Reliability Evaluation of Power Systems with WTGs and Energy Storage

Z. Y. Gao School of Electrical and Electronic Engineering

Nanyang Technological University Singapore

gaoz0004@ntu.edu.sg

Peng Wang School of Electrical and Electronic Engineering

Nanyang Technological University Singapore

epwang@ntu.edu.sg

Abstract—Renewable energy is increasingly being treated as a promising solution to the global warming and other environment issues. Due to the intermittent and uncertain nature of these energy resources, energy storage is required to provide certain wind generation capacity. An analytical method is presented in this paper to evaluate the reliability of power systems with wind turbine generators (WTGs) and energy storage. The Expected Energy Not Supplied (EENS) index is used to investigate the impacts of the rated capacity of energy storage and charging/discharging rate, and the wind speed on system reliability. Expected Energy Not Used (EENU) index is defined to represent the wind energy produced but not used to serve system load.

Keywords- Reliability Evaluation, Wind Energy, Energy Storage

I. INTRODUCTION Wind power is attracting considerable attention due to the increasing concerns of environment issues. Wind generation has been considered to be the substitute for conventional generation because of its huge potential [1]. Many countries have planned to significantly increase the percentage of wind power capacity in total power generation. In early 2008, global installed wind capacity passed the threshold of 100 GW from only about 74 GW in 2006. Denmark, Germany and Spain are the countries getting 20% of their electricity from WTGs [2]. In developing countries such as China, India and Brazil, the installed wind capacity is increasing rapidly. By 2020, China plans to have 30 GW of wind power [3].

Many researchers have extensively studied the reliability issues in power systems with wind energy [4-6]. The four indices, the wind generation interrupted energy benefit (WGIEB), the wind generation interruption cost benefit (WGICB), the equivalent number of conventional generators (ENCG) and the equivalent conventional generator capacity (ECGC) have been proposed and widely used to evaluate the reliability benefit of a distribution system including wind energy [4]. In [5], the authors used the Universal Generating Function (UGF) to simulate the fluctuation of wind speed, reliability of wind turbine generators and uncertainty of load. From the application of the proposed method, this technique was found to be easily used to determine the hydro/thermal reserve for a give load and wind penetration. Roy Billinton et al created an analytical model of a multi-unit wind farm to be used in conventional generating capacity or composite

generation and transmission system reliability evaluation [6]. The multiple wind farms can make more significant reliability contrition than a single wind farm in a composite generation and transmission system, providing there is a very strong transmission system.

Energy storage has been used to smooth high variability of wind power and to provide spinning reserve to improve the system reliability [7-11]. P. Hu et al presented three different energy storage operating scenarios and looked for the potentially useful one for both power system operators and wind farm owners [8]. The effect of several factors of energy storage on LOLE, LOEE (Loss of Energy Expectation) and ESWE (Expected Surplus Wind Energy) were investigated. These factors include charging/discharging constraints of energy storage, energy storage capacity and wind energy dispatch restrictions. A stochastic optimization approach, which considers the rating of energy storage, wind penetration levels, storage efficiency and diesel operating strategies, was presented in [9]. The optimization approach is applicable to isolated wind-diesel power systems. It was found that the diesel operating strategies have the most important effect to minimize the cost of supplied energy. A methodology for determining the optimal size of energy storage system integrated with thermal power system was presented in [10]. The optimal size of energy storage system is the one that can achieve maximum revenue considering the life-cycle cost of energy storage system, production cost savings, emission cost savings, and distribution network savings. The authors in [11] presented a simple probabilistic method to predict the ability of energy storage to increase the penetration of wind power. Different energy storage technologies were selected for different applications over different time scales.

In this paper, an analytical procedure is proposed to evaluate the reliability of power systems with WTGs and energy storage. The Expected Energy Not Supplied (EENS) is used to investigate the impacts of the rated capacity of energy storage and charging/discharging rate, and the wind speed on system reliability. A new defined index, Expected Energy Not Used (EENU), is used to represent the wind energy produced but not used to serve system load. Section II describes the modeling of wind farm and load. The energy storage system is modeled in Section III. The calculation formulae of the indices EENS and EENU are introduced in Section IV and the analytical reliability evaluation procedure is also presented in this section.

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In Section V, the proposed procedure is applied to the IEEE-RTS. A conclusion is presented in Section VI.

II. MODELING OF WIND FARM AND LOAD Wind speed is usually modeled by hourly mean wind speed from the historical wind speed data in a specific wind site. A WTG power output is calculated using a mathematical relationship between wind speed and power output. The WTG power output reliability model and wind farm power output reliability model are presented in this section. An hourly peak load variation curve is used to represent the system load.

A. Wind Speed Model There may have quite different types of wind regimes at different geographic locations. Different wind speed models such as the Weibull distribution model, multi state wind speed model and ARMA time-series model have been used in reliability evaluation [6, 12-15]. The wind speed model used in this paper is the hourly mean wind speed model, which is based on sufficient wind speed data from the wind site. Twenty-year wind speed data for the city Ijmuiden, Dutch obtained from the "KNMI HYDRA Project" by Royal Netherlands Meteorological Institute are used to form the hourly mean wind speed model [16]. The main statistical characteristics of the twenty years wind speed data for Ijmuiden City are shown in Table I. The mean wind speed V can be calculated using (1)

1

nii

VV

n== ∑ (1)

where iV is the ith wind speed observation and n is the number of the observations.

TABLE I. MAIN STATISTICAL CHARACTERISTICS OF THE WIND SPEED DATA FOR IJMUIDEN CITY

Year Mean wind speed (m/s)

Standard deviation

(m/s) Year Mean wind

speed (m/s)

Standard deviation

(m/s) 1982 6.57 3.41 1995 7.08 3.37 1984 6.21 3.25 1996 6.74 3.36 1987 6.38 3.22 1997 6.57 3.32 1988 7.31 3.36 1998 7.49 3.65 1989 6.51 3.31 2000 7.23 3.55 1990 7.16 3.69 2001 7.01 3.38 1991 6.47 3.37 2002 6.92 3.61 1992 6.89 3.24 2003 6.18 3.03 1993 6.73 3.30 2004 6.67 3.49 1994 6.96 3.46 2005 6.55 3.25

B. WTG Power Output Model The power output P(V) of a WTG can be calculated using

equation (2), which shows the relationship between wind speed and wind turbine power output [17-18].

2( ) ( )

0

r ci r

r r co

A B V C V P V V VP V P V V V

otherwise

⎧ + ⋅ + ⋅ ⋅ ≤ <⎪= ≤ ≤⎨⎪⎩

(2)

where V is the wind speed in (m/s), Vci is the cut-in wind speed in (m/s), Vr is the rated wind speed in (m/s), Vco is the cut-out wind speed in (m/s), Pr is the rated power (MW) of the WTG and A, B, C are constant parameters, which can be obtained using (3),(4) and (5) [17].

3ci r

ci ci r ci r2rci r

1 V VA V (V V ) 4(V V )2V(V V )

⎡ ⎤⎡ ⎤+⎢ ⎥= × + − ⎢ ⎥− ⎢ ⎥⎣ ⎦⎣ ⎦ (3)

3ci r

ci r ci r2rci r

1 V VB 4(V V ) ( 3V V )2V(V V )

⎡ ⎤⎡ ⎤+⎢ ⎥= × + − +⎢ ⎥− ⎢ ⎥⎣ ⎦⎣ ⎦ (4)

3ci r

2rci r

1 V VC 2 42V(V V )

⎡ ⎤⎡ ⎤+⎢ ⎥= × − ⎢ ⎥− ⎢ ⎥⎣ ⎦⎣ ⎦ (5)

C. WTG Power Output Reliability Model The power output of a WTG also depends on its reliability. A WTG can be either in operating or failure state. The power output is zero when a WTG is in failure state and P(V) when the WTG is in operating state. The WTG power output reliability model for a WTG with the forced outage rate (FOR) or unavailability (U) is shown as Table II.

TABLE II. THE WTG POWER OUTPUT RELIABILITY MODEL

State Capacity in (MW) Probability

1 0 U

2 P(V) 1-U

D. Wind Farm Reliability Model A wind farm consists of many WTGs. Each of them can be out of service due to the forced outages. Consider a wind farm consisting of n identical Pr MW WTGs. If the forced outages of WTGs are not considered, the available power output of the wind farm is the summing of n WTG power outputs, i.e. n×Pr MW. If each WTG has a FOR of q, the cumulative probability that up to k (0 ≤ k ≤ n) WTGs are on forced outage is given by (6) and the individual probability of i units being on forced outage is given by (7) [19].

1

(1 )k

i n ik

i

nP q q

i−

=

⎛ ⎞= −⎜ ⎟

⎝ ⎠∑ (6)

(1 )i n ii

np q q

i−⎛ ⎞

= −⎜ ⎟⎝ ⎠

(7)

The wind farm reliability model can be obtained using the individual probability pi and the WTG power output model, as shown in (8) [19-20]

0 0( ) ( / )

k s

j j j ii j

P X q u x i C p= =

⎛ ⎞= −⎜ ⎟

⎝ ⎠∑ ∑ (8)

where P(Xj) is the probability of the output power of the wind farm, s is the number of wind power outputs, Cj is the jth capacity state, pi is the probability of i units being available (using (7)), qj is the probability of a WTG operating in output

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state Cj, and u(x/i-Cj) is the unit step function (equal to 1 for i = 0 & all j, and for i ≥ 1 & j = 0; equal to 0 elsewhere). If different WTGs in a wind farm to be modeled, a computationally efficient recursive algorithm has been developed in [20].

E. Load Model Load modeling is very important to power system reliability evaluation. To obtain accurate model of load is a difficult task due to lack of precise information of the composition of load, weather forecast errors, and more. Different load models including constant load models and load duration curve (LDC) have been used in reliability evaluation [4, 21-23]. A time varying load model, the hourly peak load variation curve of the IEEE-RTS [24] is used in this study, as shown in Fig. 1.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000500

1000

1500

2000

2500

3000

Time (hour)

Load

(M

W)

Figure 1: The hourly peak load variation curve of the IEEE-RTS

III. ENERGY STORAGE SYSTEM MODELING

Energy storage has been used to improve reliability of power systems with wind energy. Several energy storage models have been proposed in [8, 9, 25-27]. Four parameters are mainly used to characterize an energy storage unit in reliability evaluation. They are Storage Capacity, Charging/Discharging Rate (power rating of the storage unit) (Rc/Rd), Charging/Discharging Efficiency (ηc/ηd) and Charging/Discharging Limit (Lc/Ld) (i.e. maximum/minimum capacity of energy storage). The ηc/ηd and Lc/Ld are actually associated with the charging/discharging rate and storage capacity, respectively. Therefore the two most important parameters to characterize an energy storage unit are the charging/discharging rate and capacity, which are also the two main parameters to determine the price of energy storage units. The charging/discharging efficiency and charging/discharging limit are assumed to be 100% and no limits, respectively.

In addition to the capacity and charging/discharging rate, the operating strategy of energy storage also characterizes the energy storage system. The factors that impact the operating strategy include the purposes of storage, such as peak load shaving [28], providing standing reserve [29], smoothing WTG power output fluctuation and maximizing wind power utilizing [11], and priority of wind power. In this study, the operating strategy of the energy storage is to offset the deficiency of the available generation in some states and the wind power has priority to supply load. The detailed operating strategy is as follows

1) If the available conventional generating units in a time step can supply system demand, all the wind energy produced is available to be stored in energy storage. The available wind energy is not always be stored in the energy storage due to the limits of left space and charging rate of the energy storage.

2) If the available conventional generating units in a time step cannot supply system demand, the produced wind energy will be incorporated to supply system demand. When the combination of the conventional generation and wind generation is adequate to supply system demand, the excess wind energy is available to be stored and the storing is also limited by the left space and charging rate of energy storage.

3) If the available conventional generating units and WTGs cannot supply system demand, the stored energy in energy storage will be discharged to supply system demand.

4) If all the energy from the conventional generating units, WTGs and energy storage still cannot supply demand, the load curtailment is required to balance supply and demand.

IV. RELIABILITY EVALUATION TECHNIQUES

A. Reliability Indices Expected Energy Not Supplied (EENS) is one of the most important indices in generating capacity adequacy evaluation. The EENS for a time period can be calculated using the following equation

1 1

( ) j iN N

ji dj ji jj i

EENS p A AG t= =

= × − ×∑∑ (9)

where pji is the individual probability of state i at time step j, Adj is the load level at step j, AGji is the available capacity of state i at time step j, tj is the step duration at time step j and Nj, Ni are the number of steps and states, respectively. pji and AGji are calculated using (10) and (11)

Goi G G Woi G W

Goi G G Woi

M M M M M M

ji cG cG cW cWc 1 c M 1 c M 1 c M M 1

p A U A U+ +

= = + = + = + +

= ∏ ∏ ∏ ∏ (10)

Goi G Woi

G

M M M

ji cG cW s jc 1 c M 1

AG AG AG AG+

= = +

= + +∑ ∑ (11)

where AcG , AcW, UcG and UcW are availability of conventional generating units, availability of WTGs, unavailability of conventional generating units and unavailability of WTGs, respectively; AGcG and AGcW are available capacity of conventional generating units and WTGs, respectively; AGsj is the dischargeable energy in energy storage at time step j; MGoi is the number of conventional generating units being operating at state i, MG is the total number of conventional generating units, MWoi is the number of WTGs being operating at state i, and MW is the total number of WTGs.

When a wind farm is included in the reliability evaluation, its generation can be evaluated by many indices [30-32], as

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shown in Table III. A new index, expected energy not used (EENU), is defined to represent the wind energy produced by WTGs but not used to service system load. The EENU results from the operating strategy of the wind farm: only when the conventional generating units cannot supply system load, the wind generation joins together with the conventional units to supply system load. The EENU for a time period can be calculated using (12)

,

j i

j i

N N

ji W ch j G djj 1 i 1

N N

ji ji s j d j ch j G djj 1 i 1

p ( AG E ) if AG AEENU

p ( AG AG A E ),if AG A

= =

= =

=

⎧× − ≥⎪

⎪⎨⎪ × − − − <⎪⎩

∑∑

∑∑

(12)

where AGW, AGG are the energy produced by WTGs and conventional generating units, respectively; Echj is the wind energy absorbed by energy storage at time step j, which is subject to the following constraints (13) and (14)

0 ch j c jE R t≤ ≤ ⋅ (13)

( 1)0 ( )ch j slimit s jE AG AG −≤ ≤ − (14)

where Rc is the charging rate, AGslimit is the storage capacity limit and AGs(j-1) is the left energy stored in storage at time step (j-1).

TABLE III. INDICES FOR WIND FARM GENERATION EVALUATION

Index Definition

IWE Installed Wind Energy is the product of installed capacity and the number of hours in the period

IWP Installed Wind Power is the sum of the nominal power of all the WTGs in the wind farm

EAWE Expected Available Wind Energy is the sum of energies that wind farm produces in the period

EGWE Expected Generated Wind Energy is the sum of energies that all effectively available WTGs produce in the period

CF Capacity Factor is the ratio of EGWE to IWE

GR Generation Ratio is the ratio of the power delivered at the point of common coupling (PCC) to the power injection generated by the wind farm

B. Evaluation Precedure The analytical evaluation technique for evaluating the EENU and EENS consists of the following steps:

Step 1: Pre-process the historical wind speed data and form the hourly mean wind speed model using (1).

Step 2: Obtain the power output model of a single WTG using the relationship (2)-(5).

Step 3: Combine the WTG two-state reliability model and the power output model from Step 2 to form the WTG power output reliability model.

Step 4: According to the types of WTGs in the wind farm, form the wind farm reliability model.

Step 5: Obtain the hourly peak load model.

Step 6: Calculate the capacity outage probability table (COPT) for conventional generating units in the power system using the recursive algorithm in [33].

Step 7: For every time step j, add the wind farm to the generating unit list and form new COPTj.

Step 8: Determine the energy storage model and its operating strategy.

Step 9: For a time step j, combine the load at this time step, COPTj and the operating strategy of energy storage, to calculate the EENUj and EENSj.

Step 10: Repeat Step 9 for all time steps, obtain the EENS and EENU for whole time period.

Step 11: Adjust the power system parameters, such as the parameters of conventional generating units, the wind conditions, the parameters of WTGs and wind farm, the parameters of energy storage, repeat Step 1-10.

V. SYSTEM STUDIES The proposed procedure is applied to the IEEE-RTS [24]. The total installed capacity in the IEEE-RTS is 3405 MW and the generating unit data are shown in Table IV. There are 32 conventional generating units including fossil steam, combustion turbine, hydro, and nuclear steam types.

TABLE IV. GENERATING UNIT RELIABILITY DATA

Unit size (MW) Unit type Number of

units FORs MTTF (hours)

MTTR (hours)

12 Oil/steam 5 0.02 2940 60 20 Oil/CT 4 0.10 450 50 50 Hydro 6 0.01 1980 20 76 Coal/steam 4 0.02 1960 40 100 Oil/steam 3 0.04 1200 50

1545 Coal/steam 4 0.04 960 40 197 Oil/steam 3 0.05 950 50 350 Coal/steam 1 0.08 1150 100 400 nuclear 2 0.12 1000 150

The peak system load is 2850 MW and the one month load data in June are selected for usage. Different cases have been studied to illustrate the impacts of wind speed, storage capacity and charging/discharging rate of energy storage on the EENU and EENS.

A. Without Energy Storage For the IEEE-RTS without WTGs, the EENS is 122.2698 MWh/month and there is no EENU since it only represents the unused wind energy.

A wind farm with 50 identical 10.0 MW WTGs is incorporated into the IEEE-RTS. The cut-in, rated, and cut-out speeds of these wind turbines are 3 m/s, 14 m/s and 25 m/s, respectively. The capacity of the wind farm is 500 MW, which accounts for about 13% of the total power system capacity, i.e. the penetration level of wind power is 13%. The FOR of WTGs is assumed to be 0.05. The wind farm can produce maximal energy of 3.1815×104 MWh/month. The EENS is decreased to 57.8406 MWh/month and the EENU is 3.1764×104 MWh/month. The value of EENU is almost equal to the total

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produced wind energy in that month. The reason is simple: the generation system of the IEEE-RTS is relatively strong and there have very low probabilities that the generation system cannot supply system load and hence, the wind power has few chances to offset the deficiency of the conventional generation to supply load. Hence, the unused wind energy is very much.

B. With Energy Storage The energy storage is incorporated into the IEEE-RTS with WTGs. The operating strategy is described in Section III. The capacity and charging/discharging rate are 800 MWh and 300 MW, respectively. It is assumed that the energy storage has no initial stored energy. The EENU and EENS are changed to 3.088×104 MWh/month and 2.7141MWh/month, respectively. Comparing to the values when without energy storage, the EENU and EENS decreases by 2.7% and 95.2%, respectively, i.e. incorporating energy storage has larger impact on the EENS than on the EENU in this system.

1) Effect of Rated Capacity of Energy Storage

The impact of the rated capacity of energy storage on reliability indices is studied in this case. When the rated storage capacity increases from 0 MWh to 1900 MWh, the corresponding EENS and EENU are shown in Fig. 2. The EENU decreases a little bit faster when the capacity of energy storage is increased from 0 MWh to 400 MWh. For example, when the capacity is changed from 0 to 100 MWh, the EENU decreases from 3.1764×104 MWh/month to 3.1611×104 MWh/month, i.e. the increase of 100 MWh capacity of energy storage leads to 153 MWh/month decrease of EENU. However, when the capacity of energy storage is over 400 MWh, the EENU starts to decrease slowly and the increase of 100 MWh energy storage leads to 100 MWh/month decrease of EENU. The EENS decreases significantly when the capacity of storage is increased from 0 MWh to 400 MWh and keeps constant at 2.7141 MWh/month when the capacity of energy storage is over 400 MWh. This is to say that, from the EENS point of view, the energy storage of 400 MWh is suitable for this power system.

0 200 400 600 800 1000 1200 1400 1600 1800 20002.9

3

3.1

3.2x 10

4

Capacity of Energy Storage (MWh)

EE

NU

(M

Wh/

mon

th)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

20

40

60

Capacity of Energy Storage (MWh)

EE

NS

(M

Wh/

mon

th)

Figure 2: Impact of storage capacity on EENU and EENS

2) Effect of Charging/Discharging Rate

The charging/discharging rate is changed from 0 MW/hour to 95 MW/hour. Fig. 3 shows the changes of EENU and EENS with the change of charging/discharging rate. It can be seen

from Fig. 3 that the charging/discharging rate has small effect on the EENU but has large effect on the EENS. Actually, the EENU is impacted mainly by the charging rate since wasted wind energy is produced during charging period while the EENS is impacted mainly by the discharging rate because insufficient discharging leads to EENS. From the top curve in Fig. 3, it can be found that a charging rate larger than 5 MW/hour has small benefit to the EENU. The EENS decreases from 57.8406 MWh/month to 23.3838 MWh/month when the charging/discharging rate increases from 0 MW to 95 MW. Hence, a large charging/discharging rate benefits the EENS more.

3) Effect of Wind Speed

The wind speed is ranging from 80% to 175% of its original value and the impact of wind speed on the EENU and EENS are shown in Fig. 4. It can be seen from Fig. 4 that the increase of wind speed leads to quite large increase of EENU while only results in small reduce of EENS. Hence, for this system, increasing of wind speed cannot bring about much reliability benefit and on the other hand it leads to a large amount of waste of wind energy. The two curves are not straight lines because the power output of wind farm is not changing continuously with the increase of wind speed.

0 10 20 30 40 50 60 70 80 90 1003.14

3.16

3.18x 10

4

Charging/Discharging Rate (MW/hour)

EE

NU

(M

Wh/

mon

th)

0 10 20 30 40 50 60 70 80 90 10020

40

60

Charging/Discharging Rate (MW/hour)

EE

NS

(M

Wh/

mon

th)

Figure 3: Impact of charging/discharging rate on EENU and EENS

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80

5

10

15x 10

4

EE

NU

(M

Wh/

mon

th)

Wind Speed / Original Wind Speed

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.81

2

3

4

Wind Speed / Original Wind Speed

EE

NS

(M

Wh/

mon

th)

Figure 4: Impact of wind speed on EENU and EENS

VI. CONCLUSION This paper presents an analytical method to evaluate the reliability of power systems with WTGs and energy storage.

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The simulation results show that the increase of storage capacity can benefit the EENU and EENS when the capacity is not over 400 MWh. The increase of charging rate has relatively small impact on the EENU and increase of discharging rate benefit the EENS much. Higher wind speed leads to significant increase of EENU and relatively less improvement of the EENS when the energy storage capacity is fixed. Other parameters such as the wind power penetration level, operating strategies of energy storage system, system load level and system generating capacity, can be incorporated to evaluate the reliability. This procedure can also be extended to determine the impacts on other reliability indices, such as LOEE (Loss of Energy Expectation), LOLE (Loss of Load Expectation), etc.

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