CN107846040B - Distributed photovoltaic and energy storage coordination planning method and system based on second-order cone relaxation - Google Patents

Distributed photovoltaic and energy storage coordination planning method and system based on second-order cone relaxation Download PDF

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CN107846040B
CN107846040B CN201711064792.9A CN201711064792A CN107846040B CN 107846040 B CN107846040 B CN 107846040B CN 201711064792 A CN201711064792 A CN 201711064792A CN 107846040 B CN107846040 B CN 107846040B
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state
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energy storage
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CN107846040A (en
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王建国
徐瑞林
陈涛
周婧婧
李俊杰
李哲
吴志
顾晨骁
刘亚斐
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Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
Southeast University
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State Grid Corp of China SGCC
Southeast University
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    • H02J3/383—
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/28—Arrangements for balancing of the load in a network by storage of energy
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E70/00—Other energy conversion or management systems reducing GHG emissions
    • Y02E70/30—Systems combining energy storage with energy generation of non-fossil origin

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Abstract

The invention discloses a distributed photovoltaic and energy storage coordination planning method and system based on second-order cone relaxation, which comprises the following steps of S1: carrying out site selection and volume fixing on the constructed distributed power supply model to obtain constraint conditions and a cost objective function; s2: carrying out relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model by using a second-order cone algorithm to obtain a converted constraint condition and a converted cost objective function; s3: and solving the objective function converted in the step S2, and performing coordinated planning on the photovoltaic data and the energy storage data by using the solved result. The beneficial effects obtained by the invention are as follows: the photovoltaic output can be adjusted and the load can be balanced according to the electric quantity stored or discharged by the load demand; the photovoltaic output fluctuation can be restrained within a certain range, and the quality of photovoltaic output electric energy is improved; and the model is subjected to relaxation conversion by using a second-order cone algorithm, so that the model is effectively simplified, and the objective function is solved more quickly.

Description

Distributed photovoltaic and energy storage coordination planning method and system based on second-order cone relaxation
Technical Field
The invention belongs to the field of power distribution of an electric power system, relates to a second-order cone relaxation algorithm, and more particularly relates to a distributed photovoltaic and energy storage coordination planning method and system based on second-order cone relaxation.
Background
Photovoltaic power generation is a power generation mode for converting light energy irradiated by the sun into direct current energy, but the output rate of photovoltaic power generation has the characteristic of intermittency.
In the existing photovoltaic and energy storage coordination planning method, modeling of photovoltaic and energy storage is not very accurate, power supply characteristics cannot be described in detail, the model is complex, and solving difficulty is increased.
Disclosure of Invention
In view of the above defects in the prior art, the present invention provides a method and a system for distributed photovoltaic and energy storage coordination planning based on second-order cone relaxation, which can store or discharge electric quantity according to load demand, adjust photovoltaic output, and balance load; the photovoltaic output fluctuation can be restrained within a certain range through charging and discharging, and the quality of photovoltaic output electric energy is improved; the model can be effectively simplified, and the objective function can be solved more quickly.
One of the purposes of the invention is realized by the technical scheme, and the distributed photovoltaic and energy storage coordination planning method based on the second-order cone relaxation comprises the following steps: the method comprises the following steps:
s1: carrying out site selection and volume fixing on the constructed distributed power supply model to obtain constraint conditions and a cost objective function;
s2: carrying out relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model by using a second-order cone algorithm to obtain a converted constraint condition and a converted cost objective function;
s3: and solving the objective function converted in the step S2, and performing coordinated planning on the photovoltaic data and the energy storage data by using the solved result.
Further, the photovoltaic and energy storage data comprises: solar radiation, solar panel output, energy storage system output, and load value of the test distribution system.
Further, the building step of the distributed power source model in step S1 includes:
s11: simplification of continuous time;
dividing any day into 24 time periods in turn, namely each time period corresponds to one hour in any day in turn;
s12: modeling of random solar radiation;
uncertainty in solar irradiance is represented using stochastic theory with Beta distribution:
Figure GDA0002967969540000021
wherein f(s) represents the probability of solar irradiance being s, smaxIs the upper limit of the specific time in kW/m2(ii) a α, β are shape parameters of the Beta distribution;
for each time period, the shape parameter of the Beta distribution may be determined by statistical analysis of historical data; let mu letgAnd σgThe mean and standard deviation of the historical data representing the time period g; then α, β for the g segment can be calculated as:
Figure GDA0002967969540000022
Figure GDA0002967969540000023
discretizing a continuous probability density function PDF using multi-state theory based on a specific Beta distribution corresponding to each time period; the continuous probability density function PDF of each time period is divided into N states, and each state has the same span of S;
using sk-maxAnd sk-minRepresenting the upper and lower limits of state k, the probability of solar irradiance falling in state k may be expressed as:
Figure GDA0002967969540000024
wherein s isk-maxIs the upper limit value of state k, sk-minIs the offline value of state k;
s13: modeling the output of the solar panel;
the active power output of the PV is simply expressed in relation to the solar radiation by means of a piecewise function:
Figure GDA0002967969540000025
wherein PV refers to solar power generation, PsIs the active power output of PV under solar irradiance s, Ps-ratedIs the rated output of the PV under rated solar irradiation;
s14: modeling of energy storage system output.
Further, the step of constructing the load model of the distributed power source in step S1 further includes:
s15: ignoring the load fluctuations in a test distribution system that can be used, only the peak load of the distribution system is provided, i.e. a set of hourly peak loads is taken as statistical data for the annual peak load percentage.
Further, the cost objective function in step S1 includes:
the planning goal is to minimize the annual total cost, including annual investment costs, annual operating costs, annual maintenance costs and annual grid loss costs of the distributed power supply; the objective function can be expressed as:
Figure GDA0002967969540000031
wherein, CIIs the annual investment cost;
Figure GDA0002967969540000032
is the operating maintenance cost of the distributed power supply;
Figure GDA0002967969540000033
is the network loss cost corresponding to state k for time period t; prob (S)t,k) Representing the probability of the solar irradiance falling in state k for time period t; n is the number of states in each time segment.
Further, the calculation methods of the annual investment cost, the annual operation cost, the annual maintenance cost and the annual network loss cost are respectively as follows:
annual investment cost CIThe calculation method of (2) is as follows:
Figure GDA0002967969540000034
wherein
Figure GDA0002967969540000035
d is the discount rate, yPVIs the economic life of the PV; y isESEconomic life for ES; ES refers to an energy storage system; n is a radical ofbusIs the total number of buses in the power distribution system;
Figure GDA0002967969540000036
investment cost per unit volume for PV;
Figure GDA0002967969540000037
for the investment cost per unit volume of the ES,
Figure GDA0002967969540000038
installed capacity for PV at bus i;
Figure GDA0002967969540000039
installed capacity at bus i for ES;
cost of operation and maintenance
Figure GDA00029679695400000310
The calculation method of (2) is as follows:
Figure GDA00029679695400000311
wherein the content of the first and second substances,
Figure GDA00029679695400000312
operating maintenance costs for each unit of PV;
Figure GDA00029679695400000313
operating maintenance cost, P, for each unit of ESPV，iThe active power output of the PV under the bus i in a specific state; pES，iOutputting active power of a bus i in a specific state for the ES; Δ t is the span of each time period, set to 1 hour;
loss of network cost
Figure GDA0002967969540000041
The calculation method of (2) is as follows:
Figure GDA0002967969540000042
where u (i) represents the set of downstream buses connected to bus i; c. CLIs the unit cost of network loss; i isijIs the branch current from i to j in a given state; rijIs the branch resistance from i to j.
Further, the constraint conditions in step S1 include:
power flow equation:
Figure GDA0002967969540000043
Figure GDA0002967969540000044
Figure GDA0002967969540000045
v (j), u (j) represent the upstream and downstream bus sets connected to bus j respectively; pij、PjlRespectively representing active power in the branches ij and jl in the designated state; qij、QjlRespectively representing the reactive power in the branches ij and jl under the specified state; u shapeiRepresenting the voltage amplitude of the bus i in a specified state; xijRepresents the branch reactance from i to j; pjIs the equivalent active power demand at bus j under a specified state; qjIs the equivalent reactive power requirement at bus j under a specified state; omegaNIs a collection of buses in a power distribution system; omegaLIs a collection of branches in a power distribution system;
and voltage amplitude limitation:
Figure GDA0002967969540000046
wherein U ismaxAnd UminAre the upper and lower limits of the allowed voltage amplitude;
and (3) branch current limiting:
Figure GDA0002967969540000047
wherein Iij，maxRepresents the upper limit of the branch current from i to j;
discrete size constraints of distributed power sources:
Figure GDA0002967969540000051
Figure GDA0002967969540000052
output constraint of ES:
Figure GDA0002967969540000053
wherein N isPV，iAn integer variable representing the installed number of PVs on bus i; n is a radical ofES，iAn integer variable representing the installed number of ESs on bus i,
Figure GDA0002967969540000054
representing the available unit capacity of the PV to be installed;
Figure GDA0002967969540000055
indicating the available unit capacity of the ES to be installed.
Further, the step of performing relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model by using a second-order cone algorithm to obtain the transformed constraint condition and the transformed cost objective function includes:
s21: defining a new variable;
Figure GDA0002967969540000056
Figure GDA0002967969540000057
it is clear that:
Figure GDA0002967969540000058
wherein the content of the first and second substances,
Figure GDA0002967969540000059
representing the average voltage amplitude of the bus i in a specified state;
Figure GDA00029679695400000510
is the average current of the branch from i to j in a given state;
s22: from the newly defined variables, reformulating the new constraints, equations (11) through (13) can be written as follows:
Figure GDA00029679695400000511
Figure GDA00029679695400000512
Figure GDA00029679695400000513
meanwhile, the constraints of equation (14) and equation (15) may re-describe the following linear inequality:
Figure GDA0002967969540000061
Figure GDA0002967969540000062
processing the non-linear equation (21) to satisfy the standard form of SOCP, equation (21) can be relaxed to an inequality:
Figure GDA0002967969540000063
it was reformed into the following standard second order cone:
Figure GDA0002967969540000064
after the relaxation and the conversion, the original model of the optimal addressing and the size adjustment of the distributed power supply is redefined as follows:
Figure GDA0002967969540000065
further, in step S4, the objective function converted in step S2 is solved by using a commercial solver CPLEX through the yalmap platform.
Another object of the present invention is to provide a distributed photovoltaic and energy storage coordination planning system based on second order cone relaxation, which includes:
the model building module is used for building an output model and a load model of the distributed power supply;
the locating and sizing module is used for acquiring a cost objective function of the photovoltaic power generation system and a constraint condition of normal operation of the photovoltaic power generation system;
the relaxation optimization module is used for performing relaxation optimization on the cost objective function and the constraint condition of normal operation;
and the solving module is used for solving the cost objective function after the relaxation optimization and the constraint condition of normal operation.
Due to the adoption of the technical scheme, the invention has the following advantages:
(1) the energy storage system can effectively reduce the influence of photovoltaic output power intermittency on a power grid;
(2) the energy storage system has the functions of balancing, adjusting, storing electricity and peak clipping and valley filling;
(3) the photovoltaic output can be adjusted and the load can be balanced according to the electric quantity stored or discharged by the load demand; the photovoltaic output fluctuation can be restrained within a certain range through charging and discharging, and the quality of photovoltaic output electric energy is improved;
(4) the second-order cone planning is used as an important branch in the field of mathematical planning, and the power distribution planning problem of the power system can be effectively solved;
(5) the model is subjected to relaxation conversion by using a second-order cone algorithm, so that the model can be effectively simplified, and the objective function can be solved more quickly.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
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The drawings of the invention are illustrated as follows:
FIG. 1 is a schematic flow chart of the method of the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example (b): as shown in fig. 1; a distributed photovoltaic and energy storage coordination planning method based on second-order cone relaxation comprises the following steps: the method comprises the following steps:
s1: carrying out site selection and volume fixing on the constructed distributed power supply model to obtain constraint conditions and a cost objective function;
s2: carrying out relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model by using a second-order cone algorithm to obtain a converted constraint condition and a converted cost objective function;
s3: and solving the objective function converted in the step S2, and performing coordinated planning on the photovoltaic data and the energy storage data by using the solved result.
Step S1 also includes output modeling of the distributed power source, where the modeling process is as follows:
s11: simplification of continuous time;
dividing any day into 24 time periods in turn, namely each time period corresponds to one hour in any day in turn; thus, a planned year may represent 96 time periods on four typical days, which means that four days are selected that represent the average over a period of time.
S12: modeling of random solar radiation;
uncertainty in solar irradiance is represented using stochastic theory with Beta distribution:
Figure GDA0002967969540000081
wherein f(s) represents the probability of solar irradiance being s, smaxIs the upper limit of the specific time in kW/m2(ii) a α, β are shape parameters of the Beta distribution;
for each time period, the shape parameter of the Beta distribution may be determined by statistical analysis of historical data; let mu letgAnd σgThe mean and standard deviation of the historical data representing the time period g; then α, β for the g segment can be calculated as:
Figure GDA0002967969540000082
Figure GDA0002967969540000083
discretizing a continuous probability density function PDF using multi-state theory based on a specific Beta distribution corresponding to each time period; the continuous probability density function PDF of each time period is divided into N states, and each state has the same span of S;
using sk-maxAnd sk-minRepresenting the upper and lower limits of state k, the probability of solar irradiance falling in state k may be expressed as:
Figure GDA0002967969540000084
wherein s isk-maxIs the upper limit value of state k, sk-minThe lower line value for state k.
The output modeling of the distributed power supply in step S1 further includes:
s13: modeling the output of the solar panel;
the active power output of the PV is simply expressed in relation to the solar radiation by means of a piecewise function:
Figure GDA0002967969540000091
wherein PV refers to solar power generation, PsIs the active power output of PV under solar irradiance s, Ps-ratedIs the rated output of the PV under rated solar irradiation;
s14: modeling of energy storage system output. The energy storage system can enable the distributed power supply to operate at a relatively stable output level, the influence of photovoltaic output power intermittence on a power grid is reduced, and the output of the distributed power supply is adjustable within a certain range.
The step of constructing the load model of the distributed power source in step S1 further includes:
s15: ignoring the load fluctuations in a test distribution system that can be used, only the peak load of the distribution system is provided, i.e. a set of hourly peak loads is taken as statistical data for the annual peak load percentage.
The cost objective function in step S1 includes:
the planning goal is to minimize the annual total cost, including annual investment costs, annual operating costs, annual maintenance costs and annual grid loss costs of the distributed power supply; the objective function can be expressed as:
Figure GDA0002967969540000092
wherein, CIIs the annual investment cost;
Figure GDA0002967969540000093
is the operating maintenance cost of the distributed power supply;
Figure GDA0002967969540000094
is the network loss cost corresponding to state k for time period t; prob (S)t,k) Representing the probability of the solar irradiance falling in state k for time period t; n is the number of states in each time segment.
Several cost calculation methods in step S21 are as follows:
annual investment cost CIThe calculation method of (2) is as follows:
Figure GDA0002967969540000095
wherein
Figure GDA0002967969540000101
d is the discount rate, yPVIs the economic life of the PV; y isESEconomic life for ES; ES refers to an energy storage system; n is a radical ofbusIs the total number of buses in the power distribution system;
Figure GDA0002967969540000102
investment cost per unit volume for PV;
Figure GDA0002967969540000103
for the investment cost per unit volume of the ES,
Figure GDA0002967969540000104
installed capacity for PV at bus i;
Figure GDA0002967969540000105
installed capacity at bus i for ES; the constant 96 represents the number of time segments for all four seasons of the year, for a total of 96 × N states considered in the planning model. The constant 91.25 is the average number of days per season.
Cost of operation and maintenance
Figure GDA0002967969540000106
The calculation method of (2) is as follows:
Figure GDA0002967969540000107
wherein the content of the first and second substances,
Figure GDA0002967969540000108
for each sheet of the PVThe cost of operation and maintenance of the elements;
Figure GDA0002967969540000109
operating maintenance cost, P, for each unit of ESPV，iThe active power output of the PV under the bus i in a specific state; pES，iOutputting active power of a bus i in a specific state for the ES; Δ t is the span of each time period, set to 1 hour;
loss of network cost
Figure GDA00029679695400001010
The calculation method of (2) is as follows:
Figure GDA00029679695400001011
where u (i) represents the set of downstream buses connected to bus i; c. CLIs the unit cost of network loss; i isijIs the branch current from i to j in a given state; rijIs the branch resistance from i to j.
The constraints in step S1 include:
power flow equation:
Figure GDA00029679695400001012
Figure GDA00029679695400001013
Figure GDA0002967969540000111
v (j), u (j) represent the upstream and downstream bus sets connected to bus j respectively; pij、PjlRespectively representing active power in the branches ij and jl in the designated state; qij、QjlRespectively representing the reactive power in the branches ij and jl under the specified state; u shapeiRepresenting the voltage amplitude of the bus i in a specified state; xijRepresents the branch reactance from i to j; pjIs the equivalent active power demand at bus j under a specified state; qjIs the equivalent reactive power requirement at bus j under a specified state; omegaNIs a collection of buses in a power distribution system; omegaLIs a collection of branches in a power distribution system;
and voltage amplitude limitation:
Figure GDA0002967969540000112
wherein U ismaxAnd UminAre the upper and lower limits of the allowed voltage amplitude;
and (3) branch current limiting:
Figure GDA0002967969540000113
wherein Iij,maxRepresents the upper limit of the branch current from i to j;
discrete size constraints of distributed power sources:
Figure GDA0002967969540000114
Figure GDA0002967969540000115
output constraint of ES:
Figure GDA0002967969540000116
wherein N isPV，iAn integer variable representing the installed number of PVs on bus i; n is a radical ofES，iAn integer variable representing the installed number of ESs on bus i,
Figure GDA0002967969540000117
representing the available unit capacity of the PV to be installed;
Figure GDA0002967969540000118
indicating the available unit capacity of the ES to be installed. This limitation is a consideration of the cost-effective and negative impact on the economic life of an ES for frequent start-up.
The step of utilizing a second-order cone algorithm to perform relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model to obtain the converted constraint condition and the converted cost objective function comprises the following steps:
s21: defining a new variable;
Figure GDA0002967969540000121
Figure GDA0002967969540000122
it is clear that:
Figure GDA0002967969540000123
wherein the content of the first and second substances,
Figure GDA0002967969540000124
representing the average voltage amplitude of the bus i in a specified state;
Figure GDA0002967969540000125
is the average current of the branch from i to j in a given state.
S22: from the newly defined variables, reformulating the new constraints, equations (11) through (13) can be written as follows:
Figure GDA0002967969540000126
Figure GDA0002967969540000127
Figure GDA0002967969540000128
meanwhile, the constraints of equation (14) and equation (15) may re-describe the following linear inequality:
Figure GDA0002967969540000129
Figure GDA00029679695400001210
processing the non-linear equation (21) to satisfy the standard form of SOCP, equation (21) can be relaxed to an inequality:
Figure GDA00029679695400001211
it was reformed into the following standard second order cone:
Figure GDA0002967969540000131
after the relaxation and the conversion, the original model of the optimal addressing and the size adjustment of the distributed power supply is redefined as follows:
Figure GDA0002967969540000132
in step S4, the objective function converted in step S2 is solved by the YALMIP platform using the commercial solver CPLEX.
A distributed photovoltaic and energy storage coordinated planning system based on second order cone relaxation comprises:
the model building module is used for building an output model and a load model of the distributed power supply;
the locating and sizing module is used for acquiring a cost objective function of the photovoltaic power generation system and a constraint condition of normal operation of the photovoltaic power generation system;
the relaxation optimization module is used for performing relaxation optimization on the cost objective function and the constraint condition of normal operation;
and the solving module is used for solving the cost objective function after the relaxation optimization and the constraint condition of normal operation.
The energy storage system is applied to the photovoltaic system, so that the influence of the photovoltaic output power intermittency on a power grid can be effectively reduced. The energy storage system has the effects of balancing, adjusting, storing electricity and clipping peak and filling valley, on one hand, the energy storage system can store or discharge electricity according to the load demand, adjust the photovoltaic output and balance the load, on the other hand, through charging and discharging, the photovoltaic output fluctuation can be restrained within a certain range, and the quality of the photovoltaic output electric energy is improved. According to the operating characteristics of a photovoltaic power generation system and an energy storage system, economic and technical factors and other factors are reasonably and comprehensively considered, and the optimal configuration with practical significance can be obtained.
The second-order cone planning is used as an important branch in the field of mathematical planning, has wide application field and practical significance, and can effectively solve the power distribution planning problem of the power system. The standard SOCP problem consists of a linear objective function and some constraints, including a second order cone constraint, a linear equality constraint and a linear inequality constraint. The model is subjected to relaxation conversion by using a second-order cone algorithm, so that the model can be effectively simplified, and the objective function can be solved more quickly.
The invention has the following beneficial effects:
(1) the energy storage system can effectively reduce the influence of photovoltaic output power intermittency on a power grid;
(2) the energy storage system has the functions of balancing, adjusting, storing electricity and peak clipping and valley filling;
(3) the photovoltaic output can be adjusted and the load can be balanced according to the electric quantity stored or discharged by the load demand; the photovoltaic output fluctuation can be restrained within a certain range through charging and discharging, and the quality of photovoltaic output electric energy is improved;
(4) the second-order cone planning is used as an important branch in the field of mathematical planning, and the power distribution planning problem of the power system can be effectively solved;
(5) the model is subjected to relaxation conversion by using a second-order cone algorithm, so that the model can be effectively simplified, and the objective function can be solved more quickly.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (3)

1. A distributed photovoltaic and energy storage coordination planning method based on second-order cone relaxation is characterized by comprising the following steps:
the method comprises the following steps of carrying out site selection and volume fixing on a constructed distributed power supply model to obtain constraint conditions and a cost objective function, and specifically comprises the following steps:
1) simplification of continuous time;
dividing any day into 24 time periods in turn, namely each time period corresponds to one hour in any day in turn;
2) modeling of random solar radiation;
uncertainty in solar irradiance is represented using stochastic theory with Beta distribution:
Figure FDA0003126963820000011
wherein f(s) represents the probability of solar irradiance being s, smaxIs the upper limit of the specific time in kW/m2(ii) a α, β are shape parameters of the Beta distribution;
for each time period, the shape parameter of the Beta distribution may be determined by statistical analysis of historical data; let mu letgAnd σgThe mean and standard deviation of the historical data representing the time period g; then α, β for the g segment can be calculated as:
Figure FDA0003126963820000012
Figure FDA0003126963820000013
discretizing a continuous probability density function PDF using multi-state theory based on a specific Beta distribution corresponding to each time period; the continuous probability density function PDF of each time period is divided into N states, and each state has the same span of S;
using sk-maxAnd sk-minRepresenting the upper and lower limits of state k, the probability of solar irradiance falling in state k may be expressed as:
Figure FDA0003126963820000014
wherein s isk-maxIs the upper limit value of state k, sk-minIs the offline value of state k;
3) modeling the output of the solar panel;
the active power output of the PV is simply expressed in relation to the solar radiation by means of a piecewise function:
Figure FDA0003126963820000021
wherein PV refers to solar power generation, PsIs the active power output of PV under solar irradiance s, Ps-ratedIs the rated output of the PV under rated solar irradiation;
4) modeling of energy storage system output;
5) ignoring the load fluctuations in a test distribution system that can be used, only providing the peak load of the distribution system, i.e. taking a set of hourly peak loads as statistical data for the annual peak load percentage;
6) cost objective function for building planning model
The planning objective is to minimize the total annual cost, including annual investment costs, annual operating costs, annual maintenance costs and annual grid loss costs of the distributed power supply, and the objective function can be expressed as:
Figure FDA0003126963820000022
wherein, CIIs the annual investment cost;
Figure FDA0003126963820000023
is the operating maintenance cost of the distributed power supply;
Figure FDA0003126963820000024
is the network loss cost corresponding to state k for time period t; prob (S)t,k) Representing the probability of the solar irradiance falling in state k for time period t; n is the number of states in each time segment;
the calculation methods of the annual investment cost, the annual operation cost, the annual maintenance cost and the annual network loss cost in the objective function are respectively as follows:
annual investment cost CIThe calculation method of (2) is as follows:
Figure FDA0003126963820000025
wherein
Figure FDA0003126963820000031
d is the discount rate, yPVIs the economic life of the PV; y isESEconomic life for ES; ES refers to an energy storage system; n is a radical ofbusIs the total number of buses in the power distribution system;
Figure FDA0003126963820000032
investment cost per unit volume for PV;
Figure FDA0003126963820000033
for the investment cost per unit volume of the ES,
Figure FDA0003126963820000034
installed capacity for PV at bus i;
Figure FDA0003126963820000035
installed capacity at bus i for ES;
cost of operation and maintenance
Figure FDA0003126963820000036
The calculation method of (2) is as follows:
Figure FDA0003126963820000037
wherein the content of the first and second substances,
Figure FDA0003126963820000038
operating maintenance costs for each unit of PV;
Figure FDA0003126963820000039
operating maintenance cost, P, for each unit of ESPV,iThe active power output of the PV under the bus i in a specific state; pES,iOutputting active power of a bus i in a specific state for the ES; Δ t is the span of each time period, set to 1 hour;
loss of network cost
Figure FDA00031269638200000310
The calculation method of (2) is as follows:
Figure FDA00031269638200000311
where u (i) represents the set of downstream buses connected to bus i; c. CLIs the unit cost of network loss; i isijIs the branch current from i to j in a given state; rijIs the branch resistance from i to j;
7) establishing constraint conditions of a planning model, which specifically comprises the following steps:
power flow equation:
Figure FDA00031269638200000312
Figure FDA0003126963820000041
Figure FDA0003126963820000042
v (j), u (j) represent the upstream and downstream bus sets connected to bus j respectively; pij、PjlRespectively representing active power in the branches ij and jl in the designated state; qij、QjlRespectively representing the reactive power in the branches ij and jl under the specified state; u shapeiRepresenting the voltage amplitude of the bus i in a specified state; xijRepresents the branch reactance from i to j; pjIs the equivalent active power demand at bus j under a specified state; qjIs the equivalent reactive power requirement at bus j under a specified state; omegaNIs a collection of buses in a power distribution system; omegaLIs a collection of branches in a power distribution system;
and voltage amplitude limitation:
Figure FDA0003126963820000043
whereinUmaxAnd UminAre the upper and lower limits of the allowed voltage amplitude;
and (3) branch current limiting:
Figure FDA0003126963820000044
wherein Iij,maxRepresents the upper limit of the branch current from i to j;
discrete size constraints of distributed power sources:
Figure FDA0003126963820000045
Figure FDA0003126963820000046
output constraint of ES:
Figure FDA0003126963820000047
wherein N isPV,iAn integer variable representing the installed number of PVs on bus i; n is a radical ofES,iAn integer variable representing the installed number of ESs on bus i,
Figure FDA0003126963820000051
representing the available unit capacity of the PV to be installed;
Figure FDA0003126963820000052
indicating an available unit capacity of an ES to be installed;
8) carrying out relaxation optimization on the constraint condition and the cost objective function of the distributed power supply model by using a second-order cone algorithm to obtain a converted constraint condition and a converted cost objective function;
defining a new variable;
Figure FDA0003126963820000053
Figure FDA0003126963820000054
it is clear that:
Figure FDA0003126963820000055
wherein the content of the first and second substances,
Figure FDA0003126963820000056
representing the average voltage amplitude of the bus i in a specified state;
Figure FDA0003126963820000057
is the average current of the branch from i to j in a given state;
from the newly defined variables, reformulating the new constraints, equations (11) through (13) can be written as follows:
Figure FDA0003126963820000058
Figure FDA0003126963820000059
Figure FDA00031269638200000510
meanwhile, the constraints of equation (14) and equation (15) may re-describe the following linear inequality:
Figure FDA00031269638200000511
Figure FDA00031269638200000512
processing the non-linear equation (21) to satisfy the standard form of SOCP, equation (21) can be relaxed to an inequality:
Figure FDA0003126963820000061
it was reformed into the following standard second order cone:
Figure FDA0003126963820000062
after the relaxation and the conversion, the original model of the optimal addressing and the size adjustment of the distributed power supply is redefined as follows:
Figure FDA0003126963820000063
Figure FDA0003126963820000064
Figure FDA0003126963820000065
Figure FDA0003126963820000066
Figure FDA0003126963820000067
Figure FDA0003126963820000068
Figure FDA0003126963820000069
Figure FDA00031269638200000610
Figure FDA00031269638200000611
Figure FDA00031269638200000612
2. the second order cone relaxation-based distributed photovoltaic and energy storage coordination planning method according to claim 1, wherein the photovoltaic and energy storage data comprises: solar radiation, solar panel output, energy storage system output, and load value of the test distribution system.
3. The distributed photovoltaic and energy storage coordination planning method based on second-order cone relaxation as claimed in claim 1, characterized in that the objective function transformed in step S2 is solved through yalmap platform by using commercial solver CPLEX.
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