Total output power variation of several small wind turbines

Abstract

There is a concern that connection of several small wind turbines may cause severe voltage fluctuation and voltage flicker in low-voltage distribution lines due to their output power variations. In this study, output power variations of four 5-kW-class small wind turbine systems were measured with an interval of 0.1 s at a site in Wakkanai, Hokkaido, and their correlations and smoothing effect in the frequency range from $~ 10^{- 4}$ to 5 Hz were analyzed and compared with those of five residential photovoltaic power systems. The results indicate that a smoothing effect occurs more in small wind turbines than in photovoltaic systems, because of lower correlation coefficients in lower frequency ( $\underset{~}{>} 3 \times 10^{- 3}$ Hz) components. Voltage flicker at the point of common coupling was also measured and it was confirmed that the impact of small wind turbines on voltage flicker is low enough at the site. In addition, the upper limits of the installation number and/or the system resistance are estimated theoretically using the measured flicker values.

Keywords

Small wind turbine output power variation smoothing effect correlation coefficient voltage flicker

Introduction

Recently, installation of dispersed power generated by solar photovoltaics (PVs), wind turbines (WTs), and other energy resources have been increasing all over the world. However, they have some negative impacts on power systems that must be addressed, such as frequency deviation and voltage fluctuation (Zhang et al., 2019). In WT systems, these negative impacts are caused especially by aerodynamic factors such as turbulence and wind shifts. Studies of methods to address these problems, such as controls of WTs and energy storage systems, have been conducted (Abbasi et al., 2019; Shangfeng et al., 2017; Xing et al., 2019; Yang and Yang, 2019). On one hand, these methods compensate only low-frequency components of output power fluctuation with a response delay of several seconds at least. On the other hand, a problem called voltage flicker is caused by higher frequency components (mainly $\underset{~}{>} 1$ Hz) of the fluctuation.

Voltage flicker is the phenomenon of flickering of light fixtures that is caused by system voltage fluctuation. Because it annoys the human eyes, it needs to be suppressed (Kumar Sharma et al., 2017). Its main causes are abrupt changes in the power consumption of large-capacity loads (electrical arc furnaces, etc.) in the system (Alasooly and Redha, 2010; Blavette et al., 2016) and inrush current at the startup of induction machines (Chen et al., 2016; Leinonen and Laketic, 2018; Rahman et al., 2018), but it is recognized that severe output variation of wind power may also be another cause of voltage flicker (Ammar and Ammar, 2016). Thus, studies to analyze the voltage flicker caused by large-scale WTs have been conducted under numerical simulations (Alaboudly et al., 2013; Ammar and Ammar, 2016; Fooladi and Akbari Foroud, 2016; Hu et al., 2009; Mascarella et al., 2015).

Consideration of the smoothing effect is important in evaluating the impact of multiple variable-power generation units in power systems. The total output power fluctuation could be relieved by integrating variable-power generation units, thanks to the smoothing effect (Holttinen and Hirvonen, 2012; Lakmal Wevita et al., 2014). In addition, it is expected that the negative impact of power fluctuation could be mitigated by frequency and/or demand control (Kim et al., 2017). The results of previous studies on the smoothing effect indicate that these schemes can smooth the output power fluctuation by adjusting the control gain with respect to the rotor speed and thereby improve the speed-regulating capability of a variable-speed WT. This can also mitigate the output power fluctuation associated with a high level of wind penetration into the grid (Kim et al., 2017).

These factors have been analyzed with respect to large-scale WTs. Small wind turbines (SWTs), whose rated power is less than approximately 50 kW (Zammit et al., 2018), also have potential as renewable energy systems. SWTs can generate the energy required by rural homes, farms (Ahshan et al., 2018; Verde et al., 2018), schools/campuses, and medium-sizes businesses in regions where the average wind speed is high and the grid infrastructure is limited (Artal-Sevil et al., 2018). According to global investigations (Alsop et al., 2017), these regions need energy production by systems such as SWTs. Experiments conducted in some countries, such as Oman (Ahshan et al., 2018), Ethiopia, and Nepal (Latoufis et al., 2018), have demonstrated the practicality of SWTs. Because of their small size, SWTs can be put on the roofs of buildings (Lee et al., 2018; Proulx et al., 2016), and SWT systems can be designed and implemented easily. They can generate power at low wind speeds (e.g. 4 m/s) (Ani et al., 2013; Hsieh and Yeh, 2013; Majeed et al., 2019; Rasmussen and Johansen, 2017), and can operate in wind turbulence with pitch and yaw controls (Chalise et al., 2016; De Zutter et al., 2017; Engleitner et al., 2018). SWT systems combined with storage systems, such as batteries and supercapacitors (Atur et al., 2018), have been proposed. These systems can smooth the output variation of SWTs quickly and can address long-term imbalances.

However, there have been few studies on the impact of SWTs on power systems, because they have not been as widely used as PV power systems and large-scale WTs. In addition, utilities have recognized the general characteristic that the output fluctuation of a single SWT is more intense than that of a single residential PV and voltage fluctuation is severe due to low X/R ratio in low-voltage distribution lines. Thus, they have great concern for installing more SWTs to their grids. Conversely, it has been observed that multiple smaller WTs produce less bus voltage drop and less frequency deviation than a single larger WT with the same total rated power (Thiringer et al., 2014). The reason for this is that the total output fluctuation of N units of WTs is smaller than N times the output fluctuation of an individual WT, because of the smoothing effect. However, no study has yet been conducted to analyze the roles of output fluctuations and the smoothing effect of SWTs in voltage flicker quantitatively as far as the authors know. This study was conducted to analyze the smoothing effect and voltage flicker at the point of common coupling (PCC) of several SWTs.

For this purpose, the outputs of SWTs measured in Wakkanai, Hokkaido, were analyzed, and those of PVs measured in Ota, Gunma, were analyzed for comparison. Section “Facility overview” presents an overview of each system. The results of an analysis of correlations between the SWTs’ output power and voltage flicker are presented in section “Result.” Conclusions drawn from the results of the study are presented in section “Conclusion.”

Facility overview

In this study, the output power fluctuations of four 5-kW-class small WTs and five 4-kW-class residential PV power generators were analyzed using their data sets with high sampling rates as shown in Table 1. Their locations are about 1200 km away from each other, and their measuring periods do not overlap at all. However, it does not matter since the subject of this study is not the analysis of smoothing effect of the total output power from a hybrid system with SWTs and PVs. The aim of this article is to analyze the output power variation of multiple SWTs and their impact on an electric power quality. This section presents an overview of these systems. Their capacity factors are described in Appendix 1.

Table 1.

Data description.

Data set	Rated power of a unit (kW)	Number of units	Measurement duration	Sampling rate	Location
SWTs	4.9	4	A. 4 months B. A few days	A. 10 Hz B. 50 Hz	Wakkanai, Hokkaido
PVs	4	5	1 year	1 Hz	Ota, Gunma

SWTs: small wind turbines; PV: photovoltaic power.

5-kW-class small WT generation

Operational data for four horizontal-axis propeller-type small WTs (Zephyr 9000, Zephyr Corporation, Tokyo, Japan) installed on a flat hill facing the Soya Bay in Wakkanai, Hokkaido, Japan were collected from 15 December 2017 to 24 April 2018. Although the measurement period does not cover a full year, it is enough to analyze the impact on the distribution line voltage since the period includes the season (winter) with the highest energy yield. Figure 1 shows the layout of the site. Table 2 shows the distances of each WT unit. The distance from Unit 1 to Soya Bay is approximately 400 m in the north, and the hill covered by Sasa bamboos has an elevation of 46–47 m.

Figure 1.

Layout of small wind turbines.

Table 2.

Distances between two SWTs.

Units	Distance (m)
1 and 2	103
1 and 3	124
1 and 4	168
2 and 3	27
2 and 4	70
3 and 4	43

SWTs: small wind turbines.

Figure 2 shows the appearance of one of the turbines. The wind power generation units considered in this study have a rated power of 4.9 kW per unit, a rotor diameter of 5.5 m, and a hub height of 12.1 m. It should be noted that the rated power of SWTs is defined as the maximum continuous electrical output power to the PCC under normal operation, so the instantaneous power can be sometimes higher than the rated power (IEC 61400-2:2013, 2013).

Figure 2.

The appearance of an SWT monitored.

The alternating current (AC) from each WT generator, which varies in magnitude and frequency according to the rotor speed, is converted to direct current (DC) by a rectifier and then input to a power conversion system (PCS) in a hut via more than 100 m of cable. The PCS, which is connected to the grid, converts the DC to 200 V AC with a commercial frequency of 50 Hz (Artal-Sevil et al., 2018; Atur et al., 2018). At this site, the AC output power of the four units flows into the same PCC. The active and reactive power and AC current of each WT and the AC voltage at the PCC were measured with four clamp-on power meters (3169-01, Hioki Electric). In addition, the voltage flicker index at the PCC was measured using a flicker meter (IFK-40, Kyuden Technosystems Co., Ltd). The measuring instruments were set in the hut with PCSs. The analog outputs of the measured values from the measurement instruments were recorded on a 32-GB SD memory card at every 0.1 s in a paperless recorder (GP10, Yokogawa Electric, Tokyo, Japan), and the created data files were transferred remotely through wireless communication. The measured values were saved at every cycle (i.e. every 20 ms in the 50 Hz system) on a 1-GB CF memory card in the power meter 3169-01, although the period for this high sampling rate measurement was limited to a few days due to the capacity limit and the necessity of the manual exchange of the card.

The wind speed and direction near the hut were measured using an ultrasonic anemometer (WindObserver 65, Gill Instruments, Hampshire, UK) installed 8 m above the ground at the top of a pole erected at a point approximately 126 m from SWT Unit 4. In principle, an ultrasonic anemometer has no response delay caused by the moment of inertia of any rotating parts, as a cup-type anemometer has. The analog outputs of the measurement values from the anemometer were updated at every 0.1 s, and they were also recorded with the GP10.

Unit 2 had a fault and generated no energy from 15 December to 11 January. The data collected for the other three units during this period have been analyzed previously (Kashiwaya and Kondoh, 2018). The data collected after 12 January were used for the analyses of output power variation described in this article.

Figure 3(a) and (b) presents the wind speed and output power profiles of an individual SWT system and all four 5-kW-class SWT systems on a high wind speed day (1 March) and on a medium wind speed day (29 January), respectively. According to the measurements obtained with the ultrasonic anemometer, the average wind speeds during the periods reflected in Figure 3(a) and (b) were 12.9 m/s and 4.8 m/s, respectively. During the period of high wind speed, the output power was often close to the rated output power, as shown in Figure 3(a). During the period of medium wind speed, the total output power from the four units fluctuated from 0 to 20 kW. This is the reason why these two periods were chosen for the analyses in this study. Since the output is controlled to be constant by the pitch control at high wind speeds, the output fluctuation is less than at medium wind speeds.

Figure 3.

Output power profiles of the SWT systems at high and medium wind speeds. (a) On 1 March with high wind speed.(b) On 29 January with medium wind speed.

4-kW-class PV power generation

The output power variations of five 4-kW-class residential PV power generation systems were also analyzed. The data were measured in Ota, Gunma, Japan, as part of a demonstration project on grid connection of clustered PV power generation systems, funded by NEDO (Kandenko, 2008). In this project, 553 grid-connected residential PV power systems with a total capacity of 2519 kW were monitored, and the time series of the DC and AC output power from the respective PV systems at an interval of 1 s were made available with the permission of NEDO. The five PV systems (Units 6, 9, 10, 17, and 203) analyzed in this study were connected to the same low-voltage distribution lines, which means they were at most approximately 100 m apart from each other.

Figure 4(a) and (b) presents the daily output power profiles on 9 and 15 October, respectively. As shown in Figure 4(a), the output power profiles were close to the cyclic curves on 9 October, a sunny day. However, Figure 4(b) shows that the fluctuation of the output power on 15 October, a cloudy day, was intense. This was the day on which the maximum total output power variation was recorded by the 553 PV systems in time widths of 10 and 20 s during the period from August 2006 to January 2008 (Kondoh and Watanabe, 2013).

Figure 4.

Output power profiles of the PV systems on sunny and cloudy days. (a) On 9 October, sunny day. (b) On 15 October, cloudy day.

Result

Duration curves

Figure 5 shows the load duration curves of the individual and total output power from the SWT and PV systems. In Figure 5, T_total on the horizontal axis is the effective measurement period, and P_acrate on the vertical axis is 5.0 kW for the individual SWT system (Unit 2), 4.0 kW for the individual PV system (Unit 10), and 20 kW for both groups of all systems. Flattening of duration curves are caused by smoothing long-term power variation (Holttinen and Hirvonen, 2012). Thus, a comparison of the individual and total outputs indicates a slight smoothing effect acted on both the SWT and PV systems, but the effect was limited because the distribution area of each site was not very large (approximately 10³–10⁴ m²).

Figure 5.

Duration curves of the SWT and PV systems.

Spectra of output power and correlation coefficients

To ascertain whether fluctuations in the output power from the respective systems are mutually synchronized or independent, the correlation coefficients among the output powers of the respective units were analyzed for each frequency component. Figures 6 to 9 show the results of this analysis for the SWTs at high and low wind speeds. Figures 6 and 8 show the power spectra of the output power of Unit 2 and of all the four units multiplied by the frequency $f {p_{2} (f)}^{2}$ and $f {p_{all} (f)}^{2}$ , respectively, obtained by a fast Fourier transform of 2¹⁸ time series data points for the periods from 16:00 to 23:30 on the 2 days represented in Figure 3. They also show the frequency dependency of the ratio of the total-to-individual output power, $p_{all} (f) / p_{2} (f)$ , and that of the correlation coefficients of each combination of SWTs.

Figure 6.

Power spectra and ratio of total-to-individual output power and frequency dependency of correlation coefficients of each combination of four SWT systems at high wind speed on 1 March.

Figure 7.

Component of ≤0.0001 Hz of output power of four SWTs on 1 March during the same period as in Figure 3(a).

Figure 8.

Power spectra and ratio of total-to-individual output power and frequency dependency of correlation coefficients of each combination of four SWT systems at low wind speed on 29 January.

Figure 9.

Component of ≤0.0001 Hz of output power of four SWTs on 29 January during the same period as in Figure 3(b).

The method used to obtain the correlation coefficients is as follows. The spectra of output power were divided into 13–16 ranges of frequency components with the same logarithmic intervals. To obtain the output power variation $P_{n}^{f} (t)$ of Unit $n$ with a sole frequency component, the magnitude of the other component out of the range was modified to 0, and then, an inverse Fourier transform was performed. Figures 7 and 9 show the output power variation with the lowest frequency range ( $\underset{~}{<}$ 0.0001 Hz) component of the SWTs for the same period represented in Figure 3(a) and (b), respectively. Using $P_{m}^{f} (t_{i})$ and $P_{n}^{f} (t_{i})$ , the output power variation of each range of frequency f of units m and n obtained by the inverse Fourier transform at time, $t_{i}$ , the correlation coefficient $Γ_{m, n}^{f}$ for frequency range f was calculated as shown in equation (1) (Syahiman et al., 2015), where $\bar{P_{m}^{f}} and \bar{P_{n}^{f}}$ are the average values of $P_{m}^{f} (t_{i})$ and $P_{n}^{f} (t_{i})$ , respectively

Γ_{m, n}^{f} = \frac{\sum_{i} {P_{m}^{f} (t_{i}) - \bar{P_{m}^{f}}} {P_{n}^{f} (t_{i}) - \bar{P_{n}^{f}}}}{{((\sum_{i} {P_{m}^{f} (t_{i}) - \bar{P_{m}^{f}}}^{2}) (\sum_{i} {P_{n}^{f} (t_{i}) - \bar{P_{n}^{f}}}^{2}))}^{1 / 2}}

(1)

Using this equation, correlation coefficients of output power variation between the respective units were obtained for each frequency range.

As Figure 8 shows, the correlation coefficients are high in the low-frequency components of $f_{l} \underset{~}{<} 10^{- 3}$ Hz and low in the high-frequency components of $f_{h} \underset{~}{<} 10^{- 2}$ Hz. In other words, the output power fluctuation is almost synchronized in the low-frequency components and is thought to be almost independent in the high-frequency components. The output power fluctuation of all four SWTs is quadruple that of any individual SWT system if the output power fluctuations are completely synchronized, but it is only double if they are independent of each other (Lakmal Wevita et al., 2014). From the bin average of $p_{all} (f) / p_{2} (f)$ in Figures 6 and 8, we see that the output power variations of the SWTs are synchronized ( $p_{all} (f) / p_{2} (f) ≅$ 4) in the low-frequency ( $f \underset{~}{<} f_{l}$ ) components and independent ( $p_{all} (f) / p_{2} (f) ≅ 2$ ) in the high-frequency ( $f \underset{~}{>} f_{h}$ ) components.

On the other hand, the correlation coefficients between Unit 1 and any other unit are low even in the low-frequency components, as shown in Figures 6 and 8. The reasons for this are that Unit 1 can be influenced much more by the blow-up wind along the hillside with an elevation difference of $~ 40$ m than the other three units and that Unit 1 is relatively far from the other units. Thus, the output power fluctuation of Unit 1 can be seen as being more independent even in the low-frequency components. Even excluding Unit 1, the correlation coefficients between any pair of the other three units are still low in the low-frequency components compared with those of the PV systems, which are shown later in Figures 10 and 12. This means the fluctuation of the output power of the SWTs would be independent, regardless of the distances between the WTs.

Figure 10.

Power spectra and ratio of total-to-individual output power and frequency dependency of correlation coefficients of each combination of five PV systems on 9 October.

The reason for the frequency dependencies of the correlation coefficients of the SWT systems shown in Figure 6 being more complicated than those in Figure 8 is the upper limit of the output power. On 1 March, the output power was very close to its rated output power for the high wind speed represented in Figure 3(a). Thus, the fluctuations of the $f_{l} \underset{~}{<} 10^{- 3}$ Hz components of output power are not fully reflected by wind speed variation, because of the blades’ pitch control, with smaller correlations between units. Thus, even the lowest component is rather independent in Figure 7, especially in the range surrounded by the black dotted line, compared with Figure 9.

Next, the analysis results for the PVs are discussed for comparison with the results for the SWTs. Figures 10 to 13 show the same results for PVs on sunny and cloudy days, respectively, for comparison with the results for the SWTs. Figures 10 and 12 show the power spectra of the output power multiplied by the frequency, which were obtained by fast Fourier transforms of 2¹⁴ time series data points from 9:00 to 13:30 on the 2 days. In Figures 10 to 13, P₆–P₂₀₃ are the output AC power of units 6–203, respectively, and P_total is the total output power of the five units. Figures 10 and 12 show that the correlation coefficients are high in the low-frequency components of $f_{l} \underset{~}{<} 5 \times 10^{- 2}$ Hz and low in the high-frequency components of $f_{h} \underset{~}{>} 3 \times 10^{- 1}$ Hz. It should be noted that the threshold frequencies of $f_{l}$ and $f_{h}$ are different for the SWTs and PVs. The total output power fluctuation of the five PVs is five times higher than that of any individual PV system if the power output fluctuations are completely synchronized, but it is only higher by a factor of $\sqrt{5}$ if they are independent of each other (Lakmal Wevita et al., 2014). From the bin average of $p_{all} (f) / p_{10} (f)$ in Figures 10 and 12, we see that the output power variations of all five PVs are almost synchronized in the low-frequency components ( $p_{all} (f) / p_{10} (f)$ $≅ 5$ ) and independent in the high-frequency components ( $p_{all} (f) / p_{10} (f)$ $≅ \sqrt{5}$ ).

Figure 11.

Component of ≤0.0001-Hz of output power of five PVs on 9 October.

Figure 12.

Power spectra and ratio of total-to-individual output power and frequency dependency of correlation coefficients of each combination of five PV systems on 15 October.

Figure 13.

Component of ≤0.0001-Hz component of output power of five PVs on 15 October.

The reason for the frequency dependencies of the correlation coefficients of the PV systems shown in Figure 10 being more complicated than those shown in Figure 12 is uncloudy weather conditions. On 9 October, the long-term output power variation was limited, except for the daily sinusoidal one, as shown in Figure 4(a). Thus, the fluctuations of the $\underset{~}{<} 0.01$ Hz components of the output power were low, as shown in Figure 10, compared with those shown in Figure 12.

To determine which type of system exhibits a greater smoothing effect, the SWT and PV data for the day represented in Figures 8 and 12, in which their characteristics appear clearly, were analyzed. A smoothing effect occurs when the output power fluctuations of the respective units are independent, which means that the correlation coefficients are approximately 0 (Rahman et al., 2018; Syahiman et al., 2015). In Figure 12, the correlation coefficients are almost 1 for the frequency components of $f_{l} \underset{~}{<} 5 \times 10^{- 2}$ Hz. However, in Figure 8, the correlation coefficients are almost 1 for the frequency components of $f_{l} \underset{~}{<} 10^{- 3}$ Hz only and almost 0 for the frequency components of $f_{h} \underset{~}{>} 3 \times 10^{- 3}$ Hz. This means that the output power fluctuation of the SWT systems is more independent in the lower frequency components. Thus, it is presumed that the smoothing effect acts in the SWT systems more than in the PV systems.

Power variation at different time intervals

Output power variation ΔP_Δt for a time interval Δt was also analyzed. If P_max and P_min are defined as the maximum and minimum output power, respectively, from all data for the period of Δt, ΔP_Δt is defined as P_max − P_min. The ΔP_Δt values of the individual and the groups of all systems for both SWT and PV systems were calculated for the effective measurement period T_total for three cases of Δt = 10 s, and 1 and 10 min. Figure 14 shows the ΔP_Δt in descending order. Figure 14 indicates that the output fluctuation of the SWT system is more intense than that of the PV system. However, it also shows that the total output power variation of all units is smoothed in comparison to the variation for individual units, and the difference is greater for the SWTs than for the PVs. Based on these results, it is clear that a greater smoothing effect acts in the SWT systems than in the PV systems.

Figure 14.

Output power variation of individual and combined 5-kW-class SWTs and 4-kW-class PV systems in descending order. (a) Time interval Δt = 10 s. (b) Time interval Δt = 1 min. (c) Time interval Δt = 10 min.

Voltage flicker

To confirm the negative impact of bus voltage fluctuation on nearby consumers, the voltage flicker of multiple SWTs was analyzed. The voltage rise $Δ V$ due to active and lagging reactive output power increments, $Δ P and Δ Q$ , respectively, at the PCC of the small-scale WT generator was calculated as follows (Alaboudly et al., 2013; Ammar and Ammar, 2016; Hu et al., 2009)

Δ V ≅ \frac{R \cdot Δ P + X \cdot Δ Q}{V}

(2)

where $V$ is the voltage at the PCC and $R + jX$ is the system impedance. In general, in a low-voltage distribution system, the resistance $R$ is almost equal to or greater than the reactance $X$ . Therefore, the active power variation $Δ P$ has a great influence on $Δ V$ . Since the PCSs are designed to operate at a power factor of 1.0 as long as V is lower than the upper threshold, the reactive power fluctuation $Δ Q$ is not the main cause of voltage fluctuation (De Zutter et al., 2017).

A scatter diagram of the total AC output power, $P_{all}$ , and the AC voltage, $V$ , is shown in Figure 15. The AC voltage $V$ constantly fluctuates, even with other factors on the grid side, so the scatter diagram in Figure 15 has a distributed width. However, if the fluctuation of $V$ is due only to the AC output power $P_{all}$ , $V$ should be close to a linear function of $P_{all}$ , according to equation (2) and substituting $P_{all}$ for $Δ P$ . When the approximate linear relation is determined by the least squares method, the slope is 0.16–0.26 V/kW, with little difference depending on the evaluation period. Because the bus voltage is almost 200 V, this corresponds to 0.033–0.052 V/A. Thus, the resistance $R$ per line is estimated to be 0.016 to 0.026 Ω. Because the line resistance value used in PCS certification tests in Japan is 0.19 Ω, it is considered that the voltage fluctuation at this site is almost one-tenth as low as the case supposed in the PCS certification tests.

Figure 15.

Correlation between the total AC output power, P_all, and the AC voltage, V, on 17 December 2017.

In Japan, voltage flicker is evaluated using the index $Δ V_{10}$ developed by Central Research Institute of Electric Power Industry (CRIEPI) (Leinonen and Laketic, 2018). According to the definition of the $Δ V_{10}$ criterion, different frequency components of voltage fluctuations have different degrees of influence on the flicker level. The influence is calculated as follows

Δ V_{10} = \sqrt{\sum_{n = 1}^{\infty} {(a_{n} \times Δ v_{n})}^{2}}

(3)

where $Δ v_{n}$ are amplitudes of voltage fluctuation components with frequency $f_{n}$ , and $a_{n}$ is a sensitivity coefficient. Figure 16 illustrates the approximated flicker sensitivity curve. In general, $Δ V_{10}$ is calculated at every 1 min, and the fourth highest value among 60 calculated values for an hour is used to evaluate the voltage flicker. If the value is below 0.45 V, voltage flicker at the PCC is considered to be practically acceptable (Kandenko, 2008).

Figure 16.

Flicker sensitivity curve.

Figure 17 shows the scatter diagram of the 1 min average of AC output power, ${\bar{P}}_{all}$ , and $Δ V_{10}$ from 12 January to 24 April 2018. $Δ V_{10}$ was measured using an IFK-40 flicker meter. The red markers indicate the respective $Δ V_{10}$ values for the 4 months. The highest value of $Δ V_{10}$ was 0.193 over the 4 months of measurement, which was less than 1/2 the limit value of 0.45 V, although we should keep in mind that the system resistance R at this PCC is low. Figure 18 shows the time variation of each value during the measurement period for 3 min around the highest $Δ V_{10}$ (0:00 on 18 April). Figure 18 indicates that V_ac has a short-period variation, which seems to increase $Δ V_{10}$ . However, such a short-period variation was not observed for $P_{all}$ . In addition, the fluctuation of the total output power of the four units is smoother than those of the respective individual units in Figure 18. This means that a smoothing effect acted on the time, as mentioned above.

Figure 17.

${\bar{P}}_{all} - Δ V_{10}$ scatter plot at the PCC of the four 5-kW SWT systems.

Figure 18.

Time variation of four SWTs at Wakkanai at approximately 0:00 on 18 April.

In Figure 17, the top 1%, 5%, and average values of $Δ V_{10}$ in the 1-kW interval bins are also shown. These values indicate that $Δ V_{10}$ has a tendency to reach its peak value when the 1-min average output is 15–16 kW, and it tends to decrease as ${\bar{P}}_{all}$ approaches the rated output. That is, $Δ V_{10}$ for small WTs tends to decrease when the output power is both low and approaching the rated output.

As mentioned above, the voltage flicker is evaluated by the fourth highest value among the 60 calculated values over an hour. This study focuses on the top 5% values, which correspond to the third highest value among the 60 calculated values, while considering a minor safety factor. In Figure 17, the voltage flicker $Δ V_{10}^{ot}$ is 0.070 V at ${\bar{P}}_{all} = 0 kW$ , which implies that it is not caused by the SWTs. Then, the voltage flicker $Δ V_{10}^{all}$ reaches 0.126 V at ${\bar{P}}_{all} = 16 kW$ , which is engendered by several factors, including the SWTs as well as the load variation in a nearby consumer, the on-load tap changing in substations, and so on. As the voltage fluctuation due to the output power variation of the SWTs is not related to the other factors, the voltage flicker $Δ V_{10}^{SWT}$ caused only by the SWTs is evaluated at $Δ V_{10}^{SWT} = \sqrt{{(Δ V_{10}^{all})}^{2} - {(Δ V_{10}^{ot})}^{2}} = 0.104 V$ (JEAC-9701:2012, 2013). Conversely, if $Δ V_{10}^{SWT}$ reaches 0.444 V, which is 4.27 times higher than the present value, $Δ V_{10}^{all}$ at the PCC reaches the upper limit of 0.45 V. Section 3.2 indicates that the correlation coefficients are approximately 0 in the high-frequency components of $f \underset{~}{>} 3 \times 10^{- 2}$ Hz with high-sensitivity coefficients $a_{n}$ . Therefore, the voltage flicker due to each SWT can be considered independent. This implies that $Δ V_{10}^{SWT}$ is estimated theoretically to reach 0.444 V if the number of the SWTs increases to 73, which is 4.27² times as high as the present number, or if the system resistance $R$ is 4.27 times as high as the present value. It is better to measure and analyze data at the site with more multiple SWTs in order to validate the estimation.

Next, the 2¹⁵ time series data points measured at every 20 m were used to analyze the frequency components of the $v (f)$ and $p_{all} (f)$ of the AC voltage V at the PCC and the total output power $P_{all}$ . The results of the analysis are shown in Figure 19.

Figure 19.

Power spectra and ratio of total output power and output voltage and frequency dependency of correlation coefficient of total output power and voltage.

Figure 19 shows the average value for each equal interval in a logarithmic representation, and the $v (f) / p_{all} (f)$ ratios are also shown. If $p_{all} (f)$ is the main factor of $v$ occurring at each frequency f, $v (f) / p_{all} (f)$ should be close to 0.16 − 0.26 V/kW, which is the slope related to system impedance, as shown in Figure 15. In fact, $v (f) / p_{all} (f)$ was in the range of 0.16–0.26 V/kW for the long-period fluctuation components of $f \underset{~}{>}$ 0.2 Hz, but for the shorter period fluctuation components of $f \underset{~}{>}$ 0.2 Hz, $v (f) / p_{all} (f)$ was much larger. These larger voltage fluctuation components cannot be explained by the output power fluctuation $p_{all} (f)$ and equation (2). Therefore, the main factor in the short-period voltage fluctuation components of $f \underset{~}{>}$ 0.2 Hz is not derived from the output fluctuation from the small wind power generation systems. Furthermore, the correlation coefficients between $v (f)$ and $p_{all} (f)$ are high in the low-frequency components, except for 3 × 10⁻⁴ Hz, and low in the high-frequency components. This indicates the same characteristics as illustrated in Figure 18. In addition, the impact of long-period fluctuation on $Δ V_{10}$ is low because of low-sensitivity coefficients a_n. Thus, the total output power variation has little influence on $Δ V_{10}$ .

Since $Δ V_{10}$ is used in Japan only, an analysis with the international indexes of voltage flicker, P_st and P_lt, was also conducted. These indexes are established in IEC standards 61000-4-30:2008 and EN 50160:2010. P_st is determined from the values of the cumulative weighted probability of flicker perception levels at 0.1%, 1%, 3%, 10%, and 50%, as

P_{st} = \sqrt{0.0314 P_{0.1} + 0.0525 P_{1} + 0.0657 P_{3} + 0.28 P_{10} + 0.08 P_{50}}

(4)

where the percentiles P_0.1, P₁, P₃, P₁₀, and P₅₀ are the flicker levels exceeded for 0.1%, 1%, 3%, 10%, and 50% of every 10-min interval, respectively. They reflect the ratio of the relative voltage difference (ΔV = V_max − V_min) to the base voltage (V) (Alaboudly et al., 2013; Blavette et al., 2016; Chen et al., 2016). P_lt is measured as an average of 12 values of P_st levels over a 2-h duration using (5) as

P_{lt} = \sqrt[3]{\frac{1}{12} \sum_{i = 1}^{12} {P_{st} (i \cdot Δ t_{10})}^{3}}

(5)

where $Δ$ t₁₀ = 10 min. P_st and P_lt were also measured using an IFK flicker meter. If P_st and P_lt are below 1 and 0.8, respectively, voltage flicker at the PCC in a low-voltage distribution system is considered as practically acceptable (Rahman et al., 2018).

Figures 20 and 21 show the scatter plots of the 10 min and 2 h averages of AC output power, ${\bar{P}}_{all}$ , and P_st and P_lt from 12 January to 24 April 2018 (Rahman et al., 2018).

Figure 20.

${\bar{P}}_{all} - P_{st}$ scatter plot of four 5-kW SWT systems at Wakkanai.

Figure 21.

${\bar{P}}_{all} - P_{lt}$ scatter plot of four 5-kW SWT systems at Wakkanai.

In Figures 20 and 21, we see that P_st and P_lt were almost always less than 1/2 the limit values of 1 and 0.8, respectively. The red markers indicate the P_st and P_lt during the 4 months. This confirms that the voltage flicker caused by the SWTs is low at this site, according to the international evaluation criteria. The top 1%, 5%, and average values of P_st and P_lt in the 1-kW interval bins were also analyzed, but the characteristics shown in Figure 17 were not clearly evident compared with the characteristics of $Δ V_{10}$ shown in Figure 17. Therefore, the results of a linear regression analysis of P_st and P_lt are represented by black lines and equations in the respective figures. The small positive slopes of the P_st and P_lt regression lines indicate a slight positive relation between flicker and AC output power. To confirm the effects of the 10-min and 2-h averages of AC output power, ${\bar{P}}_{all}$ on P_st and P_lt more clearly, the correlation coefficients between ${\bar{P}}_{all}$ and P_st and P_lt (Rahman et al., 2018) were analyzed. The resulting values in the case of P_st and P_lt were 0.141 and 0.181 respectively. Furthermore, the values of P_st and P_lt were not very related to ${\bar{P}}_{all}$ . The reason seems to be that the output power variation of the SWTs is too frequent to be distinguished in the measurement with an interval of 10 min or longer like P_st and P_lt. Anyway, the results of the linear regressions and correlation analyses show that the flicker produced by SWT systems is lower than that created by other causes in the cases of the investigated SWT systems, at least at the existing penetration level.

Conclusion

SWT systems have not been as widely used as PV power systems and large-scale WTs. In addition, utilities have recognized the general characteristic that the output fluctuation of SWTs is more intense than that of PV. Thus, they have great concern for installing more SWTs to their grids. This article aims to analyze the output fluctuations of multiple SWTs and their negative impacts (especially voltage flicker) quantitatively. For this purpose, the output power fluctuations of four 5-kW-class SWT systems were analyzed using time series data measured at 0.1-s intervals and compared with those of five 4-kW-class PV systems. First, it was confirmed that the output power of the SWT systems fluctuates much more than that of the PV systems in terms of both spectra and variation in some time intervals. Next, the characteristics of the correlation coefficients of output power variation between any two units are made clear under the influence of certain weather conditions, such as those on cloudy and breezy days, when the output power fluctuation is intense. The result indicates that a smoothing effect occurs more in the SWT systems than in the PV systems, because of the narrower frequency range with high correlation.

The voltage flicker caused by voltage fluctuations in the four 5-kW-class SWT systems was also analyzed using different indices ( $Δ V_{10}$ , P_st, and P_lt) to assess its impact on the bus voltage fluctuation. The results confirmed that the flicker produced by the SWT systems was sufficiently lower than the limit value to be considered practically acceptable, at least in the case of the site considered in this study. Furthermore, the voltage flicker evaluated by $Δ V_{10}$ has a clear dependency on the 1-min average output power; the impact of SWTs on $Δ V_{10}$ can be evaluated with other factors, and the upper limits of the installation number and/or the system resistance can be estimated theoretically with the voltage flicker of the four 5-kW-class SWTs, although measurement and analyses of data at the site with more multiple SWTs are required to validate the estimation. However, correlation between the voltage flicker evaluated by P_st and P_lt and output power was analyzed, revealing only a minor positive relationship.

Footnotes

Appendix 1 Acknowledgements

The authors express their appreciation to Daito Petroleum Sales Co., Ltd. and Zephyr Corporation for their support of the measurements at the site in Wakkanai.

Author contributions

K.K. and J.K. took charge of the conceptualization, methodology, software, and validation. K.K. conducted formal analysis, investigation, data curation, and writing of the original draft. J.K. supervised the research project. K.F. took charge of review and editing the draft.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the Collaborative Research Program of the Research Institute for Applied Mechanics, Kyushu University.

ORCID iD

Kenta Kashiwaya

Patents

This section is not mandatory, but may be added if there are patents resulting from the work reported in this article.

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