Numerical definitions of wind power output fluctuations for power system operations

Accepted Manuscript Numerical definitions of wind power output fluctuations for power system operations Takashi Ikegami, Chiyori T. Urabe, Tetsuo Saitou, Kazuhiko Ogimoto PII:

S0960-1481(17)30761-9

DOI:

10.1016/j.renene.2017.08.009

Reference:

RENE 9107

To appear in:

Renewable Energy

Received Date: 19 December 2016 Revised Date:

14 June 2017

Accepted Date: 4 August 2017

Please cite this article as: Ikegami T, Urabe CT, Saitou T, Ogimoto K, Numerical definitions of wind power output fluctuations for power system operations, Renewable Energy (2017), doi: 10.1016/ j.renene.2017.08.009. 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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Numerical Definitions of Wind Power Output Fluctuations for Power System Operations

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Takashi Ikegamia,, Chiyori T. Urabeb , Tetsuo Saitoub , Kazuhiko Ogimotob a Division

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of Advanced Mechanical Systems Engineering, Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo, 184-8588, JAPAN b Collaborative Research Center for Energy Engineering, Institute of Industrial Science, the University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, JAPAN

Abstract

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Because of unpredictable fluctuations in wind power output caused by sudden changes in weather conditions, operations that balance supply and demand in power systems will gradually become more difficult with the massive deployment of wind power generation. Therefore, it is necessary to quantitatively evaluate wind power output fluctuations in a way that corresponds to frequency controls in power system operations. In this study, we analyzed data for the fluctuations of actual wind power output at 20 wind farms, as designated by three basic definitions: the changes in time-averaged values, the maximum power-fluctuation range within a time window, and the deviations from a centered moving average value. The results indicated relevant differences between the definitions and demonstrated the importance of percentile analysis. We proposed a novel quantitative definition of the output fluctuations associated with the frequency controls of power systems: primary turbine-governor control, secondary load-frequency control, and tertiary economic load-dispatch control. Using these definitions to quantify fluctuations demonstrates how each smoothing technique can contribute to reducing the reserve capacity necessary for frequency control in the power system operations. Our proposed definitions for dividing the frequency ranges of the fluctuations were confirmed as a convenient and practical method for quantitatively evaluating the fluctuations and determining the reserve capacity required for stable power system operations.

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1. Introduction

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Keywords: wind power, fluctuation, smoothing effect, power system operation, load frequency control, supply-demand analysis

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Wind power (WP) generation is one of the most widely integrated renewable energy technologies in power systems. With increasing WP penetration of the power market, operations that balance supply and demand in power systems will gradually become more difficult because of the unpredictable fluctuations in WP output caused by sudden changes in weather conditions. Output fluctuations cause not only local voltage problems, such as static voltage fluctuations, instantaneous voltage drops, and voltage flickers, but also whole system problems related to balancing operations [1, 2, 3]. These problems have a negative impact on the further development of renewable energy. In order to mitigate this negative influence, it is absolutely imperative to introduce technologies for reducing output fluctuations. Email address: [email protected] (Takashi Ikegami) Preprint submitted to Elsevier (Renewable Energy)

First of all, quantitative evaluation of output fluctuations is necessary for the introduction and implementation of these technologies. Some studies have analyzed impacts of fluctuations on the power system [4, 5, 6, 7]. To evaluate future total WP output fluctuations in a power system, we must quantitatively understand geographical smoothing effects. If no definite correlation exists between any two output fluctuations of geographically dispersed wind turbines or wind farms, the synthesized fluctuation is expected to decrease because positive and negative changes in outputs cancel each other. Therefore, the number of wind turbines or wind farms and their geographical distribution are important factors in smoothing effects. Many analyses of geographical smoothing effects have been conducted, as has been reported in many papers. In some studies, the smoothing effects due to the aggregation of multiple wind turbines in a August 7, 2017

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WP fluctuations and the associated forecasting errors [46, 47, 48, 49]. For example, the required spinning reserve capacity was set at 3% of the load and 5% of the forecasted renewable production [50]. The idea of dividing fluctuation into several components with different frequencies is indicated in previous studies [51, 52]. Our proposed definition is characterized by fluctuation cycles corresponding to the power systems operations. In this paper, we propose a novel quantitative definition of WP output fluctuations associated with the frequency controls of the power systems: primary turbine-governor control (TGC), secondary load-frequency control (LFC), and tertiary economic load-dispatch control (EDC). Using this definition for quantification can demonstrate that each smoothing technique can contribute to reducing the reserve capacity required for stable frequency control in power system operations. Moreover, the definition will make it possible to analyze the timing and the required capacity of equipment and technologies, such as battery-storage systems, by simulating the power system operations using quantified fluctuations for frequency controls. On the power system scale, studies based on data with high temporal resolution had hardly been conducted. In this study, we analyzed WP output fluctuations using actual operational data with 10-second temporal resolution from 20 wind farms in the Tohoku region, a windy area in the northern part of the main island of Japan. To quantitatively evaluate fluctuations, we applied several indices based on the definitions in current use along with indices based on our proposed definitions and analyzed the characteristics of the indices of each definition. In addition, the applicability of our proposed definition to power system operations was evaluated.

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wind farm were analyzed [8, 9, 10]. Furthermore, the output fluctuations themselves or the smoothing effects on output fluctuations in distributed wind farms has become the subject of analysis in many countries [4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. An approach for artificially generating the synthetic timeseries of aggregate WP output was also studied [25, 26]. In photovoltaic (PV) power generation as well as WP generation, there are similar problems of output fluctuations caused by the movement of clouds. Therefore, the quantification of output fluctuations [27] and geographical smoothing effects [28, 29, 30, 31, 32, 33, 34, 35] in multiple PV sites have also been under investigation for many years. The development of various control techniques for mitigating output fluctuations is proceeding. These techniques offer controlled smoothing effects to compensate for WP output fluctuations. Some studies have analyzed the effects of control techniques using the equipment in a WP system, such as the pitch control of wind-turbine blades [36, 37, 38], or the control of windenergy converters [39]. Novel control techniques for a battery-based energy-storage system have also been studied for output stabilization and fluctuation smoothing [40, 41]. Charging and discharging control can respond quickly to changes in WP output. Therefore, despite the economic disadvantages, the battery-storage system is one of the most powerful solutions. Control techniques corresponding to the primary frequency using variable speed wind turbines have also been developed [42, 43, 44]. For PV power generation systems, research on control methods for mitigating output fluctuations using battery-storage systems has also been conducted [45]. In these research efforts and studies, various numerical indices were used to evaluate output fluctuations or their geographical and controlled smoothing effects. The quantitative indices in previous studies are discussed in Section 3.1. Because of the different indices, it is not easy to compare the magnitude of fluctuations or the smoothing effects. Furthermore, we have no way of judging which technique is the most effective. Therefore, a unified quantitative definition of the fluctuation magnitudes is needed for a fair evaluation. The existence of a proper evaluation index makes it possible to simulate power system operations while evaluating the impact of stochastic WP output fluctuations. The unit-commitment models used in recent years for simulating the operations of conventional power plants have become the models that can account for the spinning reserve of thermal power plants while considering not only load fluctuations but also PV and

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2. Frequency Control in Power Systems 2.1. Target Domains of Frequency Control In order to mitigate the frequency fluctuations within a certain range, the thermal power output of a system is controlled so as to constantly follow the fluctuations in the demand, and the balance between supply and demand is thus maintained. Because PV and WP outputs fluctuate in addition to fluctuations in demand, there is concern about difficulties in controlling the balance over various time ranges made up of seconds, minutes, hours, days, or years. In power systems, the power fluctuations separate into three components corresponding to three ranges of cycle length, or in other words, three frequency ranges. 2

to frequency deviations quickly, but it can only be adjusted over limited range. Grid Inertia, Self-regulating of Load

2.3. Load-Frequency Control Load frequency control (LFC) provides automatic control for maintaining a constant system frequency from the load-dispatch center of a power system. The load-dispatch center sends an order for power output to each power plant, and the operators at the power plants receiving the order control the fuel valves, feedwater valves, and turbine governors to adjust the flow rate of fuel and feedwater to the boiler and the flow rate of steam to the turbine. The LFC is also a type of feedback control, and has a wider adjustable range than the TGC because it is based on controlling the amount of fuel and feedwater. However, the response speed is restricted based on the rate at which power output can be changed. Unpredictable short-cycle and medium-cycle output fluctuations of PV and WP must be compensated for by TGC and LFC.

EDC (Tertiary)

LFC (Secondary) TGC (Primary) 0.5 sec

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Load Fluctuation Width

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Load / Frequency Fluctuation Cycle [min]

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Output Change by EDC

TGC Range

LFC Range

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Figure 1: Assigned target domains for each type of frequency control [53].

2.4. Economic Load-Dispatch Control

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Figure 2: Thermal power output controls [54].

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The TGC domain consists of short-cycle fluctuations with a cycle lasting a few minutes or less; the LFC domain consists of medium-cycle fluctuations with a cycle lasting from a few miniutes to 20 minutes, and the EDC domain consists of long-cycle fluctuations with a cycle lasting about 20 minutes or more. As in Figure 1, different controls are assigned to each component of the fluctuations based on the response speed and range of generator power output [53]. For periodic fluctuations with a cycle of a few seconds, the frequency is controlled by the grid inertia, which is stored as rotational kinetic energy in the turbines of thermal power plants, and the self-regulating characteristics of the load. Figure 2 shows the output adjustment of thermal power generators using each of the three control components within their appropriate ranges [54, 55].

Economic load-dispatch control (EDC) is scheduled feedforward control from a load-dispatch center. For large load fluctuations throughout the course of a day, load-dispatch for power plants is controlled to minimize costs based on forecasts of electricity demand, PV output, and WP output. Because it is controlled in advance, including start and stop control of the generation units, EDC has a large adjustment range and provides control of longcycle output fluctuations. In the future, because the differences in net load between day and night will increase along with the massive deployment of PV generation, it is assumed that the fluctuations in the EDC domain will also increase.

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3. Definitions of Power Output Fluctuations 3.1. Quantitative Indices in Previous Studies Many kinds of definitions or quantitative indices of the output fluctuations have been used in previous studies to evaluate geographical or controlled smoothing effects. The spectral analysis of time-series data using the Fourier transform, which is the most powerful technique in analyzing the output fluctuation characteristics for each frequency, was used in many studies [9, 11, 14, 16, 18, 19, 20, 21, 26, 28, 31, 34, 35, 40]. Although spectral analysis is excellent for capturing the fluctuation amplitude at a specific frequency, it is not

2.2. Turbine-Governor Control

The turbine-governor is the device that controls the flow rate of steam from boiler to turbine. In a thermal power plant, turbine-governor control (TGC) controls the rotation speed of the turbine and automatically stabilizes the system frequency by measuring its deviation. Because of automatic feedback control, it can respond 3

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suitable for estimating the reserve capacity needed to cope with problematic fluctuations in power system operations. Using a filter to extract short-cycle components by means of a fast Fourier transform [30, 31] is quite useful for analyzing the smoothing effects; however, due to its computational cost, this method is inappropriate for capturing increasing and decreasing trends in real time and for maintaining control. For such reasons, analyses that do not use the Fourier transform have also been performed. As the simplest indicator, the standard deviation of the power output itself was evaluated [10, 13, 15, 36]. In some studies, the output changes at fixed time intervals and the difference between two adjacent average values were used [5, 12, 13, 18, 23, 25, 32]. This definition is described in Section 3.2. The index of fluctuation (IOF) obtained by integrating the absolute values of these differences, as in Eq. (1), was used to evaluate the smoothing effects [37, 38]. X IOF = |Pt+1 − Pt |. (1)

5-min average

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Flu tuation e

Figure 3: Example of Definition 1 of output fluctuations.

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In this study, we used three definitions from previous studies: the change of time-averaged values, the maximum fluctuation width in the time window, and the deviation from the centered moving average (CMA).

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3.2. Definition 1: Change of Time-Averaged Values First, we defined the amount of change in timeaveraged values as the range of fluctuations. For instance, when the sampling period is 30 seconds or when the average values during 30 seconds are used, the fluctuation range is calculated by Eq. (5), where it is defined as the difference between the value at time step t and the value at the previous time step (t − 1) as shown in Figure 3.

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In this equation, Pt is the power output at time step t, and t represents the time step within the target period. The maximum fluctuation width within the time window, detailed in Section 3.3, have been used as the evaluation index in many studies [9, 40, 41], especially in studies of PV output fluctuations [29, 30, 31, 33, 45]. The average value of the deviation from the mean power output (AVD) calculated by Eq. (2) was used [39]. 1 X Pt − Pavg AV D = . (2) N t Pavg

In this equation, N denotes the number of the time step t, and Pt and Pavg are the power output at time t and average power output in an entire period, respectively. A moving average filter was used to eliminate shortcycle fluctuations, and the difference between two values at fixed intervals was used as the index for the variations [16]. The reverse fluctuation count (RFC) was defined as the number of time steps when the power output trend was reversed. The average fluctuation magnitude (AF M) was defined by Eq. (3). The moving fluctuation intensity (MFI) was defined as the product of AF M and RFC in Eq. (4) [27]. =

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AF MN × RFC N .

(3) (4)

(5)

Here, rt(1) is the fluctuation range in per-unit (p.u.) value based on Definition 1 at time step t, and p¯ t is the timeaveraged power output in p.u. at time step t. When average values during 1 minute are used, the fluctuations occurring within a time shorter than 1 minute are eliminated. In the same way, when hourly values are used, the fluctuations within 1 hour are not considered. 3.3. Definition 2: Maximum Fluctuation Width in the Time Window Second, the fluctuation range at time step t was defined as the difference between the largest and smallest power values in a certain period chosen as the time window. Figure 4 shows an example with a time window of 20 minutes’ width. The fluctuation range at time step t is calculated by Eq. (6).

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rt(1) = p¯ t − p¯ t−1 .


at − bt rt(2) = pat − pbt · . |at − bt |

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Here, rt(2) is the fluctuation range in p.u. based on Definition 2 at time step t with w steps of time window 4

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Figure 5: Example of Definition 3 of output fluctuations.

width. The symbol pt denotes the power output in p.u. at time step t, and at , bt are the time steps where the power output takes on its largest and smallest values, respectively. If at ≥ bt holds, then the fluctuation range rt(2) is a positive value, and if bt > at holds, then the fluctuation rt(2) is a negative value. When the fluctuation range is determined in a time window of 20 minutes’ width, the fluctuations occurring over a duration longer than 20 minutes are not included.

length of their controls. Using the Definition 3 with 1and 30-minute CMA filters, we divided the WP output data into three components: the EDC domain fluctuations (rt(EDC) ), the LFC domain fluctuations (rt(LFC) ), and the TGC domain fluctuations (rt(TGC) ). The long-cycle fluctuations followed by the EDC are represented as 30minute CMAs as shown in Eq. (8). The fluctuations followed by the LFC are represented as the difference between the 1-minute CMAs and the 30-minute CMAs as shown in Eq. (9). Finally, the fluctuations compensated for by the TGC are represented as deviation from 1-minute CMAs as shown in Eq. (10).

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Figure 4: Example of Definition 2 of output fluctuations.

3.4. Definition 3: Deviation from the Centered Moving Average

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Third, the range of fluctuations was defined by the deviation from the CMA calculated in Eq. (7) as the basic definition.

t+s 1 X . (7) pk = pt − CMA(period) t 2s + 1 k=t−s

= =

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, − CMA(30min) t (1min) pt − CMAt .

(8) (9) (10)

In these equations, rt(EDC) denotes the EDC domain fluctuations, rt(LFC) denotes the LFC domain fluctuations, and rt(TGC) denotes the TGC domain fluctuations. By dividing the power output fluctuations into components in this way, all fluctuations are allocated to one of the indices as shown in Eq. (11).

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rt(3) = pt −

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= CMA(30min) , t

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Here, rt(3) is the fluctuation range in p.u. based on Definition 3 at time step t, the expression 2s + 1 denotes the number of time steps within the moving average period, and CMA(period) represents the centered moving average t at time step t within the (period). Figure 5 shows an example of the definition using a 20-minute CMA. When the 20-minute CMAs are subtracted from the output, the fluctuations occurring over a time longer than 20 minutes are eliminated. However, the information about long-cycle fluctuations of a period longer than 20 minutes remains in the 20-minute CMA information that was subtracted.

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rt(EDC) + rt(LFC) + rt(TGC) .

(11)

This dividing method using CMAs has advantageous not only in the simplicity of calculation but also in the utilization of data in real time operation. Since calculation of CMA requires past and future values, it is not possible to grasp the present CMA value in real time only with actual measurement data. If 30-minute ahead forecast data are available, we can simply incorporate the forecast to real time system operation. Figure 6 shows examples of application in real time operation utilizing forecast values every 5 minutes. As of 12:00 noon, 30-minute CMAs calculated by using the actual measurement data can only be obtained up to 11:45 am. If the forecast values are available, we can obtain the

3.5. Proposed Definitions of Domain Fluctuations in Power System Operations To form a connection to the frequency controls in power system operations, we attempted to divide the output into three components according to the cycle 5

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output in per unit values are calculated by dividing the total power output from all the farms by the total capacity of the WP generators on all the farms.

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4.2. Analyses of Fluctuations Based on the Three Definitions

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Using these actual WP output data, we evaluated the fluctuations using the indices obtained from the three definitions described in Sections 3.2, 3.3, and 3.4. Based on Definition 1, 2, and 3, we calculated probability density distribution of their fluctuations, analyzed distribution shape and cumulative probability density function, and estimated the maximum increment and decrement values and the 0.1 and 99.9 percentile values. Time index, which is the dominant parameter, is completely different among the three definitions: the periods of average in Definition 1, the time window width in Definition 2, and the periods of CMA filter in Definition 3. In Definition 1, short-cycle fluctuations disappear by using a long period of average, whereas long-cycle ones disappear by using a short period of average. The fluctuations that can be captured in Definition 2 change depending on the time window width. In Definition 3, because the long-cycle fluctuations are eliminated by CMA filter, the short-cycle fluctuations depend on the length of the moving average period. In order to analyze the dependence of the fluctuations on the time index, the fluctuations were evaluated using multiple time indices in each definition, as we discuss in Sections 5.1, 5.2, and 5.3.

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Figure 6: Examples of application in real time operation utilizing forecast values.

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current value at 12:00 noon. In the case of the forecast 1 (black point), CMAs become gray dotted line; the current EDC domain fluctuation has an increasing (EDC) trend; r12:00 = 0.369; the sum of the fluctuation components of the LFC and TGC domains has a negative (LFC) (TGC) value; r12:00 + r12:00 < 0. On the other hand, in the case of the forecast 2 (square outline), CMAs become gray dot-dash line; the current EDC domain fluctuation has (EDC) a decreasing trend; r12:00 = 0.333; the sum of the fluctuation components of the LFC and TGC domains has (LFC) (TGC) a positive value; r12:00 + r12:00 > 0. While the forecast accuracy is important because the current trends are different depending on the forecast values, even if the temporal resolutions of actual data and forecast data are different, it is possible to easily calculate CMAs. In this study, the method using CMA filters was adopted because it is easy to grasp the current fluctuation trend using forecast data.

4.3. Analysis of proposed TGC, LFC, EDC Domain Fluctuations

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We analyzed the fluctuations in the TGC, the LFC, and the EDC domains with the distributions and the amplitude spectra, as we discuss in Section 5.4. This was done to confirm that the proposed division of the data into groups using the definitions is a suitable and convenient methods for quantitatively evaluating the fluctuations and for determining the required reserve capacity for power system operations.

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4. Analysis Procedure and Data Used

4.1. Actual High Temporal Resolution Wind Power Output Data In this study, we used the total WP output in the Tohoku region in the northern part of the main island of Japan. The output was measured by the Supervisory Control And Data Acquisition (SCADA) system for one year from 0:00 on April 1, 2012 to 0:00 on March 31, 2013. The temporal resolution of the original data was 10 seconds. We were able to collect data for 20 wind farms with a total of 303 wind turbines and a total wind generation capacity of 442 MW. We used a per unit system (p.u.) for the power output and fluctuations. The

5. Calculation Results 5.1. Analysis of Changes in Time-Averaged Values (Def. 1) First, using the time-series data at a temporal resolution of 10 s, we calculated the time-series average data for several intervals. We then calculated the changes in these values. Based on Definition 1 in Section 3.2, we 6

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Figure 7: Calculation results of changes in time-averaged values (Def. 1): (A) probability density distributions, (B) cumulative probability distribution functions, (C) enlarged view of cumulative probability distribution functions and the Gaussian distribution, and (D) maximum increments/decrements and 99.9 and 0.1 percentiles of fluctuations with each average. The periods of average are 1 min, 5 min, and 20 min in (A) and (B), 20 min in (C), and from 10 s to 6 h in (D).

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obtained the probability density distribution of the output fluctuations. The results of the cases for intervals of 1 min, 5 min, and 20 min are shown in Figure 7(A). In this figure, we also show the probability density of the Gaussian distribution with the same mean and the same standard deviation of the fluctuations as determined for the 20 min interval. The vertical axis is a logarithmic scale, and the integral of this probability density function over all ranges of p.u. values becomes one. In all cases, we find that the probability that fluctuation values are around zero is extremely high. The larger the interval is, the wider the distribution of the fluctuation range is. It can be also seen from this figure that the tails of the distribution functions of three cases are substantially linear. This means that the probability decreases exponentially with increasing fluctuation range. The cumulative probability distribution functions of these three cases are shown in Figure 7(B). The cumulative probability distribution functions of the 20 min interval case and the Gaussian distribution with same mean and same standard deviation in this case are shown in an enlarged view in Figure 7(C). It is obvious from the definition of fluctuations that the average values of fluctuations were almost exactly zero in all cases. In addition, the fluctuations were also zero when the cumulative probabilities were 0.5. This means that the increases and decreases in average power output occurred

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at approximately the same frequency. In a comparison between the line for the 20 min interval and the curve of the Gaussian distribution, the tails of the distribution of the output fluctuation for the 20 min interval are heavier than those of the Gaussian distribution as shown in Figures 7(A) and 7(C). In quantifying the fluctuations for the electric power system, rare events with large fluctuations are also important. In many previous studies, the average ±3σ was used as the range from which nearly all values were taken. This is known as the 3σ rule of thumb because 99.73% of the values lie within three standard deviations (σ) of the mean in the Gaussian distribution. However, as Figure 7(C) shows, it was found that the values of the cumulative probabilities in the 3σ band between the actual WP output fluctuation and the Gaussian distribution differed greatly. In actual wind data, the probability that the fluctuation range is 3σ (= 0.0648) or more was about 1%. Therefore, when using this definition, it is important to recognize that a range that assumes ±3σ is not sufficient when using actual WP output fluctuation data. In this study, we used as the indices not only the maximum increment/decrement values, but also the 0.1 and 99.9 percentile values for expressing a near-certainty. Figure 7(D) shows these values for various time intervals. In this figure, the maximum increment values and

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analysis of PV output, the frequency of the decreasing trend was higher than the one of the increasing trend. This means that, in general, the power output of a PV system increases rapidly and decreases slowly. It was found that the rates of the increases and decreases in the WP output were almost the same. We evaluated the maximum increment and decrement values and the 0.1 and 99.9 percentile values, as shown in Figure 8(D). In this analysis, these four indices steadily decreased as the time window width became narrower. The maximum decrement values did not decrease because of the rare decreasing event described in Section 5.4.

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the 99.9 and 0.1 percentile values gradually decreased as the interval was shortened. However, the maximum decrement values did not always decrease. A single event that is a rare and rapid decrease of the output induced these decrement values. Therefore, we confirmed that the 0.1 and 99.9 percentile values are more statistically representative as the near-certainty values for the fluctuation range. Details of this event are described in Section 5.4.

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5.2. Analysis of Maximum Fluctuation Widths (Def. 2) Second, we calculated the maximum fluctuation width in the time window using several time window widths based on Definition 2 in Section 3.3. The results of the probability density distribution of these fluctuations for time window widths of 1 min, 5 min, and 20 min are shown in Figure 8(A). In this figure, the probability density of the Gaussian distribution was calculated for the same mean and the same standard deviation of the maximum fluctuation widths in the 20 min time window. The greater the time window width is, the wider the distribution of fluctuation width is. It was found that, unlike the case of Definition 1, the shapes of the probability distribution of fluctuation widths become more similar to that of the Gaussian distribution with increasing window width. Only when there is no change in output in the time window, the maximum fluctuation widths become zero. Therefore, near zero, the curves of the probability distributions form deep valleys. In the cases where the time window width was set to 2 hours or more, the probability of the maximum fluctuation width becoming zero was zero. Figure 8(B) shows the cumulative probability distribution functions of these three cases. Figure 8(C) shows an enlarged view of Figure 8(B) including the Gaussian distribution with same mean and same standard deviation as the case with a window width of 20 min. Near the zero fluctuation value, especially in the case of the 20 min time window width, the slope temporarily decreased for the same reason as above. In the analysis results that used this definition, the probability that the maximum fluctuation width becomes 3σ (= 0.1319) or more in the actual data was 99.76% and that probability in the Gaussian distribution was 99.87%, which is almost the same. As is the case for Definition 1, it was found that the frequencies of occurrence of the increasing and the decreasing trends were approximately equal. Kato [33] showed the graph of the cumulative distribution functions of the maximum fluctuation width in the time window with respect to the fluctuation of PV output. In the

5.3. Analysis of Fluctuations Divided by CMA Filters (Def. 3)

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Third, we calculated the fluctuation range using Eq. (7) with several moving average periods. The results of the probability density distribution of these fluctuations with moving average periods of 1 min, 5 min, and 20 min are shown in Figure 9(A). The shapes of these graphs are very similar to the shapes in the Figure 7(A), which shows the results of Definition 1. The tails of the distribution of the actual data were heavier in comparison with those of the Gaussian distribution as shown in Figure 9(B) and 9(C). In addition, it was also found that the value of cumulative probabilities in 3σ between the actual data and the Gaussian distribution were greatly different. In the actual wind data, the 3σ value was 0.0237, and the cumulative probability was 99.21%, which is smaller by 0.66% than the 3σ value of the Gaussian distribution. We evaluated the maximum increment and decrement values and the 0.1 and 99.9 percentile values, as shown in Figure 9(D). In this analysis, the values of the 0.1 and 99.9 percentiles also steadily decreased as the moving average period became shorter. The differences between the maximum increments and the 99.9 percentile values, and the differences between the maximum decrements and the 0.1 percentile values were quite large in all cases. The maximum increment and decrement values were greatly influenced by the rare event described in Section 5.4. Figure 10 shows the comparison of the fluctuation based on Definitions 1 to 3. The common horizontal axis in Figure 10 indicates the periods of average data in Definition 1, time window widths in Definition 2, and periods of CMA filter in Definition 3 as a time index. On the vertical axis, fluctuation ranges between 0.1 and 99.9 percentiles are shown. There are approximately power law relationships between the time index and the

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5.4. Proposed TGC, LFC, EDC Domain Fluctuations We obtained the fluctuations in the TGC, LFC, and EDC domains based on the proposed definitions and method. An example of the result of dividing the WP output into three components is shown in Figure 11. This figure shows the power output, including the fluctuations in the EDC, LFC, and TGC domains, between 11:10 am and 12:30 pm on November 27, 2012. By dividing the data in this way, the entire range of fluctuations was necessarily included in one of the EDC, LFC, or TGC domains. Figure 12 shows the results of the spectral analyses of the fluctuations of the three domains in the double logarithmic chart. These curves in this figure denote the

amplitude spectra, which were averaged over the interval obtained by dividing each section on the horizontal axis between 10k and 10k+1 (k is an integer from −8 to −2) into nine parts. In the time region longer than 48 minutes, the fluctuations of the EDC domain were most prominent. And in the time region shorter than 105 seconds, the fluctuations of the TGC domain were dominant. The fluctuations with periods between these two values were included in the LFC domain. It can be confirmed that these fluctuations correspond relatively well to the respective frequency control regions of power sys9

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Figure 9: Calculation results of deviations from CMA filters (Def. 3): (A) probability density distributions, (B) cumulative probability distribution functions, (C) enlarged view of cumulative probability distribution functions and the Gaussian distribution, and (D) maximum increments/decrements and 99.9 and 0.1 percentiles of fluctuations with each CMA filter. The periods of CMA filter are 1 min, 5 min, and 20 min in (A) and (B), 20 min in (C), and from 20 s to 6 h in (D).

Figure 11: Time-series outputs and the TGC, LFC, and EDC domain fluctuations between 11:10 am and 12:30 pm on November 27, 2012.

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Figure 12: Amplitude spectrum of the fluctuations in each domain.

capacity that must be secured. It was found that the reserve capacity required for the TGC to compensate for WP output fluctuations should be set to ±1.2% of the total capacity of the WP generation when a twosided 98% confidence interval is assumed. Furthermore, it was found that the reserve capacity for the LFC to compensate for WP output fluctuations should be set to about ±4.4% of the total capacity of the WP generation. We must be careful that the reserve capacity is originally allocated for net load fluctuations. The reserve capacity for the net load fluctuations must be estimated using re-

tem operations. In Figures 13 and 14 are shown the monthly and yearly maximum increments/decrements and the 99.9 and 0.1 percentiles of the TGC and LFC domain fluctuations, respectively. The figures indicate that there are differences corresponding to the seasons; the fluctuation is small in the summer and large in the winter. Yearly values of the indices of these two domains are shown in Table 1. These indices can be used to determine the reserve 10

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Table 1: Yearly values of maximum increments/decrements and 99.9 and 0.1 percentiles of the TGC and LFC domain fluctuations.

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Figure 15: Time-series outputs and the TGC, LFC, and EDC domain fluctuations between 2:10 am and 3:30 am on November 27, 2012.

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serve capacities for the fluctuations of WP output, PV output, and load and taking their offset effects into account. The fluctuation of WP output is imperative for the estimation. In November, the maximum increment and maximum decrement values were larger than the other monthly values. A rare and serious event, during which the fluctuation reached a maximum, occurred around 2:34 am on November 27, 2012. Figure 15 shows the power output and the fluctuations of the EDC, LFC, and TGC domains between 2:10 am and 3:30 am on this day. Around 2:34 am, WP output dropped sharply from 0.40 p.u. to 0.11 p.u. within 10 seconds. This event was caused by sharp decrease of WP generation of 10 wind farms because of cutout events. When the wind speed exceeded the cutout speed of the wind generators, which is usually set to 25 m/s, WP generations decreased to zero within 10 seconds. These 10 wind farms are concentrated in a narrow area, approximately 15 km east to west and 50 km north to south, with a total wind generation capacity of 230 MW. It is uneconomical to secure capacity for such a rare event. A different response

should be made in cases; for example, WP output could be gradually decreased when the wind speed approaches the cutout speed. 6. Conclusions

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A quantitative definition of power output fluctuations is required for power system operations and simulation studies thereof. In this study, we analyzed fluctuations in WP output based on three basic definitions: changes in the time-averaged values, referred to as Definition1; the maximum fluctuation widths within a specific time window, referred to as Definition 2; and the deviations from the centered moving average value, referred to as Definition 3. The results are described in the following text. (1) The distributions of the fluctuations using Definition 2 were similar to the Gaussian distribution; however, the fluctuations using Definitions 1 and 3 differed significantly from the Gaussian distribution. (2) The 3σ values of the distributions of Definitions 1 and 3 were approximately 99.04% and 99.21%, respectively, which were much smaller than the 99.87% value of the Gaussian distribution. (3) The occurrence frequencies of the increasing and decreasing trends were substantially equal, and the fluctuation widths of the increases and the decreases that defined the 99.9 and 0.1 11

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References

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Integration of Variable Renewable Energy: Mitigation Technologies on Output Fluctuations of Renewable Energy Generations in Power Grid, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

percentile values, respectively, were also approximately equal. These results indicate that it is important to recognize that the evaluations and the operations using 3σ fluctuation values involve a higher risk of a reserve capacity shortage. Therefore, we propose using the 0.1 and 99.9 percentile values as the indices, because they indicate near-certainty. Moreover, we propose a novel quantitative definition of the output fluctuations associated with the frequency controls of power systems; they involve the TGC-, LFC, and EDC-frequency domains. We analyzed the distributions and the amplitude spectra of the fluctuations in the TGC, LFC, and EDC domains. The results are the following. (4) The fluctuations in the TGC domain were most prominent in the time region shorter than 105 seconds, the fluctuations in the LFC domain were most prominent in the time region between 105 seconds and 48 minutes, and the fluctuations in the EDC domain were most prominent in the time region longer than 48 minutes. (5) The fluctuations in the TGC and LFC domains were small in the summer and larger in the winter. (6) The fluctuations between the 99.9 and 0.1 percentile values in the TGC and LFC domains were ±1.2% and ±4.4% of the total capacity of the WP generation, respectively. These results indicate that the fluctuations between the 99.9 and 0.1 percentile values in each domain can be used to determine the reserve capacity for control in each domain. Our proposed definitions for dividing the frequency ranges were confirmed as a convenient and practical method for quantitatively evaluating the fluctuations to determine the reserve capacity required for stable power system operations. When comparing the fluctuations in different regions, it is important to use a unified definition to estimate the fluctuations. For future work, using the definition corresponding to the power systems operations proposed in this paper, the difference in the fluctuation rate by region and the geographical smoothing effects of the fluctuations in each control domain will be quantitatively evaluated. Furthermore, estimations will be performed of the fluctuations that occur following the predicted, massive introduction of WP generation.

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Acknowledgements Wind data used in this work was collected through collaborative research by the University of Tokyo and Japan Wind Power Association, and provided by the Ogimoto Laboratory in the University of Tokyo. This work was partially supported by R&D Project on Grid 12

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ACCEPTED MANUSCRIPT Highlights


Comparing several definitions for fluctuations, the wind power output fluctuation was discussed. One year’s worth of high temporal resolution data in 10-sec intervals was analyzed.




A novel definition of the fluctuations corresponding to power system operations was proposed.




The fluctuations divided into TGC, LFC, and EDC domains was analyzed.

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