CN112531788B - Transparent micro-grid group planning method considering multiple uncertainties and self-optimization-approaching operation - Google Patents

Transparent micro-grid group planning method considering multiple uncertainties and self-optimization-approaching operation Download PDF

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CN112531788B
CN112531788B CN202011500781.2A CN202011500781A CN112531788B CN 112531788 B CN112531788 B CN 112531788B CN 202011500781 A CN202011500781 A CN 202011500781A CN 112531788 B CN112531788 B CN 112531788B
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microgrid
load
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CN112531788A (en
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赵家悦
郭创新
陈晓刚
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Zhejiang University ZJU
State Grid Zhejiang Electric Power Co Ltd
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State Grid Zhejiang Electric Power Co Ltd
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    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
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    • GPHYSICS
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    • G06Q10/063Operations research, analysis or management
    • G06Q10/0631Resource planning, allocation, distributing or scheduling for enterprises or organisations
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Abstract

The invention discloses a transparent microgrid cluster planning method considering multiple uncertainties and self-optimization-seeking operation, which comprises the steps of firstly, carrying out microgrid cluster source-storage-load modeling by considering multiple uncertainties, wherein the microgrid cluster source-storage-load modeling comprises a distributed power supply, an energy storage unit, an active load and the like; then establishing a self-optimizing single transparent microgrid planning model; and establishing a self-optimizing transparent micro-grid group double-layer optimization planning model, and finally solving to obtain an optimal planning scheme. The planning method is applied to the planning layer of the transparent microgrid group, so that multi-energy complementation can be realized, planning optimization of the microgrid group is guaranteed to be completed on the basis that a single microgrid tends to be optimal, and a cooperative win-win situation is achieved. On the basis of ensuring the economy, the environmental protection, the reliability and the flexibility of the system are effectively improved; and multiple uncertainties are taken into consideration, so that the utilization rate of renewable energy sources and the system initiative are improved.

Description

Transparent micro-grid group planning method considering multiple uncertainties and self-optimization-seeking operation
Technical Field
The invention belongs to the technical field of electrical information, and particularly relates to a transparent micro-grid group planning method considering multiple uncertainties and self-optimization-approaching operation.
Background
The traditional power grid faces three problems of high energy consumption, high pollution and high cost, the renewable energy power generation technology with low energy consumption and low pollution solves the difficulty of the traditional power grid to a certain extent, but the volatility and the randomness of the renewable energy power generation technology bring challenges to the safe and stable operation of the power grid. In order to solve the contradiction between the distributed power generation technology and the stable operation of the power grid, the micro-grid technology is developed. The modern information technology is combined with the microgrid to form a transparent microgrid, so that social parties can participate in various links such as power production, transmission, consumption and the like, and the safe, efficient, green and low-carbon development of energy and power is promoted in a synergetic manner. The single transparent micro-grid comprises a distributed power supply, an energy storage and a load, and the combined supply of cold, heat, electricity and gas is realized; the device can be operated independently, and realizes automatic control, self-protection and self-care; the micro-grid can also be connected with other micro-grids according to a certain topological structure to form a transparent micro-grid group. The distributed power generation in the transparent micro-grid group can realize safe power supply, energy conservation and emission reduction, and can provide high-quality and reliable power for loads by matching with an energy storage technology, so that the power failure economic loss of important loads can be reduced.
At present, optimization planning of the transparent micro-grid group is mostly concentrated on the aspect of a single micro-grid system, multi-objective optimization is carried out by considering system economy, renewable energy permeability and carbon emission level, and research on optimal planning of the transparent micro-grid group is lacked. In addition, as the permeability of new energy increases and a great deal of active load and energy storage is invested, the complexity of source-storage-load coupling is greatly increased, and more obvious uncertainty is presented. Therefore, transparent microgrid group planning should pay attention to matching source-storage-load uncertainty and describing the initiative of the microgrid group, seek overall optimization while considering different benefit requirements of all parties, balance global and local optimization, and research a transparent microgrid group planning method considering multiple uncertainties and self-optimization operation.
Disclosure of Invention
The invention aims to provide a transparent microgrid group planning method considering multiple uncertainties and self-optimization operation aiming at the defects of the prior art.
The purpose of the invention is realized by the following technical scheme: a transparent microgrid group planning method considering multiple uncertainties and self-optimization-seeking operation is disclosed, wherein a transparent microgrid group comprises a plurality of transparent microgrids which are connected through connecting lines; the single transparent microgrid comprises distributed power supplies, energy storage units and active loads, and the method comprises the following steps:
step 1, modeling the internal structure of the transparent microgrid, wherein the internal structure comprises distributed power supplies such as wind power and photovoltaic power supplies, an energy storage unit and active loads such as a reducible load and a transferable load.
And 2, modeling a typical planning scene of the single transparent microgrid by considering multiple uncertainties according to the source-storage-load modeling in the step 1, and establishing a lower-layer objective function and constraint conditions.
Step 3, establishing a transparent micro-grid group typical planning model based on self-optimization-trending operation, and establishing an upper-layer objective function and constraint conditions;
and 4, decoupling the double-layer optimization model constructed in the steps 2 and 3, adding the cost variation of the sub-micro-grid, which is changed due to the network loss variation, into an upper-layer optimization target, and finally solving to obtain an optimal planning scheme.
Further, in step 1, the source-storage-load modeling of the internal structure of the transparent microgrid is as follows:
P i (t)=P i pre (t)+ΔP i (t)
ΔP i (t)=ΔP i,max α-ΔP i,max (1-α)
Figure BDA0002843548260000021
Figure BDA0002843548260000022
Figure BDA0002843548260000023
Figure BDA0002843548260000024
wherein, P i (t) represents the i-node renewable energy actual output at the time t, P i pre (t) represents the predicted value of i-node renewable energy output at t moment, delta P i And (t) represents the renewable energy output prediction deviation of the i node at the time t. Delta P i,max Expressing the maximum value of the predicted deviation of the i-node renewable energy output, and expressing the deviation coefficient by alpha so that delta P i (t) has a value in the range [ - Δ P i,max ,ΔP i,max ]Between, P i (t) has a value in the range of [ P ] i pre (t)-ΔP i,max ,P i pre (t)+ΔP i,max ]In the meantime. P is ES,i (t) the energy storage active power of a node i at the moment t is represented, the charging state is represented when the positive power is taken, and the discharging state is represented when the negative power is taken; a is dis,i And b dis,i Representing a state relation coefficient of the energy storage battery in a charging state; a is ch,i And b ch,i And the state relation coefficient of the energy storage battery in a discharging state is shown. P cut,i (t)、P mov,i (t) the reducible load and the transferable load active power of the inode at the time t are respectively;
Figure BDA0002843548260000025
load reducible and transferable load predicted values of the i node at the time t are respectively; delta P cut,i (t)、ΔP mov,i (t) load reducible and transferable load prediction error correction values of the i node at the time t respectively; c (t) is a predicted value of the electricity price at the moment t; c cut To reduce electricity prices; c mov Is transferable electricity price. Correction of Δ P by introducing a deviation factor β cut,i (t)、ΔP mov,i The method of (t) is the same as in the previous section and is not described herein again.
Figure BDA0002843548260000026
The maximum value of the forecast deviation of the reducible load and the transferable load of the inode at the time t is shown.
Further, in step 2, the lower layer objective function in the typical planning method for the single transparent microgrid is as follows:
min f=C inv +C mat +C opr +C rel
Figure BDA0002843548260000027
Figure BDA0002843548260000031
Figure BDA0002843548260000032
Figure BDA0002843548260000033
wherein, λ represents the discount rate, the variable x to be solved y,ig,θ ,x y,j ,x y,k And x es.l Whether a line ig of the type theta, a fan unit j, a photovoltaic unit k and an energy storage unit l are built in the y year is described respectively, and when 1 is taken, the building is represented, and when 0 is taken, the non-building is represented. X y,ig,θ ,X y,i,θ ,X y,j ,X y,k And X es.l Whether the line ig, the fan unit j, the photovoltaic unit k and the stored energy l of the type theta in the y year exist or not is respectively described, and the existence is represented when the line ig, the fan unit j, the photovoltaic unit k and the stored energy l are taken as 1, and the nonexistence is represented when the line ig, the fan unit j, the photovoltaic unit k and the stored energy l are taken as 0.
Figure BDA0002843548260000034
Respectively represents the unit construction cost of the line, the photovoltaic unit, the wind turbine unit and the energy storage unit,
Figure BDA0002843548260000035
respectively representing the unit maintenance costs of the line, the photovoltaic unit, the wind turbine and the stored energy, C loss The cost of the loss of the network is represented,
Figure BDA0002843548260000036
and
Figure BDA0002843548260000037
a penalty factor, L, representing reducible and transferable loads, respectively ig Denotes the length, s, of the line ig w,j Denotes the capacity, s, of fan j pv,k Denotes the capacity, s, of the photovoltaic k es,l Representing the storage capacity, P, of the stored energy l ysh,ig 、Q ysh,ig Respectively representing active power and reactive power of power flow flowing through the power distribution network line ig in the s-quarter h period of the y year; r is ig Represents the resistance of line ig;
Figure BDA0002843548260000038
representing the real power that node i can interrupt the load during the h-th time period of the s-th quarter of the y-th year,
Figure BDA0002843548260000039
representing the real power representing the transferable load of node i during the h-th time period of the s-th quarter of the y-th year; u represents the node voltage.
Further, in step 2, the lower layer constraint conditions in the typical planning method for a single transparent microgrid include: state variable constraints, radial constraints, node power balance constraints, capacity constraints, reliability constraints, and energy storage constraints.
The state variable constraints include:
Figure BDA00028435482600000310
X y-1,i,θ ≤X y,i,θ
wherein omega type Representing the set of models to be built for all lines.
One line can be constructed by selecting only one type, and cannot be changed within the planning years; the equipment is changed once the commissioning state is changed and is not dismantled within the planning years.
The radial constraint comprises:
z ysh,ig ≥0
Figure BDA00028435482600000311
in the formula, z ysh,ig Represents the current direction, z, of the line ig during the ith quarter of the y year ysh,gi Representing the trend direction of the line gi in the ith quarter of the y year; Ωel representing the collection of all lines inside the transparent microgrid.
The node power balancing constraints include:
for any time, the input and output power of the node should satisfy the following conditions:
Figure BDA0002843548260000041
Figure BDA0002843548260000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002843548260000043
the method comprises the steps of (1) collecting nodes of the micro power grid; p ysh,ig And P ysh,ki Respectively representing the active power flows of the distribution lines ig and ki in the ith quarter of the y year; q ysh,ig And Q ysh,ki Respectively representing the reactive power flow of the distribution lines ig and ki in the ith quarter of the y year;
Figure BDA0002843548260000044
representing the output power of the distributed energy source at the node i in the h-th time period of the s-th quarter of the y year;
Figure BDA0002843548260000045
indicating that node i may interrupt the reactive power of the load during the h-th time period of the s-th quarter of the y-th year,
Figure BDA0002843548260000046
representing the reactive power of the transferable load of the node i in the h-th time period of the s-th quarter of the y-th year; l is a radical of an alcohol ysh,i And
Figure BDA0002843548260000047
respectively representing the active and reactive loads of node i during the h-th time of the s-th quarter of the y-th year.
The line capacity constraints are specifically:
Figure BDA0002843548260000048
Figure BDA0002843548260000049
in the formula (I), the compound is shown in the specification,
Figure BDA00028435482600000410
and
Figure BDA00028435482600000411
respectively representing the upper limit values of the active power and the reactive power of the power flow of the line ig.
The renewable energy capacity constraint is specifically as follows:
Figure BDA00028435482600000412
Figure BDA00028435482600000413
Figure BDA00028435482600000414
Figure BDA00028435482600000415
in the formula (I), the compound is shown in the specification,
Figure BDA00028435482600000416
represents the upper limit of the installation capacity of the fan j;
Figure BDA00028435482600000417
represents an upper limit of the installation capacity of the photovoltaic k;
Figure BDA00028435482600000418
representing the upper limit of the output power of the fan j;
Figure BDA00028435482600000419
representing the lower limit of the output power of the fan j;
Figure BDA00028435482600000420
represents the upper limit of the output power of the photovoltaic k;
Figure BDA00028435482600000421
represents the lower output power limit of the photovoltaic k.
The reliability constraints include:
the requirements are satisfied that the load shedding amount and the load transferring amount do not exceed a prescribed maximum value, for
Figure BDA00028435482600000422
Figure BDA00028435482600000423
Figure BDA00028435482600000424
In the formula (I), the compound is shown in the specification,
Figure BDA00028435482600000425
and
Figure BDA00028435482600000426
respectively, the allowable load shedding and the maximum transfer amount of the node i in the h-th period of the s-th quarter of the y-th year.
Figure BDA00028435482600000427
In the formula (I), the compound is shown in the specification,
Figure BDA0002843548260000051
and
Figure BDA0002843548260000052
the average load transfer duration and the maximum allowed load transfer duration of the node i in the s-th quarter of the y-th year are respectively.
The energy storage constraint includes:
Figure BDA0002843548260000053
SOC l,min ≤SOC l,ysh ≤SOC l,max
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002843548260000054
represents the upper limit of the installation capacity of the stored energy l; SOC l,min Represents the lower state of charge (SOC) limit of the stored energy (l); SOC l,max Represents the SOC upper limit of the stored energy l.
Further, in step 3, the upper-layer objective function in the transparent microgrid group planning method is specifically as follows:
min f=C inv '+C mat '+C opr '+C C
Figure BDA0002843548260000055
Figure BDA0002843548260000056
Figure BDA0002843548260000057
Figure BDA0002843548260000058
in the formula, the variable x to be solved y,IJ,θ Described is whether or not a tie IJ of type θ is constructed in the y-th year, which represents construction when 1 is taken and represents non-construction when 0 is taken. X y,IJ,θ Whether a connecting line IJ of type θ exists in year y is described, and it represents existence when 1 is taken and represents nonexistence when 0 is taken.
Figure BDA0002843548260000059
Presentation classThe unit construction cost of the type theta tie IJ,
Figure BDA00028435482600000510
unit maintenance cost, C, of a tie IJ of type θ loss ' represents a loss cost, C co2 Represents the carbon emission cost, δ represents the carbon emission factor, L IJ The length of the tie line IJ is shown,
Figure BDA00028435482600000511
and
Figure BDA00028435482600000512
respectively representing the amount of electricity purchased and sold from an upper level grid during the period of s quarter h of the y year, P ysh,IJ And Q ysh,IJ Respectively representing the active and reactive power, r, of the IJ power flow of the tie line in the s-th quarter h period of the y year IJ Representing the resistance of the tie line IJ and U' the node voltage.
Further, the upper-layer constraint conditions in the transparent microgrid group planning method comprise state variable constraints, node power balance constraints and capacity constraints.
The node power balancing constraints include:
for any time, the input and output power of the node should satisfy the following conditions:
Figure BDA00028435482600000513
Figure BDA00028435482600000514
in the formula, P ysh,IJ And P ysh,KI Respectively representing the active power of the power flow flowing through the connecting lines IJ and KI in the ith quarter of the y year; q ysh,IJ And Q ysh,KI Respectively representing the reactive power of the power flow flowing through the connecting lines IJ and KI in the ith quarter of the y year;
Figure BDA00028435482600000515
and
Figure BDA0002843548260000061
respectively representing the active electric quantity purchased and sold by the sub-microgrid I from an upper-level power grid in the time period of s quarter h in the y year,
Figure BDA0002843548260000062
and
Figure BDA0002843548260000063
respectively representing the reactive power purchased and sold by the sub-microgrid I from the upper-level power grid in the time period of s quarter h of the y year.
The capacity constraint includes:
the tie line capacity constraint is specifically:
Figure BDA0002843548260000064
Figure BDA0002843548260000065
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002843548260000066
representing the active power of the electricity delivered by the other piconets to the piconet I,
Figure BDA0002843548260000067
the maximum value of the active power of the electric quantity transmitted to the sub-microgrid I by other sub-microgrids is represented;
Figure BDA0002843548260000068
the active power of the electric quantity transmitted to other sub-micro grids by the sub-micro grid I is represented,
Figure BDA0002843548260000069
and the maximum value of the active power of the electric quantity transmitted to other sub-micro grids by the sub-micro grid I is represented.
The upper-level purchased electricity quantity capacity constraint is as follows:
Figure BDA00028435482600000610
Figure BDA00028435482600000611
wherein the content of the first and second substances,
Figure BDA00028435482600000612
the maximum value of the active electric quantity purchased by the sub-microgrid I from the upper-level power grid is represented,
Figure BDA00028435482600000613
and the maximum value of the active electric quantity sold by the sub-microgrid I to the upper-level power grid is represented.
Further, in step 4, a double-layer optimization decoupling method is adopted, the cost variation of the sub-microgrid due to the change of the network loss is added into an upper-layer optimization target, and the updated upper-layer target function formula is as follows:
min f=C inv '+C mat '+C opr '+C C +ΔC
ΔC=C opr1 -C opr0
wherein, C opr1 Sum of network loss values, C, after a single microgrid has been connected to a network group opr0 The sum of the network loss values of the single microgrid during independent operation is obtained.
Further, in the step 4, a double-layer optimization decoupling method is adopted, the upper-layer optimization problem is solved based on the NSGA-II multi-target genetic algorithm, the lower-layer optimization problem is solved based on the robust optimization method, an optimal planning scheme is generated, and the feasibility of the optimal planning scheme is verified.
The invention has the beneficial effects that: the method comprises the steps of establishing a source-storage-load and transparent microgrid cluster grid frame uncertainty model, wherein the model comprises wind-light output, interruptible load, transferable load and energy storage unit modeling considering uncertainty; establishing a single transparent microgrid model based on self-optimization-seeking operation, and taking investment cost, maintenance cost, environmental cost and reliability cost as objective functions as lower-layer objective functions; establishing a transparent micro-grid group model based on self-optimization-approaching operation, and performing multi-objective planning by taking new investment cost, maintenance cost, operation cost and carbon emission cost as objective functions as upper-layer objective functions; has the following characteristics:
(1) The invention adopts a transparent micro-grid group planning method considering self-optimization-drive operation, establishes a double-layer optimization model based on self-optimization-drive operation, performs multi-objective planning, and effectively solves the contradiction between the distributed power generation technology and the stable operation of a power grid.
(2) The invention adopts a transparent microgrid group planning method considering multiple uncertainties, and performs uncertainty modeling on a distributed power supply and an active load, so that the initiative and the flexibility of a system and the utilization rate of renewable energy are improved.
Drawings
FIG. 1 is a diagram of a typical planning model of a single transparent microgrid according to the present invention;
fig. 2 is a diagram of a typical planning model of a transparent microgrid group according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limitations of the present invention.
The invention relates to a transparent micro-grid group planning method considering multiple uncertainties and self-optimization-seeking operation, which comprises the following parts:
part one is as follows: establishing a microgrid group source-storage-load model:
in order to meet the economic, reliability and safety requirements of the system, multiple uncertainties are considered for modeling the microgrid group source-storage-load. The internal structure of the transparent microgrid is modeled, and the transparent microgrid comprises distributed power supplies such as wind power and photovoltaic power, an energy storage unit and active loads such as loads which can be reduced and loads which can be transferred.
1.1 Power supply side
Distributed generation output has obvious influence on the operation control and planning of the micro-grid, is easily influenced by factors such as environment, weather and the like, and has strong randomness and volatility. Therefore, when the predicted value of the output is known, uncertainty correction is performed on the predicted value:
P i (t)=P i pre (t)+ΔP i (t)
ΔP i (t)=ΔP i,max α-ΔP i,max (1-α)
in the formula, P i (t) represents the i-node renewable energy actual output at the time t, P i pre (t) represents the predicted value of i-node renewable energy output at t moment, delta P i And (t) represents the renewable energy output prediction deviation of the i node at the time t. Delta P i,max Expressing the maximum value of the predicted deviation of the i-node renewable energy output, and expressing the deviation coefficient by alpha, so that delta P i (t) has a value in the range [ - Δ P i,max ,ΔP i,max ]Between, P i (t) has a value in the range of [ P ] i pre (t)-ΔP i,max ,P i pre (t)+ΔP i,max ]In the meantime.
1.2 side of energy storage
Remember phi ES Is a set of energy storage nodes. Knowing the real-time electricity price prediction value C (t), the stored energy can be modeled as:
Figure BDA0002843548260000071
in the formula, P ES,i (t) the energy storage active power of a node i at the moment t is shown, the charging state is shown when the positive power is taken, and the discharging state is shown when the negative power is taken; a is dis,i And b dis,i Representing the state relation coefficient of the energy storage battery in a charging state; a is ch,i And b ch,i And the state relation coefficient of the energy storage battery in a discharging state is shown.
1.3 load side
And the demand response load is considered in the planning, so that the system economy, reliability and safety are improved. Record omega cut To reduce the set of load nodes, Ω mov For a transferable load node set, knowing the time of use price data and the load forecast value, the reducible load and the transferable load can be described as:
Figure BDA0002843548260000081
Figure BDA0002843548260000082
Figure BDA0002843548260000083
in the formula, P cut,i (t)、P mov,i (t) reducible load and transferable load active power of inode at time t, respectively;
Figure BDA0002843548260000084
load reducible and load transferable predicted values of the i node at the time t are respectively; delta P cut,i (t)、ΔP mov,i (t) load reducible and transferable load prediction error correction values of the i node at the time t respectively; c (t) is a predicted value of the electricity price at the moment t; c cut To reduce electricity prices; c mov Is transferable electricity price. Correction of Δ P by introducing a deviation factor β cut,i (t)、ΔP mov,i The method of (t) is the same as in the previous section, and is not described herein again.
Figure BDA0002843548260000085
The maximum value of the forecast deviation of the reducible load and the transferable load of the inode at the time t is shown.
And part two: establishing a single transparent microgrid planning model:
a typical planning model of a single transparent microgrid can be described by using fig. 1, wherein a power supply side comprises internal wind power and photovoltaic output, and meanwhile, the outside can receive electric quantity transmitted by other transparent microgrids and electric quantity purchased to an upper-level power grid; the energy storage side comprises an energy storage battery; the load side comprises common loads which can reduce loads, can transfer loads and do not participate in active dispatching, and meanwhile, the load side transmits electric quantity to other micro-grids and sells the electric quantity to the upper-level grids. And modeling a typical planning scene of the single transparent microgrid by considering multiple uncertainties, and establishing a lower-layer objective function and constraint conditions.
(1) Lower layer objective function
From the economic perspective, the objective function for constructing the single transparent microgrid plan can be described as:
min f=C inv +C mat +C opr +C rel
wherein the indexes are respectively construction cost C inv Maintenance cost C mat And running cost C opr And a reliability cost C rel Can be further described as:
Figure BDA0002843548260000086
Figure BDA0002843548260000087
Figure BDA0002843548260000091
Figure BDA0002843548260000092
in the formula, λ represents the discount rate, the variable x to be solved y,ig,θ ,x y,j ,x y,k And x es.l Whether a line ig of the type theta, a fan unit j, a photovoltaic unit k and an energy storage unit l are built in the y year is described respectively, and when 1 is taken, the building is represented, and when 0 is taken, the non-building is represented. X y,ig,θ ,X y,i,θ ,X y,j ,X y,k And X es.l Lines of type theta in year y are described separately ig And whether the fan unit j, the photovoltaic unit k and the energy storage l exist or not is judged, the existence is shown when the 1 is taken, and the nonexistence is shown when the 0 is taken.
Figure BDA0002843548260000093
Respectively representing line, photovoltaicUnit construction costs of the generator set, the wind turbine set and the energy storage,
Figure BDA0002843548260000094
respectively represents the unit maintenance cost of the line, the photovoltaic unit, the wind turbine unit and the stored energy, C loss The cost of the loss of the network is represented,
Figure BDA0002843548260000095
and
Figure BDA0002843548260000096
a penalty factor, L, representing reducible and transferable loads, respectively ig Denotes the length, s, of the line ig w,j Denotes the capacity, s, of fan j pv,k Denotes the capacity, s, of the photovoltaic k es,l Representing the storage capacity, P, of the stored energy l ysh,ig 、Q ysh,ig Respectively representing active power and reactive power of power flow flowing through the power distribution network line ig in the s-quarter h period of the y year; r is ig Represents the resistance of line ig;
Figure BDA0002843548260000097
representing the real power that node i can interrupt the load during the h-th time period of the s-th quarter of the y-th year,
Figure BDA0002843548260000098
representing the real power representing the transferable load of node i during the h-th time period of the s-th quarter of the y-th year; u represents the microgrid internal node voltage.
(2) Lower layer constraint
The constraint conditions of the single transparent microgrid planning model comprise:
(1) constraint of state variable
One line can be constructed by selecting only one type, and cannot be changed within the planning years; the equipment is changed once the commissioning state is changed, and is not dismantled within the planning years:
Figure BDA0002843548260000099
X y-1,i,θ ≤X y,i,θ
wherein omega type Representing the set of models to be built for all lines.
(2) Radial constraint
The reliability level of the distributed power supply and the energy storage unit in the microgrid is obviously improved by connecting the distributed power supply and the energy storage unit, and the reliability is not required to be improved through an annular grid frame, so that a radial structure is adopted. In order to meet the requirement of radial operation of the distribution network, the following constraints need to be met:
z ysh,ig ≥0
Figure BDA0002843548260000101
in the formula, z ysh,ig Represents the current direction, z, of the line ig during the ith quarter of the y year ysh,gi Representing the trend direction of the line gi in the ith quarter of the y year; omega el Representing the collection of all lines inside the transparent microgrid.
(3) Node power balance constraints
For any time, the input and output power of the node should satisfy the following conditions:
Figure BDA0002843548260000102
Figure BDA0002843548260000103
in the formula (I), the compound is shown in the specification,
Figure BDA0002843548260000104
the method comprises the steps of (1) collecting nodes of the micro-grid; p ysh,ig And P ysh,ki Respectively representing the active power flows of the distribution lines ig and ki in the ith quarter of the y year; q ysh,ig And Q ysh,ki Respectively representing the reactive power flow of the distribution lines ig and ki in the ith quarter of the y year;
Figure BDA0002843548260000105
representing the output power of the distributed energy source at the node i in the h-th time period of the s-th quarter of the y year;
Figure BDA0002843548260000106
indicating that node i may interrupt the reactive power of the load during the h-th time period of the s-th quarter of the y-th year,
Figure BDA0002843548260000107
indicating that node i can transfer reactive power of load in the h-th time period of the s-th quarter of the y-th year; l is ysh,i And
Figure BDA0002843548260000108
respectively representing the active and reactive loads of node i during the h-th time of the s-th quarter of the y-th year.
(4) Capacity constraints
The line capacity constraints are specifically:
Figure BDA0002843548260000109
Figure BDA00028435482600001010
in the formula (I), the compound is shown in the specification,
Figure BDA00028435482600001011
and
Figure BDA00028435482600001012
respectively representing the upper limit values of the active power and the reactive power of the power flow of the line ig.
The renewable energy capacity constraints are specifically:
Figure BDA00028435482600001013
Figure BDA0002843548260000111
Figure BDA0002843548260000112
Figure BDA0002843548260000113
in the formula (I), the compound is shown in the specification,
Figure BDA0002843548260000114
represents the upper limit of the installation capacity of the fan j;
Figure BDA0002843548260000115
represents the upper limit of the installation capacity of the photovoltaic k;
Figure BDA0002843548260000116
representing the upper limit of the output power of the fan j;
Figure BDA0002843548260000117
represents the lower limit of the output power of the fan j;
Figure BDA0002843548260000118
represents the upper limit of the output power of the photovoltaic k;
Figure BDA0002843548260000119
represents the lower output power limit of the photovoltaic k.
(5) Reliability constraints
The requirements are satisfied that the load shedding amount and the load transferring amount do not exceed a prescribed maximum value, for
Figure BDA00028435482600001110
Figure BDA00028435482600001111
Figure BDA00028435482600001112
In the formula (I), the compound is shown in the specification,
Figure BDA00028435482600001113
and
Figure BDA00028435482600001114
the maximum value of the allowable load reduction amount and the maximum value of the load transfer amount of the node i in the h-th time of the s-th quarter of the y-th year are respectively.
Long time load shifting increases system scheduling costs, so load shifting is required not to exceed a specified duration:
Figure BDA00028435482600001115
in the formula (I), the compound is shown in the specification,
Figure BDA00028435482600001116
and
Figure BDA00028435482600001117
the average load transfer duration of the node i in the s-th quarter of the y-th year and the maximum allowed value of the average load transfer duration are respectively.
(6) Restraint of stored energy
The energy storage constraints are specifically described as:
Figure BDA00028435482600001118
SOC l,min ≤SOC l,ysh ≤SOC l,max
wherein the content of the first and second substances,
Figure BDA00028435482600001119
represents the upper limit of the installation capacity of the stored energy l; SOC l,min Representing the lower limit of the state of charge (SOC) of the stored energy (l); SOC l,max Represents the SOC upper limit of the stored energy l.
And part three: establishing a transparent micro-grid group planning model:
transparent little electric wire netting crowd couples together a plurality of little electric wire netting through the junctor, and the inside economic operation of major network crowd and little electric wire netting can be guaranteed to reasonable net crowd structure, effective reduce cost, promotion reliability and renewable energy's utilization ratio. The difference of the network group structure can affect the trend of a single microgrid, bring about the change of network loss, further affect the planning result of the single microgrid, and the result is reflected in the planning of the microgrid group, so that the method has great optimization potential, and a typical model is shown in fig. 2.
(1) Upper layer objective function
And establishing a transparent micro-grid group typical planning model based on self-optimization-trending operation, and establishing an upper-layer objective function and constraint conditions.
From the economic perspective, the objective function for constructing the transparent microgrid group planning can be described as follows:
min f=C inv ′+C mat ′+C opr ′+C C
wherein the indexes are respectively construction cost C inv ', maintenance cost C mat ', running cost C opr ' and carbon emission cost C C Can be further described as:
Figure BDA0002843548260000121
Figure BDA0002843548260000122
Figure BDA0002843548260000123
Figure BDA0002843548260000124
in the formula, the variable x to be solved y,IJ,θ Is described inIn the y-th year, if a tie IJ of the type θ is constructed, the construction is indicated when 1 is taken, and the non-construction is indicated when 0 is taken. X y,IJ,θ Whether or not the tie IJ of type θ exists in the y-th year is described, and it represents existence when it takes 1 and nonexistence when it takes 0.
Figure BDA0002843548260000125
Represents the unit construction cost of the tie IJ of type theta,
Figure BDA0002843548260000126
cost per maintenance, C, of a tie IJ of type θ loss ' represents a loss cost, C co2 Represents the carbon emission cost, δ represents the carbon emission factor, L IJ The length of the connecting line IJ is shown,
Figure BDA0002843548260000127
and
Figure BDA0002843548260000128
respectively representing the amount of electricity purchased and sold from an upper level grid during the period of s quarter h of the y year, P ysh,IJ And Q ysh,IJ Respectively representing the active and reactive power, r, of the IJ power flow of the tie line in the s-th quarter h period of the y year IJ Representing the resistance of tie line IJ and U' the mains network node voltage.
(2) Upper layer constraint
The constraint conditions of the transparent microgrid group planning model comprise:
(1) constraint of state variable
The state variable constraint is similar to that in the lower-layer constraint condition, one tie line only can select one type for construction, and the tie line cannot be changed within the planning year; once the commissioning state changes, and is not torn down within the planning years:
Figure BDA0002843548260000131
X y-1,IJ,θ ≤X y,IJ,θ
wherein the content of the first and second substances,
Figure BDA0002843548260000132
representing the set of models to be built for all links.
(2) Node power balance constraints
For any time, the input and output power of the node should satisfy the following conditions:
Figure BDA0002843548260000133
Figure BDA0002843548260000134
in the formula, P ysh,IJ And P ysh,KI Respectively representing the active power of the power flow flowing through the connecting lines IJ and KI in the ith quarter of the y year; q ysh,IJ And Q ysh,KI Respectively representing the reactive power of the power flow flowing through the connecting lines IJ and KI in the ith quarter of the y year;
Figure BDA0002843548260000135
and
Figure BDA0002843548260000136
respectively representing the active electric quantity purchased and sold by the sub-microgrid I from an upper-level power grid in the time period h of the year s of the y year,
Figure BDA0002843548260000137
and
Figure BDA0002843548260000138
respectively representing the reactive power purchased and sold by the sub-microgrid I from the upper-level power grid in the time period of s quarter h of the y year.
(3) Capacity constraints
The tie line capacity constraint is specifically:
Figure BDA0002843548260000139
Figure BDA00028435482600001310
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00028435482600001311
representing the active power of the electricity delivered by the other piconets to the piconet I,
Figure BDA00028435482600001312
the maximum value of the active power of the electric quantity transmitted to the sub-microgrid I by other sub-microgrids is represented;
Figure BDA00028435482600001313
the active power of the electric quantity transmitted from the sub-microgrid I to other sub-microgrids is represented,
Figure BDA00028435482600001314
and the maximum value of the active power of the electric quantity transmitted to other sub-micro grids by the sub-micro grid I is represented.
The upper-level purchased electricity quantity capacity constraint is as follows:
Figure BDA00028435482600001315
Figure BDA00028435482600001316
wherein the content of the first and second substances,
Figure BDA0002843548260000141
the maximum value of the active electric quantity purchased by the sub-microgrid I from the upper-level power grid is represented,
Figure BDA0002843548260000142
and the maximum value of the active electric quantity sold to the upper-level power grid by the sub-microgrid I is represented.
And 4, step 4: decoupling the upper and lower layer optimization targets, adding the cost variation delta C of the sub-micro-grid, which is changed due to the network loss variation, into the upper layer optimization target, wherein the upper layer target function after the target is newly added is as follows:
min f=C inv '+C mat '+C opr '+C C +ΔC
ΔC=C opr1 -C opr0
wherein, C opr1 Sum of network loss values, C, after the access of a group to a single microgrid opr0 The sum of the network loss values of the single microgrid during independent operation is obtained.
And 5: solving an upper-layer optimization problem based on the NSGA-II multi-target genetic algorithm, solving a lower-layer optimization problem based on a robust optimization method, generating an optimal planning scheme and verifying the feasibility of the optimal planning scheme.
The method is applied to the planning level of the transparent microgrid group, and a double-layer planning optimization model based on self-optimization-seeking operation is established on the basis of considering multiple uncertainties, so that the environmental protection, reliability and flexibility of the system can be effectively improved on the basis of ensuring the economy, multi-energy complementation is realized, the planning optimization of the microgrid group is ensured to be completed on the basis of self-optimization seeking of a single microgrid, and the purpose of cooperative win-win is achieved.

Claims (6)

1. A transparent microgrid group planning method considering multiple uncertainties and self-optimization-seeking operation is disclosed, wherein the transparent microgrid group comprises a plurality of transparent microgrids which are connected through connecting lines; the single transparent microgrid comprises distributed power supplies, energy storage units and active loads, and is characterized by comprising the following steps:
step 1, modeling an internal structure of a transparent microgrid, wherein the internal structure comprises a wind power and photovoltaic distributed power supply, an energy storage unit and an active load capable of reducing load and transferring load;
step 2, modeling a typical planning scene of the single transparent microgrid by considering multiple uncertainties according to the source-storage-load modeling in the step 1, and establishing a lower-layer objective function and constraint conditions;
the lower objective function is:
min f=C inv +C mat +C opr +C rel
wherein, C inv Is a wireConstruction cost and C of road ig, fan unit j, photovoltaic unit k and energy storage l mat Maintenance cost and C for line ig, fan unit j, photovoltaic unit k and energy storage l opr To running cost and C rel Cost for reliability; are all related to the discount rate;
the lower layer constraint conditions include: state variable constraint, radial constraint, node power balance constraint, capacity constraint, reliability constraint and energy storage constraint;
step 3, establishing a transparent micro-grid group typical planning model based on self-optimization-trending operation, and establishing an upper-layer objective function and constraint conditions; the upper layer objective function is:
min f=C inv ′+C mat ′+C opr ′+C C
wherein, C inv ' construction cost, C for Link IJ mat ' maintenance cost, C for the tie IJ opr ' is running cost and C C Is the carbon emission cost; are all related to the discount rate;
the upper layer constraint conditions comprise state variable constraints, node power balance constraints and capacity constraints;
step 4, decoupling the double-layer optimization model constructed in the steps 2 and 3, adding the cost variation of the sub-microgrid, which is changed due to the change of the network loss, into an upper-layer optimization target, solving an upper-layer optimization problem by adopting a double-layer optimization decoupling method and a multi-objective genetic algorithm based on NSGA-II, solving a lower-layer optimization problem based on a robust optimization method, and finally solving to obtain an optimal planning scheme;
in the step 4, a double-layer optimization decoupling method is adopted, the cost variation of the sub-micro-grid, which is changed due to the change of the network loss, is added into an upper-layer optimization target, and the updated upper-layer target function formula is as follows:
min f=C inv '+C mat '+C opr '+C C +ΔC
ΔC=C opr1 -C opr0
wherein, C opr1 Sum of network loss values, C, after the access of a group to a single microgrid opr0 The sum of the network loss values of the single microgrid during independent operation is obtained.
2. The transparent microgrid cluster planning method considering multiple uncertainties and self-optimization operation according to claim 1, characterized in that in step 1, the source-storage-load modeling of the internal structure of the transparent microgrid is as follows:
P i (t)=P i pre (t)+ΔP i (t)
ΔP i (t)=ΔP i,max α-ΔP i,max (1-α)
Figure FDA0003885843200000021
Figure FDA0003885843200000022
Figure FDA0003885843200000023
Figure FDA0003885843200000024
wherein, P i (t) represents the i-node renewable energy actual output at the time t, P i pre (t) represents the predicted value of i-node renewable energy output at t moment, delta P i (t) representing the output prediction deviation of the i node renewable energy at the t moment; delta P i,max Expressing the maximum value of the predicted deviation of the i-node renewable energy output, and expressing the deviation coefficient by alpha so that delta P i (t) has a value in the range [ - Δ P i,max ,ΔP i,max ]Between, P i (t) has a value in the range of [ P ] i pre (t)-ΔP i,max ,P i pre (t)+ΔP i,max ]In the middle of; p is ES,i (t) the energy storage active power of a node i at the moment t is represented, the charging state is represented when the positive power is taken, and the discharging state is represented when the negative power is taken; a is dis,i And b dis,i Indicating the state of charge of the energy storage batteryA state relation coefficient; a is ch,i And b ch,i Representing the state relation coefficient of the energy storage battery in a discharging state; p cut,i (t)、P mov,i (t) reducible load and transferable load active power of inode at time t, respectively;
Figure FDA0003885843200000025
load reducible and load transferable predicted values of the i node at the time t are respectively; delta P cut,i (t)、ΔP mov,i (t) load reducible and transferable load prediction error correction values of the i node at the time t respectively; c (t) is a predicted value of the electricity price at the moment t; c cut To reduce electricity prices; c mov Is transferable electricity price; correction of Δ P by introducing a deviation factor β cut,i (t)、ΔP mov,i (t);
Figure FDA0003885843200000026
The maximum value of the forecast deviation of the reducible load and the transferable load of the inode at the time t is shown.
3. The transparent microgrid group planning method considering multiple uncertainties and self-optimization running according to claim 2, characterized in that in step 2, the lower objective function in the typical planning method for a single transparent microgrid is:
min f=C inv +C mat +C opr +C rel
Figure FDA0003885843200000027
Figure FDA0003885843200000028
Figure FDA0003885843200000029
Figure FDA0003885843200000031
wherein, λ represents the discount rate, the variable x to be solved y,ig,θ ,x y,j ,x y,k And x es.l Whether a line ig of the type theta, a fan unit j, a photovoltaic unit k and an energy storage unit l are built in the y year or not is described respectively, and when 1 is taken, the building is represented, and when 0 is taken, the non-building is represented; x y,ig,θ ,X y,j ,X y,k And X es.l Respectively describing whether a line ig of the type theta in the y year, a fan unit j, a photovoltaic unit k and an energy storage l exist or not, wherein the existence is shown when 1 is taken, and the nonexistence is shown when 0 is taken;
Figure FDA0003885843200000032
respectively represents the unit construction cost of the line, the photovoltaic unit, the wind turbine unit and the energy storage unit,
Figure FDA0003885843200000033
respectively represents the unit maintenance cost of the line, the photovoltaic unit, the wind turbine unit and the stored energy, C loss The cost of the loss of the network is represented,
Figure FDA0003885843200000034
and
Figure FDA0003885843200000035
a penalty factor, L, representing the reducible load and the transferable load, respectively ig Denotes the length, s, of the line ig w,j Denotes the capacity, s, of fan j pv,k Denotes the capacity, s, of the photovoltaic k es,l Representing the storage capacity, P, of the stored energy l ysh,ig 、Q ysh,ig Respectively representing active power and reactive power of power flow flowing through the power distribution network line ig in the s-quarter h period of the y year; r is ig Represents the resistance of line ig;
Figure FDA0003885843200000036
indicating that node i may be in the ith quarter of the y yearThe active power of the load is interrupted,
Figure FDA0003885843200000037
representing the active power that node i can transfer the load during the h-th time period of the s-th quarter of the y-th year; u represents the node voltage.
4. The method for planning a transparent microgrid cluster taking multiple uncertainties into account and self-optimizing operation according to claim 3, characterized in that in step 2:
the state variable constraints include:
Figure FDA0003885843200000038
X y-1,ig,θ ≤X y,ig,θ
wherein omega type Representing a set of models to be built of all lines;
one line can be constructed by selecting only one type, and cannot be changed within the planning years; once the equipment is put into operation, the state is changed and the equipment is not dismantled within the planning years;
the radial constraint comprises:
z ysh,ig ≥0
Figure FDA0003885843200000039
in the formula, z ysh,ig Represents the current direction, z, of the line ig during the ith quarter of the y year ysh,gi Representing the power flow direction of the line gi in the ith quarter of the y year; Ωel representing all line sets inside the transparent microgrid;
the node power balancing constraints include:
for any time, the input and output power of the node should satisfy the following conditions:
Figure FDA00038858432000000310
Figure FDA0003885843200000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003885843200000042
the method comprises the steps of (1) collecting nodes of the micro power grid; p ysh,ig And P ysh,ki Respectively representing the active power flows of the distribution lines ig and ki in the ith quarter of the y year; q ysh,ig And Q ysh,ki Respectively representing the reactive power flow of the distribution lines ig and ki in the ith quarter of the y year;
Figure FDA0003885843200000043
representing the output power of the distributed energy source at the node i in the h-th time period of the s-th quarter of the y year;
Figure FDA0003885843200000044
indicating that node i may interrupt the reactive power of the load during the h-th time period of the s-th quarter of the y-th year,
Figure FDA0003885843200000045
representing the reactive power of the transferable load of the node i in the h-th time period of the s-th quarter of the y-th year;
Figure FDA0003885843200000046
representing the real power that node i can interrupt the load during the h-th time period of the s-th quarter of the y-th year,
Figure FDA0003885843200000047
representing the active power that node i can transfer the load during the h-th time period of the s-th quarter of the y-th year; l is ysh,i And
Figure FDA0003885843200000048
respectively representing the real power of the node i in the h period of the s quarter of the y yearAnd reactive load;
the capacity constraints include line capacity constraints and renewable energy capacity constraints;
the line capacity constraints are specifically:
Figure FDA0003885843200000049
Figure FDA00038858432000000410
in the formula (I), the compound is shown in the specification,
Figure FDA00038858432000000411
and
Figure FDA00038858432000000412
respectively representing the upper limit values of the active power and the reactive power of the power flow of the line ig;
the renewable energy capacity constraint is specifically as follows:
Figure FDA00038858432000000413
Figure FDA00038858432000000414
Figure FDA00038858432000000415
Figure FDA00038858432000000416
in the formula (I), the compound is shown in the specification,
Figure FDA00038858432000000417
represents the upper limit of the installation capacity of the fan j;
Figure FDA00038858432000000418
represents the upper limit of the installation capacity of the photovoltaic k;
Figure FDA00038858432000000419
representing the upper limit of the output power of the fan j;
Figure FDA00038858432000000420
represents the lower limit of the output power of the fan j;
Figure FDA00038858432000000421
represents the upper limit of the output power of the photovoltaic k;
Figure FDA00038858432000000422
represents the lower output power limit of photovoltaic k;
the reliability constraints include:
the requirements are satisfied that the load shedding amount and the load transferring amount do not exceed a prescribed maximum value, for
Figure FDA00038858432000000423
Figure FDA00038858432000000424
Figure FDA00038858432000000425
In the formula (I), the compound is shown in the specification,
Figure FDA00038858432000000426
and
Figure FDA00038858432000000427
respectively the allowable load reduction and the maximum transfer amount of the node i in the h-th time period of the s-th quarter of the y-th year;
Figure FDA00038858432000000428
in the formula (I), the compound is shown in the specification,
Figure FDA0003885843200000051
and
Figure FDA0003885843200000052
respectively the average load transfer duration and the maximum allowable value of the load of the node i in the s-th quarter of the y-th year;
the energy storage constraint includes:
Figure FDA0003885843200000053
SOC l,min ≤SOC l,ysh ≤SOC l,max
wherein the content of the first and second substances,
Figure FDA0003885843200000054
represents the upper limit of the installation capacity of the stored energy l; SOC (system on chip) l,min Representing the lower limit of the state of charge (SOC) of the stored energy (l); SOC l,max Represents the SOC upper limit of the stored energy l.
5. The transparent microgrid cluster planning method considering multiple uncertainties and self-optimization operation according to claim 4, characterized in that in step 3, an upper layer objective function in the transparent microgrid cluster planning method is specifically:
min f=C inv '+C mat '+C opr '+C C
Figure FDA0003885843200000055
Figure FDA0003885843200000056
Figure FDA0003885843200000057
Figure FDA0003885843200000058
in the formula, the variable x to be solved y,IJ,θ Describing whether a connecting line IJ of the type theta is built in the y-th year, wherein the building is represented when 1 is taken, and the non-building is represented when 0 is taken; x y,IJ,θ Describing whether a connecting line IJ of the type theta in the y year exists or not, wherein the connecting line IJ is 1 to indicate that the connecting line exists, and 0 to indicate that the connecting line does not exist;
Figure FDA0003885843200000059
represents the unit construction cost of the tie IJ of type theta,
Figure FDA00038858432000000510
unit maintenance cost, C, of a tie IJ of type θ loss ' represents a loss cost, C co2 Represents the carbon emission cost, δ represents the carbon emission factor, L IJ The length of the tie line IJ is shown,
Figure FDA00038858432000000511
and
Figure FDA00038858432000000512
respectively representing the amount of electricity purchased and sold from an upper level grid during the period of s quarter h of the y year, P ysh,IJ And Q ysh,IJ Respectively representing the active and reactive power, r, of the IJ power flow of the tie line in the s-th quarter h period of the y year IJ Representing the resistance of the tie line IJ and U' the node voltage.
6. The transparent microgrid group planning method considering multiple uncertainties and self-optimization operation according to claim 5, characterized in that in the transparent microgrid group planning method:
the node power balancing constraints include:
for any time, the input and output power of the node should satisfy the following conditions:
Figure FDA00038858432000000513
Figure FDA00038858432000000514
in the formula, P ysh,IJ And P ysh,KI Respectively representing the active power of the power flow flowing through the connecting lines IJ and KI in the ith time period of the s-th quarter of the y year; q ysh,IJ And Q ysh,KI Respectively representing the reactive power of the power flow flowing through the connecting lines IJ and KI in the ith quarter of the y year;
Figure FDA0003885843200000061
and
Figure FDA0003885843200000062
respectively representing the active electric quantity purchased and sold by the sub-microgrid I from an upper-level power grid in the time period of s quarter h in the y year,
Figure FDA0003885843200000063
and
Figure FDA0003885843200000064
respectively representing the reactive power quantity purchased and sold by the sub-microgrid I from the upper-level power grid in the time period h of the s quarter of the y year;
the capacity constraint includes:
the tie line capacity constraint is specifically:
Figure FDA0003885843200000065
Figure FDA0003885843200000066
wherein the content of the first and second substances,
Figure FDA0003885843200000067
representing the active power of the electricity delivered by the other piconets to the piconet I,
Figure FDA0003885843200000068
the maximum value of the active power of the electric quantity transmitted to the sub-microgrid I by other sub-microgrids is represented;
Figure FDA0003885843200000069
the active power of the electric quantity transmitted from the sub-microgrid I to other sub-microgrids is represented,
Figure FDA00038858432000000610
the maximum value of the active power of the electric quantity transmitted to other sub-micro grids by the sub-micro grid I is represented;
the upper-level purchased electricity quantity capacity constraint is as follows:
Figure FDA00038858432000000611
Figure FDA00038858432000000612
wherein the content of the first and second substances,
Figure FDA00038858432000000613
the maximum value of the active electric quantity purchased by the sub-microgrid I from the upper-level power grid is represented,
Figure FDA00038858432000000614
and the maximum value of the active electric quantity sold to the upper-level power grid by the sub-microgrid I is represented.
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