**1. Introduction**

The most often used standards related to power quality (PQ) are EN 50160:2010 [1] with further amendment EN 50160:2015 [2] as well as IEC 61000-4-30 [3] and IEEE 1159 [4]. The classical method of assessing power quality is based on choosing a representative period of time, normally 1 week, which should represent normal operating conditions of the observed electrical power network (EPN). The parameters which are taken into consideration in PQ assessment are as follows: frequency variation (*f*), voltage variation ( *U*), flicker represented by long-term flicker severity ( *P*lt) and short-term flicker severity ( *P*st), asymmetry (*k*u2), total harmonic distortion in voltage (*THDu*), content of harmonic from 2nd to 50th. In the methodology of power quality assessment, the measurement time interval and aggregation time interval have to be distinguished. The basic measurement time interval for the parameter magnitudes (supply voltage, harmonics, interharmonics and unbalance) is a 10-cycle time interval for a 50 Hz power system or a 12-cycle time interval for a 60 Hz power system. Then, the measurement time intervals are aggregated over a 150/180-cycle interval (150 cycles for 50 Hz nominal or 180 cycles for 60 Hz nominal), 10 min interval and 2 h interval.

The review of present literature indicates that there is some discussion related to the assessment of power quality in terms of the influence of the aggregation time interval on the effect of the assessment. This issue has a significant meaning in terms of the assessment of power quality at the point of the common coupling (PCC) of the distributed generation (DG), especially when the observed DG is characterized by high variations of the energy production. Common examples are PV installations with their inherent relation of generated energy with cloud effect. The discussed aspect has already been reflected in the amendment to standard EN 50160:2015 where a 1 min aggregation interval is suggested for the assessment of voltage variation in low voltage (LV) power systems. Selected issues related to aggregation interval influence can be found in the below works:


obtained results are similar. However, both papers have recommended a further verification of the results for grids with a significantly di fferent structure. This recommendation was a motivation for the presented paper. That is why this paper is focused on the investigation of the possible impact of the aggregation interval on power quality assessment in a particular case of the point of common coupling of a photovoltaic plant when the variability of the parameters is more expected.

The presented state of the art supports the need for further verification of the influence of the aggregation interval on power quality assessment for power grids with di fferent structures. Nowadays the widely discussed issue is the integration of distributed energy resources with a power system and its impact on power quality. One of the main contributions of this work compared to previous research dedicated to the investigation of the influence of the aggregation interval on power quality assessment is to expand research into a real measurement case of a 100 kW photovoltaic plant directly connected to a low voltage power network. The investigated case is interesting due to the variability of power quality parameters associated with variable nature of energy production a ffected by weather conditions. Additionally, this work explores an additional aspect of the possible impact of the aggregation interval which is its influence on the correlation analysis between weather conditions and power quality parameters. The presented results highlight some di fferences between the correlation coe fficient obtained using 10 min and 1 min aggregation intervals.

Taking into consideration the e ffects of the quoted discussion, the aim of this paper is to present a comparative investigation of the application of 1 and 10 min aggregation times in power quality assessment. The selected times are based on the demands of PQ assessment in accordance with the amendment to the standard EN 50160 where both 1 min and 10 min aggregation intervals are considered [1,2]. The observed object is the 100 kW PV power plant connected directly to LV power network. Additionally, the paper extends the discussion of using di fferent aggregation intervals in the context of correlation analysis of the PQ parameters and weather conditions. The obtained results highlight the impact of PV energy production on PQ level at the PCC when di fferent aggregation times are used.

#### **2. Comparative Study of Recent Developments in Power Quality Requirements**

The permissible levels of power quality parameters used for the assessment of public distribution networks is based on standard EN 50160. This standard was changed significantly in 2015. The comparison of demand levels for standard EN 50160:2010 [1] and standard EN 50160:2015 [2] were involved in Table 1.

Studying contents of Table 1 it can be noticed that the most significant di fference is the extended requirement for the time period when the parameters should preserve the permissible levels. The acceptance level for parameters are similar for both [1] and [2] but the time to maintain the parameter at a given level is required at 100% of the observations in [2] while the previous version of the standard [1] generally uses 95% for the time of observation. This indicates that the trend is toward continuous maintenance of power quality parameters (*f*, *U*, *P*lt, *k*u2, *THDu*, harmonic 2nd to 50th) for the acceptance level.

A significant change is noted for frequency. For the systems with a synchronous connection, the requirements for the 50 Hz systems is setup to 50 Hz ± 0.1 Hz for 100% of the time. The acceptance level corresponding to 100% of measurement data was restricted from 47 Hz to 49.9 Hz. The frequency is a grid parameter and local changes generally have no significant influence on frequency but the formulated requirement might be a very restrictive demand for distribution system operators.

The next di fference between the documents is the mentioned aggregation time for voltage variations. In [1], the 10 min aggregation was used. In [2], the 1 min aggregation is proposed for a LV power network. The reduction of aggregation time as well as the demand for 100% of the data to be in the permissible range creates a serious question for the sensitivity of the assessment when a single aggregated 1 min value can cause a negative assessment of voltage variation.

The next difference is the introduction of the requirement for short-term flicker severity which uses 10 min aggregation interval. Until 2015, long-term flicker severity was used, where 2 h aggregation is applied. It creates the next question about the sensitivity of the assessment when rapid changes of power demand or power generation might be considered.

Standard [2] introduced the requirement level for harmonic from 26th to 50th. Additionally, the mean value of *THDu* measured data was defined. It indicates that when the *THDu* level is high (higher than 5%) for a long period of time it may lead to a negative assessment [15]


**Table 1.** Comparison of permissible levels of power quality parameters in EN 50160:2010 [1] and EN 50160:2015 [2] for a 50 Hz system.

#### **3. Description of Investigated PV Power Plant**

The investigated photovoltaic power plant (PVPP) consists of numerous of small photovoltaic systems. The range of installed power of the PV systems are: 3 kWp, 5 kWp, 17 kWp, 25 kWp, 30 kWp with a total power of 132.37 kWp, however referring to an agreemen<sup>t</sup> with the local distribution system operator, the generated power is limited to 100 kW. Thus, technically one of the 30 kWp system works in the regulatory mode in order to keep maximum of generated power to 100 kW. The diagram with the assignment of specific PV technologies and range of installed power is shown in Figure 1. PV modules are made on the basis of different technologies which have been marked in in Figure 1 with given colors:

• First generation—silicon cells, from crystalline silicon: - - Monocrystalline (sc-Si) (yellow),
	- - Cadmium telluride cells (CdTe) (pink),
	- - Burns from CuInGaSe2 copper-indium selenide (Copper-Indium-Gallium-Diselenide —CIGS) (green).

**Figure 1.** The diagram of investigated photovoltaic power plant with the assignment of rated power and photovoltaic (PV) technologies related to particular PV systems. Note: sc-Si—monocrystalline, mc-Si—multicrystalline, CdTe—Cadmium telluride cells, CIGS—Copper-Indium-Gallium-Diselenide, CC—connector cable, MSS—main switching station, MS—measuring system, PVSS—photovoltaic switching station.

The PV power plant (PVPP) is located in the south-western part of Poland. The angle of the PV panel position is β = 31◦.

The database of measurements consists of electric and non-electrical quantities associated with individual PV installations. The elements of non-electrical quantities are irradiance, temperature of the panels and wind. Electrical quantities come from the particular PV inverters on the AC and DC sides. Additionally, power quality parameters are measured at the point of common coupling of the PV power plant, noted as MS (measuring systems). The energy production is also measured by energy meters.

Additionally, the weather data are collected by a separate weather station including:


In order to investigate the influence of the aggregation time interval, PQ parameters and weather condition measurements were conducted from selected period of 12 July, 2018 to 18 July, 2018. This period of observation can be treated as a representative week of measurement data consisting of high and low irradiance levels and di fferent weather conditions. Methods of the measurement and aggregation times were conducted in accordance with class A of standard [3]. The PQ recorder was set up so that the 1 min and 10 min aggregations were collected simultaneously. In order to demonstrate the PV power plant behavior in the selected period of observation in Figure 2, the active power generation in the week for both 1 min and 10 min aggregation is shown. Negative active power during the night is caused by the energy consumption of the plant, mainly related to supplying the database server and cooling the technical container. The application of a 1 min aggregation interval in comparison to a 10 min interval allows the real changeability or power generation to be expressed better, especially in view of extremum values caused by the cloud e ffect.

**Figure 2.** Active power generation of observed PV power plant during selected week using 1 min and 10 min aggregation intervals.

To demonstrate the variation of the weather conditions, the changes of ambient temperature, global horizontal irradiance and di ffuse horizontal irradiance is presented in Figure 3 using a 10 min aggregation interval and in Figure 4 using a 1 min aggregation interval. Comparison of the application of 1 min and 10 min of data indicates the higher changeability and extremum values of observed measurements.

**Figure 3.** Weather conditions during the selected week of observation using a 10 min aggregation interval.

**Figure 4.** Weather conditions during the selected week of observation using a 1 min aggregation interval.

### **4. Results of the PQ Assessment and Correlation Analysis for Di**ff**erent Aggregation Time Intervals**

*4.1. General Comparison of the PQ Assessment Results Using Requirements of EN 50160:2010 and EN 50160:2015*

The results of the PQ assessment for both EN 50160:2010 [1] and EN 50160:2015 [2] are presented in Table 2. The analysis indicates that PQ assessment in accordance with [1,2] gives different results of the assessment. The differences appear mainly when the assessment considers 100% of the measurement data set.

**Table 2.** Comparison of general results of the power quality assessment obtained using 50160:2010 [1] and 50160:2015 [2].


#### *4.2. Voltage Variation Analysis Using 1 Min and 10 Min Aggregation Intervals*

The standard EN 50160:2015 [2] has introduced the analysis of voltage variation in 1 min aggregation time. Previously, referring to EN 50160:2010 [1], the analysis was based on a 10 min aggregation interval. Table 3 presents the obtained values of minimal, mean, maximal, variance, standard deviation and median values of voltage variations aggregated in 1 min and 10 min. The analysis indicates that:


Using 1 min or 10 min aggregation intervals has preserved the general character of the investigated connection point. For example, using 1 min and 10 min aggregations indicate some asymmetry in the voltage in the connection point of the observed PV power plant. The differences between values of voltage in particular phases are the effect of the structure of the investigated PV power plant. The PV power plant consists of a number of one-phase PV installations which are connected to different phases and can bring some differences in voltages in particular phases. Generally, it can be concluded that application of a 1 min aggregation interval in comparison to a 10 min interval introduces better observability of variations of voltage that exhibits itself by the higher level of extreme values and standard deviation. Table 3 shows that the voltage variation parameters including minimal and maximal values or standard deviations better express the variability of the observed parameters when 1 min aggregation is used. Generally, it can be concluded that the application of a 1 min aggregation interval in comparison to 10 min introduces better observability of variations of voltage that exhibits itself by a higher level of extreme values and standard deviation.


**Table 3.** Comparison of voltage variation parameters of 1 min and 10 min aggregation intervals.

In order to highlight the impact of the aggregation interval on the assessment of PQ parameters at the point of the connection of the PV power plant, Figure 5 presents the analysis of voltage variations in classic term (10 min), short term (1 min) and very short term (200 ms extreme minimum and maximum values of each 10 min aggregated data) for two opposite weather conditions:


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**Figure 5.** Observability of voltage variations of the selected phase for di fferent aggregation intervals at di fferent solar irradiance levels.

The results are presented for one representative phase. In order to minimalize the impact of the network operating condition, the comparison was performed for similar working conditions i.e., working day and working hour (12:00), but the selected days represent di fferent conditions of solar irradiance. Using both 10 min and 1 min aggregation intervals, an expected relationship between solar irradiance and the voltage is represented. The high solar irradiance level directly indicates the higher level of active power generation that naturally increases voltage in the connection point. However, using 1 min aggregation data additional observations and conclusions can be done. From having 1 min data it can be seen that the envelope of voltage variation is wider for the higher irradiance level than for the smaller solar irradiance It can be stated that using a 1 min aggregation interval the cloud e ffect on voltage variation is better represented than when a 10 min aggregation is applied. It can be concluded generally that a shorter aggregation interval allows the variable nature of observed parameter to be expressed better. Instead of one mean 10 min value, a time series of 1 min values is considered.

#### *4.3. Correlation Analysis Using 1 Min and 10 Min Aggregation Intervals*

The next issue concerns the possible impact of the aggregation interval that can be considered in terms of the e ffect on the result of the correlation analysis of selected power quality parameters and weather condition. The correlation was calculated for 1 min and 10 min aggregation time respectively. Correlation analysis was performed using the Statistica software. A correlation matrix function was used, which is based on determining the linear correlation of the straight line (r-Pearson). It defines the degree of proportional relations of the values of two variables. Correlation analysis was performed between pairs of parameters representing power quality, weather condition, level of active power production. No preliminary data standardization was performed. Correlation levels were determined on the basis of the *rxy* correlation coe fficient defined as [16]:

$$r\_{xy} = \frac{\sum\_{i=1}^{N} (\mathbf{x}\_i - \overline{\mathbf{x}})(y\_i - \overline{y})}{\sum\_{i=1}^{N} (\mathbf{x}\_i - \overline{\mathbf{x}})^2 \sum\_{i=1}^{N} (y\_i - \overline{y})^2} \tag{1}$$

The interpretation of the correlation level based on the determined *rxy* coe fficient is presented in Table 4.


**Table 4.** Correlation level description [17].

The prepared matrix of correlation is an extended matrix which consists of PQ parameters and weather condition measurements together so that the analysis of the correlation coe fficient can be performed simultaneously between particular power quality themselves, for example between voltage level and harmonic contents, as well as between power quality parameters and weather condition, for example between horizontal irradiance and voltage level. The results of the correlation coe fficients using 10 min aggregated data is presented in Table 5. Comparative results obtained 1 min aggregated data is collected in Table 6. Additionally, the correlation diagrams of all pairs of parameters is shown in Figure 6 for the 10 min data and in Figure 7 for the 1 min data.


**Table 5.** Correlation matrix of power quality (PQ) and weather parameters for 10 min aggregated data.

Note: 1—*AtmP* (air pressure), 2—*Ta* (ambient temperature), 3—*RH* (relative humidity), 4—*WS* (wind speed), 5—*Gh* (global horizontal irradiance), 6—*Gd* (diffuse horizontal irradiance), 7—*UL1* (voltage variation L1), 8—*UL2* (voltage variation L2), 9—*UL3* (voltage variation L3), 10—*P*stL1 (short-term flicker severity L1), 11—*P*stL2 (short-term flicker severity L2), 12—*P*stL3 (short-term flicker severity L3), 13—*k*u2 (asymmetry), 14—*THDu*L1 (total harmonic distortion L1), 15—*THDu*L2 (total harmonic distortion L2), 16—*THDu*L3 (total harmonic distortion L3), 17—*P*L1 (active power change L1), 18—*P*L2 (active power change L2), 19—*P*L3 (active power change L3).

**Table 6.** Correlation matrix of PQ and weather parameters for 1 min aggregated data.


Note: 1—*AtmP* (air pressure), 2—*Ta* (ambient temperature), 3—*RH* (relative humidity), 4—*WS* (wind speed), 5—*Gh* (global horizontal irradiance), 6—*Gd* (diffuse horizontal irradiance), 7—*UL1* (voltage variation L1), 8—*UL2* (voltage variation L2), 9—*UL3* (voltage variation L3), 10—*P*stL1 (short-term flicker severity L1), 11—*P*stL2 (short-term flicker severity L2), 12—*P*stL3 (short-term flicker severity L3), 13—*k*u2 (asymmetry), 14—*THDu*L1 (total harmonic distortion L1), 15—*THDu*L2 (total harmonic distortion L2), 16—*THDu*L3 (total harmonic distortion L3), 17—*P*L1 (active power change L1), 18—*P*L2 (active power change L2), 19—*P*L3 (active power change L3).

**Figure 6.** Correlation diagrams for all pairs of parameters (PQ and weather) when 10 min aggregation interval is used. Note: 1—*AtmP* (air pressure), 2—*Ta* (ambient temperature), 3—*RH* (relative humidity), 4—*WS* (wind speed), 5—*Gh* (global horizontal irradiance), 6—*Gd* (diffuse horizontal irradiance), 7—*UL1* (voltage variation L1), 8—*UL2* (voltage variation L2), 9—*UL3* (voltage variation L3), 10—*P*stL1 (short-term flicker severity L1), 11—*P*stL2 (short-term flicker severity L2), 12—*P*stL3 (short-term flicker severity L3), 13—*k*u2 (asymmetry), 14—*THDu*L1 (total harmonic distortion L1), 15—*THDu*L2 (total harmonic distortion L2), 16—*THDu*L3 (total harmonic distortion L3), 17—*P*L1 (active power change L1), 18—*P*L2 (active power change L2), 19—*P*L3 (active power change L3).

**Figure 7.** Correlation diagrams for all pairs of parameters (PQ and weather) when 1 min aggregation interval is used. Note: 1—*AtmP* (air pressure), 2—*Ta* (ambient temperature), 3—*RH* (relative humidity), 4—*WS* (wind speed), 5—*Gh* (global horizontal irradiance), 6—*Gd* (diffuse horizontal irradiance), 7—*UL1* (voltage variation L1), 8—*UL2* (voltage variation L2), 9—*UL3* (voltage variation L3), 10—*P*stL1 (short-term flicker severity L1), 11—*P*stL2 (short-term flicker severity L2), 12—*P*stL3 (short-term flicker severity L3), 13—*k*u2 (asymmetry), 14—*THDu*L1 (total harmonic distortion L1), 15—*THDu*L2 (total harmonic distortion L2), 16—*THDu*L3 (total harmonic distortion L3), 17—*P*L1 (active power change L1), 18—*P*L2 (active power change L2), 19—*P*L3 (active power change L3).

The analysis of the correlation matrix of PQ parameters and weather conditions using a 10 min aggregation interval, presented in Table 4 and Figure 6, indicates that there is:


Using both 10 min and 1 min aggregation intervals, an expected relationship between solar irradiance and the active power production as well as voltage level is represented by the high level of correlation coefficients. The higher solar irradiance level, the higher level of active power generation is observed that naturally has an influence on voltage level in the connection point. The correlation analysis is sensitive enough to show small differences between phases which can be explained by the structure of the investigated PV power plant. The PV power plant consists of many small individual PV installations including one-phase installations thus the active power or voltage level may differ slightly in particular phases. It has resulted in a correlation coefficient related to the phases.

Analyzing the correlation matrix of PQ parameters and weather conditions for the 1 min aggregation interval, presented in Table 6 and Figure 7, confirms generally the same correlation results as for the 10 min interval. However, in order to highlight the impact of the aggregation interval on the results of the correlation analysis, a separate matrix of differences was prepared and presented in Table 7. The matrix consists of differences calculated between the absolute value of adequate correlation coefficients obtained using 10 min and 1 min aggregation intervals. A positive value of the difference denotes that the correlation coefficient calculated using the 10 min aggregation is higher than that calculated using the 1 min aggregation. The obtained result of the investigated differences indicates that the correlation results using 10 min and 1 min aggregation are characterized by comparative level of correlation coefficient for all measured parameters. The comparative means that the maximal difference is slight and less than 0.1. The exception of this result is the correlation between flicker severity (*P*st) and voltage level (*U*) and total harmonic distortion in voltage (*THDu*). For these parameters, the maximal value of difference is 0.15. Generally, it can be concluded that using a 10 min aggregation interval in comparison to a 1 min aggregation results in a slightly higher level of correlation coefficients. The sign of the coefficients remains the same. In other words, it can be concluded generally that the application of different aggregation time intervals does not change the direction of the correlation but has an influence on the absolute value of the correlation coefficient. Shorter aggregation time intervals assure sharper observability of the process but exhibit a higher level of standard deviation and wider envelope of parameter variation. Compared to the 1 min time series, the 10 min data are more "monotonous" than the 1 min data due to the averaging process over the 10 min interval. Thus, the correlation analysis performed using 10 min data, which are more smoothed, results in higher values of correlation coefficient.


**Table 7.** Matrix of differences between correlation coefficients obtained using 1 and 10 min aggregation intervals.

Note: 1—*AtmP* (air pressure), 2—*Ta* (ambient temperature), 3—*RH* (relative humidity), 4—*WS* (wind speed), 5—*Gh* (global horizontal irradiance), 6—*Gd* (diffuse horizontal irradiance), 7—*UL1* (voltage variation L1), 8—*UL2* (voltage variation L2), 9—*UL3* (voltage variation L3), 10—*P*stL1 (short-term flicker severity L1), 11—*P*stL2 (short-term flicker severity L2), 12—*P*stL3 (short-term flicker severity L3), 13—*k*u2 (asymmetry), 14—*THDu*L1 (total harmonic distortion L1), 15—*THDu*L2 (total harmonic distortion L2), 16—*THDu*L3 (total harmonic distortion L3), 17—*P*L1 (active power change L1), 18—*P*L2 (active power change L2), 19—*P*L3 (active power change L3).
