CN102436631B - Method for evaluating reliability of wind/diesel/ storage hybrid system - Google Patents

Abstract

The invention provides a method for evaluating the reliability of a wind/diesel/ storage hybrid system, which comprises the following steps of: collecting the original data of a distribution network, building a wind speed time sequence, building a WTG (Wind Turbine Generator) power output model, building the off-stream model of a WTG and a diesel group, building an energy storage equipment charging and discharging model, and finally calculating the reliability index of the system by blocks. The method proposes a strategy that energy storage equipment stores energy when the total power output of the WTG and the diesel group is more than a load, and the energy storage equipment releases the energy when the total power output is less than the load. Under the strategy, the energy storage equipment charging and discharging model is built so as to evaluate system reliability. With the method, the operation characteristics of the energy storage equipment are counted, and the reliability of the hybrid system can be accurately evaluated.

Description

A kind of wind/bavin/storage commingled system reliability estimation method

Technical field

The present invention relates to a kind of distribution network reliability evaluation method, be specifically related to a kind of wind/bavin/storage commingled system reliability estimation method taking into account energy storage device operation reserve, belong to electric power project engineering field.

Background technology

In recent years, wind energy power technology obtains fast development, but the randomness of wind energy makes output power fluctuation of wind farm very large, and wind-electricity integration brings series of problems to the stable operation of electric system.Energy storage device has Dynamic Absorption energy and the feature of release in good time, and at Wind turbines, English full name is: Wind Turbine Generator, adds energy storage device and effectively can solve the unstable problem of wind-powered electricity generation output in abbreviation WTG.

Wind/bavin/storage commingled system is made up of WTG, diesel generator set and energy storage device, and the operation reserve of energy storage device and the reliability of operation characteristic to wind/bavin/storage commingled system have material impact.The operation reserve of prior art energy storage device has: (1) a kind of energy storage device operation reserve (wind farm energy storage capacity reasonable value surface analysis [J], University Of Chongqing's journal, 2010,33 (8): 46-51 balancing wind power and export, Large-scale Wind Power field stored energy capacitance prioritization scheme [J], electric power network technique, 2010,34 (1): 169-173), this policy grounds calculates the optimum capacity of energy storage device, but do not take into account the reliability model that this strategy sets up energy storage device, reliability assessment is carried out to the wind generator system containing energy storage device, (2) energy storage device three kinds of operation reserve (Reliability evaluation of generating systems containing wind power and energy storage [J] of wind energy permeability is taken into account, IET Gener Transm Distrib, 2009, 3 (8): 783-791), this strategy adopts sequential Monte Carlo simulation to carry out reliability assessment to the large-scale wind power field containing energy storage device, but do not consider the impact of energy storage device charge-discharge electric power, and existing energy storage technology also cannot be used for large-scale wind power field, carry out long-time energy storage, (3) a kind of Reliability Evaluation Model (wind/bavin/energy storage device generating capacity adequacy evaluation [J] of wind/bavin/storage commingled system, Proceedings of the CSEE, 2006,26 (16): 62-67), in this model, the operation reserve of energy storage device is fairly simple, does not consider the impact of energy storage device charge-discharge electric power, (4) analytical method assessment wind/bavin/storage commingled system (Reliability evaluation of a wind-diesel hybrid power system with battery bank using discrete wind speed frame analysis [C] is adopted, 9th International Conference Probabilistic Methods Applied to Power Systems, KTH, Stockholm, Sweden, 2006:11-15), the method effectively reduces calculated amount, but do not take into account the factors such as the reparation characteristic of genset, and cannot calculated rate class reliability index, (5) a kind of wind/bavin based on cost effectiveness analysis/storage commingled system planing method (uses the wind/bavin/accumulator system planing method [J] of cost effectiveness analysis, Power System and its Automation journal, 2010,22 (3): 67-72) cost-benefit model that, the method is set up does not take into account the cost in serviceable life of energy storage device.

Summary of the invention

For the problems referred to above that prior art exists, the present invention proposes one and takes into account energy storage device operation reserve wind/bavin/storage commingled system reliability estimation method, can make and assessing exactly wind/bavin/storage commingled system reliability.

The present invention is achieved in that a kind of wind/bavin/storage commingled system reliability estimation method, and concrete steps comprise:

step 1:gather the raw data of power distribution network: the air speed data of electric field; The incision wind speed of WTG, wind rating, cut-out wind speed; Connecting relation in power distribution network between circuit, transformer, switchgear, load point and WTG, energy storage device and diesel generator set; The max cap. of energy storage device, minimum capacity and maximum charge-discharge electric power and diesel engine unit send rated power when normally working; The Mean continuous working period of system unit and mean repair time;

step 2:build wind speed time series

Carry out matching with Weibull distribution to original air speed data, sequential produces corresponding Weibull random number, obtains wind speed time series, and the Weibull distribution function of wind speed is:

(1)

(2)

In formula, v is actual wind speed, and c is scale coefficient, and k is shape coefficient, f (v, c, k) is probability density function, F (v, c, k) be accumulated probability density function, use inverse transformation law theory, obtain the wind speed time series of Follow Weibull Distribution:

(3)

In formula, v _tthe simulation wind speed of t hour, x _tgenerate (0,1) equally distributed stochastic variable in t hour;

step 3:build WTG power stage model

Obtain WTG power stage by the nonlinear relationship of WTG power stage and wind speed, general expression is:

(4)

In formula, v _ci, v _r, v _coand P _rbe respectively the incision wind speed of WTG, wind rating, cut-out wind speed and output rating; Constant A, B, C are about v _ci, v _r, v _coexpression formula;

step 4:build the outage model of WTG and diesel engine unit

WTG and diesel engine unit all adopt normal work and two state models of stopping transport, when WTG normally works, power stage is drawn by formula (4), rated power is sent when diesel engine unit normally works, adopt sequential Monte-Carlo simulation, the operation of WTG and diesel engine unit-idle time sequence by unit Mean continuous working period MTTF and mean repair time MTTR simulate and obtain, the sample value obeys index distribution of state duration, expression formula is:

(5)

(6)

In formula, t ₁and t ₂represent the normal duration of operation and repair time respectively, x ₁and x ₂represent (0,1) equally distributed stochastic variable; Pass through t ₁and t ₂obtain basis operation/idle time sequence;

step 5:set up energy storage device charging and recharging model

WTG and diesel engine unit general power export and are greater than load, energy storage device storage power; Be less than load, energy storage device releases energy, and sets up energy storage device charging and recharging model based on this kind of strategy:

1)obtained the power stage time series of energy storage device by basis operation/idle time sequence and Load Time Series, represented by formula (9):

（9）

2)taking into account the restriction of energy storage device operation characteristic, formula (9) is rewritten as formula (11):

（11）

3)through type (11) obtains energy storage device energy time sequence:

(12)

(9), in (11) and (12) formula, i represents i-th hour (i=1,2,3 in simulated time T ... T), P _bat(i) and E _bati () represents i-th hour energy storage device power stage and storage power respectively, P _w(i), P _d(i) and P _li () represents i-th hour WTG power stage, diesel generator set power stage and load respectively, P _ch-maxand P _dch-maxrepresent the maximum charge power of energy storage device and maximum discharge power respectively, E _maxand E _minrepresent the minimum and maximum capacity of energy storage device respectively;

step 6:the reliability index of section technique system

In simulated time inner analysis system state, reliability of statistics index: expected loss of load LOLE, expected loss of energy LOEE, power-off frequency expectation value LOLF, energy storage device delivery expect E _eESBSSe is expected with energy storage device charge and discharge cycles number of times _eCDCTOSSindex; Represent to formula (17) by formula (13) respectively;

(13)

(14)

(15)

(16)

(17)

Wherein, K represents the complete or collected works losing load condition, represent and be in state power off time, represent and be in state dead electricity amount, represent total frequency of power cut, S represents the complete or collected works of energy storage device discharge condition in simulated time, DIC _kfor system is in the discharge capacity of state k, N represents simulation year number, and n represents the total charge and discharge cycles number of times in simulated time.

Accompanying drawing explanation

Fig. 1-wind/bavin/storage commingled system model.

Fig. 2-wind speed is on the impact of LOLE.

Energy storage device power stage curve in Fig. 3-sampling time.

Energy storage device storage power curve in Fig. 4-sampling time.

Energy storage device power stage curve in Fig. 5-sampling time.

Energy storage device storage power curve in Fig. 6-sampling time.

Fig. 7-energy storage device capacity is to E _eESBSSimpact.

Fig. 8-energy storage device charge-discharge electric power is to E _eESBSSimpact.

Embodiment

Below to being described in further detail the present invention by reference to the accompanying drawings.

With reference to the accompanying drawings 1, a kind of wind/bavin/storage commingled system reliability estimation method: concrete steps comprise:

step 1:gather the raw data of power distribution network: the air speed data of electric field; The incision wind speed of WTG, wind rating, cut-out wind speed; Connecting relation in power distribution network between circuit, transformer, switchgear, load point and WTG, energy storage device and diesel generator set; The max cap. of energy storage device, minimum capacity and maximum charge-discharge electric power and diesel engine unit send rated power when normally working; The Mean continuous working period of system unit and mean repair time;

step 2:build wind speed time series

Carry out matching with Weibull distribution to original air speed data, sequential produces corresponding Weibull random number, obtains wind speed time series, and the Weibull distribution function of wind speed is:

(1)

(2)

In formula, v is actual wind speed, and c is scale coefficient, and k is shape coefficient, f (v, c, k) is probability density function, F (v, c, k) be accumulated probability density function, use inverse transformation law theory, obtain the wind speed time series of Follow Weibull Distribution:

(3)

In formula, v _tthe simulation wind speed of t hour, x _tgenerate (0,1) equally distributed stochastic variable in t hour;

step 3:build WTG power stage model

Obtain WTG power stage by the nonlinear relationship of WTG power stage and wind speed, general expression is:

(4)

In formula, v _ci, v _r, v _coand P _rbe respectively the incision wind speed of WTG, wind rating, cut-out wind speed and output rating; Constant A, B, C are about v _ci, v _r, v _coexpression formula;

step 4:build the outage model of WTG and diesel engine unit

WTG and diesel engine unit all adopt normal work and two state models of stopping transport, when WTG normally works, power stage is drawn by formula (4), rated power is sent when diesel engine unit normally works, adopt sequential Monte-Carlo simulation, the operation of WTG and diesel engine unit-idle time sequence by unit Mean continuous working period MTTF and mean repair time MTTR simulate and obtain, the sample value obeys index distribution of state duration, expression formula is:

(5)

(6)

In formula, t ₁and t ₂represent the normal duration of operation and repair time respectively, x ₁and x ₂represent (0,1) equally distributed stochastic variable; Pass through t ₁and t ₂obtain basis operation/idle time sequence;

step 5:set up energy storage device charging and recharging model

WTG and diesel engine unit general power export and are greater than load, energy storage device storage power; Be less than load, energy storage device releases energy, and sets up energy storage device charging and recharging model based on this kind of strategy:

5.1obtained the power stage time series of energy storage device by basis operation/idle time sequence and Load Time Series, represented by formula (9):

（9）

5.2taking into account the restriction of the maximum charge-discharge electric power of energy storage device, formula (9) is rewritten as formula (10):

(10)

On the basis of formula (9), then take into account the restriction of the minimum and max cap. of energy storage device, formula (10) be rewritten as (11):

（11）

5.3through type (11) obtains energy storage device energy time sequence:

(12)

(9), (10), in (11) and (12) formula, i represents i-th hour (i=1,2,3 in simulated time T ... T), P _bat(i) and E _bati () represents i-th hour energy storage device power stage and storage power respectively, P _w(i), P _d(i) and P _li () represents i-th hour WTG power stage, diesel generator set power stage and load respectively, P _ch-maxand P _dch-maxrepresent the maximum charge power of energy storage device and maximum discharge power respectively, E _maxand E _minrepresent the minimum and maximum capacity of energy storage device respectively;

step 6:the reliability index of section technique system

In simulated time inner analysis system state, reliability of statistics index: expected loss of load LOLE, expected loss of energy LOEE, power-off frequency expectation value LOLF, energy storage device delivery expect E _eESBSSe is expected with energy storage device charge and discharge cycles number of times _eCDCTOSSindex; Represent to formula (17) by formula (13) respectively;

(13)

(14)

(15)

(16)

(17)

Wherein, K represents the complete or collected works losing load condition, represent and be in state power off time, represent and be in state dead electricity amount, represent total frequency of power cut, S represents the complete or collected works of energy storage device discharge condition in simulated time, DIC _kfor system is in the discharge capacity of state k, N represents simulation year number, and n represents the total charge and discharge cycles number of times in simulated time.

Embodiment: operation reserve is depended in the foundation of energy storage device charging and recharging model, the application takes into account that WTG exerts oneself, diesel engine unit is exerted oneself and load, when step 5 sets up energy storage device charging and recharging model, the strategy used is: WTG and diesel engine unit general power export and be greater than load, energy storage device storage power; Be less than load, energy storage device releases energy.

Take into account in prior art that WTG exerts oneself, diesel engine unit is exerted oneself and load, the operation reserve of energy storage device has: strategy 1, WTG average output power in the calculating simulation time, when WTG power stage is greater than average output power, and energy storage device storage power; Otherwise energy storage device releases energy, WTG and energy storage device general power are exported and reaches average output power; When strategy 2, WTG and diesel engine unit general power export and are greater than load, energy storage device storage power; When being less than load, energy storage device releases energy, and WTG and energy storage device general power must not export the x% being greater than system loading.

According to the Reliability Evaluation Model that the application sets up, write Matlab program and realize system sequential Monte Carlo analog simulation, simulated time T is 500 years.As shown in Table 1 and Table 2, original air speed data derives from the Dutch a certain wind energy turbine set statistics of 10 years to system related data, and adopt IEEE-RTS sequential load curve, peak load is 35 kW.WTG incision, specified and cut-out wind speed are respectively 3 m/s, 10 m/s and 20 m/s.Calculating WTG average output power in simulated time is 7.6863 kW.Adopt vanadium oxide reduction flow battery energy storage device in the application, be called for short " VRB ", VRB system max cap. is 300 kWh, and minimum capacity is 0, and maximum charge-discharge electric power is 60 kWh/h.Table 3 gives the reliability index of system in the sampling time.

(1) energy storage device is on the impact of system reliability

Table 4 gives example reliability index in simulated time, and after adding energy storage device, system reliability significantly improves.Under the different operation reserve of energy storage device, system reliability level is different.Strategy 1 with WTG average output power for standard carries out discharge and recharge, energy storage device charge and discharge cycles number of times and delivery are expected far above strategy 2 and the application's strategy, effectively reduce the undulatory property of WTG power stage, but when load is higher, WTG or diesel engine unit be when stopping transport, and easily causes loss of outage.Strategy 2 and the application's strategy are all to reduce for the purpose of loss of outage, and the application's strategy improves wind energy utilization, is applicable to inject hard-core system to wind energy.

(2) wind speed is on the impact of system reliability

Other parameter constant of system, changes mean wind speed hourly as 0.8 to 2.0 times of original air speed data respectively into, and step-length is 0.2, calculates system reliability under different wind speed.Composition graphs 2 can be found out: reliability increases with wind speed and increases, and when wind speed increases to 1.18 times of original wind speed, strategy 1 is identical with the LOLE of tactful 2 systems; Wind speed continues to increase, and tactful 1 system reliability is better than strategy 2; Because wind speed determines WTG power stage, strategy 2 pairs of wind energies are injected with restriction, and reliability is improved less; The application's strategy, reliability is higher than strategy 1 and strategy 2, and wind speed changes smaller on the impact of system reliability .

(3) energy storage device parameter is on the impact of system reliability

Other parameter constant of system, Reliability Index under calculating energy storage device different parameters.When energy storage device max cap. and maximum charge-discharge electric power are respectively 200 kWh and 45 kWh/h, in the sampling time, the power stage of energy storage device and storage power change are as shown in Figure 3 and Figure 4; When energy storage device max cap. and maximum charge-discharge electric power are respectively 100 kWh and 30 kWh/h, in the sampling time, energy storage device power stage and storage power change are as shown in Figure 5 and Figure 6.Table 5 gives LOLE index under energy storage device different parameters, and system reliability increases with energy storage device capacity and charge-discharge electric power and increases, and this Shen policy system reliability improves and is greater than strategy 1 and strategy 2.

Can be found out further by Fig. 7 and Fig. 8, the restriction that energy storage device capacity and charge-discharge electric power improve system reliability, E _eESBSSincrease with energy storage device capacity and discharge and recharge rate and increase, when energy storage device capacity or charge-discharge electric power are respectively more than 300 kWh and 60 kWh/h, E _eESBSSincrement is little.

(4) under the application's strategy, cost benefit is high

Based on the improvement of LOLE index, take into account energy storage device charge and discharge cycles number of times, capacity and power cost etc., set up the cost-benefit model of energy storage device, represented by formula (18):

（18）

In formula (18), η represent add VRB system after often reduce the VRB system average unit cost of unit power off time, M _c, M _p, E _band P _brepresent the Capacity Cost of VRB system, power cost, max cap. and maximum charge-discharge electric power respectively, LOLE represent add VRB system after total power off time of reducing, n _brepresent the actual charge and discharge cycles number of times of VRB system, N _brepresent the maximum charge and discharge cycles number of times of VRB system.

VRB system economy data are as shown in table 6, and under various combination scheme, the charge and discharge cycles number of times change of each operation reserve is little, as shown in table 7; Table 8 gives the cost benefit of energy storage device under various combination scheme.

As can be seen from Table 8, after adding VRB system, based on the improvement of LOLE index, the application's strategy cost benefit is best.Because VRB system charge and discharge cycles least number of times, serviceable life is the longest, is better than strategy 1 and strategy 2 to the improvement of system reliability.

Claims (1)

1. wind/bavin/storage commingled system reliability estimation method, concrete steps comprise:

Step 1: the raw data gathering power distribution network: the air speed data of electric field; The incision wind speed of WTG, wind rating, cut-out wind speed; Connecting relation in power distribution network between circuit, transformer, switchgear, load point and WTG, energy storage device and diesel generator set; The max cap. of energy storage device, minimum capacity and maximum charge-discharge electric power and diesel engine unit send rated power when normally working; The Mean continuous working period of system unit and mean repair time;

Step 2: build wind speed time series

Carry out matching with Weibull distribution to original air speed data, sequential produces corresponding Weibull random number, obtains wind speed time series, and the Weibull distribution function of wind speed is:

$f(v,c,k)=\frac{k}{c^k}{v}^{k-1}{e}^{-{\left(\frac{v}{c}\right)}^k}---\left(1\right)$

$F(v,c,k)=1-e^{-{\left(\frac{v}{c}\right)}^k}---\left(2\right)$

In formula, v is actual wind speed, and c is scale coefficient, and k is shape coefficient, f (v, c, k) is probability density function, F (v, c, k) be accumulated probability density function, use inverse transformation law theory, obtain the wind speed time series of Follow Weibull Distribution:

v _t＝c(-ln x _t) ^1/k(3)

In formula, v _tthe simulation wind speed of t hour, x _tgenerate (0,1) equally distributed stochastic variable in t hour;

Step 3: build WTG power stage model

Obtain WTG power stage by the nonlinear relationship of WTG power stage and wind speed, general expression is:

$P_t=\left\{\begin{array}{cc}0& (0\&le;v_t\&le;v_{\mathrm{ci}})\\ (A+B\&times;v_t+C\&times;v_t^2)P_r& (v_{\mathrm{ci}}<v_t\&le;v_r)\\ P_r& (v_r<v_t\&le;v_{\mathrm{co}})\\ 0& (v_t>v_{\mathrm{co}})\end{array}\right.---\left(4\right)$

In formula, v _ci, v _r, v _coand P _rbe respectively the incision wind speed of WTG, wind rating, cut-out wind speed and output rating; Constant A, B, C are by v _ciand v _rcalculate;

Step 4: the outage model building WTG and diesel engine unit

WTG and diesel engine unit all adopt normal work and two state models of stopping transport, when WTG normally works, power stage is drawn by formula (4), rated power is sent when diesel engine unit normally works, adopt sequential Monte-Carlo simulation, the operation of WTG and diesel engine unit-idle time sequence by unit Mean continuous working period MTTF and mean repair time MTTR simulate and obtain, the sample value obeys index distribution of state duration, expression formula is:

t ₁＝-MTTF×ln(x ₁) (5)

t ₂＝-MTTR×ln(x ₂) (6)

In formula, t ₁and t ₂represent the normal duration of operation and repair time respectively, x ₁and x ₂represent (0,1) equally distributed stochastic variable; Pass through t ₁and t ₂obtain basis operation/idle time sequence;

Step 5: set up energy storage device charging and recharging model

WTG and diesel engine unit general power export and are greater than load, energy storage device storage power; Be less than load, energy storage device releases energy, and sets up energy storage device charging and recharging model based on this kind of strategy:

1) obtained the power stage time series of energy storage device by basis operation/idle time sequence and Load Time Series, represented by formula (9):

$P_{\mathrm{bat}}\left(i\right)=\left\{\begin{array}{cc}{P}_W\left(i\right)-(P_L\left(i\right)-P_D\left(i\right))& P_L\left(i\right)\&GreaterEqual;P_D\left(i\right)\\ P_W\left(i\right)& P_L\left(i\right)<P_D\left(i\right)\end{array}\right.---\left(9\right)$

2) in the restriction taking into account the maximum charge-discharge electric power of energy storage device, formula (9) is rewritten as formula (10):

$P_{\mathrm{bat}}\left(i\right)=\left\{\begin{array}{cc}-P_{\mathrm{dch}-\max }& P_{\mathrm{bat}}\left(i\right)\&le;-P_{\mathrm{dch}-\max }\\ P_{\mathrm{bat}}\left(i\right)& -P_{\mathrm{dch}-\max }<P_{\mathrm{bat}}\left(i\right)<P_{\mathrm{ch}-\max }\\ P_{\mathrm{ch}-\max }& P_{\mathrm{bat}}\left(i\right)\&GreaterEqual;P_{\mathrm{ch}-\max }\end{array}\right.---\left(10\right)$

On the basis of formula (9), then take into account the restriction of the minimum and max cap. of energy storage device, formula (10) be rewritten as (11):

$\begin{array}{c}{P}_{\mathrm{bat}}\left(i\right)=\\ \left\{\begin{array}{cc}{E}_{\min }-E_{\mathrm{bat}}\left(i\right)& E_{\mathrm{bat}}\left(i\right)+P_{\mathrm{bat}}\left(i\right)\&le;E_{\min }\\ P_{\mathrm{bat}}\left(i\right)& E_{\min }<E_{\mathrm{bat}}\left(i\right)+P_{\mathrm{bat}}\left(i\right)<E_{\max }\\ E_{\max }-E_{\mathrm{bat}}\left(i\right)& E_{\mathrm{bat}}\left(i\right)+P_{\mathrm{bat}}\left(i\right)\&GreaterEqual;E_{\max }\end{array}\right.\end{array}---\left(11\right)$

3) through type (11) obtains energy storage device energy time sequence and is:

E _bat(i+1)＝E _bat(i)+P _bat(i) (12)

(9), (10), in (11) and (12) formula, i represents i-th hour (i=1,2,3 in simulated time T ... T), P _bat(i) and E _bati () represents i-th hour energy storage device power stage and storage power respectively, P _w(i), P _d(i) and P _li () represents i-th hour WTG power stage, diesel generator set power stage and load respectively, P _ch-maxand P _dch-maxrepresent the maximum charge power of energy storage device and maximum discharge power respectively, E _maxand E _minrepresent the minimum and maximum capacity of energy storage device respectively;

Step 6: the reliability index of section technique system

In simulated time inner analysis system state, reliability of statistics index: expected loss of load LOLE, expected loss of energy LOEE, power-off frequency expectation value LOLF, energy storage device delivery expect E _eESBSSe is expected with energy storage device charge and discharge cycles number of times _eCDCTOSSindex; Represent to formula (17) by formula (13) respectively;

$\mathrm{LOLE}=\underset{\mathrm{\&theta;}\&Element;K}{\mathrm{\&Sigma;}}\frac{t_{\mathrm{\&theta;}}}{N}---\left(13\right)$

$\mathrm{LOEE}=\underset{\mathrm{\&theta;}\&Element;K}{\mathrm{\&Sigma;}}\frac{{\mathrm{LOEE}}_{\mathrm{\&theta;}}}{N}\mathrm{\&theta;}---\left(14\right)$

$\mathrm{LOLF}=\frac{\mathrm{\&beta;}}{N}---\left(15\right)$

$E_{\mathrm{EESBSS}}=\frac{\underset{k\&Element;S}{\mathrm{\&Sigma;}}{\mathrm{DIC}}_k}{N}---\left(16\right)$

$E_{\mathrm{ECDCTOSS}}=\frac{n}{N}---\left(17\right)$

Wherein, K represents the complete or collected works losing load condition, t _θrepresent the power off time being in state θ, LOEE _θrepresent the dead electricity amount being in state θ, β represents total frequency of power cut, and S represents the complete or collected works of energy storage device discharge condition in simulated time, DIC _kfor system is in the discharge capacity of state k, N represents simulation year number, and n represents the total charge and discharge cycles number of times in simulated time.