CN112446145A - Energy storage power station distribution robust planning method based on KL divergence - Google Patents

Energy storage power station distribution robust planning method based on KL divergence Download PDF

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CN112446145A
CN112446145A CN202011308721.0A CN202011308721A CN112446145A CN 112446145 A CN112446145 A CN 112446145A CN 202011308721 A CN202011308721 A CN 202011308721A CN 112446145 A CN112446145 A CN 112446145A
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李旭霞
张琳娜
郑晓明
李佳
梁燕
王鹏
王尧
胡迎迎
邓娇娇
荆永明
刘红丽
王庭刚
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Wuhan Hengyuan Electric Co ltd
Economic and Technological Research Institute of State Grid Shanxi Electric Power Co Ltd
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Abstract

The invention relates to a KL (Kullback-Leibler, KL) divergence-based energy storage power station distribution robust planning method, which comprises the steps of firstly establishing an energy storage power station life model of equivalent full cycle times according to a power function of electrochemical energy storage cycle life, considering energy storage power station life model constraint and system operation constraint, and constructing a planning model of an energy storage power station by taking the minimum full life cycle cost and unit operation cost of the energy storage power station as targets; and then embedding the wind power output uncertainty set based on the KL divergence into an energy storage power station planning model, and converting the energy storage power station distribution robust planning model into a mixed integer linear planning model by a sample average approximation method for solving. The distribution robust planning method for the energy storage power station searches the optimal decision of the worst probability distribution by establishing the fuzzy set of the new energy output probability distribution without assuming the probability distribution type and parameters, so that the probability statistical information of uncertain quantity can be utilized, and the robustness of the planning result can be ensured.

Description

Energy storage power station distribution robust planning method based on KL divergence
Technical Field
The invention belongs to the technical field of power grid planning in a power system, and particularly relates to a KL divergence-based energy storage power station distribution robust planning method.
Technical Field
After two hundred years of development and innovation, the electrochemical energy storage technology is widely applied to a new energy power system due to the advantages of safety performance and cost of new battery energy storage technologies such as lithium batteries, lead-carbon batteries and all-vanadium redox flow batteries. The construction of the battery energy storage power station is not limited by geographical conditions, the electric energy can be directly stored and released, the smooth new energy generated output from the power generation side is transmitted to the power grid side for peak clipping and valley filling, and then the user side participates in demand response, so that the application value and the prospect of the battery energy storage are very bright.
The construction of the battery energy storage power station is not limited by geographical conditions, and any position on the side of the power grid can be selected for installation in principle, however, how to fully exert the economic value of the battery energy storage power station in the planning period needs to reasonably optimize and configure the capacity and the position of the battery energy storage power station. The battery energy storage power station is different from a pumped storage power station with a fixed calendar life, the service life of the battery energy storage power station is influenced by operation parameters such as charging and generating depth, charging and discharging rate, state of charge (SOC) and the like, and the reduction of the service life of the battery energy storage directly influences the operation cost in a planning period, so that the variable life characteristic of the battery energy storage power station must be considered in the optimal configuration of the battery energy storage power station.
On the other hand, in order to deal with the uncertainty of the new energy output, the energy storage planning method is gradually developed into a stochastic planning method and a robust planning method from a deterministic planning method. The traditional random planning method is mainly used for optimizing an expected value based on a typical scene set, but the comprehensiveness of typical scenes formed by intercepting, reducing and combining a large number of scenes is difficult to ensure; the robust planning method based on the interval set does not consider probability distribution information of new energy output, and seeks a planning result of the worst scene within the range of the new energy output interval, so that the planning result is relatively conservative. Therefore, the energy storage power station planning method must overcome the modeling accuracy of the conventional stochastic planning and the conservatism of the conventional robust planning method.
Disclosure of Invention
In order to solve the technical problem, the invention provides an energy storage power station distribution robust planning method based on KL divergence.
The technical scheme of the invention is an energy storage power station distribution robust planning method based on KL divergence, which is characterized by comprising the following steps of:
step 1: setting parameters of a planning model of the energy storage power station;
step 2, respectively establishing a target function of an energy storage power station planning model, an energy storage power station life model of equivalent full cycle times, an energy storage power station life model constraint condition and a system operation constraint condition;
and step 3: the power function of the equivalent full cycle times is subjected to piecewise linearization to obtain the linearly optimized equivalent full cycle times, the cyclic discharge depth is subjected to linear optimization to obtain the linearly optimized cyclic discharge depth, the full life cycle cost of the energy storage power station is subjected to linear fitting to obtain the full life cycle cost of the linearly fitted energy storage power station, the full life cycle cost of the linearly fitted energy storage power station is further subjected to binary quantization to obtain a full life cycle cost model of the binary post-energy storage power station, and therefore the deterministic mixed integer nonlinear programming model of the energy storage power station is established;
and 4, step 4: establishing a deterministic energy storage power station mixed integer linear programming model according to the steps 1 to 3, and further quantifying the distance between the actual probability distribution and the empirical distribution of the output of the wind power plant through the KL divergence to establish a distribution robust programming model of the energy storage power station;
and 5: the distribution robust planning model of the energy storage power station is converted into a deterministic mixed integer planning model, and a mature branch-and-bound method is adopted for solving to obtain the optimized distribution robust planning model of the energy storage power station.
Preferably, the setting of the energy storage power station planning model parameters in the step 1 is as follows:
setting a scheduling period, a unit time interval, a system rotation standby proportion, a generator cost piecewise linearization number, a wind abandoning rate confidence level, a current rate and a residual value recovery rate in a planning model;
preferably, the objective function of establishing the energy storage power station planning model in the step 2 is as follows:
Figure BDA0002789090810000021
in the formula, CTotal_ESSFor the life-cycle cost of energy-storage power stations, CUCFor the unit combination running cost, the unitThe combined operation cost comprises the coal consumption cost of the unit and the start-up and shut-down cost generated by the start-up and shut-down of the unit;
the total life cycle cost of the energy storage power station is specifically calculated as follows:
CTotal_ESS＝CINV_ESS+COM_ESS-CRES_ESS
wherein, CINV_ESSFor one-off investment costs of energy-storage power stations, COM_ESSFor operating maintenance costs of energy storage power stations, CRES_ESSThe method is the retired recovery value of the energy storage power station.
The unit combination operation cost is specifically calculated as follows:
Figure BDA0002789090810000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002789090810000032
representing the fuel cost of the ith thermal power generating unit in the t dispatching cycle period,
Figure BDA0002789090810000033
representing the starting cost of the ith thermal power generating unit in the t scheduling cycle period,
Figure BDA0002789090810000034
representing the shutdown cost of the ith thermal power generating unit in the T scheduling cycle period, wherein T is the number of the scheduling cycle periods, and N is the total number of the thermal power generating units;
step 2, establishing an energy storage power station life model with equivalent full cycle times:
the cycle life of an electrochemical cell can be determined using a power function fit as:
Figure BDA0002789090810000035
wherein: n is a radical oflifeThe number of cycles at which the electrochemical cell reaches the end of its life; n is a radical of0100% discharge for electrochemical cellsCycle number of deep charge and discharge; DODcycThe actual cycle discharge depth of the battery is obtained; k is a radical ofpAre constants obtained by fitting. For different kinds of batteries, kpThe values of (a) and (b) are different and are typically provided by the battery manufacturer.
Establishing equivalent full cycle times of scheduling period under different depth of discharge cycles, and obtaining the number N of cycles of each charge-discharge cycle to the service life by converting the depth of discharge to 100 percent of the depth of discharge0The breaking times are as follows:
Figure BDA0002789090810000036
wherein the content of the first and second substances,
Figure BDA0002789090810000037
representing the depreciation times of the energy storage power station corresponding to the kth node in the period of the t-th scheduling cycle,
Figure BDA0002789090810000038
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the period of the t-th scheduling period,
the daily equivalent full cycle times of the electrochemical cell are as follows:
Figure BDA0002789090810000039
wherein the content of the first and second substances,
Figure BDA00027890908100000310
representing the daily equivalent full cycle times of the electrochemical battery of the energy storage power station corresponding to the kth node,
Figure BDA00027890908100000311
representing the breaking times of the energy storage power station corresponding to the kth node in the t-th scheduling period;
step 2, establishing constraint conditions of the life model of the energy storage power station:
the energy storage power station restricts in the operation process and comprises the following steps: charge-discharge state constraint, charge-discharge rate constraint, charge-discharge energy balance constraint, charge-discharge process constraint and charge-discharge cycle judgment variable constraint;
the charge and discharge state constraints are as follows:
Figure BDA0002789090810000041
wherein the content of the first and second substances,
Figure BDA0002789090810000042
representing the charging state of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle,
Figure BDA0002789090810000043
showing the discharge state of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
the charge and discharge rate constraints are:
Figure BDA0002789090810000044
in the formula:
Figure BDA0002789090810000045
the power upper limit of the energy storage power station corresponding to the kth node, k chPis the lower limit of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000047
is the upper limit of the discharge power of the energy storage power station corresponding to the kth node, k disPis the lower limit of the discharge power of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000049
representing the charging power of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
Figure BDA00027890908100000410
the discharge power of the energy storage power station corresponding to the kth node in the t scheduling cycle period is represented;
the charge-discharge energy balance constraint is as follows:
Figure BDA00027890908100000411
Figure BDA00027890908100000412
in the formula: SoC (system on chip)k,tThe state of charge, eta, of the energy storage power station corresponding to the kth node in the t-th scheduling periodch,kFor charging the energy-storing power station corresponding to the kth node, etadis,kIs the discharge efficiency of the energy storage power station corresponding to the kth node, delta t is the time interval of the scheduling period,
Figure BDA00027890908100000413
is the upper limit of the state of charge of the energy storage power station corresponding to the kth node, kSoCis the lower limit of the state of charge of the energy storage power station corresponding to the kth node,
Figure BDA00027890908100000415
and configuring a binary variable of the energy storage power station for the energy storage power station corresponding to the kth node.
The charge and discharge process constraints are as follows:
Figure BDA00027890908100000416
Figure BDA0002789090810000051
Figure BDA0002789090810000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002789090810000053
a binary variable is set for the energy storage power station corresponding to the kth node in the charging process of the t-th scheduling cycle period,
Figure BDA0002789090810000054
a binary variable of an energy storage power station corresponding to the kth node in the discharging process of the t scheduling period;
if and only if
Figure BDA0002789090810000055
Or
Figure BDA0002789090810000056
And when the energy storage power station is switched from a chargeable power generation state, the charge-discharge cycle judgment variable constraint is as follows:
Sk，t＝0，t＝1
Figure BDA0002789090810000058
wherein S isk,tRepresenting a binary variable of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the depth of discharge of the energy storage power station corresponding to the kth node in the t-th scheduling cycle period is specifically calculated as follows:
Figure BDA0002789090810000059
wherein, DoDk,tThe discharging depth of the energy storage power station corresponding to the kth node in the t scheduling cycle period, namely SoCk,tThe charge state of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the t-th scheduling period is specifically calculated as follows:
Figure BDA00027890908100000510
wherein the content of the first and second substances,
Figure BDA00027890908100000511
the cyclic discharge depth S of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,tRepresenting the binary variable, DoD, of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,t-1The discharge depth of the energy storage power station corresponding to the kth node in the t-1 th scheduling cycle period;
the actual cycle life cycle of the electrochemical battery of the energy storage power station corresponding to the kth node is as follows:
Figure BDA0002789090810000061
wherein, TkRepresenting the actual cycle life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000062
and the number of daily equivalent full cycles of the energy storage power station corresponding to the kth node.
The expected life cycle of the energy storage plant is greater than or equal to its actual cycle life cycle, i.e.
Figure BDA0002789090810000063
Wherein the content of the first and second substances,
Figure BDA0002789090810000064
indicating the expected life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
step 2, establishing system operation constraints as follows:
the system operating constraints include: real-time energy balance constraint, branch flow constraint, system rotation standby constraint and wind abandoning rate constraint;
the system energy balance constraint is:
Figure BDA0002789090810000065
in the formula: pw,tRepresents the output, P, of the w wind farm in the t scheduling periodl,tRepresenting the active demand of the ith load in the t-th scheduling cycle period, Pi,tThe output of the ith thermal power generating unit in the t scheduling cycle period; omegaWind、ΩGenAnd ΩLoadAnd respectively representing a wind power plant access node set, a thermal power generating unit set and a load node set.
The branch flow constraint is as follows:
Figure BDA0002789090810000067
Figure BDA0002789090810000068
in the formula: b isi,jRepresenting admittance of a branch between an ith node and a jth node in the direct current power flow model; thetai,tRepresenting the phase angle of the ith node voltage during the t-th scheduling cycle period;
Figure BDA0002789090810000069
representing the upper limit of the branch power flow between the ith node and the jth node, i，jPrepresenting the lower limit of the branch power flow between the ith node and the jth node, iθrepresents the lower voltage phase angle limit of the ith node,
Figure BDA0002789090810000073
representing the upper voltage phase angle limit of the ith node.
The system rotation standby constraints are:
Figure BDA0002789090810000074
wherein u isi,tA binary variable representing the operation state of the ith thermal power generating unit in the t-th scheduling cycle period,
Figure BDA0002789090810000075
the output upper limit of the ith thermal power generating unit is shown,
Figure BDA0002789090810000076
representing the rated power of the energy storage power station corresponding to the kth node; and R is a power grid rotation standby proportion coefficient.
The wind abandon rate constraint is as follows:
Figure BDA0002789090810000077
in the formula:
Figure BDA0002789090810000078
predicted possible maximum output, D, for the w-th wind farmcurtThe air abandon rate is;
preferably, in step 3, the linear-optimized equivalent full cycle number obtained by piecewise linearization of the power function of the equivalent full cycle number is:
Figure BDA0002789090810000079
Figure BDA00027890908100000710
Figure BDA00027890908100000711
Figure BDA00027890908100000712
in the formula: d is the total number of piecewise linearization, gk,t,dThe discharge depth of the energy storage power station corresponding to the kth node in the t scheduling period is represented
Figure BDA00027890908100000713
The binary variable at the d-th segment,
Figure BDA00027890908100000714
indicating the discharge depth of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle
Figure BDA00027890908100000715
In the d segment; kk,dLinearly fitting a first-order coefficient for the energy storage power station corresponding to the kth node in the d section; b isk,dLinear fitting constant term coefficients of the energy storage power station corresponding to the kth node in the d section,
Figure BDA00027890908100000716
indicating that the energy storage power station corresponding to the kth node is limited in the depth of discharge of the d-th section, k，dDoDand limiting the energy storage power station corresponding to the kth node under the d-section discharge depth. "
And 3, linearly optimizing the cyclic discharge depth to obtain linearly optimized cyclic discharge depth:
Figure BDA0002789090810000082
in the formula: m is a sufficiently large positive number, and the above-described Big-M method can be similarly applied to linearization of products of continuous variables and binary variables;
and 3, performing linear fitting on the total life cycle cost of the energy storage power station to obtain the linearly-fitted total life cycle cost of the energy storage power station, wherein the linearly-fitted total life cycle cost is as follows:
Figure BDA0002789090810000083
in the formula (I), the compound is shown in the specification,
Figure BDA0002789090810000084
linearly fitting a first-order coefficient of the energy storage power station corresponding to the kth node with respect to the rated power;
Figure BDA0002789090810000085
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node with respect to rated power,
Figure BDA0002789090810000086
linear fitting first-order coefficient of rated capacity for the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000087
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node about rated capacity;
Figure BDA0002789090810000088
indicating the rated power of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000089
and the rated capacity of the energy storage power station corresponding to the kth node is shown.
Step 3, further carrying out binary quantization on the full-life cycle cost of the energy storage power station after linear fitting to obtain a full-life cycle cost model of the energy storage power station after binary quantization, wherein the model comprises the following steps:
the energy storage power station considered by the invention is formed by assembling single electrochemical batteries, and the capacity and the power of the energy storage power station are respectively several times of the capacity and the power of the single electrochemical batteries, namely
Figure BDA00027890908100000810
ekIs a positive integer corresponding to the energy storage power station corresponding to the kth node,
Figure BDA00027890908100000811
capacity of energy storage power station cell container corresponding to kth node, CTotal_ESSContaining discrete variables
Figure BDA00027890908100000812
And continuous variable
Figure BDA00027890908100000813
Product term of ekCan be equivalently expressed as a combination of a series of binary variables, namely:
Figure BDA00027890908100000814
in the formula, sk,0、sk,1、sk,vjIs v isjA number +1 of virtual binary variables,
Figure BDA0002789090810000091
is ekThe upper limit of (d);
integer vjIs determined by the following formula:
Figure BDA0002789090810000092
further, the method can be used for preparing a novel material
Figure BDA0002789090810000093
Can be converted into:
Figure BDA0002789090810000094
the above formula is converted into product linearization of discrete variables and continuous variables, and the product linearization can be further linearized by adopting a Big-M method.
Preferably, the deterministic energy storage power station mixed integer linear programming model in step 4 is:
Figure BDA0002789090810000095
Figure BDA0002789090810000096
in the formula: x is a decision variable; g is a linear equation constraint condition; c is a linear inequality constraint condition;
step 4, further quantifying the distance between the actual probability distribution and the empirical distribution of the wind power plant output through the KL divergence to construct a distribution robust planning model of the energy storage power station, wherein the distribution robust planning model comprises the following steps:
KL divergence is used to describe the actual distribution P and the empirical distribution P0A distance d betweenKLI.e. the KL divergence. For a discrete distribution, dKLCan be expressed as:
Figure BDA0002789090810000097
in the formula: pin、
Figure BDA0002789090810000098
Are respectively P, P0In the sample xinThe discrete probability of (2).
By adjusting dKLThe range of variation of the actual probability distribution density function can be varied, and therefore, the inequality constraint failure probability becomes a failure probability estimate for a cluster of probability density distribution functions. Further, the energy storage power station planning model considering the wind power plant prediction output randomness is equivalently converted into:
Figure BDA0002789090810000099
Figure BDA00027890908100000910
in the formula: pr (Pr) of0(A) Is event A atEmpirical probability distribution function alpha1+The probability of occurrence; alpha is alpha1+For the reliability correction value, the calculation method is as follows:
Figure BDA0002789090810000101
further defining a binary auxiliary variable zc(1),zc(2),…,zc(q) to characterize all scenarios that may invalidate the opportunistic constraint inequality when zc(k) 1 denotes scene ξkThe chance constrained inequality fails, so the probability of the chance constrained inequality failing is determined by all zc(k) The sum of the energy storage power station and the total scene number is determined by a ratio q, and the sample average approximation equivalent form of the distribution robust planning model of the energy storage power station is as follows:
Figure BDA0002789090810000102
Figure BDA0002789090810000103
the distribution robust planning method for the energy storage power station searches the optimal decision of the worst probability distribution by establishing the fuzzy set of the new energy output probability distribution without assuming the probability distribution type and parameters, so that the probability statistical information of uncertain quantity can be utilized, and the robustness of the planning result can be ensured.
Drawings
FIG. 1 is a schematic diagram of a distributed robust planning model solution for an energy storage power station;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. For the parameters that need to be analyzed in the actual situation, we have noted the parameter setting method above and will not be described herein.
The invention is further described in the following patent with reference to the accompanying drawings:
FIG. 1 is a schematic diagram of a distributed robust planning model of an energy storage power station. The planning model of the energy storage power station mainly comprises a planning target and a constraint condition. The specific implementation steps of the invention can be summarized as follows:
step 1: setting and inputting parameters of a planning model of the energy storage power station;
setting a scheduling period T of 24h, a unit time interval delta T of 1h, a system rotation standby proportion R of 5%, a generator cost piecewise linearization number of 20 and a wind abandoning rate D in a planning modelcurtThe confidence level alpha of the air abandoning rate is 95 percent, the rate of the present application r is 5 percent, and the recovery rate of the residual value is 5 percent;
step 2, respectively establishing a target function of an energy storage power station planning model, an energy storage power station life model of equivalent full cycle times, an energy storage power station life model constraint condition and a system operation constraint condition;
the invention converts the total life cycle cost of the energy storage power station to the day, and calculates the planning total cost by taking the day as the cycle; step 2, establishing an objective function of the energy storage power station planning model as follows:
Figure BDA0002789090810000111
in the formula, CTotal_ESSFor the life-cycle cost of energy-storage power stations, CUCThe unit combination running cost comprises the unit coal consumption cost and the start-up and shut-down cost generated by the start-up and shut-down of the unit;
the total life cycle cost of the energy storage power station is specifically calculated as follows:
CTotal_ESS＝CINV_ESS+COM_ESS-CRES_ESS
wherein, CINV_ESSFor one-off investment costs of energy-storage power stations, COM_ESSFor operating maintenance costs of energy storage power stations, CRES_ESSThe method is the retired recovery value of the energy storage power station.
The unit combination operation cost is specifically calculated as follows:
Figure BDA0002789090810000112
in the formula (I), the compound is shown in the specification,
Figure BDA0002789090810000113
representing the fuel cost of the ith thermal power generating unit in the t dispatching cycle period,
Figure BDA0002789090810000114
representing the starting cost of the ith thermal power generating unit in the t scheduling cycle period,
Figure BDA0002789090810000115
the shutdown cost of the ith thermal power generating unit in the T-th scheduling cycle period is represented, T is the number of the scheduling cycle periods 24, and N is 5 and is the total number of the thermal power generating units;
step 2, establishing an energy storage power station life model with equivalent full cycle times:
the cycle life of an electrochemical cell can be determined using a power function fit as:
Figure BDA0002789090810000116
wherein: n is a radical oflifeThe number of cycles at which the electrochemical cell reaches the end of its life; n is a radical of0Cycle number for 100% deep discharge charge and discharge for an electrochemical cell; DODcycThe actual cycle discharge depth of the battery is obtained; k is a radical ofpAre constants obtained by fitting. For different kinds of batteries, kpThe values of (a) and (b) are different and are typically provided by the battery manufacturer.
Establishing equivalent full cycle times of scheduling period under different depth of discharge cycles, and obtaining the equivalent full cycle times by converting each depth of discharge to 100% depth of dischargeNumber of cycles to life N per charge-discharge cycle0The breaking times are as follows:
Figure BDA0002789090810000121
wherein the content of the first and second substances,
Figure BDA0002789090810000122
representing the depreciation times of the energy storage power station corresponding to the kth node in the period of the t-th scheduling cycle,
Figure BDA0002789090810000123
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the period of the t-th scheduling period,
the daily equivalent full cycle times of the electrochemical cell are as follows:
Figure BDA0002789090810000124
wherein the content of the first and second substances,
Figure BDA0002789090810000125
representing the daily equivalent full cycle times of the electrochemical battery of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000126
representing the breaking times of the energy storage power station corresponding to the kth node in the t-th scheduling period;
step 2, establishing constraint conditions of the life model of the energy storage power station:
the energy storage power station restricts in the operation process and comprises the following steps: charge-discharge state constraint, charge-discharge rate constraint, charge-discharge energy balance constraint, charge-discharge process constraint and charge-discharge cycle judgment variable constraint;
the charge and discharge state constraints are as follows:
Figure BDA0002789090810000127
wherein the content of the first and second substances,
Figure BDA0002789090810000128
representing the charging state of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle,
Figure BDA0002789090810000129
showing the discharge state of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
the charge and discharge rate constraints are:
Figure BDA00027890908100001210
in the formula:
Figure BDA00027890908100001211
the power upper limit of the energy storage power station corresponding to the kth node, k chPis the lower limit of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000131
is the upper limit of the discharge power of the energy storage power station corresponding to the kth node, k disPis the lower limit of the discharge power of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000133
representing the charging power of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
Figure BDA0002789090810000134
the discharge power of the energy storage power station corresponding to the kth node in the t scheduling cycle period is represented;
the charge-discharge energy balance constraint is as follows:
Figure BDA0002789090810000135
Figure BDA0002789090810000136
in the formula: SoC (system on chip)k,tThe state of charge, eta, of the energy storage power station corresponding to the kth node in the t-th scheduling periodch,kFor charging the energy-storing power station corresponding to the kth node, etadis,kIs the discharge efficiency of the energy storage power station corresponding to the kth node, delta t is the time interval of the scheduling period,
Figure BDA0002789090810000137
is the upper limit of the state of charge of the energy storage power station corresponding to the kth node, kSoCis the lower limit of the state of charge of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000139
and configuring a binary variable of the energy storage power station for the energy storage power station corresponding to the kth node.
The charge and discharge process constraints are as follows:
Figure BDA00027890908100001310
Figure BDA00027890908100001311
Figure BDA00027890908100001312
in the formula (I), the compound is shown in the specification,
Figure BDA00027890908100001313
a binary variable is set for the energy storage power station corresponding to the kth node in the charging process of the t-th scheduling cycle period,
Figure BDA00027890908100001314
a binary variable of an energy storage power station corresponding to the kth node in the discharging process of the t scheduling period;
if and only if
Figure BDA00027890908100001315
Or
Figure BDA00027890908100001316
And when the energy storage power station is switched from a chargeable power generation state, the charge-discharge cycle judgment variable constraint is as follows:
Sk，t＝0，t＝1
Figure BDA0002789090810000142
wherein S isk,tRepresenting a binary variable of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the depth of discharge of the energy storage power station corresponding to the kth node in the t-th scheduling cycle period is specifically calculated as follows:
Figure BDA0002789090810000143
wherein, DoDk,tThe discharging depth of the energy storage power station corresponding to the kth node in the t scheduling cycle period, namely SoCk,tThe charge state of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the t-th scheduling period is specifically calculated as follows:
Figure BDA0002789090810000144
wherein the content of the first and second substances,
Figure BDA0002789090810000145
the cyclic discharge depth S of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,tRepresenting the binary variable, DoD, of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,t-1The discharge depth of the energy storage power station corresponding to the kth node in the t-1 th scheduling cycle period;
the actual cycle life cycle of the electrochemical battery of the energy storage power station corresponding to the kth node is as follows:
Figure BDA0002789090810000146
wherein, TkRepresenting the actual cycle life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000147
and the number of daily equivalent full cycles of the energy storage power station corresponding to the kth node.
The expected life cycle of the energy storage plant is greater than or equal to its actual cycle life cycle, i.e.
Figure BDA0002789090810000148
Wherein the content of the first and second substances,
Figure BDA0002789090810000151
indicating the expected life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
step 2, establishing system operation constraints as follows:
the system operating constraints include: real-time energy balance constraint, branch flow constraint, system rotation standby constraint and wind abandoning rate constraint;
the system energy balance constraint is:
Figure BDA0002789090810000152
in the formula: pw,tRepresents the output, P, of the w wind farm in the t scheduling periodl,tRepresenting the active demand of the ith load in the t-th scheduling cycle period, Pi,tThe output of the ith thermal power generating unit in the t scheduling cycle period; omegaWind、ΩGenAnd ΩLoadAnd respectively representing a wind power plant access node set, a thermal power generating unit set and a load node set.
The branch flow constraint is as follows:
Figure BDA0002789090810000154
Figure BDA0002789090810000155
in the formula: b isi,jRepresenting admittance of a branch between an ith node and a jth node in the direct current power flow model; thetai,tRepresenting the phase angle of the ith node voltage during the t-th scheduling cycle period;
Figure BDA0002789090810000156
representing the upper limit of the branch power flow between the ith node and the jth node, i，jPrepresenting the lower limit of the branch power flow between the ith node and the jth node, iθrepresents the lower voltage phase angle limit of the ith node,
Figure BDA0002789090810000159
representing the upper voltage phase angle limit of the ith node.
The system rotation standby constraints are:
Figure BDA00027890908100001510
wherein u isi,tA binary variable representing the operation state of the ith thermal power generating unit in the t-th scheduling cycle period,
Figure BDA00027890908100001511
the output upper limit of the ith thermal power generating unit is shown,
Figure BDA00027890908100001512
representing the rated power of the energy storage power station corresponding to the kth node; and R is a power grid rotation standby proportion coefficient.
The wind abandon rate constraint is as follows:
Figure BDA0002789090810000161
in the formula:
Figure BDA0002789090810000162
predicted possible maximum output, D, for the w-th wind farmcurtThe air abandon rate is;
and step 3: the power function of the equivalent full cycle times is subjected to piecewise linearization to obtain the linearly optimized equivalent full cycle times, the cyclic discharge depth is subjected to linear optimization to obtain the linearly optimized cyclic discharge depth, the full life cycle cost of the energy storage power station is subjected to linear fitting to obtain the full life cycle cost of the linearly fitted energy storage power station, the full life cycle cost of the linearly fitted energy storage power station is further subjected to binary quantization to obtain a full life cycle cost model of the binary post-energy storage power station, and therefore the deterministic mixed integer nonlinear programming model of the energy storage power station is established;
step 3, the power function of the equivalent full cycle times is linearized in sections to obtain the linearly optimized equivalent full cycle times
The cycle times are as follows:
Figure BDA0002789090810000163
Figure BDA0002789090810000164
Figure BDA0002789090810000165
Figure BDA0002789090810000166
in the formula: d is the total number of piecewise linearization, gk,t,dThe discharge depth of the energy storage power station corresponding to the kth node in the t scheduling period is represented
Figure BDA0002789090810000167
The binary variable at the d-th segment,
Figure BDA0002789090810000168
indicating the discharge depth of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle
Figure BDA0002789090810000169
In the d segment; kk,dLinearly fitting a first-order coefficient for the energy storage power station corresponding to the kth node in the d section; b isk,dLinear fitting constant term coefficients of the energy storage power station corresponding to the kth node in the d section,
Figure BDA00027890908100001610
indicating that the energy storage power station corresponding to the kth node is limited in the depth of discharge of the d-th section, k，dDoDand limiting the energy storage power station corresponding to the kth node under the d-section discharge depth. "
And 3, linearly optimizing the cyclic discharge depth to obtain linearly optimized cyclic discharge depth:
Figure BDA0002789090810000171
in the formula: m is a sufficiently large positive number, and the above-described Big-M method can be similarly applied to linearization of products of continuous variables and binary variables;
and 3, performing linear fitting on the total life cycle cost of the energy storage power station to obtain the linearly-fitted total life cycle cost of the energy storage power station, wherein the linearly-fitted total life cycle cost is as follows:
Figure BDA0002789090810000172
in the formula (I), the compound is shown in the specification,
Figure BDA0002789090810000173
linearly fitting a first-order coefficient of the energy storage power station corresponding to the kth node with respect to the rated power;
Figure BDA0002789090810000174
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node with respect to rated power,
Figure BDA0002789090810000175
linear fitting first-order coefficient of rated capacity for the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000176
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node about rated capacity;
Figure BDA0002789090810000177
indicating the rated power of the energy storage power station corresponding to the kth node,
Figure BDA0002789090810000178
and the rated capacity of the energy storage power station corresponding to the kth node is shown.
Step 3, further carrying out binary quantization on the full-life cycle cost of the energy storage power station after linear fitting to obtain a full-life cycle cost model of the energy storage power station after binary quantization, wherein the model comprises the following steps:
the energy storage power station considered by the invention is formed by assembling single electrochemical batteries, and the capacity and the power of the energy storage power station are respectively several times of the capacity and the power of the single electrochemical batteries, namely
Figure BDA0002789090810000179
ekIs a positive integer corresponding to the energy storage power station corresponding to the kth node,
Figure BDA00027890908100001710
capacity of energy storage power station cell container corresponding to kth node, CTotal_ESSContaining discrete variables
Figure BDA00027890908100001711
And continuous variable
Figure BDA00027890908100001712
Product term of ekCan be equivalently expressed as a combination of a series of binary variables, namely:
Figure BDA00027890908100001713
in the formula, sk,0、sk,1、sk,vjIs v isjA number +1 of virtual binary variables,
Figure BDA00027890908100001714
is ekThe upper limit of (d);
integer vjIs determined by the following formula:
Figure BDA0002789090810000181
further, the method can be used for preparing a novel material
Figure BDA0002789090810000182
Can be converted into:
Figure BDA0002789090810000183
the above formula is converted into product linearization of discrete variables and continuous variables, and the product linearization can be further linearized by adopting a Big-M method.
And 4, step 4: establishing a deterministic energy storage power station mixed integer linear programming model according to the steps 1 to 3, and further quantifying the distance between the actual probability distribution and the empirical distribution of the output of the wind power plant through the KL divergence to establish a distribution robust programming model of the energy storage power station;
step 4, the deterministic energy storage power station mixed integer linear programming model is as follows:
Figure BDA0002789090810000184
Figure BDA0002789090810000185
in the formula: x is a decision variable; g is a linear equation constraint condition; c is a linear inequality constraint condition;
step 4, further quantifying the distance between the actual probability distribution and the empirical distribution of the wind power plant output through the KL divergence to construct a distribution robust planning model of the energy storage power station, wherein the distribution robust planning model comprises the following steps:
KL divergence is used to describe the actual distribution P and the empirical distribution P0A distance d betweenKLI.e. the KL divergence. For a discrete distribution, dKLCan be expressed as:
Figure BDA0002789090810000186
in the formula: pin、
Figure BDA0002789090810000187
Are respectively P, P0In the sample xinThe discrete probability of (2).
By adjusting dKLThe range of variation of the actual probability distribution density function can be varied, and therefore, the inequality constraint failure probability becomes a failure probability estimate for a cluster of probability density distribution functions. Further, the energy storage power station planning model considering the wind power plant prediction output randomness is equivalently converted into:
Figure BDA0002789090810000188
Figure BDA0002789090810000189
in the formula: pr (Pr) of0(A) Is the empirical probability distribution function alpha of event A1+The probability of occurrence; alpha is alpha1+For the reliability correction value, the calculation method is as follows:
Figure BDA0002789090810000191
further defining a binary auxiliary variable zc(1),zc(2),…,zc(q) to characterize all scenarios that may invalidate the opportunistic constraint inequality when zc(k) 1 denotes scene ξkThe chance constrained inequality fails, so the probability of the chance constrained inequality failing is determined by all zc(k) The sum of the energy storage power station and the total scene number is determined by a ratio q, and the sample average approximation equivalent form of the distribution robust planning model of the energy storage power station is as follows:
Figure BDA0002789090810000192
Figure BDA0002789090810000193
and 5: the distribution robust planning model of the energy storage power station is converted into a deterministic mixed integer planning model, and a mature branch-and-bound method is adopted for solving to obtain the optimized distribution robust planning model of the energy storage power station;
and 5, calling a Cplex solver to solve through a Matlab platform, modeling by using a Matlab toolbox Yalmip, directly calling a commercial solver Cplex in the Yalmip to solve, and outputting the optimized distribution robust planning model of the energy storage power station.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (5)

1. A distribution robust planning method of an energy storage power station based on KL divergence is characterized by comprising the following steps:
step 1: setting parameters of a planning model of the energy storage power station;
step 2, respectively establishing a target function of an energy storage power station planning model, an energy storage power station life model of equivalent full cycle times, an energy storage power station life model constraint condition and a system operation constraint condition;
and step 3: the power function of the equivalent full cycle times is subjected to piecewise linearization to obtain the linearly optimized equivalent full cycle times, the cyclic discharge depth is subjected to linear optimization to obtain the linearly optimized cyclic discharge depth, the full life cycle cost of the energy storage power station is subjected to linear fitting to obtain the full life cycle cost of the linearly fitted energy storage power station, the full life cycle cost of the linearly fitted energy storage power station is further subjected to binary quantization to obtain a full life cycle cost model of the binary post-energy storage power station, and therefore the deterministic mixed integer nonlinear programming model of the energy storage power station is established;
and 4, step 4: establishing a deterministic energy storage power station mixed integer linear programming model according to the steps 1 to 3, and further quantifying the distance between the actual probability distribution and the empirical distribution of the output of the wind power plant through the KL divergence to establish a distribution robust programming model of the energy storage power station;
and 5: the distribution robust planning model of the energy storage power station is converted into a deterministic mixed integer planning model, and a mature branch-and-bound method is adopted for solving to obtain the optimized distribution robust planning model of the energy storage power station.
2. The KL divergence-based energy storage power station distribution robust planning method of claim 1, characterized in that:
step 1, setting parameters of an energy storage power station planning model as follows:
setting a scheduling period, a unit time interval, a system rotation standby proportion, a generator cost piecewise linearization number, a wind abandoning rate confidence level, an occurrence rate and a residual value recovery rate in a planning model.
3. The KL divergence-based energy storage power station distribution robust planning method of claim 1, characterized in that:
step 2, establishing an objective function of the energy storage power station planning model as follows:
Figure FDA0002789090800000011
in the formula, CTotal_ESSFor the life-cycle cost of energy-storage power stations, CUCThe unit combination running cost comprises the unit coal consumption cost and the start-up and shut-down cost generated by the start-up and shut-down of the unit;
the total life cycle cost of the energy storage power station is specifically calculated as follows:
CTotal_ESS＝CINV_ESS+COM_ESS-CRES_ESS
wherein, CINV_ESSFor one-off investment costs of energy-storage power stations, COM_ESSFor operating maintenance costs of energy storage power stations, CRES_ESSRecovering value for the retirement of the energy storage power station;
the unit combination operation cost is specifically calculated as follows:
Figure FDA0002789090800000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002789090800000022
representing the fuel cost of the ith thermal power generating unit in the t dispatching cycle period,
Figure FDA0002789090800000023
representing the starting cost of the ith thermal power generating unit in the t scheduling cycle period,
Figure FDA0002789090800000024
representing the shutdown cost of the ith thermal power generating unit in the T scheduling cycle period, wherein T is the number of the scheduling cycle periods, and N is the total number of the thermal power generating units;
step 2, establishing an energy storage power station life model with equivalent full cycle times:
the cycle life of an electrochemical cell can be determined using a power function fit as:
Figure FDA0002789090800000025
wherein: n is a radical oflifeThe number of cycles at which the electrochemical cell reaches the end of its life; n is a radical of0Cycle number for 100% deep discharge charge and discharge for an electrochemical cell; DODcycThe actual cycle discharge depth of the battery is obtained; k is a radical ofpIs a constant obtained by fitting; for different kinds of batteries, kpThe values of (a) and (b) are different and are typically provided by the battery manufacturer;
establishing equivalent full cycle times of scheduling period under different depth of discharge cycles, and obtaining the number N of cycles of each charge-discharge cycle to the service life by converting the depth of discharge to 100 percent of the depth of discharge0The breaking times are as follows:
Figure FDA0002789090800000026
wherein the content of the first and second substances,
Figure FDA0002789090800000027
represents the k < th >The breakage times of the energy storage power station corresponding to the node in the t-th scheduling cycle period,
Figure FDA0002789090800000028
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the period of the t-th scheduling period,
the daily equivalent full cycle times of the electrochemical cell are as follows:
Figure FDA0002789090800000029
wherein the content of the first and second substances,
Figure FDA0002789090800000031
representing the daily equivalent full cycle times of the electrochemical battery of the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000032
representing the breaking times of the energy storage power station corresponding to the kth node in the t-th scheduling period;
step 2, establishing constraint conditions of the life model of the energy storage power station:
the energy storage power station restricts in the operation process and comprises the following steps: charge-discharge state constraint, charge-discharge rate constraint, charge-discharge energy balance constraint, charge-discharge process constraint and charge-discharge cycle judgment variable constraint;
the charge and discharge state constraints are as follows:
Figure FDA0002789090800000033
wherein the content of the first and second substances,
Figure FDA0002789090800000034
representing the charging state of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle,
Figure FDA0002789090800000035
showing the discharge state of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
the charge and discharge rate constraints are:
Figure FDA0002789090800000036
in the formula:
Figure FDA0002789090800000037
the power upper limit of the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000038
is the lower limit of the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000039
is the upper limit of the discharge power of the energy storage power station corresponding to the kth node,
Figure FDA00027890908000000310
is the lower limit of the discharge power of the energy storage power station corresponding to the kth node,
Figure FDA00027890908000000311
representing the charging power of the energy storage power station corresponding to the kth node in the t scheduling cycle period,
Figure FDA00027890908000000312
the discharge power of the energy storage power station corresponding to the kth node in the t scheduling cycle period is represented;
the charge-discharge energy balance constraint is as follows:
Figure FDA00027890908000000313
Figure FDA00027890908000000314
in the formula: SoC (system on chip)k,tThe state of charge, eta, of the energy storage power station corresponding to the kth node in the t-th scheduling periodch,kFor charging the energy-storing power station corresponding to the kth node, etadis,kIs the discharge efficiency of the energy storage power station corresponding to the kth node, delta t is the time interval of the scheduling period,
Figure FDA00027890908000000315
is the upper limit of the state of charge of the energy storage power station corresponding to the kth node, kSoCis the lower limit of the state of charge of the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000041
whether a binary variable of the energy storage power station is configured for the energy storage power station corresponding to the kth node or not is judged;
the charge and discharge process constraints are as follows:
Figure FDA0002789090800000042
Figure FDA0002789090800000043
Figure FDA0002789090800000044
in the formula (I), the compound is shown in the specification,
Figure FDA0002789090800000045
a binary variable is set for the energy storage power station corresponding to the kth node in the charging process of the t-th scheduling cycle period,
Figure FDA0002789090800000046
a binary variable of an energy storage power station corresponding to the kth node in the discharging process of the t scheduling period;
if and only if
Figure FDA0002789090800000047
Or
Figure FDA0002789090800000048
And when the energy storage power station is switched from a chargeable power generation state, the charge-discharge cycle judgment variable constraint is as follows:
Sk，t＝0,t＝1
Figure FDA0002789090800000049
wherein S isk,tRepresenting a binary variable of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the depth of discharge of the energy storage power station corresponding to the kth node in the t-th scheduling cycle period is specifically calculated as follows:
Figure FDA00027890908000000410
wherein, DoDk,tThe discharging depth of the energy storage power station corresponding to the kth node in the t scheduling cycle period, namely SoCk,tThe charge state of the energy storage power station corresponding to the kth node in the t-th scheduling period;
the cyclic discharge depth of the energy storage power station corresponding to the kth node in the t-th scheduling period is specifically calculated as follows:
Figure FDA0002789090800000051
wherein the content of the first and second substances,
Figure FDA0002789090800000052
the cyclic discharge depth S of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,tRepresenting the binary variable, DoD, of the energy storage power station corresponding to the kth node in the t-th scheduling periodk,t-1The discharge depth of the energy storage power station corresponding to the kth node in the t-1 th scheduling cycle period;
the actual cycle life cycle of the electrochemical battery of the energy storage power station corresponding to the kth node is as follows:
Figure FDA0002789090800000053
wherein, TkRepresenting the actual cycle life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000054
the number of daily equivalent full cycles of the energy storage power station corresponding to the kth node;
the expected life cycle of the energy storage plant is greater than or equal to its actual cycle life cycle, i.e.
Figure FDA0002789090800000055
Wherein the content of the first and second substances,
Figure FDA0002789090800000056
indicating the expected life cycle of the electrochemical cell of the energy storage power station corresponding to the kth node,
step 2, establishing system operation constraints as follows:
the system operating constraints include: real-time energy balance constraint, branch flow constraint, system rotation standby constraint and wind abandoning rate constraint;
the system energy balance constraint is:
Figure FDA0002789090800000057
in the formula: pw,tRepresents the output, P, of the w wind farm in the t scheduling periodl,tRepresenting the active demand of the ith load in the t-th scheduling cycle period, Pi,tThe output of the ith thermal power generating unit in the t scheduling cycle period; omegaWind、ΩGenAnd ΩLoadRespectively representing a wind power plant access node set, a thermal power generating unit set and a load node set;
the branch flow constraint is as follows:
Figure FDA0002789090800000061
Figure FDA0002789090800000062
in the formula: b isi,jRepresenting admittance of a branch between an ith node and a jth node in the direct current power flow model; thetai,tRepresenting the phase angle of the ith node voltage during the t-th scheduling cycle period;
Figure FDA0002789090800000063
representing the upper limit of the branch power flow between the ith node and the jth node, i,jPrepresenting the lower limit of the branch power flow between the ith node and the jth node, iθrepresents the lower voltage phase angle limit of the ith node,
Figure FDA0002789090800000064
representing the upper voltage phase angle limit of the ith node;
the system rotation standby constraints are:
Figure FDA0002789090800000065
wherein u isi,tA binary variable representing the operation state of the ith thermal power generating unit in the t-th scheduling cycle period,
Figure FDA0002789090800000066
the output upper limit of the ith thermal power generating unit is shown,
Figure FDA0002789090800000067
representing the rated power of the energy storage power station corresponding to the kth node; r is a power grid rotation standby proportion coefficient;
the wind abandon rate constraint is as follows:
Figure FDA0002789090800000068
in the formula:
Figure FDA0002789090800000069
predicted possible maximum output, D, for the w-th wind farmcurtThe air abandon rate is.
4. The KL divergence-based energy storage power station distribution robust planning method of claim 1, characterized in that:
step 3, after the power function of the equivalent full-cycle times is subjected to piecewise linearization, the equivalent full-cycle times after linear optimization are obtained as follows:
Figure FDA00027890908000000610
Figure FDA00027890908000000611
Figure FDA00027890908000000612
Figure FDA00027890908000000613
in the formula: d is the total number of piecewise linearization, gk,t,dThe discharge depth of the energy storage power station corresponding to the kth node in the t scheduling period is represented
Figure FDA0002789090800000071
The binary variable at the d-th segment,
Figure FDA0002789090800000072
indicating the discharge depth of the energy storage power station corresponding to the kth node in the period of the t scheduling cycle
Figure FDA0002789090800000073
In the d segment; kk,dLinearly fitting a first-order coefficient for the energy storage power station corresponding to the kth node in the d section; b isk,dLinear fitting constant term coefficients of the energy storage power station corresponding to the kth node in the d section,
Figure FDA0002789090800000074
indicating that the energy storage power station corresponding to the kth node is limited in the depth of discharge of the d-th section, k,dDoDlimiting the energy storage power station corresponding to the kth node under the d-section discharge depth; "
And 3, linearly optimizing the cyclic discharge depth to obtain linearly optimized cyclic discharge depth:
Figure FDA0002789090800000075
in the formula: m is a sufficiently large positive number, and the above-described Big-M method can be similarly applied to linearization of products of continuous variables and binary variables;
and 3, performing linear fitting on the total life cycle cost of the energy storage power station to obtain the linearly-fitted total life cycle cost of the energy storage power station, wherein the linearly-fitted total life cycle cost is as follows:
Figure FDA0002789090800000076
in the formula (I), the compound is shown in the specification,
Figure FDA0002789090800000077
linearly fitting a first-order coefficient of the energy storage power station corresponding to the kth node with respect to the rated power;
Figure FDA0002789090800000078
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node with respect to rated power,
Figure FDA0002789090800000079
linear fitting first-order coefficient of rated capacity for the energy storage power station corresponding to the kth node,
Figure FDA00027890908000000710
linear fitting constant term coefficients of the energy storage power station corresponding to the kth node about rated capacity;
Figure FDA00027890908000000711
indicating the rated power of the energy storage power station corresponding to the kth node,
Figure FDA00027890908000000712
representing the rated capacity of the energy storage power station corresponding to the kth node;
step 3, further carrying out binary quantization on the full-life cycle cost of the energy storage power station after linear fitting to obtain a full-life cycle cost model of the energy storage power station after binary quantization, wherein the model comprises the following steps:
the energy storage power station considered by the invention is formed by assembling single electrochemical batteries, and the capacity and the power of the energy storage power station are respectively the capacity and the power of the single electrochemical batteriesSeveral times, i.e.
Figure FDA00027890908000000713
ekIs a positive integer corresponding to the energy storage power station corresponding to the kth node,
Figure FDA0002789090800000081
capacity of energy storage power station cell container corresponding to kth node, CTotal_ESSContaining discrete variables
Figure FDA0002789090800000082
And continuous variable
Figure FDA0002789090800000083
Product term of ekCan be equivalently expressed as a combination of a series of binary variables, namely:
Figure FDA0002789090800000084
in the formula, sk,0、sk,1、
Figure FDA0002789090800000085
Is v isjA number +1 of virtual binary variables,
Figure FDA0002789090800000086
is ekThe upper limit of (d);
integer vjIs determined by the following formula:
Figure FDA0002789090800000087
further, the method can be used for preparing a novel material
Figure FDA0002789090800000088
Can be converted into:
Figure FDA0002789090800000089
the above formula is converted into product linearization of discrete variables and continuous variables, and the product linearization can be further linearized by adopting a Big-M method.
5. The KL divergence-based energy storage power station distribution robust planning method of claim 1, characterized in that:
step 4, the deterministic energy storage power station mixed integer linear programming model is as follows:
Figure FDA00027890908000000810
Figure FDA00027890908000000811
in the formula: x is a decision variable; g is a linear equation constraint condition; c is a linear inequality constraint condition;
step 4, further quantifying the distance between the actual probability distribution and the empirical distribution of the wind power plant output through the KL divergence to construct a distribution robust planning model of the energy storage power station, wherein the distribution robust planning model comprises the following steps:
KL divergence is used to describe the actual distribution P and the empirical distribution P0A distance d betweenKLThe KL divergence is obtained; for a discrete distribution, dKLCan be expressed as:
Figure FDA00027890908000000812
in the formula: pin、
Figure FDA0002789090800000091
Are respectively P, P0In the sample xinThe discrete probability of (d);
by adjusting dKLThe variation range of the actual probability distribution density function can be changed, so that inequality constraint condition failure probability becomes failure probability evaluation of a cluster of probability density distribution functions; further, the energy storage power station planning model considering the wind power plant prediction output randomness is equivalently converted into:
Figure FDA0002789090800000092
Figure FDA0002789090800000093
in the formula: pr (Pr) of0(A) Is the empirical probability distribution function alpha of event A1+The probability of occurrence; alpha is alpha1+For the reliability correction value, the calculation method is as follows:
Figure FDA0002789090800000094
further defining a binary auxiliary variable zc(1),zc(2),…,zc(q) to characterize all scenarios that may invalidate the opportunistic constraint inequality when zc(k) 1 denotes scene ξkThe chance constrained inequality fails, so the probability of the chance constrained inequality failing is determined by all zc(k) The sum of the energy storage power station and the total scene number is determined by a ratio q, and the sample average approximation equivalent form of the distribution robust planning model of the energy storage power station is as follows:
Figure FDA0002789090800000095
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