Multi-objective Expansion Planning Method for Distribution Network Considering the Access of Large-scale Electric Heat Storage Equipment

Abstract

The present invention discloses a multi-objective expansion planning method for a distribution network considering the access of large-scale electric heat storage equipment. First, to improve the effectiveness of typical scenarios, the heat load is generated by comprehensively considering meteorological factors such as building structure, indoor and outdoor heat transfer characteristics, and light intensity. At the same time, the influence of wind speed is considered in terms of heat transfer factors, and this method can more accurately realize the modeling of the heat load. Secondly, in the decision-making of the operation strategy of the heat storage electric boiler, the present invention considers the output characteristics of wind and solar power sources at each time period, and determines the operation strategy of the heat storage electric boiler with the lowest carbon emission as the goal. While reducing carbon emissions, the more flexible operation strategy can also effectively shift peaks and fill valleys, reducing the power supply pressure of the distribution network during peak electricity consumption periods. Finally, the present invention conducts multi-objective expansion planning for the distribution network with the goals of economy and load rate uniformity, and uses a nested hybrid particle swarm optimization algorithm for solution. The solution results have the characteristics of low total cost and strong load rate uniformity of the lines.

Description

Technical Field

[0001] The invention belongs to the technical field of distribution network planning, and particularly relates to a multi-objective expansion planning method for distribution network considering the access of large-scale electric heat storage equipment. Background Art

[0002] The load growth caused by the access of large-scale electric heat equipment to the distribution network will lead to insufficient load-carrying capacity of the distribution network, while the access of electric heat storage equipment to the distribution network can effectively shift the peak and fill the valley, reducing the load demand during the peak electricity consumption period. In the prior art, firstly, the heat load is generated for the purpose of improving the effectiveness of the scenario, but the existing modeling methods consider relatively single factors and have insufficient modeling accuracy. Then, it is the decision-making of the operation strategy of the heat storage electric boiler. The traditional two-stage operation strategy and the grouped input / withdrawal operation strategy lack flexibility and cannot effectively utilize clean power sources such as wind and light for power supply. Finally, it is the expansion planning of the distribution network. Most of the existing technologies are single-objective planning with economy as the goal, and it is difficult to take into account both the operation reliability of the distribution system and the uniformity of the line load rate at the same time. Summary of the Invention

[0003] The purpose of the invention is to provide a multi-objective expansion planning method for distribution network considering the access of large-scale electric heat storage equipment, which has the characteristics of high accuracy in heat load modeling and strong uniformity of the line load rate after the distribution network planning.

[0004] The technical solution adopted by the invention is that the multi-objective expansion planning method for distribution network considering the access of large-scale electric heat storage equipment is specifically implemented according to the following steps:

[0005] Step 1: Combine the wind speed in the analysis of heat transfer characteristics to establish a time-varying equation of the internal temperature of the heating building formed by the building envelope structure, and establish an electric heat load model according to the time-varying equation;

[0006] Step 2: Establish a model for the heat storage electric boiler;

[0007] Step 3: Establish a two-layer multi-objective planning model for the distribution network;

[0008] Step 4: Solve by the nested hybrid particle swarm optimization algorithm.

[0009] The characteristics of the invention also lie in that:

[0010] The specific process of Step 1 is as follows:

[0011] Calculate The heat obtained by the interior of the building space through heat transfer with the outside through the wall at time , which is expressed as:

[0012] (1)

[0013] In the formula: is the heating area; is the equivalent wall area per unit heating area; is the heat transfer coefficient between the inner surface of the wall per unit area and the air, which is related to the temperature of the inner surface of the wall; , are respectively the indoor and outdoor temperatures at time

[0014] The heat obtained by the indoor through heat transfer through the window to the outdoor at time is expressed as:

[0015] (2)

[0016] In the formula, is the equivalent window area per unit heating area; is the solar radiation heat gain coefficient of the window per unit area; is the glass cooling load coefficient; is the shading coefficient of the glass;

[0017] The heat obtained by the indoor through air exchange at time , is expressed as:

[0018] (3)

[0019] In the formula: is the outdoor wind speed; is the comprehensive heat transfer coefficient;

[0020] The heat sent into the indoor by the heating system at time , is expressed as:

[0021] (4)

[0022] In the formula, is the heat provided by the heat storage electric boiler at time is the heat provided by the direct electric heating equipment at time

[0023] The time-varying equation of the internal temperature of the heating building formed by the building envelope is:

[0024] (5)

[0025] In the formula, is the demand for electric heating load;

[0026] According to the time-varying temperature equation, an electric heating load model is established, which is C in formula (5) a .

[0027] Step 2: The electric boiler with thermal energy storage includes an electric boiler and a thermal energy storage device. The specific process of Step 2 is as follows:

[0028] An output model of the electric boiler is established, expressed as:

[0029] (6)

[0030] In the formula: and are respectively the electricity consumption and heat production of the electric boiler in the period;

[0031] A mathematical model of the heat storage capacity of the thermal energy storage device is established, expressed as:

[0032] (7)

[0033] In the formula: is the heat storage amount of the thermal energy storage device in the period; is the heat dissipation loss rate; and are the heat absorption and release power at the moment;

[0034] In Step 3, the distribution network's two-layer multi-objective planning model includes an upper-layer planning model and a lower-layer planning model;

[0035] The two-layer multi-objective planning of the distribution network specifically refers to:

[0036] The upper-layer planning makes decisions on the operation strategy of the electric boiler with thermal energy storage to minimize carbon emissions;

[0037] The lower-layer planning takes the total cost of the distribution network planning and the uniformity of the system load rate as objectives to conduct a multi-objective extended planning of the distribution network.

[0038] The specific process of establishing the upper-layer planning model in Step 3 is as follows:

[0039] The objective function and constraint conditions of the upper-layer planning model are established, specifically:

[0040] The upper-layer planning model establishes an objective function with the minimum carbon emissions as the goal, expressed as:

[0041] (8)

[0042] In the formula, is the total system carbon emissions; is the equipment operation time cycle; is the comprehensive carbon emission factor of thermal power units; is the thermal power unit output during a period; is the time interval;

[0043] The constraint conditions of the upper-level planning model are expressed as:

[0044] Power balance constraint:

[0045] (9)

[0046] (10)

[0047] In the formula, and are the total active and reactive power outputs of node respectively; , are the active and reactive power flowing out of node respectively; , are the active power consumed and the heat stored by the electric boiler with thermal energy storage at node respectively; is the set of adjacent nodes of node ; is the voltage phase angle difference between two nodes;

[0048] Node voltage constraint:

[0049] (11)

[0050] In the formula, is the voltage of node ; , are the upper and lower limits of the voltage of node respectively;

[0051] Branch current constraint:

[0052] (12)

[0053] In the formula, is the current of line ; is the maximum current-carrying capacity of the line;

[0054] Output constraint of the electric boiler with thermal energy storage:

[0055] (13)

[0056] (14)

[0057] (15)

[0058] In equations (13), (14), and (15), is the heat storage capacity of the heat storage device at the end of the time period; and are the input and output heat powers at the moment; and are the upper and lower limits of the capacity of the heat storage device, respectively; , and , are the upper and lower limits of the input and output heat powers, respectively;

[0059] Reliability constraint:

[0060] (16)

[0061] In the formula, is the total output of thermal power, wind, and photovoltaic units at the moment; is the demand for the electro-thermal load at the moment under extreme meteorological conditions;

[0062] Power output constraint:

[0063] (17)

[0064] (18)

[0065] (19)

[0066] In the formula, , , are the outputs of photovoltaic, wind power, and thermal power units at the moment, respectively; , , , , , are the upper and lower limits of the outputs of photovoltaic, wind power, and thermal power units at the moment, respectively.

[0067] The specific process of establishing the lower-level planning model in step 3 is as follows:

[0068] Establish the objective function and constraint conditions of the lower-level planning model, specifically:

[0069] Establish the objective function of the lower-level planning model with economy and load rate uniformity as the objectives, expressed as:

[0070] 1) Uniformity objective function:

[0071] The load rate is the ratio of the actual transmission power of the distribution line to its maximum transmission power, and it is used as an index to measure the uniformity of the distribution network. The i load rate L i is expressed as follows:

[0072] (20)

[0073] In the formula: i = 1, 2, 3… M , 、 are the actual transmission power and the maximum transmission power of the distribution line respectively; define the vector as the load rate vector of all lines in the distribution network during a certain period, is average value, and the non-uniformity is expressed as follows:

[0074] (21)

[0075] (22)

[0076] (23)

[0077] In the formula: is the variance of the distribution network load rate, which characterizes the average distribution of the load rate in the system; is the range of the distribution network load rate, which characterizes the worst deviation value of the load rate in the system; and are the weight coefficients of the two, which respectively characterize and influence degree, and the sum of the two is 1;

[0078] 2) Economic objective function

[0079] In the distribution network planning, the goal is to minimize the annual comprehensive cost of the whole society, which includes the investment cost and operation cost of the distribution network, and is expressed as:

[0080] (24)

[0081] In the formula: is the investment cost of the distribution network; is the operation cost of the distribution network;

[0082] The constraint conditions of the lower-level planning model are:

[0083] Distribution network planning investment cost constraint:

[0084] The total construction cost is required to be less than the cost ceiling during the entire planning period, i.e.,

[0085] (27)

[0086] In the formula: is the candidate set of lines; is the cost of newly built lines per unit capacity; is the capacity of a single newly built line; is a 0, 1 variable for line construction. When , the line is constructed. When , the line is not constructed. is the maximum cost of the investment cost of the distribution network lines;

[0087] In the distribution network planning, the upper and lower limits of the line transmission capacity are

[0088] (28)

[0089] In the formula: is the actual transmission capacity of line ; , are the upper and lower limits of the transmission capacity of the -th line respectively;

[0090] In the distribution network planning, the number of newly built lines should not exceed a certain limit, and its constraint is:

[0091] (29)

[0092] In the formula: is the upper limit value of the number of candidate lines;

[0093] Node power balance constraint:

[0094] In the distribution network, the difference between the power injected into the node and the node load demand should be equal to the power consumed on the branch, i.e.,

[0095] (30)

[0096] In the formula: and are the active power injected into node and the load demand of node respectively; is the susceptance of the line between nodes , ; , are the phase angles between nodes , ; is the set of distribution network nodes, where , ;

[0097] Line power flow constraint:

[0098] It is required that the transmission power on the line between two nodes does not exceed the maximum allowable transmission power of this line, that is

[0099] (31)

[0100] In the formula: is the node and the sum node The power upper limit of the line between.

[0101] The specific process of step 4 is as follows:

[0102] Step 4.1: Establish a node power distribution system model of the distribution network, and input the distribution network parameters, initial grid structure, distribution network line selection and installation operation costs into the model;

[0103] Step 4.2: Initialize the upper-layer particle population and the number of iterations. According to formula (5), model the typical daily electric and thermal load curves, superimpose them on the typical daily electric load curve to obtain the load curve including electric and thermal loads, perform integer coding on the ordinate of the load curve including electric and thermal loads, and randomly generate the upper-layer initial particle swarm;

[0104] Step 4.3: From the upper-layer objective function and conditional constraints, and the output of the original electric heating equipment at each time period, use the particle swarm optimization algorithm to find the output of the electric boiler with heat storage at each time period, eliminate and update the solutions that do not meet the constraint conditions, superimpose the electric load demand generated by the heat storage capacity of the electric boiler with heat storage on the load curve including electric and thermal loads, and use the curve obtained after superposition as the basic parameter and input it into the lower-layer model;

[0105] Step 4.4: Initialize the number of iterations and population of the lower-layer particles, perform binary coding on the installation positions of the lines to be built, randomly generate the lower-layer particle velocities and positions, and initialize the lower-layer particle swarm;

[0106] Step 4.5: Expand the lines according to the output scheme of the electric boiler with heat storage determined by the upper layer, and return to step 4.3;

[0107] Step 4.6: Calculate the construction cost, operation cost, variance of load rate, and range of system load rate, execute the objective function of the lower-layer planning model, update the individual extreme values and overall extreme values of the line decision variables corresponding to each grid structure scheme in the lower layer according to the curve obtained after superposition in step 4.3, and use the overall extreme value as the optimal solution corresponding to each scheme; update the velocities and positions of the lower-layer particles;

[0108] Step 4.7: Determine whether the convergence condition of the lower-layer planning model is satisfied. If yes, proceed to the next step; otherwise, return to Step 4.5;

[0109] Step 4.8: According to the lower-layer planning results, calculate the upper-layer carbon emissions. Combine the lower-layer data and execute the objective function of the upper-layer planning model to obtain the upper-layer individual extreme value. Take the upper-layer individual extreme value as the global extreme value and update the velocity and position of the upper-layer particles;

[0110] Step 4.9: Determine whether the convergence condition of the upper-layer planning model is satisfied. If yes, execute Step 4.10; otherwise, return to Step 4.3;

[0111] Step 4.10: Output the lower-layer global extreme value as the optimal planning scheme.

[0112] The beneficial effects of the present invention are as follows.

[0113] The multi-objective expansion planning method for a distribution network considering the access of large-scale electric heat storage equipment of the present invention has the characteristics of high accuracy in heat load modeling and strong uniformity of line load rates after distribution network planning. First, to improve the effectiveness of typical scenarios, heat loads are generated by comprehensively considering building structures, indoor and outdoor heat transfer characteristics, and meteorological factors such as light intensity. At the same time, the influence of wind speed is considered in terms of heat transfer factors, and this method can more accurately realize the modeling of heat loads. Secondly, in the decision-making of the operation strategy of electric boilers with heat storage, the present invention considers the output characteristics of wind and solar power sources at each time period and determines the operation strategy of electric boilers with heat storage with the lowest carbon emissions as the goal. While reducing carbon emissions, a more flexible operation strategy can also effectively shift peaks and fill valleys, reducing the power supply pressure on the distribution network during peak electricity consumption periods. Finally, the present invention conducts multi-objective expansion planning for the distribution network with the goals of economy and load rate uniformity, and uses a nested hybrid particle swarm optimization algorithm for solution. The solution results have the characteristics of low total cost and strong uniformity of line load rates. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 is a diagram of influencing factors of the building heat process for the multi-objective expansion planning of a distribution network considering the access of large-scale electric heat storage equipment of the present invention;

[0115] Figure 2 is a two-layer planning structure diagram for the multi-objective expansion planning of a distribution network considering the access of large-scale electric heat storage equipment of the present invention;

[0116] Figure 3 is a flow chart for solving by a nested hybrid particle swarm optimization algorithm;

[0117] Figure 4 is the initial network structure diagram of the IEEE33 distribution system;

[0118] Figure 5It is the typical scenario data curve graph in the embodiment of the present invention;

[0119] Figure 6 It is the typical daily outdoor temperature curve graph in the embodiment of the present invention;

[0120] Figure 7 It is the typical daily load curve graph with electric heating load in the embodiment of the present invention;

[0121] Figure 8 It is the graph of the heat storage time period and the change of heat storage quantity of three models in the embodiment of the present invention;

[0122] Figure 9 It is the optimized load curve graph of three models in the embodiment of the present invention;

[0123] Figure 10 It is the schematic diagram of the change of the load rate uniformity of three models in the embodiment of the present invention. Detailed implementation manners

[0124] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0125] The multi-objective expansion planning method for taking into account the access of large-scale electric heat storage equipment to the distribution network is specifically implemented according to the following steps:

[0126] Step 1. When modeling the building heat load characteristics, it is necessary to fully consider the influence of outdoor temperature, building structure and indoor-outdoor heat transfer. The influence of wind speed is considered in the analysis of heat transfer characteristics to make the modeling result of the heat load more accurate. Various factors affecting the building heat process, such as Figure 1 , based on the analysis of the influencing factors of the building heat process, the time-varying equation of the internal temperature of the heating building formed by the building envelope structure is:

[0127] (5)

[0128] In the formula, is the demand for electric heating load; is the heat obtained by heat transfer between the interior of the building space and the outside through the wall at time is the heat obtained by heat transfer between the interior and the outside through the window at time is the heat obtained by air exchange in the interior at time is the heat sent into the interior through the heating system at time

[0129] An electric heating load model is established according to the temperature time-varying equation, that is, C in formula (5) a .

[0130] Establish time-varying equations for each part in formula (5):

[0131] (1) Calculate The heat obtained by heat transfer through the wall from the outside to the inside of the building space at time , which is expressed as:

[0132] (1)

[0133] In the formula: is the heating area; is the equivalent wall area per unit heating area; is the heat transfer coefficient between the inner surface of the wall per unit area and the air, which is related to the temperature of the inner surface of the wall; , are respectively the indoor and outdoor temperatures at time

[0134] (2) The heat obtained by heat transfer through the window from the outside to the inside of the room at time, which is expressed as:

[0135] (2)

[0136] In the formula, is the equivalent window area per unit heating area; is the solar radiation heat gain coefficient of the window per unit area; is the glass cooling load coefficient; is the shading coefficient of the glass;

[0137] (3) The heat obtained by air exchange in the room at time , which is expressed as:

[0138] (3)

[0139] In the formula: is the outdoor wind speed; is the comprehensive heat transfer coefficient;

[0140] (4) The heat output of the heating equipment refers to the heat transferred into the room by the heating system. The heating system specifically refers to the direct-heating electric heating equipment and the heat storage electric boiler here; The heat sent into the room by the heating system at time , which is expressed as:

[0141] (4)

[0142] In the formula, is the heat provided by the heat storage electric boiler at time is Heat provided by the instant direct electric heating equipment

[0143] Step 2: Establish a model for the electric heat storage boiler, which includes an electric boiler and a heat storage device; the specific process is as follows:

[0144] The electric boiler is also a coupling unit for energy form conversion, and it relies on the energization of electrical components to achieve the heating purpose. At the same time, the electric boiler does not produce combustion chemical reactions, can achieve zero carbon emissions, and has high heating efficiency and automation level. Establish an output model for the electric boiler, which is expressed as:

[0145] (6)

[0146] In the formula: and are respectively The electricity consumption and heat production of the electric boiler during the is the electro-thermal conversion efficiency of the electric boiler, and its value is generally greater than 95%;

[0147] After the electric boiler is equipped with a heat storage device, it breaks the traditional "electricity determined by heat" operation mode, can effectively shift the peak and fill the valley, makes the electricity consumption of the electric boiler not restricted by the heat load demand, and can flexibly decide the operation strategy of the electric heat storage boiler according to the output of wind and photovoltaic power sources. Establish a mathematical model for the heat storage capacity of the heat storage device, which is expressed as:

[0148] (7)

[0149] In the formula: is The heat storage of the heat storage device during the is the heat dissipation loss rate; 、 are The heat absorption and release power at the 、 are The heat absorption and release efficiency at the

[0150] Step 3: The upper and lower layers of the bilevel programming model respond to each other, and at the same time, information is transmitted between the upper and lower layers. On the premise of meeting the reliability of power grid operation, comprehensively consider the total cost of distribution network planning, load rate uniformity, carbon emissions, etc., and establish a bilevel programming model. The upper-level planning realizes the minimization of carbon emissions by making decisions on the operation strategy of the heat storage electric boiler. On the basis of the operation strategy determined by the upper level, the lower-level planning aims at the total cost of distribution network planning and system load rate uniformity, and conducts a multi-objective expansion planning for the distribution network. The bilevel planning structure is as Figure 2 shown.

[0151] The upper layer combines the output characteristics of wind and photovoltaic power sources, makes decisions on the operation strategy of heat storage electric boilers with the goal of minimizing carbon emissions, and superimposes the impact of the decision results on the load onto the typical daily load curve and transmits it to the lower layer as the basis for the distribution network expansion planning. The upper layer model makes decisions on the operation strategy of heat storage electric boilers in a more flexible way, and while achieving the low-carbon goal, it can also transmit relevant information to the lower layer to improve the uniformity of the distribution system.

[0152] The specific process of establishing the upper layer planning model is as follows:

[0153] Establish the objective function and constraint conditions of the upper layer planning model, specifically:

[0154] The upper layer takes the minimum carbon emissions as the objective function. On the power source side, wind and photovoltaic power sources can achieve zero carbon emissions, and the main source of carbon emissions is thermal power units. Therefore, only the carbon emissions of thermal power units need to be calculated, and the expression is as follows:

[0155] (8)

[0156] In the formula, is the total carbon emissions of the system; is the equipment operation time period, with a value of 24 h ; is the comprehensive carbon emission coefficient of thermal power units, with a value of 0.85 - 0.95 ; is the output of thermal power units during the time period; h is the time interval, with a value of 1

[0157] Combined with the operation requirements of the actual distribution network, the constraints of the upper layer model include:

[0158] 1) Power balance constraint:

[0159] (9)

[0160] (10)

[0161] In the formula, and are the total active and reactive power outputs of node respectively; , are the active and reactive power flowing out of node respectively; , are the active power consumed by the heat storage electric boiler and the heat stored on node respectively; is the set of adjacent nodes of node ; is the voltage phase angle difference between two nodes;

[0162] 2) Node voltage constraint:

[0163] (11)

[0164] In the formula, is the voltage of node ; , are respectively the upper and lower limits of the voltage of node ;

[0165] 3) Branch current constraint:

[0166] (12)

[0167] In the formula, is the current of line ; is the maximum carrying capacity of the line;

[0168] 4) Output constraint of the electric heat storage boiler:

[0169] (13)

[0170] (14)

[0171] (15)

[0172] In formulas (13), (14), and (15), is the heat storage capacity of the heat storage device at the end of period; and are the input and output heat powers at moment; and are respectively the upper and lower limits of the capacity of the heat storage device; , and , are respectively the upper and lower limits of the input and output heat powers;

[0173] 5) Reliability constraint:

[0174] (16)

[0175] In the formula, is the total output of thermal power, wind, and photovoltaic units at moment; is the demand for the electric heat load at moment under extreme meteorological conditions;

[0176] 6) Power output constraint:

[0177] (17)

[0178] (18)

[0179] (19)

[0180] In the formula, 、 、 are respectively the power outputs of the photovoltaic, wind power, and thermal power generation units at time 、 、 、 、 、 are respectively the upper and lower limits of the power outputs of the photovoltaic, wind power, and thermal power generation units at time

[0181] The lower-level planning aims at the total cost of the distribution network planning and the uniformity of the system load rate, and conducts multi-objective expansion planning for the distribution network. The specific process of establishing the lower-level planning model is as follows:

[0182] Establish the objective function and constraint conditions of the lower-level planning model, specifically:

[0183] Establish the objective function of the lower-level planning model with economy and load rate uniformity as the objectives, expressed as:

[0184] 1) Uniformity objective function:

[0185] During the operation of the distribution network, due to the differences in the parameters of various equipment and the distribution network grid during operation, and various random factors affecting each equipment during operation, when the distribution system fluctuates, it will have non-uniform characteristics in space and time. The load rate is the ratio of the actual transmission power of the distribution line to its limit transmission power, and it is reasonable to use it as an index to measure the uniformity of the distribution network. The load rate i of line L i has the following expression:

[0186] (20)

[0187] In the formula: i = 1, 2, 3… M , 、 are respectively the actual transmission power and the maximum transmission power of the distribution line; define the vector as the load rate vector of all lines in the distribution network during a certain period, is the average value, and the unevenness is expressed as follows:

[0188] (21)

[0189] (22)

[0190] (23)

[0191] In the formula: is the variance of the load rate of the distribution network, which characterizes the average distribution of the load rate in the system; is the range of the load rate of the distribution network, which characterizes the worst deviation value of the load rate in the system; and are the weight coefficients of the two, respectively characterizing and the influence degree, and the sum of the two is 1;

[0192] 2) Economic objective function

[0193] In the distribution network planning, the goal is to minimize the annual comprehensive cost of the whole society, which includes the investment cost of the distribution network and the operation cost of the distribution network, and is expressed as:

[0194] (24)

[0195] In the formula: is the investment cost of the distribution network; is the operation cost of the distribution network; the specific calculation methods of each cost are as follows.

[0196] Investment cost of the distribution network:

[0197] In the distribution network planning, according to the construction cost and capacity of each line, the investment cost of the newly built lines of the distribution network is expressed as:

[0198] (25)

[0199] In the formula: is the candidate set of lines; is the cost of newly built lines per unit capacity; is the capacity of a single newly built line; is the 0, 1 variable for line construction. When the line is built, and when the line is not built.

[0200] Operation cost of the distribution network:

[0201] The operation cost needs to be considered during the planning period of the distribution network. The annual operation cost is expressed as a certain proportion of the investment cost of the distribution network, and is specifically expressed as

[0202] (26)

[0203] Wherein: represents the original line set; is the capacity of the th line in the original line set; is the operation and maintenance cost coefficient of the line, which can take values from 2% to 5%.

[0204] The constraint conditions of the lower-level planning model are:

[0205] Distribution network planning investment cost constraint:

[0206] During the entire planning period, it is required that the total construction cost is less than the cost upper limit, that is

[0207] (27)

[0208] Wherein: is the candidate set of lines; is the cost of newly built lines per unit capacity; is the capacity of a single newly built line; is a 0, 1 variable for line construction. When , the line is constructed. When , the line is not constructed. is the maximum cost of distribution network line investment cost;

[0209] In distribution network planning, the upper and lower limits of line transmission capacity are

[0210] (28)

[0211] Wherein: is the actual transmission capacity of line ; , are the upper and lower limits of the transmission capacity of the th line respectively;

[0212] In distribution network planning, the number of newly built lines should not exceed a certain limit, and its constraint is:

[0213] (29)

[0214] Wherein: is the upper limit value of the number of candidate lines;

[0215] Node power balance constraint:

[0216] In the distribution network, the difference between the power injected into the node and the node load demand should be equal to the power consumed on the branch, that is

[0217] (30)

[0218] Wherein: and are respectively the active power of the injection node and the load demand of the node ; is the line susceptance between nodes , ; , are the phase angles between nodes , ; is the set of distribution network nodes, where , ;

[0219] Line power flow constraint:

[0220] It is required that the transmission power on the line between two nodes does not exceed the maximum allowable transmission power of this line, that is

[0221] (31)

[0222] Wherein: is the power upper limit of the line between node and node .

[0223] Step 4. Solve using the nested hybrid particle swarm optimization algorithm. In the model, the operation strategy of the upper-layer heat storage electric boiler is transmitted to the lower layer, and the lower layer transmits the distribution network planning results to the upper layer. After the upper layer updates the parameters, the upper and lower layers are iteratively solved in the next round. The upper and lower layers are iteratively looped to obtain the final operation strategy of the heat storage electric boiler and the distribution network expansion planning results.

[0224] The nested hybrid particle swarm optimization algorithm is used for optimization and solution. The double-layer optimization model has an interactive correlation in the respective optimization processes. The lower-layer distribution network expansion planning is based on the operation strategy of the upper-layer heat storage electric boiler and the decision results of typical scenarios. At the same time, the total operation cost and load rate uniformity obtained by the lower-layer simulation will be returned to the upper layer as part of the upper-layer optimization goal. Through double-layer iterative optimization, the final planning results are improved. The algorithm flow chart is as Figure 3 shown, and the specific process is as follows:

[0225] Step 4.1. Establish a node distribution system model of the distribution network, and input distribution network parameters, initial grid structure, distribution network line selection, and installation and operation costs into the model;

[0226] Step 4.2: Initialize the upper-layer particle population and the number of iterations. Model the typical daily electric and heat load curve according to formula (5), and superimpose it on the typical daily electric load curve to obtain the load curve including electric and heat loads. Perform integer encoding on the ordinate of the load curve including electric and heat loads, and randomly generate the initial upper-layer particle swarm;

[0227] Step 4.3: From the upper-layer objective function and conditional constraints, and based on the output of the original electric heating equipment at each time period, use the particle swarm optimization algorithm to find the output of the electric boiler with heat storage at each time period. Eliminate and update the solutions that do not meet the constraint conditions. Superimpose the electric load demand generated by the heat storage of the electric boiler with heat storage on the load curve including electric and heat loads, and use the superimposed curve as the basic parameter to input into the lower-layer model;

[0228] Step 4.4: Initialize the number of iterations and population of the lower-layer particles. Perform binary encoding on the installation positions of the lines to be built, randomly generate the lower-layer particle velocities and positions, and initialize the lower-layer particle swarm;

[0229] Step 4.5: Expand the lines according to the output scheme of the electric boiler with heat storage determined by the upper layer, and return to Step 4.3;

[0230] Step 4.6: Calculate the construction cost, operation cost, variance of load rate, and range of system load rate. Execute the objective function of the lower-layer planning model. Update the individual extreme values and global extreme values of the decision variables of each line corresponding to each grid structure scheme in the lower layer according to the curve obtained by superimposing in Step 4.3, and use the global extreme value as the optimal solution corresponding to each scheme; Update the velocities and positions of the lower-layer particles;

[0231] Step 4.7: Determine whether the convergence condition of the lower-layer planning model is met. If yes, proceed to the next step; otherwise, return to Step 4.5;

[0232] Step 4.8: According to the lower-layer planning results, calculate the carbon emissions of the upper layer. Combine the lower-layer data and execute the objective function of the upper-layer planning model to obtain the upper-layer individual extreme value. Use the upper-layer individual extreme value as the global extreme value, and update the velocities and positions of the upper-layer particles;

[0233] Step 4.9: Determine whether the convergence condition of the upper-layer planning model is met. If yes, execute Step 4.10; otherwise, return to Step 4.3;

[0234] Step 4.10: Output the lower-layer global extreme value as the optimal planning scheme.

[0235] Embodiment

[0236] The present invention takes the IEEE33 distribution system as an example for simulation verification. The initial network of the IEEE33 distribution system is as Figure 4 :

[0237] The distribution system has 33 nodes, a base voltage of 12.66 kV, 32 lines, a power base value of 10 MV·A, and 32 candidate lines.

[0238] The total capacity of the heat storage electric boiler is 50 MW, and its expected installation locations are nodes 2, 6, 10, 14, and 30 respectively. The load, wind power output, and photovoltaic power output data used are from actual substations, wind farms, and photovoltaic power plants, and the outdoor temperature is from the actual data of a certain area in Northeast China. The typical scenarios in the heating season are selected according to the historical data of load, wind power, photovoltaic power, and outdoor temperature. The data of the typical scenarios are as Figure 5 shown, and the outdoor temperature is as Figure 6 shown.

[0239] Under the given heating building structure characteristic parameters and meteorological conditions, factors such as light intensity and building parameters (specific parameters are shown in Table 1) are substituted into equations (1) to (5) to obtain the heat load demand of the system. The heat load is superimposed on the electrical load, and the result is as Figure 7 .

[0240] Table 1

[0241]

[0242] To prove the effectiveness and rationality of the method proposed in the present invention, considering the economy, carbon emissions, and uniformity of the network topology of the distribution network planning, the model of the present invention is compared and analyzed with various models. Specifically as follows: Model 1, the heat storage electric boiler conducts single-layer multi-objective planning for the distribution network under the traditional two-stage control method; Model 2, conducts two-layer single-objective planning for the distribution network without considering uniformity; Model 3, the two-layer multi-objective planning method proposed in the present invention.

[0243] Figure 8 For the decision results of the operation strategies of the 3 models, the optimization effect after adopting Figure 8 the decision results is as Figure 9 . The carbon emissions under the 3 models are 640.99 t, 420.57 t, and 446.37 t respectively.

[0244] It can be seen from the comparison between Model 1 and Model 3 that: in Model 1, the heat storage period is fixed, all in the low electricity consumption period, while in Model 3, the heat storage period is more flexible. Compared with Model 1, the load curve after optimization in Model 3 is smoother, the peak shaving and valley filling effect is better, and the carbon emissions are reduced by 30.4%. This is because in Model 1, the operation mode of the heat storage electric boiler is the traditional two-stage control method, and a more flexible operation strategy can better play the peak shifting characteristic of the heat storage electric boiler. Moreover, Model 1 does not consider the output characteristics of wind and photovoltaic power sources, and the heat storage electric boiler stores heat during the period when thermal power units account for a large proportion, so the carbon emissions increase.

[0245] From the comparison between Model 2 and Model 3, it can be seen that: Model 2 has fewer heat storage periods, but overall, the heat storage capacity in each period is greater. After optimization, the peak shaving and valley filling effect of Model 3 is slightly better than that of Model 2, but the carbon emissions increase by 5.7%. This is because in Model 3, the lower-level objective function comprehensively considers two objectives, namely economy and load rate uniformity, and has greater restrictions on the operating conditions of the heat storage electric boiler. Model 2 has no load rate uniformity restriction and can store heat more efficiently during periods when the output ratio of wind and photovoltaic power sources is large, so the carbon emissions are less. Although Model 2 is slightly better than Model 3 in terms of total cost and carbon emissions, due to the fact that Model 2 does not consider the impact of load rate uniformity, the system reliability is poor, and the analysis of uniformity will be elaborated below.

[0246] The results of newly built distribution lines for the 3 models are shown in Table 2, and the relevant indicators such as the total planning cost are shown in Table 3. The load rate uniformity indicators of each model are as Figure 10 shown.

[0247] Table 2

[0248]

[0249] Note: m(i−j) in the newly built line represents a line numbered m built between nodes i and j.

[0250] Table 3

[0251]

[0252] From the comparison between Model 1 and Model 3, it can be seen that: The number of newly built lines in Model 3 is 2 less than that in Model 1, and the total cost is reduced by 19.7%. This is because under the two-stage control mode of the heat storage electric boiler in Model 1, the load increases significantly during the heat storage period, and the line carrying capacity is insufficient, resulting in an increase in the number of newly built lines and an increase in the total cost. In terms of uniformity, the load of the heat storage electric boiler installation nodes in Model 1 fluctuates greatly during the heat storage period, and the load rate range increases, so the uniformity of Model 1 is slightly worse.

[0253] From the comparison between Model 2 and Model 3, it can be seen that: The number of newly built lines in Model 3 is 1 more than that in Model 2, and the total cost increases by 10.2%. This is because in Model 3, the lower-level objective function considers the load rate uniformity objective and has higher requirements for the line carrying capacity. In order to maintain the load rate uniformity level, more lines need to be expanded, so the total cost is higher. In terms of uniformity, since Model 2 does not consider the impact of load rate uniformity, the load rate of some distribution lines is close to the threshold, and at this time, the lines are in a heavy load state. If a certain line fails, it is easy to cause large-scale power flow transfer and large-scale cascading failures. However, Model 3 comprehensively considers the network topology structure of the distribution network, making the line load rates of the distribution network more uniform and effectively improving the system operation reliability.

[0254] Through the above method, the multi-objective expansion planning method for the access of large-scale electric heat storage equipment to the distribution network in the present invention has the characteristics of high accuracy in heat load modeling and strong uniformity of line load rates after distribution network planning. First, to improve the effectiveness of typical scenarios, heat loads are generated by comprehensively considering building structures, indoor and outdoor heat transfer characteristics, and meteorological factors such as light intensity. At the same time, the influence of wind speed is considered in terms of heat transfer factors, and this method can more accurately realize the modeling of heat loads. Secondly, in terms of the decision-making of the operation strategy of the electric heat storage boiler, the present invention considers the output characteristics of wind and solar power sources at each time period, and determines the operation strategy of the electric heat storage boiler with the lowest carbon emission as the goal. While reducing carbon emissions, the more flexible operation strategy can also effectively shift peaks and fill valleys, reducing the power supply pressure on the distribution network during peak electricity consumption periods. Finally, the present invention conducts multi-objective expansion planning for the distribution network with the goals of economy and load rate uniformity, and uses a nested hybrid particle swarm optimization algorithm for solution. The solution results have the characteristics of low total cost and strong uniformity of line load rates.

Claims

1. A multi-objective expansion planning method for distribution networks considering the access of large-scale electric heat storage equipment, characterized in that, The implementation is carried out according to the following steps: Step 1: Combine the wind speed in the analysis of heat transfer characteristics to establish a time-varying equation of the internal temperature of a heating building formed by the building envelope structure; Step 2: Establish a model of the electric boiler with heat storage; Step 3: Establish a two-layer multi-objective planning model for the distribution network; Step 4: Solve it with a nested hybrid particle swarm optimization algorithm; The specific process of Step 1 is as follows: Calculation The heat obtained by heat transfer through the wall inside the building space at a certain moment from the outside , expressed as: （1） In the formula: is the heating area; is the equivalent wall area per unit heating area; is the heat transfer coefficient between the inner surface of the wall per unit area and the air, which is related to the temperature of the inner surface of the wall; and are respectively the indoor and outdoor temperatures at time The heat obtained by heat transfer between the indoor and outdoor through the window at a certain moment is expressed as: （2） Wherein, is the equivalent window area per unit heating area; is the solar heat gain coefficient of the window per unit area; is the glass cooling load coefficient; is the shading coefficient of the glass; Indoor heat gain through air exchange at a certain moment , expressed as: （3） In the formula: is the outdoor wind speed; is the comprehensive heat transfer coefficient; The heat sent into the room through the heating system at a certain moment , expressed as: （4） Wherein, is the heat provided by the heat storage electric boiler at time is the heat provided by the direct electric heating equipment at time The time-varying equation of the internal temperature of a heating building formed by the building envelope structure is: （5） In the formula, is the demand for electric heating load; Establish an electric heating load model according to the temperature time-varying equation, which is C in formula (5). a ; The two-layer multi-objective planning model for the distribution network described in Step 3 includes an upper-layer planning model and a lower-layer planning model; The specific meaning of the two-layer multi-objective planning for the distribution network is: The upper-layer planning realizes the minimization of carbon emissions through the decision-making of the operation strategy of the electric boiler with heat storage; The lower-layer planning conducts a multi-objective expansion planning for the distribution network with the total cost of the distribution network planning and the uniformity of the system load rate as the objectives; The specific process of establishing the upper-layer planning model in Step 3 is as follows: Establish the objective function and constraint conditions of the upper-layer planning model, specifically: The upper-layer planning model establishes an objective function with the minimum carbon emissions as the goal, expressed as: （8） In the formula, is the total carbon emissions of the system; is the operating time period of the equipment; is the comprehensive carbon emission coefficient of the thermal power unit; is the thermal power unit output during the period; is the time interval; The constraint conditions of the upper-layer planning model are expressed as: Power balance constraint: （9） （10） Wherein, and are respectively the total active and reactive power outputs of node ; , are respectively the active and reactive power flowing out of node ; , are respectively the active power consumed by the thermoelectric storage boiler and the stored heat at node ; is the set of adjacent nodes of node ; is the voltage phase angle difference between two nodes; Node voltage constraint: （11） wherein, is the node voltage; , are respectively the upper and lower limits of the node voltages; Branch current constraint: （12） Wherein, is the line current; is the maximum current-carrying capacity of the line; Output constraint of the electric boiler with heat storage: （13） （14） （15） In formulas (13), (14), and (15), is the heat storage capacity of the heat storage device at the end of time period; and are the input and output heat powers at moment; and are respectively the upper and lower limits of the capacity of the heat storage device; , and , are respectively the upper and lower limits of the input and output heat powers; Reliability constraint: （16） Wherein, is the total output of thermal power, wind, and photovoltaic units at time under extreme meteorological conditions the demand for electric and heat loads at time Power output constraint of the power source: （17） （18） （19） Wherein, , , are respectively the output powers of the photovoltaic, wind power, and thermal power generation units at the moment; , , , , , are respectively the upper and lower limits of the output powers of the photovoltaic, wind power, and thermal power generation units at the moment.

2. The multi-objective expansion planning method for considering the access of large-scale electric heat storage equipment to the distribution network according to claim 1, wherein, The electric boiler with heat storage described in Step 2 includes an electric boiler and a heat storage device. The specific process of Step 2 is as follows: Establish an output model for the electric boiler, expressed as: （6） Where: and are respectively the electricity consumption and heat output of the time-of-use electric boiler; is the electro-thermal conversion efficiency of the electric boiler; Establish a mathematical model of the heat storage capacity for the heat storage device, expressed as: （7） In the formula: is the heat storage amount of the time-period heat storage device; is the heat dissipation loss rate; , is the heat absorption and release power at time , is the heat absorption and release efficiency at time 3. The multi-objective expansion planning method for considering the access of large-scale electric heat storage equipment to the distribution network according to claim 1, wherein, The specific process of establishing the lower-layer planning model in Step 3 is as follows: Establish the objective function and constraint conditions of the lower-layer planning model, specifically: Establish the objective function of the lower-layer planning model with economy and load rate uniformity as the goals, expressed as: 1) Uniformity objective function: The load rate is the ratio of the actual transmission power of the distribution line to its limit transmission power, and it is used as an index to measure the uniformity of the distribution network. The load rate i of the line L i is expressed as follows: （20） Wherein: i = 1, 2, 3… M , and are the actual transmission power and the maximum transmission power of the distribution line respectively; define the vector as the load rate vector of all lines in the distribution network during a certain period, is average value, and the unevenness is expressed as follows: （21） （22） （23） Wherein: is the variance of the distribution network load rate, characterizing the average distribution of the load rate in the system; is the range of the distribution network load rate, characterizing the worst deviation value of the load rate in the system; and are the weight coefficients of the two, respectively characterizing and the influence degrees of, and the sum of the two is 1; 2) Economic objective function In the distribution network planning, with the minimum annual comprehensive cost of the whole society as the goal, it includes the investment cost of the distribution network and the operation cost of the distribution network, expressed as: （24） Wherein: is the investment cost of the distribution network; is the operation cost of the distribution network; The constraint conditions of the lower-layer planning model are: Investment cost constraint of the distribution network planning: It is required that the total construction cost is less than the cost upper limit during the entire planning period, that is （27） Wherein: is the candidate set of lines; is the cost of a newly built line per unit capacity; is the capacity of a single newly built line; is a 0, 1 variable for line construction. When , the line is constructed. When , the line is not constructed. is the maximum cost of the investment cost of the distribution network line; In the distribution network planning, the upper and lower limits of the line transmission capacity are （28） In the formula: is the actual transmission capacity of the line ; , are respectively the upper and lower limits of the transmission capacity of the th line; In the distribution network planning, the number of newly built lines should not exceed a certain limit, and its constraint is: （29） Wherein: is the upper limit value of the number of candidate lines; Node power balance constraint: The difference between the power injected into the node in the distribution network and the node load demand should be equal to the power consumed on the branch, that is （30） Wherein: and are respectively the active power of the injection node and the load demand of the node ; is the line susceptance between nodes and ; and are the phase angles between nodes and ; is the set of distribution network nodes, where and ; Line power flow constraint: It is required that the transmission power on the line between two nodes does not exceed the maximum allowable transmission power of this line, that is （31） Wherein: is the node is the sum node is the power upper limit of the line between them.

4. The multi-objective expansion planning method for considering the access of large-scale electric heat storage equipment to the distribution network according to claim 1, characterized in that The specific process of Step 4 is as follows: Step 4.1: Establish a node distribution system model of the distribution network, and input the distribution network parameters, initial grid structure, distribution network line selection, and installation and operation costs into the model; Step 4.2: Initialize the upper-layer particle population and the number of iterations. According to formula (5), model the typical daily electric and heat load curve, superimpose it on the typical daily electric load curve to obtain the load curve including electric and heat loads, perform integer coding on the ordinate of the load curve including electric and heat loads, and randomly generate the upper-layer initial particle swarm; Step 4.3: Based on the upper-layer objective function and conditional constraints, and the power outputs of the original electric heating equipment at each time period, the power outputs of the heat storage electric boiler at each time period are obtained through particle swarm optimization. The solutions that do not meet the constraint conditions are eliminated and updated. The electrical load demand generated by the heat storage of the heat storage electric boiler is superimposed on the load curve containing the electric heating load, and the curve obtained after superposition is used as the basic parameter and input into the lower-layer model; Step 4.4: Initialize the iteration times and population of the lower-layer particles, perform binary encoding on the installation positions of the to-be-built lines, randomly generate the velocities and positions of the lower-layer particles, and initialize the lower-layer particle swarm; Step 4.5: Expand the lines according to the power output schemes of the heat storage electric boiler determined in the upper layer, and return to Step 4.3; Step 4.6: Calculate the construction cost, operation cost, variance of the load rate, and range of the system load rate, execute the objective function of the lower-layer planning model, update the individual extreme values and the overall extreme values of the decision variables of each line corresponding to each grid structure scheme in the lower layer according to the curve obtained after superposition in Step 4.3, and use the overall extreme value as the optimal solution corresponding to each scheme; update the velocities and positions of the lower-layer particles; Step 4.7: Judge whether the convergence condition of the lower-layer planning model is met. If yes, proceed to the next step; otherwise, return to Step 4.5; Step 4.8: According to the lower-layer planning results, calculate the carbon emissions in the upper layer, combine the lower-layer data, execute the objective function of the upper-layer planning model, obtain the upper-layer individual extreme value, use the upper-layer individual extreme value as the global extreme value, and update the velocities and positions of the upper-layer particles; Step 4.9: Judge whether the convergence condition of the upper-layer planning model is met. If yes, execute Step 4.10; otherwise, return to Step 4.3; Step 4.10: Output the lower-layer global extreme value as the optimal planning scheme.

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