CN106169108B - Active power distribution network short-term active power optimization method containing battery energy storage system - Google Patents

Active power distribution network short-term active power optimization method containing battery energy storage system Download PDF

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CN106169108B
CN106169108B CN201610557005.3A CN201610557005A CN106169108B CN 106169108 B CN106169108 B CN 106169108B CN 201610557005 A CN201610557005 A CN 201610557005A CN 106169108 B CN106169108 B CN 106169108B
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赵晋泉
朱泽锋
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Abstract

The invention discloses a short-term active optimization method for an active power distribution network with a battery energy storage system, which is based on the economic considerations of time-sharing electricity price, electricity purchasing and selling cost, equivalent operation cost of the battery energy storage system, wind and light abandoning cost, operation cost of a micro gas turbine, compensation cost for adjusting controllable load and the like, provides a short-term active optimization model for the active power distribution network with the aim of minimizing the total operation cost at the side of the distribution network, and solves the problem by a branch-bound-original-dual interior point method. The economic operation of the battery energy storage system is realized by calculating the cycle life of the battery and considering the equivalent operation cost of the battery energy storage system. The method realizes the optimized dispatching management of the distributed energy and the consumption of the DGs, and improves the running economy of the active power distribution network. The invention also provides a method for applying the decoupling interior point method to the solution of the multi-period nonlinear programming problem, and the calculation efficiency is improved.

Description

Active power distribution network short-term active power optimization method containing battery energy storage system
Technical Field
The invention belongs to the technical field of optimized operation and control of a power system, and particularly relates to a short-term active optimization method for an active power distribution network with a battery energy storage system.
Background
On one hand, Distributed Generation (DG) represented by wind power and photovoltaic, which has the characteristics of volatility, intermittency, poor schedulability and the like, and is connected with the existing power distribution system in a grid manner, brings huge challenges to the operation and control of the power distribution system, meanwhile, the rapid increase of load also brings many challenges to the operation of the existing power distribution system, and it becomes more and more difficult to meet the demands by newly building a power network and increasing the capacity; on the other hand, with the development of an Active Distribution Network (ADN) technology and an energy storage and demand side response technology, which aim to solve the problem of renewable energy grid-connected operation control, the Distribution Network gradually changes from traditional passive to Active.
The active power distribution network is a main mode of a future power distribution network, has the characteristics of high DG permeability and high control requirement, has active control and management capabilities for various distributed energy sources (DG, energy storage, demand side management and the like), and can realize the economic operation of the power distribution network. The energy storage system participates in the dispatching plan of the active power distribution network, and the dispatching plan has great significance for improving the utilization efficiency of distributed energy and the operation economy of the power distribution network. The short-term active optimization of the active power distribution network can realize the optimized dispatching management of distributed energy in the active power distribution network, the consumption capacity of distributed power sources is improved, and the running economy of the active power distribution network is improved.
Disclosure of Invention
Aiming at the problems, the invention provides a short-term active power optimization method for an active power distribution network with a battery energy storage system.
The technical purpose is achieved, the technical effect is achieved, and the invention is realized through the following technical scheme:
a short-term active optimization method for an active power distribution network with a battery energy storage system is characterized by comprising the following steps:
step 1, establishing a model of active power and energy of a battery energy storage system, and specifically comprising the following steps:
step 1-a, collecting basic parameters of a battery energy storage system, comprising: rated active power P of battery energy storage systemratedMaximum apparent power SBESS,maxCharge and discharge efficiency ηinDischarge efficiency ηoutRated capacity Wrated(ii) a Setting parameters of a working battery energy storage system: battery state of charge maximum and minimum SOCmax、SOCmin；
Step 1-b, establishing an active input and output model of the battery energy storage system:
Figure GDA0001073055470000011
wherein, ItIs the charging and discharging state of the battery energy storage system in the t-th period, It1 denotes discharge, It-1 represents the charge-up of the battery,
Figure GDA0001073055470000012
the active power of the battery energy storage system in the t-th period,
Figure GDA0001073055470000013
Figure GDA0001073055470000014
and
Figure GDA0001073055470000015
respectively representing the charging active power and the discharging active power of the battery energy storage system in the t-th time period;
step 1-c, establishing an energy model of the battery energy storage system:
Figure GDA0001073055470000021
wherein the content of the first and second substances,
Figure GDA0001073055470000022
for the stored energy of the battery energy storage system during the t-th period,
Figure GDA0001073055470000023
the energy stored in the initial stage of the battery energy storage system is delta t, and the delta t is a time step;
step 2, establishing an equivalent operation cost model of the battery energy storage system;
the equivalent operation cost of the battery energy storage system comprises two parts of fixed investment cost and maintenance cost;
the fixed investment cost of the battery energy storage system can be uniformly distributed to each time of cyclic charge and discharge of the battery energy storage system, and the discharge depth of the mth cycle period of the kth battery energy storage system is defined as DoD,k,mSo the equivalent investment cost for a single cycle charge-discharge of the battery energy storage system can be expressed as:
Figure GDA0001073055470000024
wherein, CPAnd CWRespectively unit power investment cost and unit capacity investment cost of the battery energy storage system, wherein the units of the investment cost are RMB/kW and RMB/kWh; n is a radical ofctf(DoD,k,m) To depth of discharge DoD,k,mThe corresponding cycle life of the battery energy storage system;
maintenance cost and rated active power P of battery energy storage systemratedRated capacity WratedAnd operating time, expressed as:
CBESS＝Y(mPPrated+mWWrated)
wherein m isPAnd mWThe unit power and unit capacity operation maintenance cost of the battery energy storage system in unit time are respectively RMB/kW.h and RMB/kW.h2(ii) a Y is working time;
step 3, establishing an active power and energy relation model of the controllable load, and regarding the controllable load as a generator with negative output:
step 3-a, establishing an active power and energy relation model capable of directly controlling the load:
Figure GDA0001073055470000025
wherein
Figure GDA0001073055470000026
The active power of the load can be directly controlled in the t-th time period and is a negative value; eDMFDThe total electric quantity demand of the load in the dispatching cycle;
step 3-b, establishing an active and energy relation model of the storage type controllable load:
Figure GDA0001073055470000027
wherein the content of the first and second substances,
Figure GDA0001073055470000028
the energy stored in the controllable-like load is stored for the t-th period,
Figure GDA0001073055470000029
storing energy stored in the initial stage of the controllable load;
Figure GDA0001073055470000031
capacity for storage class controllable loads; mu is electric energy and stored energyThe conversion efficiency between;
Figure GDA0001073055470000032
storing active power injection of the controllable load for each time interval, wherein the active power injection is a negative value;
Figure GDA0001073055470000033
power to extract heat from the storage class controllable load for each time period;
step 4, establishing a short-term active optimization model taking the minimum total running cost of the power distribution network side as a target function on the basis of the active and energy model, the equivalent running cost model and the controllable load active and energy relation model of the battery energy storage system;
step 4-a, the objective function comprises electricity purchasing cost, equivalent operation cost of a battery energy storage system, wind and light abandoning cost, operation cost of a micro gas turbine and compensation cost for adjusting controllable load, and the objective function is expressed as:
min f＝C1+C2+C3+C4+C5
wherein, C1Sum of electricity purchasing cost and electricity selling income for distribution side, C2For equivalent operating costs of the battery energy storage system, C3To optimize the cost of wind and light rejection in the scheduling process, C4For the operating costs of micro gas turbines, C5Compensation costs for adjusting the controllable load;
step 4-b, establishing equality constraints including tidal current balance equation constraints of nodes in each time period, coupling equality constraints between the battery energy storage system and the controllable load time period;
the node power flow balance equation is constrained as follows:
Figure GDA0001073055470000034
Figure GDA0001073055470000035
wherein:
Figure GDA0001073055470000036
and
Figure GDA0001073055470000037
active and reactive power output of the wind turbine generator at a node i in the t-th time period;
Figure GDA0001073055470000038
and
Figure GDA0001073055470000039
photovoltaic active and reactive power output at a node i in the t-th time period;
Figure GDA00010730554700000310
and
Figure GDA00010730554700000311
then the active power and the reactive power at the root node of the distribution network in the t-th period are represented;
Figure GDA00010730554700000312
and
Figure GDA00010730554700000313
the charging and discharging active and reactive power output of the battery energy storage system at the node i in the t-th time period is represented;
Figure GDA00010730554700000314
and
Figure GDA00010730554700000315
the active power and the reactive power of the load can be directly controlled at a node i in the t-th period;
Figure GDA00010730554700000316
and
Figure GDA00010730554700000317
active power and reactive power of the storage type controllable load at the node i in the t-th period;
Figure GDA00010730554700000318
and
Figure GDA00010730554700000319
respectively providing active power and reactive power of the micro gas turbine at the i node in the t period;
Figure GDA00010730554700000320
and
Figure GDA00010730554700000321
the real power and the reactive power of the fixed load at the node i in the t-th period; n is the number of nodes, Vi tAnd
Figure GDA00010730554700000322
is the voltage amplitude, G, of node i during the t-th periodijAnd BijFor the real and imaginary parts of the transadmittance between nodes i and j,
Figure GDA00010730554700000323
the phase angle difference of the voltages of the two nodes i and j in the t period; the actual active power output of the wind turbine generator and the photovoltaic power system also meets the following equation:
Figure GDA00010730554700000324
Figure GDA00010730554700000325
in the formula (I), the compound is shown in the specification,
Figure GDA0001073055470000041
and
Figure GDA0001073055470000042
the active output predicted value of the wind turbine generator and the photovoltaic at the node i in the t-th time period is obtained;
Figure GDA0001073055470000043
and
Figure GDA0001073055470000044
respectively the active power of the fan abandoned wind or the photovoltaic abandoned light at the node i in the t-th time period;
the battery energy storage system and the storage type controllable load energy constraints are respectively as follows:
Figure GDA0001073055470000045
SOCT＝SOC0
Figure GDA0001073055470000046
Figure GDA0001073055470000047
wherein T is the total time period number of the scheduling period; SOCTThe residual electric quantity of the battery energy storage system at the last moment is obtained;
Figure GDA0001073055470000048
the residual capacity at the last moment of the storage type load is stored;
step 4-c, establishing inequality constraints including node voltage upper and lower limit constraints, branch power flow constraints and control variable sum
State variable dependent constraints:
and (3) limiting the upper and lower limits of the node voltage:
Vi,min＜Vi t＜Vi,max
wherein, Vi,minAnd Vi,maxRespectively the minimum value and the maximum value allowed by the voltage at the node i;
branch flow constraint:
Figure GDA0001073055470000049
wherein the content of the first and second substances,
Figure GDA00010730554700000410
apparent power, S, of branch l during period tl.maxIs the apparent power maximum for branch l;
the active power, apparent power and energy constraint of the battery energy storage system are respectively as follows:
Figure GDA00010730554700000411
Figure GDA00010730554700000412
SOCmin＜SOCt＜SOCmax
therein, SOCmaxAnd SOCminThe battery state of charge maximum and minimum values of the battery energy storage system,
Figure GDA00010730554700000413
the reactive output of the battery energy storage system in the t-th time period is represented;
active and reactive power output limitation and climbing restraint of the micro gas turbine:
Figure GDA00010730554700000414
Figure GDA00010730554700000415
Figure GDA00010730554700000416
Figure GDA0001073055470000051
wherein the content of the first and second substances,
Figure GDA0001073055470000052
for the active power output, P, of the micro gas turbine during the t-th periodMT,i,minAnd PMT,i,maxRespectively active power take-off of micro gas turbineA lower limit and an upper limit;
Figure GDA0001073055470000053
for the t-th period of time, the reactive power, Q, of the micro gas turbineMT,minAnd QMT,maxRespectively is the lower limit and the upper limit of the reactive power output of the micro gas turbine; rMT,upAnd RMT,downRespectively represents the upper limit and the lower limit of the climbing power when the micro gas turbine increases and decreases the load.
Active power and reactive power constraints of the wind turbine generator and the photovoltaic are not fixed:
Figure GDA0001073055470000054
Figure GDA0001073055470000055
Figure GDA0001073055470000056
Figure GDA0001073055470000057
wherein the content of the first and second substances,
Figure GDA0001073055470000058
the reactive power output of the wind turbine generator is the t-th time period; qW,maxAnd QW,minRespectively the maximum value and the minimum value of the reactive output of the wind turbine generator;
Figure GDA0001073055470000059
is the reactive power of photovoltaic in the t-th period, QPV,maxAnd QPV,minThe maximum value and the minimum value of the reactive output of the photovoltaic are respectively.
And (3) controllable load active power and energy constraint:
Figure GDA00010730554700000510
Figure GDA00010730554700000511
Figure GDA00010730554700000512
wherein the content of the first and second substances,
Figure GDA00010730554700000513
is the upper limit of the output of the controllable load,
Figure GDA00010730554700000514
the lower limit of the output force of the controllable load. SOCSMFD,maxAnd SOCSMFD,minRespectively the upper and lower limits of the storage-type controllable load state of charge.
And 5, considering that the active power optimization problem is a mixed integer nonlinear programming problem, solving by adopting a branch-bound-primal dual interior point method:
step 5-a, according to the prediction results of the wind power output and the load, solving the active optimization of each time interval according to the scheduling condition of the previous day to obtain the target value of each time interval, namely the value of the target function corresponding to the current time interval, and using the target value as the upper bound of each time interval in the process of processing the discrete variable by using a branch-and-bound method;
step 5-b, the charging and discharging states of each battery energy storage system in each time period are discrete variables, firstly all the discrete variables are loosened, then the optimal power flow problem only containing continuous variables is solved by adopting an original dual interior point method, the values of each control variable, each state variable and the corresponding objective function are obtained, whether the results of all the discrete variables are integers is judged, and if yes, the results are stored; otherwise, adding the relaxation problem and the objective function value thereof into a queue to be branched, marking as RP, and taking the objective function value as a new lower bound of the objective value;
step 5-c, branching the single discrete variables of the subproblems in the RP in sequence, solving each relaxation subproblem by adopting an original dual interior point method, judging whether all the discrete variables obtain integer values, if so, saving the result, and turning to step 5-f; if not, adding the branch queue into a next waiting branch queue, and recording as RRP;
step 5-d, pruning all the subproblems in the RRP according to a pruning rule, and updating the RP;
step 5-e, judging whether the queue RP to be branched is empty, if so, making an error, and quitting the calculation; if not, turning to the step 5-c;
step 5-f, calculating the depth of discharge of all scheduling modes meeting the constraint condition, and then obtaining an equivalent operation result
Adding the obtained data to the objective function value of each scheduling mode, and taking the solution with the minimum objective function value as the optimal solution
And realizing short-term active optimization of the active power distribution network.
The step 2 of establishing the mathematical relationship between the discharge depth and the cycle life thereof and calculating the discharge depth comprises the following steps:
step 2-a, life and temperature of the energy storage device, peak current, depth of discharge D during operation thereofoDAre closely related to each other in that,
the larger the depth of discharge is, the shorter the cycle life of the energy storage device is, and the polynomial function method is used for measuring the depth of discharge DoDAnd the circulation longevity
Min NctfFitting the functional relationship between them, depth of discharge DoDAnd cycle life NctfThe functional relationship between the two is as follows:
Figure GDA0001073055470000061
wherein, aiIs the coefficient corresponding to the i-th order, and N is the polynomial order;
depth of discharge D in the above equationoDIs a variable having a nonlinear relation with the charge-discharge state and the active power of the battery
Amount of, i.e.
Figure GDA0001073055470000062
It cannot give an explicit mathematical expression, so it is calculated by a rain flow counting method;
step 2-b, the rain flow counting method comprises the following steps:
1) clockwise rotating a battery charge state-time curve of a battery energy storage system by 90 degrees, regarding the curve as an eave, and starting rain flow from a starting point and each peak/valley value in sequence;
2) the rain drops vertically when flowing to the peak/valley, and the rain drops until the opposite surface has a peak value larger than the maximum value or the minimum value at the beginning or a valley value smaller than the maximum value or the minimum value at the beginning;
3) drawing a flow path of each raindrop according to the starting point and the end point of the flowing of each raindrop, namely each cycle half period, and simultaneously recording the peak-to-valley values of all the cycle half periods;
4) the horizontal length of the rain flow path in each cycle is the discharge depth of the battery energy storage system in the cycle period.
In step 4, the objective function specifically consists of:
step a, considering the situation that power exchange can be carried out between the main network and the distribution network side purchases electricity prices are different, the distribution side purchases electricity prices
The sum of the electricity cost and the electricity sales revenue can be expressed as:
Figure GDA0001073055470000063
wherein the content of the first and second substances,
Figure GDA0001073055470000071
active power delivered to the distribution network for the main network during the t-th period, CtThe purchase and sale electricity price of the main network in the t-th scheduling period for the distribution network can be expressed as:
Figure GDA0001073055470000072
wherein the content of the first and second substances,
Figure GDA0001073055470000073
and C-The unit of the distribution network electricity purchasing price and the electricity selling price are RMB/kW.h respectively in the time period of t, and
Figure GDA0001073055470000074
step b, in order to fully consider the economic benefits of the distribution network side, the equivalent operation cost of the battery energy storage system is considered besides the electricity purchasing and selling cost of the distribution network side, and the equivalent operation cost of the battery energy storage system can be expressed as:
Figure GDA0001073055470000075
wherein N isBFor the number of battery energy storage systems, MkIs the total cycle number in the scheduling period of the battery energy storage system of No. k, Ce,k,m(DoD,k,m) The m-th discharge depth of the kth battery energy storage system is DoD,k,mEquivalent investment cost under the cycle period of (1); cBESS,kEquivalent maintenance cost for No. k BESS;
and step c, considering that the wind power and the photovoltaic power generation do not need to consume fuel, assuming that the power generation cost is zero, from the aspects of economy and environmental protection, the wind and light abandonment can cause excessive emission of operators, and violates the emission permission agreed in advance, so that the cost of the wind and light abandonment needs to be paid for and violated the compensation expense, and the cost of the wind and light abandonment can be expressed as:
Figure GDA0001073055470000076
wherein, cwAnd cPVRespectively represents the cost of wind and light abandonment in unit, and the unit is as follows: RMB/kW.h; n is a radical ofwAnd NpvThe number of wind power and photovoltaic are respectively;
and d, considering that the micro gas turbine needs to consume natural gas traditional energy sources when in operation, and in order to express the relation between the active output and the fuel cost, the operation cost of the micro gas turbine can be expressed as follows:
Figure GDA0001073055470000077
wherein, cFPIs the fuel price, in units of: RMB/kW.h;
Figure GDA0001073055470000078
the active power of the r-th micro gas turbine in the t-th period, NMTNumber of micro gas turbines, ηMTFuel conversion efficiency for micro gas turbines;
and e, considering that the controllable load is an industrial load, and performing appropriate adjustment on the controllable load under the condition of ensuring the power supply amount by signing a relevant contract with the industrial load, considering that the comfort level of a consumer is necessarily influenced when the controllable load is adjusted, performing certain compensation on the controllable load, wherein the compensation cost is as follows:
Figure GDA0001073055470000079
wherein, ccl,lFor the compensation price when adjusting the l controllable load, the unit is: RMB/kW.h; n is a radical ofclIs the total controllable load number;
Figure GDA0001073055470000081
and adjusting the load active power of the ith controllable load for the t period.
The primal-dual interior point method in the step 5 is specifically realized as follows:
decoupling and solving static variables and dynamic variables by adopting an original dual interior point method, and reducing the order of a solved matrix, wherein the static variables comprise voltage amplitude and phase angle of each node, active and reactive power of a root node, active and reactive power of a wind turbine generator and photovoltaic, reactive power of a micro gas turbine, each loose variable when inequality constraint is relaxed, and lagrangian multipliers corresponding to each equality constraint and each inequality constraint; the dynamic variables include: the active and reactive powers of the battery energy storage system and the controllable load, the charge states of the battery energy storage system and the storage type controllable load and the active power of the micro gas turbine; the nonlinear programming problem comprises an objective function, an equality constraint, an inequality constraint and an inter-period coupling relation, and is in the form of:
min f(x)
s.t.ht(x)＝0 t＝1,…T
glt≤gt(x)≤gut
wherein f (x) is an objective function, ht(x) 0 is an equality constraint, glt≤gt(x)≤gutThe system is an inequality constraint, and both the equality constraint and the inequality constraint comprise a static part and a dynamic part, wherein the dynamic part comprises an energy constraint related to a battery energy storage system and a storage type controllable load and a climbing constraint of the micro gas turbine; solving by adopting a primal-dual interior point method, a series of coefficient matrixes in the form of a classical optimal power flow correction equation can be obtained:
Figure GDA0001073055470000082
wherein, WR1～WRTFor a matrix of coefficients related to the static variable, Δ X, after a reduction of the correction equation at the corresponding time intervalR1～ΔXRTLagrange multiplier variation for all static variables and equality constraints over a corresponding time period, BR1～BRTPartial derivatives of the static variables for corresponding time periods for Lagrangian functions, ER1～ERTFor a matrix of coefficients relating to the static variable after decoupling for a corresponding time period, DRFor a matrix of coefficients related to dynamic variables, Δ XRdFor dynamic variable variations, BRDCalculating the partial derivative of the dynamic variable for the Lagrange function; by utilizing the block diagonal band edge structure, the method can obtain the following results through linear transformation:
Figure GDA0001073055470000083
decoupling to obtain:
Figure GDA0001073055470000091
Δ X obtained from the above formulaRdSubstituting the formula to respectively solve the static variable delta X of each time intervalRt：
Figure GDA0001073055470000092
The branch shearing criterion in the step 5-d specifically comprises the following steps:
(1) the subproblem has no feasible solution; (2) all discrete variables have obtained integer solutions; (3) sub-problem target value greater than
Or equal to the upper bound; (4) the energy stored by the battery energy storage system does not meet the upper and lower limit constraints.
The invention has the beneficial effects that:
the active power distribution network short-term active power optimization model is provided based on the consideration of the economy of time-sharing electricity price and electricity purchasing and selling cost, equivalent operation cost of a battery energy storage system, wind and light abandoning cost, operation cost of a micro gas turbine, compensation cost for adjusting controllable load and the like, the aim of minimizing the total operation cost on the side of the distribution network is taken as the target, the solution is carried out through a branch-bound-primal-dual interior point method, the optimal scheduling management of distributed energy and the consumption of DGs are realized, and the operation economy of the active power distribution network is improved. The invention also provides a method for applying the decoupling interior point method to the solution of the multi-period nonlinear programming problem, and the calculation efficiency is improved.
Drawings
Fig. 1 is a simplified structural schematic diagram of a battery energy storage system.
Fig. 2 is a flow chart of the active power optimization algorithm of the present invention.
Fig. 3 is a charging and discharging model diagram of the battery energy storage system.
Fig. 4 is a diagram of the active and energy of a battery energy storage system.
FIG. 5 is a diagram illustrating a clipping process in a branch-and-bound method.
Fig. 6 is a schematic diagram of calculating the depth of discharge of the battery energy storage system by a rain flow counting method.
Fig. 7 is a diagram of a modified IEEE33 node system used in an example of the present method.
Fig. 8 is a daily load, wind turbine output, and photovoltaic output curve.
Fig. 9(a) is the SOC curve and the active power output curve of the BESS for case 1.
Fig. 9(b) is the active power output curve of the BESS for case 1.
FIG. 10 shows WF4 force application and subtracted contrast curves.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following 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.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, a battery energy storage system includes a power conditioning system, a monitoring system, a battery management system, and a battery module; the power regulating system is connected with an external power grid, a data transmission end of the power regulating system is respectively connected with the monitoring system and the battery module, and a data transmission end of the battery management system is respectively connected with the monitoring system and the battery module. The monitoring system sends control information to the power regulation system and the battery management system and receives state information from the power regulation system and the battery management system, and the battery management system sends control information to the battery module and receives state information from the battery.
As shown in fig. 2, a method for short-term active optimization of an active power distribution network including a battery energy storage system includes the following steps:
step 1, establishing a Battery Energy Storage System (BESS) active power and Energy model
The method comprises the following steps:
step 1-a, collecting basic parameters of a battery energy storage system, comprising: rated active power P of battery energy storage systemratedMaximum apparent power SBESS,maxCharge and discharge efficiency ηinDischarge efficiency ηoutRated capacity Wrated(ii) a Setting parameters of a working battery energy storage system: state of Charge (SOC) maximum and minimum SOC of a batterymax、SOCmin；
Step 1-b, establishing an active input/output model of the battery energy storage system, referring to a charging and discharging model diagram of the battery energy storage system shown in fig. 3, modeling the battery energy storage system into two independent generators, and respectively charging and discharging correspondingly, in particular, the battery energy storage system can not be charged and discharged at the same time:
Figure GDA0001073055470000101
wherein, ItIs the charging and discharging state of the battery energy storage system in the t-th period, It1 denotes discharge, It-1 represents the charge-up of the battery,
Figure GDA0001073055470000102
the active power of the battery energy storage system in the t-th period,
Figure GDA0001073055470000103
Figure GDA0001073055470000104
and
Figure GDA0001073055470000105
respectively representing the charging active power and the discharging active power of the battery energy storage system in the t-th time period; introducing a state variable ItThe charging and discharging state of the battery energy storage system at the moment t is represented, and the charging and discharging active power of the battery energy storage system is uniformly represented in a form of the product of a state variable and the active power; the physical characteristics of the power regulating system are considered, the external charge-discharge rate of the battery energy storage system is limited, and the range of the reactive power output of the battery energy storage system is limited by the actual active power output of the battery energy storage system through the restraint of the apparent power; for the energy of the battery energy storage system, the battery state of charge is used for representing the energy level of the battery energy storage system, and the SOC is restrained by considering the limit of the rated capacity of the battery energy storage system and the influence of the habit of a dispatcher. Step 1-c, establishing an energy model of the battery energy storage system:
Figure GDA0001073055470000106
wherein the content of the first and second substances,
Figure GDA0001073055470000107
for the stored energy of the battery energy storage system during the t-th period,
Figure GDA0001073055470000108
the energy stored in the initial stage (namely the 0 th time period) of the battery energy storage system is delta t, and the delta t is a time step;
step 2, establishing an equivalent operation cost model of the battery energy storage system;
the equivalent operation cost of the battery energy storage system comprises two parts of fixed investment cost and maintenance cost;
the fixed investment cost of the battery energy storage system can be uniformly distributed to each time of cyclic charge and discharge of the battery energy storage system, and the discharge depth of the mth cycle period of the kth battery energy storage system is defined as DoD,k,mSo the equivalent investment cost for a single cycle charge-discharge of the battery energy storage system can be expressed as:
Figure GDA0001073055470000111
wherein, CPAnd CWRespectively unit power investment cost and unit capacity investment cost of the battery energy storage system, wherein the units of the investment cost are RMB/kW and RMB/kWh; n is a radical ofctf(DoD,k,m) To depth of discharge DoD,k,mThe corresponding cycle life of the battery energy storage system;
maintenance cost and rated active power P of battery energy storage systemratedRated capacity WratedAnd operating time, expressed as:
CBESS＝Y(mPPrated+mWWrated)
wherein m isPAnd mWThe unit power and unit capacity operation maintenance cost of the battery energy storage system in unit time are respectively RMB/kW.h and RMB/kW.h2(ii) a Y is working time;
step 3, establishing an active power and energy relation model of the controllable load, and regarding the controllable load as a generator with negative output:
step 3-a, establishing an active power and energy relation model capable of Directly controlling a load (DMFD):
Figure GDA0001073055470000112
wherein
Figure GDA0001073055470000113
The active power of the load can be directly controlled in the t-th time period and is a negative value; eDMFDThe total electric quantity demand of the load in the dispatching cycle;
step 3-b, establishing an active and energy relation model of Storage class controlled Flexible Demand (SMFD):
Figure GDA0001073055470000114
wherein the content of the first and second substances,
Figure GDA0001073055470000115
the energy stored in the controllable-like load is stored for the t-th period,
Figure GDA0001073055470000116
storing energy for storing an initial stage (0 th period) of the class controllable load;
Figure GDA0001073055470000117
capacity for storage class controllable loads; μ is the conversion efficiency between electrical energy and stored energy;
Figure GDA0001073055470000118
storing active power injection of the controllable load for each time interval, wherein the active power injection is a negative value;
Figure GDA0001073055470000119
extracting heat from storage class controllable loads for each time periodThe power of (d);
step 4, establishing a short-term active optimization model taking the minimum total running cost of the power distribution network side as a target function on the basis of the active and energy model, the equivalent running cost model and the controllable load active and energy relation model of the battery energy storage system;
step 4-a, the objective function comprises electricity purchasing cost, equivalent operation cost of a battery energy storage system, wind and light abandoning cost, operation cost of a micro gas turbine and compensation cost for adjusting controllable load, and the objective function is expressed as:
minf＝C1+C2+C3+C4+C5
wherein, C1Sum of electricity purchasing cost and electricity selling income for distribution side, C2For equivalent operating costs of the battery energy storage system, C3To optimize the cost of wind and light rejection in the scheduling process, C4For the operating costs of micro gas turbines, C5Compensation costs for adjusting the controllable load;
step 4-b, establishing equality constraints including tidal current balance equation constraints of nodes in each time period, coupling equality constraints between the battery energy storage system and the controllable load time period;
the node power flow balance equation is constrained as follows:
Figure GDA0001073055470000121
Figure GDA0001073055470000122
wherein:
Figure GDA0001073055470000123
and
Figure GDA0001073055470000124
active and reactive power output of the wind turbine generator at a node i in the t-th time period;
Figure GDA0001073055470000125
and
Figure GDA0001073055470000126
photovoltaic active and reactive power output at a node i in the t-th time period;
Figure GDA0001073055470000127
and
Figure GDA0001073055470000128
then the active and reactive power at the distribution network root node (i.e. the active and reactive power delivered by the transmission network to the distribution network) at the t-th time period is represented;
Figure GDA0001073055470000129
and
Figure GDA00010730554700001210
the charging and discharging active and reactive power output of the battery energy storage system at the node i in the t-th time period is represented;
Figure GDA00010730554700001211
and
Figure GDA00010730554700001212
the active power and the reactive power of the load can be directly controlled at a node i in the t-th period;
Figure GDA00010730554700001213
and
Figure GDA00010730554700001214
active power and reactive power of the storage type controllable load at the node i in the t-th period;
Figure GDA00010730554700001215
and
Figure GDA00010730554700001216
respectively providing active power and reactive power of the micro gas turbine at the i node in the t period;
Figure GDA00010730554700001217
and
Figure GDA00010730554700001218
the real power and the reactive power of a fixed load at a node i in the t-th period (the fixed load is different from the aforementioned controllable load, and the load is uncontrollable and has a fixed size); n is the number of nodes, Vi tAnd
Figure GDA00010730554700001219
is the voltage amplitude, G, of node i during the t-th periodijAnd BijFor the real and imaginary parts of the transadmittance between nodes i and j,
Figure GDA00010730554700001220
the phase angle difference of the voltages of the two nodes i and j in the t period; the actual active power output of the wind turbine generator and the photovoltaic power system also meets the following equation:
Figure GDA00010730554700001221
Figure GDA00010730554700001222
in the formula (I), the compound is shown in the specification,
Figure GDA00010730554700001223
and
Figure GDA00010730554700001224
the active output predicted value of the wind turbine generator and the photovoltaic at the node i in the t-th time period is obtained;
Figure GDA00010730554700001225
and
Figure GDA00010730554700001226
respectively the active power of the fan abandoned wind or the photovoltaic abandoned light at the node i in the t-th time period;
the battery energy storage system and the storage type controllable load energy constraints are respectively as follows:
Figure GDA00010730554700001227
SOCT＝SOC0
Figure GDA0001073055470000131
Figure GDA0001073055470000132
wherein T is the total time period number of the scheduling period; SOCTThe residual electric quantity of the battery energy storage system at the last moment is obtained;
Figure GDA0001073055470000133
the residual capacity at the last moment of the storage type load is stored;
step 4-c, establishing inequality constraints including node voltage upper and lower limit constraints, namely voltage and branch power flow constraints in conventional Optimal Power Flow (OPF) and control and state variable related constraints: and (3) limiting the upper and lower limits of the node voltage:
Vi,min＜Vi t＜Vi,max
wherein, Vi,minAnd Vi,maxRespectively the minimum value and the maximum value allowed by the voltage at the node i;
branch flow constraint:
Figure GDA0001073055470000134
wherein the content of the first and second substances,
Figure GDA0001073055470000135
apparent power, S, of branch l during period tl.maxIs the apparent power maximum for branch l;
as shown in fig. 3 and 4, the active power, apparent power and energy constraints of the battery energy storage system are respectively:
Figure GDA0001073055470000136
Figure GDA0001073055470000137
SOCmin＜SOCt＜SOCmax
therein, SOCmaxAnd SOCminThe maximum and minimum values of the battery state of charge of the battery energy storage system,
Figure GDA0001073055470000138
the reactive output of the battery energy storage system in the t-th time period is represented;
active and reactive power output limitation and climbing restraint of the micro gas turbine:
Figure GDA0001073055470000139
Figure GDA00010730554700001310
Figure GDA00010730554700001311
Figure GDA00010730554700001312
wherein the content of the first and second substances,
Figure GDA00010730554700001313
for the active power output, P, of the micro gas turbine during the t-th periodMT,i,minAnd PMT,i,maxThe lower limit and the upper limit of the active power output of the micro gas turbine are respectively;
Figure GDA00010730554700001314
for the t-th period of time, the reactive power, Q, of the micro gas turbineMT,minAnd QMT,maxRespectively the lower limit and the upper limit of the reactive power output of the micro gas turbineLimiting; rMT,upAnd RMT,downRespectively represents the upper limit and the lower limit of the climbing power when the micro gas turbine increases and decreases the load.
Active power and reactive power constraints of the wind turbine generator and the photovoltaic are not fixed:
Figure GDA0001073055470000141
Figure GDA0001073055470000142
Figure GDA0001073055470000143
Figure GDA0001073055470000144
wherein the content of the first and second substances,
Figure GDA0001073055470000145
the reactive power output of the fan is in the t-th time period; qW,maxAnd QW,minRespectively the maximum value and the minimum value of the reactive power output of the fan;
Figure GDA0001073055470000146
reactive power output, Q, of photovoltaic power generation in the t-th periodPV,maxAnd QPV,minThe maximum value and the minimum value of the photovoltaic power generation reactive output are respectively.
And (3) controllable load active power and energy constraint:
Figure GDA0001073055470000147
Figure GDA0001073055470000148
Figure GDA0001073055470000149
wherein the content of the first and second substances,
Figure GDA00010730554700001410
is the upper limit of the output of the controllable load,
Figure GDA00010730554700001411
the lower limit of the output force of the controllable load. SOCSMFD,maxAnd SOCSMFD,minRespectively the upper and lower limits of the storage-type controllable load state of charge.
Step 5, as shown in fig. 5, in consideration of the fact that the active optimization problem is a mixed integer nonlinear programming problem, solving by using a branch-bound-primal dual interior point method:
step 5-a, according to the prediction results of the wind power output and the load, solving the active optimization of each time interval according to the scheduling condition of the previous day to obtain the target value of each time interval, namely the value of the target function corresponding to the current time interval, and using the target value as the upper bound of each time interval in the process of processing the discrete variable by using a branch-and-bound method;
step 5-b, the charging and discharging states of each battery energy storage system in each time interval are discrete variables, the original dual interior point method is adopted to solve the optimal power flow problem after the discrete variables are relaxed (for example, the relaxation process in the branch and bound method is to relax the discrete variables into the relaxation problem only containing continuous variables, if the discrete variables are { -2, -1,1}, the relaxation process becomes [ -2,1]), the values of each control variable, each state variable and the corresponding target function are obtained, whether the results of all the discrete variables are integers is judged, and if yes, the results are stored; otherwise, adding the relaxation problem and the objective function value thereof into a queue to be branched, marking as RP, and taking the objective function value as a new lower bound of the objective value;
step 5-c, branching the single discrete variables of the subproblems in the RP in sequence, solving each relaxation subproblem by adopting an original dual interior point method, judging whether all the discrete variables obtain integer values, if so, saving the result, and turning to step 5-f; if not, adding the branch queue into a next waiting branch queue, and recording as RRP;
step 5-d, pruning all the subproblems in the RRP according to a pruning rule, and updating the RP;
step 5-e, judging whether the queue RP to be branched is empty, if so, making an error, and quitting the calculation; if not, turning to the step 5-c;
and 5-f, calculating the depth of discharge of all the scheduling modes meeting the constraint conditions, then obtaining the equivalent running cost, adding the equivalent running cost into the objective function value of each scheduling mode, and taking the solution with the minimum objective function value as the optimal solution to realize the short-term active optimization of the active power distribution network.
The step 2 of establishing the mathematical relationship between the discharge depth and the cycle life thereof and calculating the discharge depth comprises the following steps:
step 2-a, life and temperature of the energy storage device, peak current, depth of discharge D during operation thereofoDClosely related, the larger the depth of discharge is, the shorter the cycle life of the energy storage device is, and the polynomial function method is used for the depth of discharge DoDAnd cycle life NctfFitting the functional relationship between them, depth of discharge DoDAnd cycle life NctfThe functional relationship between the two is as follows:
Figure GDA0001073055470000151
wherein, aiIs the coefficient corresponding to the i-th order, and N is the polynomial order;
depth of discharge D in the above equationoDIs a variable having a non-linear relationship with the charge-discharge state and the active power of the battery, i.e.
Figure GDA0001073055470000152
It cannot give an explicit mathematical expression, so it is calculated by a rain flow counting method; step 2-b, the rain flow counting method comprises the following steps, specifically referring to fig. 6:
1) clockwise rotating a battery charge state-time curve of a battery energy storage system by 90 degrees, regarding the curve as an eave, and starting rain flow from a starting point and each peak/valley value in sequence;
2) the rain drops vertically when flowing to the peak/valley, and the rain drops until the opposite surface has a peak value or a valley value larger than the maximum value or the minimum value at the beginning, namely the maximum value or the minimum value in the whole process;
3) drawing a flow path of each raindrop according to the starting point and the end point of the flowing of each raindrop, namely each cycle half period, and simultaneously recording the peak-to-valley values of all the cycle half periods;
4) the horizontal length of the rain flow path in each cycle is the discharge depth of the battery energy storage system in the cycle period.
In step 4, the objective function specifically consists of:
step a, considering the situation that power exchange can be performed between the main network and the distribution network side purchases different electricity selling prices, the sum of the electricity purchasing cost and the electricity selling income of the distribution side can be expressed as:
Figure GDA0001073055470000153
wherein the content of the first and second substances,
Figure GDA0001073055470000154
active power delivered to the distribution network for the main network during the t-th period, CtThe purchase and sale electricity price of the main network in the t-th scheduling period for the distribution network can be expressed as:
Figure GDA0001073055470000155
wherein the content of the first and second substances,
Figure GDA0001073055470000156
and C-The unit of the distribution network electricity purchasing price and the electricity selling price are RMB/kW.h respectively in the time period of t, and
Figure GDA0001073055470000157
step b, in order to fully consider the economic benefits of the distribution network side, the equivalent operation cost of the battery energy storage system is considered besides the electricity purchasing and selling cost of the distribution network side, and the equivalent operation cost of the battery energy storage system can be expressed as:
Figure GDA0001073055470000161
wherein N isBFor the number of battery energy storage systems, MkIs the total cycle number in the scheduling period of the battery energy storage system of No. k, Ce,k,m(DoD,k,m) The m-th discharge depth of the kth battery energy storage system is DoD,k,mEquivalent investment cost under the cycle period of (1); cBESS,kEquivalent maintenance cost for the k-th BESS.
And step c, considering that the wind power and the photovoltaic power generation do not need to consume fuel, assuming that the power generation cost is zero, from the aspects of economy and environmental protection, the wind and light abandonment can cause excessive emission of operators, and violates the emission permission agreed in advance, so that the cost of the wind and light abandonment needs to be paid for and violated the compensation expense, and the cost of the wind and light abandonment can be expressed as:
Figure GDA0001073055470000162
wherein, cwAnd cPVRespectively represents the cost of wind and light abandonment in unit, and the unit is as follows: RMB/kW.h; n is a radical ofwAnd NpvThe number of wind power and photovoltaic are respectively.
And d, considering that the micro gas turbine needs to consume natural gas traditional energy sources when in operation, and in order to express the relation between the active output and the fuel cost, the operation cost of the micro gas turbine can be expressed as follows:
Figure GDA0001073055470000163
wherein, cFPIs the fuel price, in units of: RMB/kW.h;
Figure GDA0001073055470000164
the active power of the r-th micro gas turbine in the t-th period, NMTNumber of micro gas turbines, ηMTThe fuel conversion efficiency of the micro gas turbine.
And e, considering that the controllable load is an industrial load, and performing appropriate adjustment on the controllable load under the condition of ensuring the power supply amount by signing a relevant contract with the industrial load, considering that the comfort level of a consumer is necessarily influenced when the controllable load is adjusted, performing certain compensation on the controllable load, wherein the compensation cost is as follows:
Figure GDA0001073055470000165
wherein, ccl,lFor the compensation price when adjusting the l controllable load, the unit is: RMB/kW.h; n is a radical ofclIs the total controllable load number;
Figure GDA0001073055470000166
and adjusting the load active power of the ith controllable load for the t period.
The primal-dual interior point method in the step 5 is specifically realized as follows:
decoupling and solving static variables and dynamic variables by adopting an original dual interior point method, and reducing the order of a solved matrix, wherein the static variables comprise voltage amplitude and phase angle of each node, active and reactive power of a root node, active and reactive power of a wind turbine generator and photovoltaic, reactive power of a micro gas turbine, each loose variable when inequality constraint is relaxed, and lagrangian multipliers corresponding to each equality constraint and each inequality constraint; the dynamic variables include: the active and reactive powers of the battery energy storage system and the controllable load, the charge states of the battery energy storage system and the storage type controllable load and the active power of the micro gas turbine; the above nonlinear programming problem includes an objective function, an equality constraint, an inequality constraint, and an inter-period coupling relationship (both the equality constraint and the inequality constraint may include the inter-period coupling relationship), and is of the form:
min f(x)
s.t.ht(x)＝0 t＝1,…T
glt≤gt(x)≤gut
wherein f (x) is an objective function, ht(x) 0 is an equality constraint, glt≤gt(x)≤gutIs notEquality constraint, and equality constraint and inequality constraint include static and dynamic two parts, the dynamic part includes the battery energy storage system and the energy constraint related to controllable load of storage type, climbing constraint of the miniature gas turbine; solving by adopting a primal-dual interior point method, a series of coefficient matrixes in the form of a classical optimal power flow correction equation can be obtained:
Figure GDA0001073055470000171
wherein, WR1～WRTFor a matrix of coefficients related to the static variable, Δ X, after a reduction of the correction equation at the corresponding time intervalR1～ΔXRTLagrange multiplier variation for all static variables and equality constraints over a corresponding time period, BR1～BRTPartial derivatives of the static variables for corresponding time periods for Lagrangian functions, ER1～ERTFor a matrix of coefficients relating to the static variable after decoupling for a corresponding time period, DRFor a matrix of coefficients related to dynamic variables, Δ XRdFor dynamic variable variations, BRDCalculating the partial derivative of the dynamic variable for the Lagrange function; by utilizing the block diagonal band edge structure, the method can obtain the following results through linear transformation:
Figure GDA0001073055470000172
decoupling to obtain:
Figure GDA0001073055470000173
Δ X obtained from the above formulaRdSubstituting the formula to respectively solve the static variable delta X of each time intervalRt：
Figure GDA0001073055470000174
All variables need to be solved, and the method only decouples the static variables and the dynamic variables and solves the variables separately, so that the calculation speed can be improved.
The branch shearing criterion in the step 5-d specifically comprises the following steps:
(1) the subproblem has no feasible solution; (2) all discrete variables have obtained integer solutions; (3) the sub-problem target value is greater than or equal to the upper bound; (4) the energy stored by the battery energy storage system does not meet the upper and lower limit constraints.
The feasibility and effectiveness of the model and algorithm of the present invention are described below with respect to fig. 7 to 10, using modified IEEE33 node calculations as specific examples:
fig. 7 is a diagram of a modified IEEE33 node system used in an example of the present method. Supposing that wind turbines are additionally arranged on nodes 10, 16, 20 and 23 respectively, wherein the fan at the node 10 is uncontrollable, and the rest wind turbines are controllable; and the No. 10 and No. 16 nodes are respectively provided with a No. 1 lead-acid battery energy storage system and a No. 2 lead-acid battery energy storage system; in addition, photovoltaic power generation equipment is additionally arranged on the node No. 31, the node No. 24 is provided with SMFD, and the node No. 31 is provided with DMFD. Other parameters of the IEEE33 node system are unchanged. Taking a certain day as an example, the load, wind turbine generator/photovoltaic active power output prediction curve and the difference curve thereof in 24 hours of the next day are shown in fig. 8. Assuming that the power factors of 24-hour loads are all 0.85, the exchange power of the connecting lines of the power distribution network and the main network is 500kW and 500kVar at most. The parameters related to BESS, photovoltaic power generation and electricity purchase and sale prices are shown in the following table 1:
TABLE 1
Parameter name Numerical value Parameter name Numerical value
Cell type 0.3MW/4MW·h SOCmin 0.4
SOCmax 0.9 ηin，ηout 0.9，0.9
C+ ￥1/kW·h C_ ￥0.3/kW·h
CP 650 CW 460
mP 0.02 mW 0.02
Photovoltaic output 0.6MW/0.6KVA ccl ￥1.2/kW·h
cw ￥0.1/kW·h cPV ￥0.1/kW·h
cFP ￥1.1/kW·h ηMT 40％
PMT,min 100kW PMT,max 300kW
RMT,up 100kW·h-1 RMT,down 100kW·h-1
The corresponding cycle life of the lead acid battery at different depths of discharge is shown in table 2:
TABLE 2
Figure GDA0001073055470000181
Consider the following two cases:
case 1: BESS is considered, but controllable load is not considered;
case 2: while accounting for the BESS and the controllable load.
Case 1 is solved by the branch-bound-primal-dual interior point method provided by the invention, and in this case, the SOC curve and the active power output of the BESS in the simulation result are shown in fig. 9(a) and fig. 9 (b).
Under the optimal strategy, the electric energy transmitted from the main network to the distribution network within 24 days is 4019.36kW & h, the electric energy transmitted from the ADN to the main network back through the main network and distribution network contact line is 1126.93kW & h, and the daily operation cost of the ADN is ￥ 9264.47. although the excess wind power and photovoltaic are stored as much as possible by using BESS in the process, the excess wind power and photovoltaic are still remained due to BESS power limitation and main network and distribution network connection line exchange power limitation, such as the BESS charging power reaches the upper limit within 15-16 time intervals, and the main network and distribution network connection point transmission power also reaches the upper limit, at the moment, only wind abandonment is carried out, and 796.84 kWh wind power needs to be abandoned in the whole scheduling process.
Table 3 shows the details of several costs in the simulation results. The depth of discharge of the two BESS is respectively 0.29, 0.19, 0.27 and 0.18, so that the equivalent operation cost is calculated.
TABLE 3
Electricity purchasing device Selling electricity Abandon wind MT BESS Sum of
Electric quantity/kW.h 4019.36 1126.93 796.84 622.68 — —
Cost/￥ 4019.36 -338.08 79.68 684.94 4818.57 9264.47
As can be seen from the table, the main cost is composed of the electricity purchase cost and the equivalent cost of BESS, wherein since BESS is relatively high in cost, the cost which is spread out to each cycle is still relatively high after calculating the equivalent cycle life by the rain flow counting method. Further, since the unit power generation cost of the micro gas turbine is high compared to others, the micro gas turbine is not used as much as possible. However, in time period 12, the sum of the BESS output and the main network connection point output still cannot balance the difference between the wind power and the load, so the balance is carried out by a micro gas turbine (149.69 kW). Meanwhile, the active power output of the micro gas turbine has a certain active power output (49.69kW) in the time periods 11 and 13 because of the climbing constraint (100 kW. h < -1 >) of the active power output of the micro gas turbine. In the whole scheduling process, the BESS is used for storing redundant wind power and photovoltaic power as much as possible due to the consideration of the compensation cost of wind abandoning and light abandoning.
In case 2, DMFD and SMFD are used to replace the original fixed load at the node, but the total load demand remains the same as in case 1, and the power factor of the load is 0.85. The adjustable time period for both DMFD and SMFD is set to 9-17, and the settings for several parameters of DMFD and SMFD are shown in table 4. The situation mainly researches BESS together with controllable load coordination optimization to exert the peak clipping and valley filling capacity.
The optimization strategy is obtained after the model and the method provided by the invention are adopted, the result shows that the electric energy transmitted from the main network to the distribution network is 3463.82 kW.h in total, the ADN transmits the electric energy to the main network in a back-transmission mode through the main network and distribution network connecting lines, the electric energy is 1126.93 kW.h, and the daily electricity purchasing cost of the ADN is ￥ 8665.38.
TABLE 4
Figure GDA0001073055470000191
Figure GDA0001073055470000201
Table 5 shows the details of several costs in the simulation results. As can be seen from the table, compared with the case 1, under the condition that the total load is not changed, the power purchasing amount and the wind abandoning amount of the power distribution network are obviously reduced, and the economical efficiency of the power distribution network is improved in the aspect of the total cost.
TABLE 5
Electricity purchasing device Selling electricity Abandon wind MT Controllable load BESS Sum of
Electric quantity/kW.h 3463.82 1126.93 257.92 0 579.4 — —
Cost/￥ 3463.82 -338.08 25.79 0 695.28 4818.57 8665.38
FIG. 10 is a WF4 minus hair contrast curve for cases 1 and 2. The power is purchased from the main network through the distribution network under the condition of reducing the power generation contrast curve and 2 conditions, the abandoned wind quantity is reduced under the condition 2, and the part of wind power is used for supplying power to part of controllable loads. Although the compensation cost exists in the adjustment of the controllable load, which is slightly larger than the operation cost of the gas turbine in the case 1, the adjustment can not only reduce the abandoned wind, but also reduce the power purchasing quantity of the distribution network, and can also reduce the load in the time interval 11-12 and reduce the use of the gas turbine.
By combining the two situations, the energy storage system is introduced in the situation 1, the peak clipping and valley filling effects of the energy storage system are exerted, and the consumption of the distributed power supply is improved, so that the operation economy of the distribution network is improved; and in case 2, the controllable load is introduced on the basis of the case 1, the coordinated control of the controllable DG, the BESS and the controllable load is realized through optimized scheduling, the controllability and the flexibility of the controllable DG, the BESS and the controllable load are fully exerted, and the operation cost is reduced.
The calculation results show that the optimization model can play the roles of BESS, the flexibility of controllable load and peak clipping and valley filling of the BESS, improve the utilization rate of renewable energy sources and the capability of a power distribution network to absorb the BESS, reduce the operation cost of the active power distribution network and improve the operation economy of the active power distribution network. The implementation of the optimization model provides an effective tool for short-term active optimization and control of the active power distribution network.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. A short-term active optimization method for an active power distribution network with a battery energy storage system is characterized by comprising the following steps:
step 1, establishing a model of active power and energy of a battery energy storage system, and specifically comprising the following steps:
step 1-a, collecting basic parameters of a battery energy storage system, comprising: rated active power P of battery energy storage systemratedMaximum apparent power SBESS,maxCharge and discharge efficiency ηinDischarge efficiency ηoutRated capacity Wrated(ii) a Setting parameters of a working battery energy storage system: battery state of charge maximum and minimum SOCmax、SOCmin；
Step 1-b, establishing an active input and output model of the battery energy storage system:
Figure FDA0002228892500000011
wherein, ItIs the charging and discharging state of the battery energy storage system in the t-th period, It1 denotes discharge, It-1 represents the charge-up of the battery,
Figure FDA0002228892500000012
the active power of the battery energy storage system in the t-th period,
Figure FDA0002228892500000013
Figure FDA0002228892500000014
and
Figure FDA0002228892500000015
respectively representing the charging active power and the discharging active power of the battery energy storage system in the t-th time period;
step 1-c, establishing an energy model of the battery energy storage system:
Figure FDA0002228892500000016
wherein the content of the first and second substances,
Figure FDA0002228892500000017
for the stored energy of the battery energy storage system during the t-th period,
Figure FDA0002228892500000018
the energy stored in the initial stage of the battery energy storage system is delta t, and the delta t is a time step;
step 2, establishing an equivalent operation cost model of the battery energy storage system;
the equivalent operation cost of the battery energy storage system comprises two parts of fixed investment cost and maintenance cost;
setting the fixed investment cost of the battery energy storage system to be evenly distributed on each cycle of charging and discharging of the battery energy storage system, and defining the discharge depth of the mth cycle period of the kth battery energy storage system as DoD,k,mSo the equivalent investment cost for a single cycle charge-discharge of the battery energy storage system can be expressed as:
Figure FDA0002228892500000019
wherein, CPAnd CWRespectively unit power investment cost and unit capacity investment cost of the battery energy storage system, wherein the units of the investment cost are RMB/kW and RMB/kWh; n is a radical ofctf(DoD,k,m) To depth of discharge DoD,k,mThe corresponding cycle life of the battery energy storage system;
maintenance cost and rated active power P of battery energy storage systemratedRated capacity WratedAnd operating time, expressed as:
CBESS＝Y(mPPrated+mWWrated)
wherein m isPAnd mWThe unit power and unit capacity operation maintenance cost of the battery energy storage system in unit time are respectively RMB/kW.h and RMB/kW.h2(ii) a Y is working time;
step 3, establishing an active power and energy relation model of the controllable load, and regarding the controllable load as a generator with negative output:
step 3-a, establishing an active power and energy relation model capable of directly controlling the load:
Figure FDA0002228892500000021
wherein
Figure FDA0002228892500000022
The active power of the load can be directly controlled in the t-th time period and is a negative value; eDMFDThe total electric quantity demand of the load in the dispatching cycle; t is the total time period number of the scheduling period;
step 3-b, establishing an active and energy relation model of the storage type controllable load:
Figure FDA0002228892500000023
wherein the content of the first and second substances,
Figure FDA0002228892500000024
the energy stored in the controllable-like load is stored for the t-th period,
Figure FDA0002228892500000025
storing energy stored in the initial stage of the controllable load;
Figure FDA0002228892500000026
capacity for storage class controllable loads; μ is the conversion efficiency between electrical energy and stored energy;
Figure FDA0002228892500000027
storing active power injection of the controllable load for each time interval, wherein the active power injection is a negative value;
Figure FDA0002228892500000028
power to extract heat from the storage class controllable load for each time period;
step 4, establishing a short-term active optimization model taking the minimum total running cost of the power distribution network side as a target function on the basis of the active and energy model, the equivalent running cost model and the controllable load active and energy relation model of the battery energy storage system;
step 4-a, the objective function comprises electricity purchasing cost, equivalent operation cost of a battery energy storage system, wind and light abandoning cost, operation cost of a micro gas turbine and compensation cost for adjusting controllable load, and the objective function is expressed as:
min f＝C1+C2+C3+C4+C5
wherein, C1Sum of electricity purchasing cost and electricity selling income for distribution side, C2For equivalent operating costs of the battery energy storage system, C3To optimize the cost of wind and light rejection in the scheduling process, C4For the operating costs of micro gas turbines, C5Compensation costs for adjusting the controllable load;
step 4-b, establishing equality constraints including tidal current balance equation constraints of nodes in each time period, coupling equality constraints between the battery energy storage system and the controllable load time period;
the node power flow balance equation is constrained as follows:
Figure FDA0002228892500000029
Figure FDA00022288925000000210
wherein:
Figure FDA00022288925000000211
and
Figure FDA00022288925000000212
active and reactive power output of the wind turbine generator at a node i in the t-th time period;
Figure FDA00022288925000000213
and
Figure FDA00022288925000000214
photovoltaic active and reactive power output at a node i in the t-th time period;
Figure FDA00022288925000000215
and
Figure FDA00022288925000000216
then the active power and the reactive power at the root node of the distribution network in the t-th period are represented;
Figure FDA0002228892500000031
and
Figure FDA0002228892500000032
the charging and discharging active and reactive power output of the battery energy storage system at the node i in the t-th time period is represented;
Figure FDA0002228892500000033
and
Figure FDA0002228892500000034
the active power and the reactive power of the load can be directly controlled at a node i in the t-th period;
Figure FDA0002228892500000035
and
Figure FDA0002228892500000036
active power and reactive power of the storage type controllable load at the node i in the t-th period;
Figure FDA0002228892500000037
and
Figure FDA0002228892500000038
respectively providing active power and reactive power of the micro gas turbine at the i node in the t period;
Figure FDA0002228892500000039
and
Figure FDA00022288925000000310
the real power and the reactive power of the fixed load at the node i in the t-th period; n is the number of nodes, Vi tAnd
Figure FDA00022288925000000311
is the voltage amplitude, G, of node i during the t-th periodijAnd BijFor the real and imaginary parts of the transadmittance between nodes i and j,
Figure FDA00022288925000000312
the phase angle difference of the voltages of the two nodes i and j in the t period; the actual active power output of the wind turbine generator and the photovoltaic power system also meets the following equation:
Figure FDA00022288925000000313
Figure FDA00022288925000000314
in the formula (I), the compound is shown in the specification,
Figure FDA00022288925000000315
and
Figure FDA00022288925000000316
the active output predicted value of the wind turbine generator and the photovoltaic at the node i in the t-th time period is obtained;
Figure FDA00022288925000000317
and
Figure FDA00022288925000000318
respectively the active power of the fan abandoned wind or the photovoltaic abandoned light at the node i in the t-th time period;
the battery energy storage system and the storage type controllable load energy constraints are respectively as follows:
Figure FDA00022288925000000319
SOCT＝SOC0
Figure FDA00022288925000000320
Figure FDA00022288925000000321
wherein T is the total time period number of the scheduling period; SOCTThe residual electric quantity of the battery energy storage system at the last moment is obtained;
Figure FDA00022288925000000322
the residual capacity at the last moment of the storage type load is stored;
step 4-c, establishing inequality constraints including node voltage upper and lower limit constraints, branch power flow constraints and control variable and state variable related constraints:
and (3) limiting the upper and lower limits of the node voltage:
Vi,min＜Vi t＜Vi,max
wherein, Vi,minAnd Vi,maxRespectively the minimum value and the maximum value allowed by the voltage at the node i;
branch flow constraint:
Figure FDA00022288925000000323
wherein the content of the first and second substances,
Figure FDA00022288925000000324
apparent power, S, of branch l during period tl.maxIs the apparent power maximum for branch l;
the active power, apparent power and energy constraint of the battery energy storage system are respectively as follows:
Figure FDA0002228892500000041
Figure FDA0002228892500000042
SOCmin＜SOCt＜SOCmax
therein, SOCmaxAnd SOCminThe battery state of charge maximum and minimum values of the battery energy storage system,
Figure FDA0002228892500000043
the reactive output of the battery energy storage system in the t-th time period is represented;
active and reactive power output limitation and climbing restraint of the micro gas turbine:
Figure FDA0002228892500000044
Figure FDA0002228892500000045
Figure FDA0002228892500000046
Figure FDA0002228892500000047
wherein the content of the first and second substances,
Figure FDA0002228892500000048
for the active power output, P, of the micro gas turbine during the t-th periodMT,i,minAnd PMT,i,maxThe lower limit and the upper limit of the active power output of the micro gas turbine are respectively;
Figure FDA0002228892500000049
for the t-th period of time, the reactive power, Q, of the micro gas turbineMT,minAnd QMT,maxRespectively is the lower limit and the upper limit of the reactive power output of the micro gas turbine; rMT,upAnd RMT,downRespectively representing the upper limit and the lower limit of the climbing power when the load of the micro gas turbine is increased or decreased;
active power and reactive power constraints of the wind turbine generator and the photovoltaic are not fixed:
Figure FDA00022288925000000410
Figure FDA00022288925000000411
Figure FDA00022288925000000412
Figure FDA00022288925000000413
wherein the content of the first and second substances,
Figure FDA00022288925000000414
the reactive power output of the wind turbine generator is the t-th time period; qW,maxAnd QW,minRespectively the maximum value and the minimum value of the reactive output of the wind turbine generator;
Figure FDA00022288925000000415
is the reactive power of photovoltaic in the t-th period, QPV,maxAnd QPV,minRespectively the maximum value and the minimum value of the reactive output of the photovoltaic;
and (3) controllable load active power and energy constraint:
Figure FDA00022288925000000416
Figure FDA00022288925000000417
Figure FDA00022288925000000418
wherein the content of the first and second substances,
Figure FDA00022288925000000419
is the upper limit of the output of the controllable load,
Figure FDA00022288925000000420
the lower limit of the output force is the controllable load; SOCSMFD,maxAnd SOCSMFD,minRespectively the upper limit and the lower limit of the storage type controllable load charge state;
and 5, considering that the active power optimization problem is a mixed integer nonlinear programming problem, solving by adopting a branch-bound-primal dual interior point method:
step 5-a, according to the prediction results of the wind power output and the load, solving the active optimization of each time interval according to the scheduling condition of the previous day to obtain the target value of each time interval, namely the value of the target function corresponding to the current time interval, and using the target value as the upper bound of each time interval in the process of processing the discrete variable by using a branch-and-bound method;
step 5-b, the charging and discharging states of each battery energy storage system in each time period are discrete variables, firstly all the discrete variables are loosened, then the optimal power flow problem only containing continuous variables is solved by adopting an original dual interior point method, the values of each control variable, each state variable and the corresponding objective function are obtained, whether the results of all the discrete variables are integers is judged, and if yes, the results are stored; otherwise, adding the relaxation problem and the objective function value thereof into a queue to be branched, marking as RP, and taking the objective function value as a new lower bound of the objective value;
step 5-c, branching the single discrete variables of the subproblems in the RP in sequence, solving each relaxation subproblem by adopting an original dual interior point method, judging whether all the discrete variables obtain integer values, if so, saving the result, and turning to 5-f; if not, adding the branch queue into a next waiting branch queue, and recording as RRP;
step 5-d, pruning all the subproblems in the RRP according to a pruning rule, and updating the RP;
step 5-e, judging whether the queue RP to be branched is empty, if so, making an error, and quitting the calculation; if not, turning to the step 5-c;
and 5-f, calculating the depth of discharge of all the scheduling modes meeting the constraint conditions, then obtaining the equivalent running cost, adding the equivalent running cost into the objective function value of each scheduling mode, and taking the solution with the minimum objective function value as the optimal solution to realize the short-term active optimization of the active power distribution network.
2. The active power distribution network short-term active power optimization method comprising the battery energy storage system according to claim 1, wherein the method comprises the following steps: the step 2 of establishing the mathematical relationship between the discharge depth and the cycle life thereof and calculating the discharge depth comprises the following steps:
step 2-a, life and temperature of the energy storage device, peak current, depth of discharge D during operation thereofoDClosely related, the larger the depth of discharge is, the shorter the cycle life of the energy storage device is, and the polynomial function method is used for the depth of discharge DoDAnd cycle life NctfFitting the functional relationship between them, depth of discharge DoDAnd cycle life NctfThe functional relationship between the two is as follows:
Figure FDA0002228892500000051
wherein, aiIs the coefficient corresponding to the i-th order, and N is the polynomial order;
depth of discharge D in the above equationoDIs a variable having a non-linear relationship with the charge-discharge state and the active power of the battery, i.e.
Figure FDA0002228892500000052
It cannot give an explicit mathematical expression, so it is calculated by a rain flow counting method;
step 2-b, the rain flow counting method comprises the following steps:
1) clockwise rotating a battery charge state-time curve of a battery energy storage system by 90 degrees, regarding the curve as an eave, and starting rain flow from a starting point and each peak/valley value in sequence;
2) the rain drops vertically when flowing to the peak/valley, and the rain drops until the opposite surface has a peak value larger than the maximum value or the minimum value at the beginning or a valley value smaller than the maximum value or the minimum value at the beginning;
3) drawing a flow path of each raindrop according to the starting point and the end point of the flowing of each raindrop, namely each cycle half period, and simultaneously recording the peak-to-valley values of all the cycle half periods;
4) the horizontal length of the rain flow path in each cycle is the discharge depth of the battery energy storage system in the cycle period.
3. The active power distribution network short-term active power optimization method comprising the battery energy storage system according to claim 1, wherein the method comprises the following steps: in step 4, the objective function specifically consists of:
step a, considering the situation that power exchange can be performed between the main network and the distribution network side purchases different electricity selling prices, the sum of the electricity purchasing cost and the electricity selling income of the distribution side can be expressed as:
Figure FDA0002228892500000061
wherein the content of the first and second substances,
Figure FDA0002228892500000062
active power delivered to the distribution network for the main network during the t-th period, CtThe purchase and sale electricity price of the main network in the t-th scheduling period for the distribution network can be expressed as:
Figure FDA0002228892500000063
wherein the content of the first and second substances,
Figure FDA0002228892500000064
and C-distribution network electricity purchasing price and electricity selling price in the time interval of t respectively, wherein the units are RMB/kW.h, and
Figure FDA0002228892500000065
step b, in order to fully consider the economic benefits of the distribution network side, the equivalent operation cost of the battery energy storage system is considered besides the electricity purchasing and selling cost of the distribution network side, and the equivalent operation cost of the battery energy storage system can be expressed as:
Figure FDA0002228892500000066
wherein N isBFor the number of battery energy storage systems, MkIs the total cycle number in the scheduling period of the battery energy storage system of No. k, Ce,k,m(DoD,k,m) The m-th discharge depth of the kth battery energy storage system is DoD,k,mEquivalent investment cost under the cycle period of (1); cBESS,kEquivalent maintenance cost for No. k BESS;
and step c, considering that the wind power and the photovoltaic power generation do not need to consume fuel, assuming that the power generation cost is zero, from the aspects of economy and environmental protection, the wind and light abandonment can cause excessive emission of operators, and violates the emission permission agreed in advance, so that the cost of the wind and light abandonment needs to be paid for and violated the compensation expense, and the cost of the wind and light abandonment can be expressed as:
Figure FDA0002228892500000067
wherein, cwAnd cPVRespectively represents the cost of wind and light abandonment in unit, and the unit is as follows: RMB/kW.h; n is a radical ofwAnd NpvThe number of wind power and photovoltaic are respectively;
and d, considering that the micro gas turbine needs to consume natural gas traditional energy sources when in operation, and in order to express the relation between the active output and the fuel cost, the operation cost of the micro gas turbine can be expressed as follows:
Figure FDA0002228892500000071
wherein, cFPIs the fuel price, in units of: RMB/kW.h;
Figure FDA0002228892500000072
the active power of the r-th micro gas turbine in the t-th period, NMTNumber of micro gas turbines, ηMTFuel conversion efficiency for micro gas turbines;
and e, considering that the controllable load is an industrial load, and performing appropriate adjustment on the controllable load under the condition of ensuring the power supply amount by signing a relevant contract with the industrial load, considering that the comfort level of a consumer is necessarily influenced when the controllable load is adjusted, performing certain compensation on the controllable load, wherein the compensation cost is as follows:
Figure FDA0002228892500000073
wherein, ccl,lFor the compensation price when adjusting the l controllable load, the unit is: RMB/kW.h; n is a radical ofclIs the total controllable load number;
Figure FDA0002228892500000074
and adjusting the load active power of the ith controllable load for the t period.
4. The active power distribution network short-term active power optimization method comprising the battery energy storage system according to claim 1, wherein the method comprises the following steps: the primal-dual interior point method in the step 5 is specifically realized as follows:
decoupling and solving static variables and dynamic variables by adopting an original dual interior point method, and reducing the order of a solved matrix, wherein the static variables comprise voltage amplitude and phase angle of each node, active and reactive power of a root node, active and reactive power of a wind turbine generator and photovoltaic, reactive power of a micro gas turbine, each loose variable when inequality constraint is relaxed, and lagrangian multipliers corresponding to each equality constraint and each inequality constraint; the dynamic variables include: the active and reactive powers of the battery energy storage system and the controllable load, the charge states of the battery energy storage system and the storage type controllable load and the active power of the micro gas turbine; the nonlinear programming problem comprises an objective function, an equality constraint, an inequality constraint and an inter-period coupling relation, and is in the form of:
Figure FDA0002228892500000075
wherein f (x) is an objective function, ht(x) 0 is an equality constraint, glt≤gt(x)≤gutThe system is an inequality constraint, and both the equality constraint and the inequality constraint comprise a static part and a dynamic part, wherein the dynamic part comprises an energy constraint related to a battery energy storage system and a storage type controllable load and a climbing constraint of the micro gas turbine; solving by adopting a primal-dual interior point method to obtain a coefficient matrix of a classical optimal power flow correction equation:
Figure FDA0002228892500000081
wherein, WR1～WRTFor a matrix of coefficients related to the static variable, Δ X, after a reduction of the correction equation at the corresponding time intervalR1～ΔXRTLagrange multiplier variation for all static variables and equality constraints over a corresponding time period, BR1～BRTPartial derivatives of the static variables for corresponding time periods for Lagrangian functions, ER1～ERTFor a matrix of coefficients relating to the static variable after decoupling for a corresponding time period, DRFor a matrix of coefficients related to dynamic variables, Δ XRdFor dynamic variable variations, BRDCalculating the partial derivative of the dynamic variable for the Lagrange function; by utilizing the block diagonal band edge structure, the method can obtain the following results through linear transformation:
Figure FDA0002228892500000082
decoupling to obtain:
Figure FDA0002228892500000083
Δ X obtained from the above formulaRdSubstituting the formula to respectively solve the static variable delta X of each time intervalRt：
Figure FDA0002228892500000084
5. The active power distribution network short-term active power optimization method comprising the battery energy storage system according to claim 1, wherein the method comprises the following steps: the branch shearing criterion in the step 5-d specifically comprises the following steps:
(1) the subproblem has no feasible solution; (2) all discrete variables have obtained integer solutions; (3) the sub-problem target value is greater than or equal to the upper bound; (4) the energy stored by the battery energy storage system does not meet the upper and lower limit constraints.
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