Reducing uncertainty accumulation in wind-integrated electrical grid

Reducing uncertainty accumulation in wind-integrated electrical grid

Accepted Manuscript Reducing uncertainty accumulation in wind-integrated electrical grid Tzu-Chieh Hung, John Chong, Kuei-Yuan Chan PII: S0360-5442(1...

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Accepted Manuscript Reducing uncertainty accumulation in wind-integrated electrical grid Tzu-Chieh Hung, John Chong, Kuei-Yuan Chan PII:

S0360-5442(17)31670-5

DOI:

10.1016/j.energy.2017.10.001

Reference:

EGY 11643

To appear in:

Energy

Received Date: 11 January 2017 Revised Date:

19 September 2017

Accepted Date: 1 October 2017

Please cite this article as: Hung T-C, Chong J, Chan K-Y, Reducing uncertainty accumulation in windintegrated electrical grid, Energy (2017), doi: 10.1016/j.energy.2017.10.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Reducing uncertainty accumulation in wind-integrated electrical grid

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Tzu-Chieh Hung, John Chong,Kuei-Yuan Chan1 , Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan Abstract

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Implementing microgrids has become a major trend in the electric power industry to move toward energy sustainability. One approach for implementing microgrids is to introduce renewable energy. With the inclusion of renewable energy in a microgrid, an appropriate energy storage capacity is needed to cope with uncertainty variation resulting from renewable energy generation fluctuation. This study proposes a probability-based dispatch strategy for determining energy storage capacity with consideration of wind and load fluctuation. The wind and load models are constructed based on their trends and uncertainty variations. The wavelet packet analysis method and the moving average technique are used to extract the trends of wind energy and load. Log-normal and extreme value distributions are used to model the uncertainties from wind speed and load. This research improves an existing method with reduced uncertainty accumulation, resulting in a more suitable battery size. To validate the proposed method, a real-time operating simulation is used to observe the behavior of a wind-integrated electrical grid. Results show that the proposed method can reduce the effects of uncertainty variation caused by wind and load. A smaller energy storage capacity with higher reliability is also obtained through optimization.

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Keywords : wind energy forecasting, electricity demand forecasting, power dispatch, energy storage sizing, microgrid, design under uncertainty

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Corresponding Author, [email protected], Fax:+886-2-2363-1755

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List of Acronyms CDF cumulative distribution function DES distributed energy storage CDES capacity of distributed energy storage

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PCDES power capacity of distributed energy storage NRPP non-renewable power plant PBPD probability-based power dispatch SOC state of charge of distributed energy storage

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WEG wind energy generator

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WIEG wind-integrated electrical grid

List of Symbols

power capacity of DES at time t

emax

upper physical limit of DES

emin

lower physical limit of DES

g(t)

power generation at time t

gw (t)

weekly trend of power generation at time t

gy (t)

yearly trend of power generation at time t

l(t)

electricity demand (load) at time t

pc,min pr pw (t)

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pc,max

power generation from central NRPPs at time t maximum power generation from central NRPPs

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pc (t)

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e(t)

minimum power generation from central NRPPs rated power of wind turbines in WEG model power generation from WEGs at time t

s

scale parameter in electricity demand model

sc

scale parameter: percentage of residential and commercial energy consumption

sg

scale parameter: annual growth rate of power generation

sp

scale parameter: percentage of regional population

v(t)

wind speed at time t

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ACCEPTED MANUSCRIPT cut-in speed of wind turbines in WEG model

vout

cut-out speed of wind turbines in WEG model

vr

rated speed of wind turbines in WEG model

vy (t)

yearly trend of wind speed at time t

εg

uncertainty variation of power generation

εv

uncertainty variation of wind speed

EV(µ, σ)

extreme value distribution with location parameter µ and scale parameter σ

N (µ, σ 2 )

normal distribution with mean µ and standard deviation σ

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success rate of electrical grid

PD[·]

power dispatch function

E[·]

average operator

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Note

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vin

Lowercase letters such as e(t) and l(t) indicate deterministic variables or parameters

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Uppercase letters such as E(t) and L(t) indicate uncertainty variables or parameters defined by probability distributions

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1 1.1

Introduction Background

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Standard power systems include the generation, transmission, distribution, and consumption of electrical energy. Since most electrical grids are macrogrids with several centralized power generation stations and a unified power dispatch strategy for power stability, a failed component might cascade to other interconnected subsystems [1]. Microgrids have been proposed to implement local power generation to meet the demand for a relatively small area. Connecting a microgrid can prevent failure from cascading and therefore improve power quality in a macrogrid. In addition, the local power generation stations within a microgrid can reduce the burden of centralized power plants in a macrogrid. Due to their flexibility, reliability, and stability, microgrids are one of the major development trends in the electric utility industry. How to systemically and efficiently transform an existing macrogrid into a number of smartly connected microgrids remains a challenge in power system design and planning. One approach for transforming a macrogrid system into a microgrid system is to introduce various forms of energy generation to reduce the dependency on non-renewable power plants (NRPPs). Two of the most popular distributed energy sources are wind and solar power due to their sustainability and environmental friendliness. However, these natural power sources have embedded uncertainty, resulting in unpredictable and fluctuating power generation. Maintaining a stable microgrid system with renewable power sources requires distributed energy storage (DES). Large DES allows a more stable power system, but has a higher installation cost. Therefore, determining a suitable storage capacity is required for the transformation of a macrogrid into microgrids. The present study considers a transformation process for part of an existing macrogrid towards a wind-integrated electrical grid (WIEG, shown in Fig. 1) with consideration of the uncertainties from both wind power generation and electricity demand. To create a sustainable electrical system, some NRPPs were replaced with wind energy generators (WEGs) and new DES devices were installed. The power dispatch strategy in a WIEG controls the output from NRPPs to optimize the performance of electrical systems, such as maximizing system reliability or minimizing operation cost. DES devices provide a bridge for matching power generation with electricity demand. Since a dispatch strategy is executed with a given equipment setup, it is directly affected by storage capacity. In other words, the dispatch strategy should be taken into account when determining the capacity of distributed energy storage (CDES). The goal of this work is to implement a dispatch strategy with CDES determination under uncertainty variation of wind and load in WIEG to obtain an optimal CDES. The specific contribution of this work is CDES determination with a probability-based power dispatch (PBPD) strategy and load model to reduce the effect of uncertainty variation.

1.2

Related Work

With the purpose of transforming macrogrid into microgrids, great effort has been put into studying microgrid implementation. Microgrid-related studies can be categorized into four types, namely wind energy forecasting, electricity demand modeling, optimal power dispatching, and DES sizing. Wind energy forecasting is used to predict short- or long-term wind energy based on local historical wind data. Several data analysis methods have been applied for wind3 4

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energy forecasting, such as statistical approaches, time series approaches, and machine learning. Statistical approaches are usually used in long-term forecasting to determine a suitable site for WEG installation. In these studies [2] and [3], Nigim et al. and Ahwide et al. used probability distributions to model the behavior of wind speed, and then a power curve of wind turbines is applied to convert wind speed into wind energy. Time series approaches are used to observe the periodic trend in wind data. An example of this is McGarrigle et al. in [4], the author created wind forecasts using an auto-regressive moving average (ARMA) model to create day ahead system schedules. Machine learning is commonly used in short-term forecasting for power system operation planning. In one study [5], Okumus et al. combines adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) for 1 hour ahead wind speed forecasts. In another study [6], daily and yearly wind speed models were built for wind energy assessment based on information from the power spectral analysis of wind data. Similar to wind energy forecasting, several data analysis methods have been applied to electricity demand modeling and forecasting. Time series trend analysis has been used to predict future energy requirements. In the study [7], weekly and yearly trends of electricity demand were extracted as models based on the autoregressive moving average (ARMA) model. In another study [8], the probability distribution of the residual between trend models and historical data was used as an index for model validation. Khraief [9] also estimated the electricity demand function for Algeria with time series analysis .The machine learning approach is usually used in very-short-term and short-term forecasting in order to manage power dispatching in electrical systems. Chae et al. [10] proposed a short term building energy usage forecasting model based on an Artificial Neural Network (ANN) model with Bayesian regularization algorithm. Optimal power dispatch is a dynamic optimization process that adjusts the power output of generators to optimize the performance of electrical systems (e.g., maximize profit, minimize operation cost, or improve system stability). Different author has his own research goal resulting in different dispatching method and research focus. Uncertainties from wind energy and electricity demand have been taken into account in WIEG for stability consideration in [11]. To achieve long-term and real-time objectives simultaneously, multi-step optimal dispatch has been proposed in both [12]. Peikherfeh et al. [13] also proposed a two stage algorithm to solve optimal power dispatch problem. Stochastic programming has also been adopted [14] to determine optimal dispatch strategies with energy storage to obtain maximum profit from wind farms. DES sizing is used to determine the CDES under resource and/or load uncertainty without overbuilding. Dutta et al. [15] optimized an installed CDES with the given rated power of WEGs based on reliability and worth analysis. Roy et al. optimized the sizes of WEGs and DES devices in an isolated wind-battery system [16]. Chen et al. sized CDES in a wind farm while considering the dispatch strategy [17]. Brekken et al. determined optimal storage size with control strategy in power flow [18]. Baker et al. take into account of uncertainties of wind forecasting by introducing chance constraints into their DES sizing formulation [19]. In a recent study [20], various scenarios are studied in an efforts to understand the conditions of meeting a desired percentage of renewable energy for policy decisions. To optimize capital investment, Whitefoot et al. built an isolated grid and integrated component sizing with optimal dispatch in a design framework [21]. This integration concept was also applied to gradually transform an existing macrogrid into microgrids in our previous study [22], which determined appropriate installation capacities of WEGs 3 5

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and DES devices with a long-term power dispatch s trategy under uncertainty. Fig. 2 shows the flowchart from [22] for clarity. Although the dispatch strategy in [22] quantified the uncertainty variation of WEGs and the power capacity of DES (PCDES) in the design stage for DES sizing, it may not be the optimal setting when the electrical grid is implemented. This is owing to uncertainty accumulation in the preset deterministic dispatch operation, which leads to DES overbuilding. Therefore, the present study aims to eliminate uncertainty accumulation by implementing the PBPD strategy with a new electricity demand (load) model. The rest of this paper is organized as follows. Previous work is briefly reviewed in Section 2. The proposed methodology is introduced in Section 3. Section 4 uses the obtained models to demonstrate the proposed method and Section 5 contains the conclusion.

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Determinisitic Power Dispatch Strategy for DES Sizing Under Uncertainty

2.1 2.1.1

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The goal of the present study is to obtain the optimal design procedure to transform a macrogrid into microgrids with wind turbines, a power dispatch strategy, and energy storage. Our previous work [22] addressed the importance of DES sizing with uncertainty. We showed that when uncertainties are ignored, the battery size obtained has a great chance of being suboptimal. Once fluctuations in wind speed are accounted for, we can provide better predictions. However, the uncertainty accumulation in storage sizing in [22] is still high since a deterministic dispatch strategy is used. In this section, we provide a brief review of [22]. Fig. 3 shows the three-step procedure of the transformation. Step 1 is getting information about the wind energy. This includes data collection and modeling. Appropriate wind energy models, combined with user demand and energy from the central power station are required to determine the optimal dispatch strategy in Step 2. The final dispatched energy is then used for the optimal component sizing in Step 3 for the final layout determination.

Wind Energy Assessment Wind Speed Model

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Weather data from the Central Weather Bureau of Taiwan at Tainan station from 2003 to 2007 were used. The historical daily wind data were analyzed and modeled using wavelet packet analysis. The low-frequency trend of the logarithmic wind data, vy (t), is represented by the dashed line in Fig. 4. The solid line in Fig. 4 represents the average trend in the 5 years as the annual trend model, v¯y (t). The uncertainty variation of the logarithmic wind data after the trend extraction, εv , shown in Fig. 5(a) and Fig. 5(b), with a probability plot and histogram fitting is a normal distribution with µ = −3.41 × 10−4 and σ = 0.30. From the results of the logarithmic wind data, the logarithmic wind speed can be modeled as: where εv ∼ N (µ, σ 2 ).

ln V (t) = v¯y (t) + εv ,

(1)

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Finally, the wind speed model with uncertainty, V (t), was obtained by taking the exponential of Eq. (1). The resulting wind speed model considering data uncertainty is shown in Fig. 6. The solid line is the trend of the wind speed, v¯y (t). The gray region includes the 95% confidence interval of the distribution (from 2.5% to 97.5%) in the wind speed model. Wind data from January 1st to July 15th, 2008, not used in the analysis stage, are plotted as the dashed line in Fig. 6 to check the accuracy of the wind speed model. The results show that almost all wind data are located in the 95% probability region. 2.1.2

Wind Energy Model

The wind energy model is used to transform the input wind speed into the output wind energy. The output wind energy, pw , can be simply modeled as a piecewise function

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(2)

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where vin , vout , and vr are the cut-in, cut-out, and rated speeds of the wind turbine, respectively. When the input wind speed is greater than the cut-in speed, the turbine starts to generate power. When the wind speed reaches the rated speed, the wind turbine outputs the rated power pr . When the wind speed is beyond vout , the wind turbine stops generating power for safety reasons.

General Dispatch Strategy

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The objective of the dispatch strategy is to minimize the generated power pc (t) from the central NRPPs subject to the energy conservation constraint while considering the uncertainty from wind power, Pw (t), and the load, L(t). Thus, the general dispatch strategy at time t can be formulated as Eq. (3). pr , emax e(t) pc (t) E(t + 1) = e(t) + pc (t) + Pw (t) − L(t) E2.5% (t + 1) ≥ emin E97.5% (t + 1) ≤ emax pc,min ≤ pc (t) ≤ pc,max w.r.t. pc (t)

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given measure min s.t.

(3a) (3b) (3c) (3d) (3e) (3f) (3g) (3h)

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Equation (3d) not only ensures energy conservation but also estimates the PCDES at the next time instant, E(t + 1), based on the current PCDES, e(t). At time t, e(t) is a deterministic variable since the estimated value can be calculated through historical charging and discharging data of DES, and thus a lowercase letter is used. E(t + 1) is estimated as the summation of two deterministic variables and two random variables, as shown in Eq. (3d). Therefore, E(t + 1), as a random variable, is expressed with an uppercase letter. Equations (3e) and (3f) constrain the 95% probability of the PCDES within its physical limits to ensure the system’s feasibility at the next time instant. The margin of the percentage of the PCDES can be modified according to the variable’s distribution and design requirements. Equation (3g) is used to ensure that pc (t) does not exceed the limits of the power generation from the central NRPPs.

2.3

Storage Sizing

The CDES is defined as the upper boundary of the PCDES divided by grid voltage to ensure electrical grid system stability and is determined with consideration of the general dispatch strategy over a long time horizon. At any time t in the future, the PCDES can be estimated as a random variable E(t) due to uncertainty. Equation (3d) then becomes3 8

ACCEPTED MANUSCRIPT E(t + 1) = E(t) + pc (t) + Pw (t) − L(t)

(4)

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The uncertainty variation of E(t+1) increases as time increases since the uncertainties from E(t), Pw (t), and L(t) in Eq. (4) are carried over to the next time instant. Although this uncertainty variation of the PCDES can be quantified, the large uncertainty variation hinders the determination of a suitable CDES. The PCDES with large uncertainty variation would result in a large sized CDES which is not optimal, as shown in Fig. 7. Therefore, our approach for power dispatching seeks to eliminate the uncertainty accumulation that results from the long-term usage of a general dispatch strategy.

Methodology

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For the presented uncertainty accumulation problem, PBPD is proposed. The framework of the present study is the substitution of the general power dispatch in Fig. 2 with the proposed PBPD method along with a new demand model during dispatch. The features of the PBPD method and the construction of the demand model are explained below.

Probability-Based Power Dispatch

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For clarity, Eq. (3) is first simplified to Eq. (5). PD [e(t)] denotes the power dispatch function with the current PCDES, e(t), as the input and the PCDES at the next time instant, and E(t + 1), as the output. The argument of the power dispatch function arg PD [e(t)] is the current power output of the central power plant, pc (t).

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E(t + 1) = PD|pr ,emax [e(t)] pc (t) = arg PD|pr ,emax [e(t)]

(5a) (5b)

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The uncertainty accumulation in the long-term usage of general power dispatch originates from the piling up of uncertainty from wind and load. The concept of the PBPD method is to define a set of pc (t), or a distribution of pc (t) at time t0 that matches the daily E(t + 1) distribution. The values of distribution pc (t) and E(t + 1) have a one-to-one correspondence in a way that their sum remains constant. Equation (5) is rewritten as Eq. (6) to expound the idea. n o n o E(t + 1) = E(t + 1) E(t + 1) = PD|pr ,emax [e(t)] , ∀e(t) ∈ E(t) n o n o pc (t) = pc (t) pc (t) = arg PD|pr ,emax [e(t)] , ∀e(t) ∈ E(t) .

(6a) (6b)

In Eq. (6), the output and the argument of the power dispatch function E(t + 1) and pc (t) form two different sets, namely {E(t + 1)} and {pc (t)} by considering all possible PCDES with e(t) ∈ E(t). At time t, e(t) will be a known variable and pc (t) will be adjusted based on e(t) to derive the value pc (t) from {pc (t)} that minimizes the uncertainty variation of E(t). Thus, the uncertainty in E(t + 1) is reduced and mainly comes from3 9

ACCEPTED MANUSCRIPT Pw (t) and L(t). In other words, the uncertainty accumulation problem is eliminated by implementing Eq. (6). After PBPD, the uncertainty variation of the PCDES at any time instant can be estimated, and the designer can determine a suitable CDES with a specific setting of the percentage bounds of the PCDES.

3.2.1

Data Analysis and Demand Model Power Generation Data Analysis

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The load data in Taiwan are not detailed enough to construct a demand model. Hence, the power generation model on which the demand model is based on is discussed here. The daily power generation data for Taiwan was provided by Taiwan Power Company. The recording period was from January 1st, 2009, to December 31st, 2012. The results of Welch’s power spectral density analysis of the data in Fig. 8(a) show that there are several peaks in the power spectrogram. The peaks at frequencies ω = 1.9531 × 10−3 , 0.1426, 0.2852, and 0.4277 correspond to cycles with periods of 512, 7, 3.5, and 2.34 days, respectively. The two smaller peaks at frequencies ω = 0.2852 and 0.4277 are the harmonics of the fundamental frequency ω = 0.1426. The two larger peaks indicate that there are two low-frequency trends with different periods hidden in the daily power generation data. 6-level wavelet packet decomposition was applied to extract the first peak in Fig. 8(a). Figure 8(b) shows the power spectrum of the residual after wavelet packet trend extraction. Since the wavelet packet decomposition was not very successful on the weekly trend extraction (second peak in Fig. 8(a)), the moving average technique (see p. 31 in [24]) was applied. Using the obtained data after wavelet packet trend extraction, the ¯ was computed using Eq. (7). average deviation d(t)

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(7)

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where t = 1, . . . , 7, 4 ≤ t + 7j ≤ 1458, x0 denotes the deviations between the original power generation data and the trend from wavelet packet analysis, and E [·] denotes the average operator. Then, the weekly trend of the power generation, gw (t), can be estimated as: 7 1X¯ ¯ d(t), (8) gw (t) = d(t) − 7 i=1 where t = 1, . . . , 7, and gw (t) = gw (t − 7) for t > 7. Figure 8(c) shows the power spectrum of the residual after the wavelet packet and moving average trend extractions. The power generation data, low-frequency trend, gy (t), and weekly trend, gw (t), are shown in Fig. 9. The residual of the power generation data, the uncertainty variation εg , was quantified from the extreme value distribution. Figure 10 shows the probability plot and histogram fitting of the extreme value distribution with parameters µ = 11.21 and σ = 19.55. 3.2.2

Electricity Demand Model

From the results in Section 3.2.1, the power generation can be modeled as the combination of the two different trends and the uncertainty variation. Figure 11 shows the two trends of the power generation data gy (t) and gw (t). The dashed line represents the low-frequency trend of the 4 years, and the solid thin line represents the weekly trend in a3 10

ACCEPTED MANUSCRIPT year. The solid bold line in Fig. 11, the average of the low-frequency trend, is the annual trend model, g¯y (t). With the ergodic assumption, the power generation, G(t), is obtained using Eq. (9). G(t) = g¯y (t) + gw (t) + εg , where εg ∼ EV(µ, σ) (9)

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The resulting power generation model considering data uncertainty is shown in Fig. 12. The gray region includes the 95% confidence interval of the distribution in the power generation model. The power generation data from January 1st to December 31st, 2013, not used in the analysis stage, are also plotted in Fig. 12 to check the accuracy of the power generation model. To obtain the energy consumption model, the power generation model, G(t), was multiplied by a scale parameter, s. The scale parameter, s, is the product of three scalers, namely the percentage of the residential and commercial energy consumption, sc , the percentage of the regional population, sp , and the annual growth rate, sg . sc is used to scale down the power generation model to the specific end-use sectors as a preliminary energy consumption model. sp is used to scale down the preliminary energy consumption model to the specific region of interest. The energy consumption model can be written as: L(t) = s · G(t), where s = sc × sp × (1 + sg ). (10)

Case Study

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As a case study to demonstrate the proposed approach, a district in Tainan was used as a model for WIEG. In this electrical grid, the residential and commercial electricity demands were the only considered loads. From Eq. (10), the electricity demand model can be constructed with the parameters sc = 30%, sp = 0.276%, and sg = 2.1% based on the statistical data from Taiwan Power Company [25] and the Ministry of the Interior of Taiwan [26]. Figure 13 shows the electricity demand model considering the distribution’s range within 95% at any time t in the electrical grid. The solid bold line at the top represents the minimal requirement of the central NRPPs, pc,max , without additional power supply. To achieve energy sustainability, wind energy was introduced into the electrical grid. After wind resource assessment in the district, a set of WEGs with 43-MW rated power was installed in the electrical grid to cover 10% of the power generation from the central NRPPs. In the wind energy model, the cut-in, cut-out, and rated speeds of the wind turbines were set as 1, 25, and 13 m/s,respectively, based on the ENERCON product overview [27]. pc,max was set to 90% of the original value to reduce the dependency on central NRPPs, as shown by the dashed line in Fig. 13. In order for the fluctuating wind energy to provide 10% of the total load, DES devices are needed in this electrical grid.

4.1

PBPD Implemention and Method Comparison

In the electrical grid with the given pr and pc,max , the proposed PBPD method and the long-term general dispatch method were applied to forecast the PCDES in a year. Since only the dispatch methods are compared in this case, variable emax is set as a constant value of 4 × 106 . Figure 14 shows the uncertainty variation range in a year for the two different methods. 3

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In Fig. 14, the dashed lines and solid lines represents PCDES and the PCDES throughout the year, respectively, and the gray region represents the 95% confidence interval of the PCDES distribution. The results clearly show that that the PBPD method has effectively reduced the uncertainty variation. The ‘x’ mark in Fig. 14 denotes a ‘failure’ occurring at that time instant. The failure is defined as the PCDES exceeding its physical limits. If the PCDES exceeds the upper limit, the additional energy is wasted. If the PCDES exceeds the lower limit, the grid will shutdown since there is insufficient energy to satisfy the energy demand. From the definition of failure, the success rate of the electrical grid in a year, S, can be calculated using Eq. (11). With this definition, the success rate of the electrical grid is 3.29% higher than long-term power dispatch when using the PBPD method as depicted in Fig. 14. number of failures (11) number of days in a year A comparison of the results of uncertainty variation range and success rate of the electrical grid confirms that the proposed PBPD method reduces uncertainty variation and is better than the long-term general dispatch.

4.2

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CDES Optimization and Results

In the previous section 4.1, the effectiveness of the PBPD method in reducing uncertainty variation and improving the success rate were demonstrated with the given pr ,pc,max , and emax . Here, PCDES, which is the variable emax , to reduce installation cost. The optimization formulation can be written as in Eq. (12) (12a) (12b) (12c) (12d) (12e)

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min emax n o n o s.t. E(t + 1) = E(t + 1) E(t + 1) = PD|pr ,emax [e(t)] , ∀e(t) ∈ E(t) n o n o pc (t) = pc (t) pc (t) = arg PD|pr ,emax [e(t)] , ∀e(t) ∈ E(t) .

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Equation (12) minimizes the CDES subject to PBPD equations with respect to the rated power of the wind turbines. The optimization results with both methods are shown in Fig. 15. In Fig. 15(a) and Fig. 15(b), the dashed line represents the rated power of WEGs, and the gray region represents the 95% confidence interval of the wind energy distribution. In Fig. 15(c) and Fig. 15(d), the solid bold line and the dashed line at the top represent the original and the new setting of pc,max , respectively, and the gray region represents the 95% confidence interval of the PBPD. In Fig. 15(e) and Fig. 15(f), the gray region represents the 95% confidence interval of the PCDES distribution. From the results in Fig. 15, the uncertainty variation range in a year is estimated, and the CDES is determined by setting the dashed line at the top of the gray region to cover at least 95% uncertainty variation. The optimization successfully minimized CDES with respect to the rated power of the wind turbines. The results are shown in Table. 1. 3

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Conclusion

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This study developed a PBPD strategy for CDES determination under wind and load uncertainty. The proposed strategy effectively eliminates the uncertainty variation effect by applying a conditional probability concept to general power dispatch. The reliability and success rate of the electrical grid were increased considerably compared to long-term power dispatch by using PBPD in the optimization of CDES. These results are especially helpful for determining an appropriate CDES and obtaining a optimal grid state in the long-term operation of a grid with wind and load uncertainty. This work provided a design framework for integrating wind energy forecasting, electricity demand forecasting, power dispatching, and DES sizing. The wavelet packet analysis method and the moving average technique were applied to extract the periodic trends from the wind speed and load data in the forecasting stage. The inverse cumulative distribution function (CDF) method was applied to estimate the distribution of wind energy in the power dispatch stage. Uncertainties from wind energy and load were considered in both the power dispatch and storage determination stages to ensure stability of the WIEG system. Finally, the unused data in the modeling were substituted into the proposed models as the actual implementation to understand the system behavior in the real world. As an example to demonstrate the data analysis, data points of daily wind speed and data points of daily power generation were used to generate annual models with uncertainty for wind energy and electricity demand forecasting. On the basis of these two models, the proposed PBPD strategy provided the 95% confidence intervals of the PCDES at each time instant and then the CDES was determined. For the actual implementation, a success rate S = 98.90% was obtained, which is greater than the confidence interval setting (95%). The proposed framework enables a systematic transformation from a pure macrogrid into one with a wind-integrated microgrid. Alternatively, without major change of the framework, one could include other energy sources such as solar energy. One could also include energy loss in transmission by providing a coefficient with generated energy source. This coefficient can be a fixed constant or a function depending on the evidence we have on the loss of transmission. In the cases of AC models of the power flow be considered to account for the losses, iterative approaches are needed. Other considerations such as unit operational constraints can also be added in the future. With more distributed energy generators and DES devices installed in the electrical grid, the dependency on the central NRPPs will decrease, eventually leading to a sustainable microgrid.

References

[1] J. E. Chadwick. How a smarter grid could have prevented the 2003 U.S. cascading blackout. In 2013 IEEE Power and Energy Conference at Illinois (PECI), pages 65–71. IEEE, 2013. [2] K. A. Nigim and P. Parker. Heuristic and probabilistic wind power availability estimation procedures: Improved tools for technology and site selection. Renewable Energy, 32(4):638–648, 2007. 3

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ACCEPTED MANUSCRIPT [17] W. Z. Chen, Q. B. Li, L. Shi, Y. Luo, D. D. Zhan, N. Shi, and K. Liu. Energy storage sizing for dispatchability of wind farm. In Environment and Electrical Engineering (EEEIC), 2012 11th International Conference on, pages 382–387. Ieee, 2012. [18] T. K. A. Brekken, A. Yokochi, A. von Jouanne, Z. Z. Yen, H. M. Hapke, and D. A. Halamay. Optimal energy storage sizing and control for wind power applications. IEEE Transactions on Sustainable Energy, 2(1):69–77, 2011.

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Centralized Non-Renewable Power Plants Localized Wind-Integrated Electrical Grid

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Wind Energy Generators

Distributed Energy Storages

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Electricity Demand

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Figure 1: System layout of a wind-integrated electrical grid.

Determine equipment sizes by optimization

Equipment Size

Long-term power dispatch

Optimal output of central power plant

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Model from data forecast

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General Power Dispatch

System state

System state forecasting at next time instant

Feasible and converge?

Optimal solution

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Update for long-term dispatch

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Figure 2: General Concept of dispatching and CDES determination

Table 1: Optimization results.

Variable Name

Long-term General Method

PBPD Method

emax Pr S

9.60 × 105 2.02 × 104 297/365

4.64 × 105 7.76 × 104 361/365

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Logarithmic wind speed

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Figure 3: Flowchart of our previous approach. [22]

ln vy (t) ln v7y (t)

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Figure 4: Trend of logarithm of wind speed.

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Figure 5: Statistical analysis of residual of logarithm of wind speed data.

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Power Capacity of DES (kWh)

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Figure 6: Wind speed model under uncertainty.

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Time (date) Figure 7: PCDES over long time horizon with large uncertainty variation 3

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(b) Residual after wavelet (c) Residual after packet trend extraction packet and moving trend extraction

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g(t) gw (t) gy (t)

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Power generation (GWh/day)

Figure 8: Welch’s power spectrogram of power generation data.

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Figure 9: Power generation data and low-frequency trends.

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Power/frequency (dB-day)

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Figure 11: Trends of power generation data. 19

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Electricity demand (kWh)

Figure 12: Power generation model under uncertainty.

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Figure 13: Electricity demand model under uncertainty.

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(a) Probability-based power dispatch

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Figure 14: Results and implementation of PBPD and long term power dispatch. 3

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(f) Power capacity of DES

Figure 15: Results of CDES optimization with long-term general dispatch and PBPD.

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National Taiwan University Department of Mechanical Engineering

1 Roosevelt Rd. Section 4, Taipei, Taiwan 10671

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T:+886-2-3366-1772 F:+886-2-2363-1755 [email protected]

Highlights of EGY-D-17-00163

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Title: A probability-based power dispatch for reducing uncertainty accumulation in wind-integrated electrical grid

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1. consider uncertainties in generation and usage of power. 2. provide a power dispatch strategy to account for uncertainty. 3. obtain the optimal equipment size without uncertainty accumulation.

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4. obtain at least 98.9% operational reliability.