500000092
Figure GDA0003513993500000093
2-2) establishing constraint conditions of an operation optimization model; the method comprises the following specific steps:
2-2-1) operation restriction of the heat accumulating type electric boiler;
power balance constraint of the heat accumulating type electric boiler;
the heat accumulating electric boiler consists of mainly electric boiler and heat accumulating tank. The heat accumulating type electric boiler operates in a mode of combining direct heat supply and heat accumulation equipment heat supply, and specifically comprises four working modes: 1) the boiler directly supplies heat to the building; 2) the boiler supplies heat to the building and stores heat to the heat storage tank at the same time; 3) the heat storage tank supplies heat to the building; 4) the boiler and the heat storage tank simultaneously supply heat to the building. The above process can be collectively represented by the following formula:
Figure GDA0003513993500000094
wherein D ism,nShowing the heat accumulating type electric boiler to heat supply buildings m (m) in the time period n
Figure GDA0003513993500000095
Figure GDA0003513993500000096
A collection of heating buildings) equivalent power of heating.
Besides the power balance constraint, the range constraint of the power consumption of the power balance device is also included:
Figure GDA0003513993500000097
wherein, PmaxAnd PminRespectively the upper and lower bounds of the heat accumulating type electric boiler power.
Energy conservation constraint of the heat storage tank;
the heat accumulating tank is an important component of the heat accumulating type electric boiler. In actual operation, in order to ensure that the heat storage tank is always at the maximum heat storage capacity, the water amount in the heat storage tank is always maintained at the maximum water amount. Therefore, the energy stored in the heat storage tank is mainly related to the water temperature. In view of the dissipation of heat energy in the heat storage tank, the stored energy thereof changes with time as shown in the following equation:
Figure GDA0003513993500000098
wherein HnRepresenting the initial heat energy of the heat storage tank in a time period n, and representing the heat storage efficiency coefficient of the heat storage tank upsilon;
the heat storage tank-related constraint includes a heat storage capacity constraint in addition to the energy conservation constraint represented by the formula:
Figure GDA0003513993500000101
in the formula, HmaxAnd HminRespectively the upper and lower limits of the heat storage capacity of the heat storage tank.
2-2-2) heat sink related constraints
Equivalent power D of radiator of building m in time period nm,nCan be controlled by the flow of hot water
Figure GDA0003513993500000102
Specific heat capacity c of waterhotAnd the temperature of the water inlet and outlet of the radiator in the time period
Figure GDA0003513993500000103
And
Figure GDA0003513993500000104
expressed, the expression is as follows:
Figure GDA0003513993500000105
heat exchange between radiator and building is performed, so that the temperature of inlet and outlet water of radiator and the temperature of building environment
Figure GDA0003513993500000106
There is the following relationship between:
Figure GDA0003513993500000107
coefficient theta reflecting integral heat dissipation effect of radiator of building m in the above formulamThe calculation method of (c) is as follows:
Figure GDA0003513993500000108
wherein K is the heat dissipation coefficient of the radiator, and F is the heat dissipation area of the radiator.
In addition, the heat exchanger device also has temperature resistance limitation, so the water inlet temperature and the water outlet temperature are within the rated range:
Figure GDA0003513993500000109
Figure GDA00035139935000001010
wherein the content of the first and second substances,
Figure GDA00035139935000001011
and
Figure GDA00035139935000001012
respectively the upper and lower limits of the water inlet temperature of the radiator,
Figure GDA00035139935000001013
and
Figure GDA00035139935000001014
respectively the upper and lower bounds of the temperature of the water outlet of the radiator.
2-2-3) building related constraints;
the building receives energy from the radiator and exchanges heat with the outdoor environment, the temperature variation of which can be expressed as:
Figure GDA00035139935000001015
in addition to this, building temperature constraints should also be added in view of the user's requirements for the temperature inside the building:
Figure GDA00035139935000001016
wherein
Figure GDA00035139935000001017
And
Figure GDA00035139935000001018
respectively, the upper and lower bounds of the temperature within the building.
3) Converting the model established in the step 2) into a distributed robust optimization model;
and (3) converting the objective function formula (6) of the optimization model into the following form by adopting a distributed robust optimization technology:
Figure GDA0003513993500000111
defining the ambient temperature for each time period
Figure GDA0003513993500000112
The formed vector is xi, and Q is a probability distribution function of the vector xi,
Figure GDA0003513993500000113
is a set of probability distributions Q. The invention adopts an uncertain set for constructing probability distribution Q based on Wasserstein distance
Figure GDA0003513993500000114
Figure GDA0003513993500000115
Wherein f represents any Lipschitz function which satisfies | f (xi) -f (xi ') | | < | | xi-xi' | | and xi is a value space of xi, and the expression is xi
Figure GDA0003513993500000116
Wherein
Figure GDA0003513993500000117
And
Figure GDA0003513993500000118
is a coefficient matrix and a vector which limit the value range of the ambient temperature,
Figure GDA0003513993500000119
is the empirical distribution of the random vector xi obtained in the step 1), and epsilon is the construction of an uncertain set
Figure GDA00035139935000001110
Radius coefficient of time.
The objective function can be converted to the following form:
Figure GDA00035139935000001111
wherein the variable gamman,k,j，sn,jAnd λnAre auxiliary variables introduced into the problem transformation,
Figure GDA00035139935000001112
can be expressed as follows:
Figure GDA00035139935000001113
4) writing the optimization model transformed in the step 3) by using a YALMIP tool package under Matlab software, and further solving the optimization model by using Gurobi solving software to obtain reported power O when the heat accumulating type electric cooker participates in peak load regulation at each time intervalnAnd finally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, and finishing the optimization.

Claims (1)

1. A heat accumulating type electric boiler participates in the operation optimization method of the peak shaving of the electric power system, characterized by that, this method utilizes historical data of predicted value of the ambient temperature and actual value of the ambient temperature to construct the corresponding empirical probability distribution function separately at first, utilize this function to transform the historical data of predicted value of the ambient temperature and actual value of the ambient temperature separately, construct the union probability distribution function of predicted value of the ambient temperature and actual value of the ambient temperature after transforming; calculating the empirical distribution of the next-day actual environment temperature by using the joint probability distribution function and the predicted value of the environment temperature at each time interval of the next day; then establishing an operation optimization model of the heat accumulating type electric boiler formed by an objective function and constraint conditions for participating in peak shaving of the power system, performing distribution robust optimization on the objective function of the model, and then solving the model to obtain an optimal solution of reported power when the heat accumulating type electric boiler participates in peak shaving at each time interval, and finally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, wherein the optimization is finished; the method comprises the following steps:
1) calculating the empirical distribution of the actual environment temperature of the next day; the method comprises the following specific steps:
1-1) obtaining the predicted value of the environmental temperature
Figure FDA0003513993490000011
Historical samples and corresponding actual values of ambient temperature TenvHistorical samples respectively obtained by using statistical method
Figure FDA0003513993490000012
Empirical probability distribution function of
Figure FDA0003513993490000013
And TenvEmpirical probability distribution function of
Figure FDA0003513993490000014
The predicted value of the environmental temperature after the transformation by using the empirical probability distribution function
Figure FDA0003513993490000015
Is recorded as corresponding value
Figure FDA0003513993490000016
Will use the empirical probability distribution function to transform TenvIs recorded as corresponding value
Figure FDA0003513993490000017
Wherein will be
Figure FDA0003513993490000018
Recording the transformed value corresponding to the ith environmental temperature predicted value historical sample, and calculating the transformed value
Figure FDA0003513993490000019
Recording the history sample as a corresponding conversion value of the ith environmental temperature actual value history sample;
1-2) order
Figure FDA00035139934900000110
Combining any two history samples for the ith history sample combination formed by the transformation in the step 1-1)
Figure FDA00035139934900000111
And
Figure FDA00035139934900000112
forming a sample pair, wherein i ≠ j;
and (3) judging: if the sample pair satisfies
Figure FDA00035139934900000113
And is
Figure FDA00035139934900000114
Or satisfy
Figure FDA00035139934900000115
And is
Figure FDA00035139934900000116
The sample pair is an ordered pair, otherwise, the sample pair is an unordered pair;
after all the sample pairs formed by combining all the historical samples are judged, calculation is carried out
Figure FDA00035139934900000117
And
Figure FDA00035139934900000118
ke of (1)And (4) the ndall rank correlation coefficient tau is expressed as follows:
Figure FDA00035139934900000119
wherein N isGeneral pairRepresents the total number of sample pairs, NSame sequence pairAnd NPair of different ordersRespectively representing the log of the same sequence and the log of the different sequence;
1-3) construction Using Gaussiancopula function
Figure FDA00035139934900000120
And
Figure FDA00035139934900000121
the joint probability distribution function of (a):
Figure FDA0003513993490000021
wherein the content of the first and second substances,
Figure FDA0003513993490000022
represents a correlation matrix of
Figure FDA0003513993490000023
Of a standard multi-source normal distribution matrix of psi-1An inverse function representing a standard normal distribution; matrix array
Figure FDA0003513993490000024
The expression of (a) is as follows:
Figure FDA0003513993490000025
wherein, the calculation expression of the parameter rho is as follows:
Figure FDA0003513993490000026
1-4) evenly dividing the next day into Z time intervals, and executing the following operations for each time interval n: predicting the ambient temperature of the time interval n
Figure FDA0003513993490000027
Using empirical probability distribution functions
Figure FDA0003513993490000028
Convert it into corresponding
Figure FDA0003513993490000029
Will be provided with
Figure FDA00035139934900000210
Substituted joint probability distribution function and according to joint probability distribution function pair
Figure FDA00035139934900000211
Sampling J times to obtain Z X J samples, and recording the samples obtained by sampling
Figure FDA00035139934900000212
Using empirical probability distribution functions
Figure FDA00035139934900000213
Will be inverse function of
Figure FDA00035139934900000214
Transforming into corresponding actual value of the environmental temperature sample in the time period
Figure FDA00035139934900000215
After the operation is finished in all the time periods, obtaining the actual values of the environmental temperature samples in all the time periods;
1-5) ambient temperature samples obtained according to steps 1-4) at all time periodsThe actual value is calculated by calculating the empirical distribution of the actual environmental temperature of the next day in the following way
Figure FDA00035139934900000216
Figure FDA00035139934900000217
The function I is an indication function, the value of the function is 1 when all comparison relations are satisfied, and the value of the function is 0 if not;
Figure FDA00035139934900000218
an actual value of ambient temperature representing time period n, n ═ 1,2, …, Z;
2) establishing an operation optimization model for the heat accumulating type electric boiler to participate in peak shaving of the electric power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
2-1) establishing an objective function of an operation optimization model, wherein the expression is as follows:
Figure FDA00035139934900000219
wherein the symbol E represents the mathematical expectation, PnRepresenting the actual power of the electric boiler in the time period n;
Figure FDA00035139934900000220
is the time-of-use electricity price of the time period n;
Figure FDA00035139934900000221
for unit capacity compensation of time period n, BnMaking a differential form determination for the baseline load for time period n; o isnIs the reported power of the time interval n when the heat accumulating electric cooker participates in peak regulation [ -sigma, sigma [ -]Bias bandwidth to avoid penalties;
Figure FDA00035139934900000222
a punishment factor of the deviation of the actual power of the electric boiler from the reported power in the period n;
Figure FDA0003513993490000031
wherein the content of the first and second substances,
Figure FDA0003513993490000032
represents the equivalent power of the boiler for storing heat to the heat storage tank of the heat storage type electric boiler in the time period n,
Figure FDA0003513993490000033
representing the equivalent power of the heat released by the heat storage tank in the time period n, eta represents the conversion efficiency of the electric boiler from electric energy to heat energy, and cbldIn order to obtain the equivalent specific heat capacity of the building,
Figure FDA0003513993490000034
for time period n the starting temperature of building m,
Figure FDA0003513993490000035
representing the coefficient of thermal conductivity between the building m and the environment,
Figure FDA0003513993490000036
is a collection of heating buildings;
by substituting equation (5) for equation (4), the objective function is expressed as follows:
Figure FDA0003513993490000037
wherein lk,nAnd hk,nIs represented by the formulae (7) and (8):
Figure FDA0003513993490000038
Figure FDA0003513993490000039
2-2) establishing constraint conditions of an operation optimization model; the method comprises the following specific steps:
2-2-1) operation restriction of the heat accumulating type electric boiler; the method comprises the following steps:
and (3) power balance constraint of the heat accumulating type electric boiler:
Figure FDA00035139934900000310
wherein D ism,nThe equivalent power of the heat accumulating type electric boiler for supplying heat to the heat supply building m in the time period n is shown;
range constraint of electric power for regenerative electric boilers:
Figure FDA00035139934900000311
wherein, PmaxAnd PminThe power of the heat accumulating type electric boiler is respectively an upper limit and a lower limit;
energy conservation constraint of the heat storage tank:
Figure FDA0003513993490000041
wherein HnRepresenting the initial heat energy of the heat storage tank in a time period n, and representing the heat storage efficiency coefficient of the heat storage tank upsilon;
and (3) heat storage capacity constraint:
Figure FDA0003513993490000042
in the formula, HmaxAnd HminThe upper limit and the lower limit of the heat storage capacity of the heat storage tank are respectively set;
2-2-2) heat sink related constraints; the method comprises the following steps:
the equivalent power constraint of the radiator:
equivalent power D of radiator of building m in time period nm,nFrom the flow of hot water
Figure FDA0003513993490000043
Specific heat capacity c of waterhotAnd the temperature of the water inlet and outlet of the radiator in the time period
Figure FDA0003513993490000044
And
Figure FDA0003513993490000045
expressed, the expression is as follows:
Figure FDA0003513993490000046
the temperature of inlet and outlet water of the radiator and the temperature of a building are restricted:
Figure FDA0003513993490000047
wherein theta ismTo reflect the coefficient of the overall heat dissipation effect of the radiator of the building m, the calculation expression is as follows:
Figure FDA0003513993490000048
wherein K is the heat dissipation coefficient of the radiator, and F is the heat dissipation area of the radiator;
restraint of temperature of inlet and outlet water of the radiator:
Figure FDA0003513993490000049
Figure FDA00035139934900000410
wherein the content of the first and second substances,
Figure FDA00035139934900000411
and
Figure FDA00035139934900000412
respectively an upper bound and a lower bound of the temperature of the water entering the radiator,
Figure FDA00035139934900000413
and
Figure FDA00035139934900000414
the upper bound and the lower bound of the water outlet temperature of the radiator are respectively set;
2-2-3) building related constraints; the method comprises the following steps:
and (3) restricting the building temperature change:
Figure FDA00035139934900000415
building temperature restraint:
Figure FDA00035139934900000416
wherein
Figure FDA0003513993490000051
And
Figure FDA0003513993490000052
upper and lower bounds for the temperature within the building, respectively;
3) converting the model established in the step 2) into a distributed robust optimization model;
and (3) converting the objective function formula (6) of the optimization model into the following form by adopting a distributed robust optimization technology:
Figure FDA0003513993490000053
wherein the ambient temperature of each time interval is recorded
Figure FDA0003513993490000054
The formed vector is xi, and Q is a probability distribution function of the vector xi,
Figure FDA0003513993490000055
is a set of probability distributions Q;
uncertain set for constructing probability distribution Q based on Wasserstein distance
Figure FDA0003513993490000056
Figure FDA0003513993490000057
Wherein f represents any Lipschitz function which satisfies | f (xi) -f (xi ') | | < | | xi-xi' | |, xi is the value space of xi, and the expression is xi
Figure FDA0003513993490000058
Figure FDA00035139934900000515
And
Figure FDA0003513993490000059
is a coefficient matrix and a vector which limit the value range of the ambient temperature,
Figure FDA00035139934900000510
is the empirical distribution of the random vector xi obtained in the step 1), and epsilon is the construction of an uncertain set
Figure FDA00035139934900000511
Radius coefficient of time;
the objective function is converted to the following form:
Figure FDA00035139934900000512
wherein the variable gamman,k,j，sn,jAnd λnAre all the auxiliary variables introduced by the conversion,
Figure FDA00035139934900000513
the expression is as follows:
Figure FDA00035139934900000514
4) solving the optimization model transformed in the step 3) to obtain reported power O when the heat accumulating type electric cooker participates in peak load regulation at each time intervalnFinally obtaining a bidding power curve of the heat accumulating type electric boiler participating in the peak shaving market, and finishing the optimization.
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