Statistical Analysis of Photovoltaic Distributed Generation Penetration Impacts on a Utility Containing Hundreds of Feeders

The increase in the number of consumers who produce part of their own electricity through photovoltaic distributed generation (PVDG) led to the need for studies on how the power system is affected. As the distribution systems were not designed to integrate PVDG, it is important for regulatory agencies and utilities to identify technical problems in the grid associated with the levels of photovoltaic penetration. In this regard, this study presents a method with indicators that quantify the technical impacts that PVDG growth causes to an actual utility that contains hundreds of feeders with different topologies, load types, and densities. Real solar irradiance and temperature values over a year, and photovoltaic system locations varying based on the Monte Carlo method were also considered in the computational simulations. This study helps the utilities to plan preventive measures to strengthen the grid, and regulatory agencies to enhance policies to support PVDG. We analyzed the impacts on voltage magnitudes, technical losses and peak demand arising from the PVDG integration. The results show that, even at low penetration levels (2%), one-third of feeders required modification in the distribution system to allow photovoltaic integration. For over 60% of feeders, penetration levels of up to 20% reduced technical losses and voltage problems, with practically no effect on peak demand. Feeders in residential and commercial/industrial areas presented increases in technical losses and voltage levels for high penetration levels. Rural areas presented reductions in these parameters for all levels of PVDG integration.


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Solar irradiation k Solar constant on the earth's surface L Hourly average active power losses of the penetration level and feeder analyzed L h Active power loss of the feeder at time h L 0 Hourly average active loss of the feeder without PVDG L Variation in the losses of the feeder due to PVDG increase n days Number of days in a month PR Performance ratio of the system PV plant PVDG power installed at the consumer unit VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

S Number of simulated PVDG locations U
Hourly average percentage of voltages outside the suitable limits of the penetration level and feeder analyzed U h Ratio between the number of nodes with voltage violation and the total number of nodes from all buses at hour h U 0 Hourly average of the voltage outside the limits of the feeder without PVDG U Variation in the voltage profile of the feeder due to PVDG increase µ Average of the voltage magnitude, technical loss or peak demand obtained for the various simulated PVDG locations σ Standard deviation of the voltage magnitude, technical loss or peak demand obtained for the various simulated PVDG locations

I. INTRODUCTION
Considering all the renewable energy technologies, photovoltaic distributed generation (PVDG) has one of the most promising growth potentials worldwide. As the investment becomes attractive, installation by consumers becomes fast and flexible [1]. According to the International Energy Agency (IEA), the distributed photovoltaic (PV) capacity grew from 63 GW between 2007 and 2012 to 139 GW between 2012 and 2018, more than doubling between the two periods. Globally, it is estimated that distributed solar PV capacity will reach 530 GW by 2024 [1].
As PVDG deployment increases, researchers in the electric power sector have been studying the positive and negative impacts that this insertion may cause to the distribution systems [2], [3]. Given that feeders were not initially designed for PVDG integration [2], the identification of technical problems -such as power quality and technical losses, for example -associated with the higher levels of PV penetration is of great concern to regulatory agencies and utilities. Improvements made to the power grid aimed at integrating more PV power can generate higher costs not only for the utility, but for all consumers, including those who do not generate their own power.
In this regard, certain studies [4]- [12] have addressed the impact of PVDG integration by evaluating hosting capacity. This approach aims to determine the highest amount of PVDG that may be connected to the grid without affecting the technical parameters. Albeit important, these studies are limited to the maximum amount of PV generation that may be connected to the distribution system. Feeder performance after PVDG integration is not addressed, and the studies only focus on whether any technical parameters are violated.
Other researchers have not aimed to determine a maximum level of PVDG that can be injected in the grid, but to determine an ''optimal'' amount of PV generation in order to maximize one or more positive impacts of this type of generation (or minimize the negative impacts). For example, these studies have sought to investigate PVDG with regard to optimal locations and sizes to minimize losses or costs, to maximize the capacity of the systems or to maintain the voltage levels within certain limits, or a combination of factors [13]- [22].
Studies attempting to address PVDG optimization have started from the hypothesis that it is possible to install PV generation at a location and with the ideal power of a feeder. However, in practice, distributed generation (DG) is generally installed by consumer units willing to invest in this type of technology. Thus, PVDG may be installed randomly at any consumer unit. The problem is then where the DG is installed and how it will affect the grid.
There are studies that have determined how the performance of a grid is altered with an increase in the level of PVDG integration. Certain authors [4], [5], [23]- [38] evaluated variations in voltage magnitudes, technical losses and peak demands, or the reversal of the power flow direction. There are also studies that analyzed the number of operations on the transformer taps, harmonic distortions, voltage unbalances and fluctuations [4], [23], [24], [27].
Most papers that have used real data investigated only one or two feeders [5], [25]- [27], [32], [35], although a given utility may possess hundreds of feeders with different topologies. According to [39], feeders have different load types (residential, commercial, industrial or a combination thereof), load densities (urban or rural), construction types, voltage levels, as well as other aspects.
Given that distribution systems are highly heterogeneous in terms of topology and type of consumer unit, in [23] the authors performed computational simulations to identify the impacts of PVDG integration on 8 typical feeders at 3 locations with different climates.
Despite the wide-ranging objective, the authors [23] did not consider in their simulations the multiple possible configurations regarding the PVDG positioning. It is important to consider uncertainties related to DG positioning, because its location may have different impacts on the distribution system [19].
Also in [23], the authors pointed out that although their study was extensive in terms of combinations of geographic scopes and types of feeders, the actual diversity of the electric system infrastructure is so large that there are feeders that would be more severely affected by PVDG than those addressed in the study. Thus, the authors [23] suggest that future studies develop a method to identify beforehand the types of feeders that would encounter technical difficulties when higher penetration levels of PVDG are integrated.
In [31], the authors evaluated the impacts of PV penetration on the energy flow in a low-voltage (LV) distribution network with 1.5 million consumer units in the United Kingdom. In this study, the differences between PV generation and demand were identified considering only the month of July and the authors did not use a time-series analysis.
It should be noted that the use of time-series analyses may be regarded as a practical tool to indicate how often the worst scenarios occur, and to identify the benefits of different integration strategies.
It is observed that there were no studies in the literature addressing an expressive number of feeders of a utility from which generalizations may be extracted. Furthermore, we did not find studies addressing the performance of the grid for different levels of PVDG penetration that jointly considered: (1) variation in the location of the PV system based on the Monte Carlo method, and; (2) random characteristics of the solar irradiance and temperature curves.
To fill the abovementioned gap, this paper proposes a method with indicators that quantify the technical impacts that PVDG growth may cause to an actual utility with many feeders. According to the IEA [40], the challenges of PVDG integration will not be as serious as may be expected, if detected at the initial stage of implementation (the current scenario of most countries).
As specific objectives, we calculate the impacts of PVDG integration on voltage magnitudes, technical losses and peak demand using the Monte Carlo method. This is the best way to consider uncertainties related to DG location, load profile, temperature and solar irradiance parameters.
Computational simulations were performed using OpenDSS, with real load consumption data for 499 feeders of a distribution system located in the Brazilian Midwest. The PV system was estimated employing real solar irradiance and temperature values over a year, and load profiles were obtained through sample measurements according to Brazilian regulations [41].
A maximum simulation period of one year and ten different penetration levels (0 to 100%) were used. Considering the great diversity of the studied load types and densities (due to the expressive number of feeders), the proposed indicators may be applied to other utilities. The results obtained are then discussed in two ways. First, all the feeders of the utility were considered, regardless of their characteristics. In the second, the feeders were grouped by load type (residential, commercial/industrial, and rural).
Therefore, the main contributions of this paper are as follows: • The present study helps utilities to plan preventive grid reinforcement measures to insert more PVDG; • The feeders are differentiated by type of load, allowing the prior identification of those that are unable to integrate larger amounts of PVDG; • A study addressing a large number of feeders may help regulatory agencies and decision-makers collect prior information on the extent of the impacts of PVDG integration on the distribution grids; • Regulatory agencies may enhance regulation to adequately allocate costs among consumers, considering the access procedures and tariff structure. The article is organized as follows: Section II describes the methodology employed, including details on the conditions of the computational simulations and the proposed indexes used to identify the impacts arising from the integration of PVDG on the voltage magnitudes, technical losses and peak demand. Section III discusses the results obtained from a case study. Section IV presents the concluding remarks.

II. METHODOLOGY
In this section, we present the methodology of the proposed study, with the indicators that quantify the technical impacts caused by PVDG growth on the distribution system, the computational tools used, and the algorithm based on the Monte Carlo method.
The flowchart of the proposed method is presented in Fig. 1. To identify the technical impacts of PVDG integration on the voltage, technical losses and peak demand of an electric power utility, the power flow is executed every hour for a simulation period of one year. The variations in solar irradiation, temperature and load consumption are updated every hour. Different PVDG locations are established.
There is a strong correlation between the technical impacts and how the PVDG is connected to the grid (location and size) and, for this reason, these were addressed in the present study. Considering this, the PVDG location, load profile, temperature and solar irradiance parameters were handled with due statistical rigor. These values are defined by the Monte Carlo method.
To quantify the technical impacts caused by PVDG growth on hundreds of feeders of an actual utility, the indicators must be calculated for each feeder and for the desired penetration level (pen).

A. PENETRATION LEVEL AND PVDG SIZE
In this study, the penetration level is defined as the ratio between the sum of the installed PV system power generation and the total power in the low-voltage feeder under analysis.
The size of each PVDG can be calculated according to the regulatory incentives. Brazilian regulation [42], [43] encourages the installation of PV plants with enough power to compensate the average consumption of the consumer unit VOLUME 8, 2020 over a period of one year. For this reason, PVDG power based on consumption is determined by: where PV plant is the PVDG power installed at the consumer unit (kW), CT is the monthly average consumption of the consumer unit (kWh), k is the solar constant on the earth's surface (kW/m 2 ), PR is the performance ratio of the system (%), n days is the number of days in a month, and Irr is the solar irradiation (kWh/m 2 /day).

B. TECHNICAL IMPACT CALCULATION
We now present the indicators used to calculate the technical impacts arising from PVDG integration on the electrical grid.

1) VOLTAGE LEVELS
The impact of PVDG integration on the voltage level of buses present in each feeder may be calculated based on the amount of voltage outside the limits established by the norm. The Brazilian National Electricity Regulatory Agency (ANEEL) determined the suitable levels of steady state voltages at the consumer unit connection points [41]. For the LV grids, voltages below 0.92 pu or above 1.05 pu are considered outside the suitable limits. For the medium-voltage (MV) grids, the minimum limit is 0.93 pu.
In this study, the hourly average percentage of voltages outside the suitable limits for a certain penetration level (U ) of the feeder under analysis is calculated by: where U h is the ratio between the number of nodes with voltage violation and the total number of nodes from all buses at hour h of the feeder under analysis, and H is the number of hours in the period under analysis.
Since U is determined for each penetration level, it is possible to calculate the variation in the voltage profile of each feeder in terms of percentage points (p.p.) resulting from the increase in PVDG penetration ( U ), as exhibited in: where U 0 is the hourly average of the voltage outside the limits (%) without PVDG (penetration level equal to zero) at the feeder under analysis.

2) TECHNICAL LOSSES
The hourly average active power losses (L) at each feeder for each penetration level is determined by: where L h is the active power loss of a feeder at time h.
Hence, the variation in the losses of the feeder due to PVDG increase ( L), for each penetration level, is given by: where L 0 is the hourly average active loss (kWh) of the feeder under analysis without PVDG.

3) PEAK DEMAND
To determine the peak demand of the feeder (D) for a given penetration level, we initially calculated the peak demand for each hour of the day (D h ). Using these values, the 95th percentile (D 95% ) in [kW] is obtained. The peak demand of the feeder (D) for each penetration level is defined as the highest D 95% for the period under analysis. Thus, the variation in the peak demand of the feeder due to PVDG increase ( D), for each penetration level, is given by: where D 0 is the peak demand (kW) of the feeder under analysis without PVDG.

4) MONTE CARLO ALGORITHM
In the present study, we developed a computational algorithm in C Sharp (C#) -the express version -to determine the impacts that PVDG may provoke on the distribution grid regarding the percentages of voltage outside the regulatory limits, the technical losses and the peak demand. The method addresses uncertainties regarding the PV system location, load profile, and the probabilistic solar irradiance and temperature features. This algorithm controls the Open Distribution System Simulator TM (OpenDSS) software package using a COM (Component Object Model) interface. The OpenDSS was selected due to: (1) its capacity of carrying out quasi-steady state simulations of distribution systems (making it suitable to study DG integration with distribution systems) [44]; (2) for being an software under an open source license [45], and; (3) it is used by Brazilian National Electricity Regulatory Agency (ANEEL) to model feeders and to calculate regulatory technical losses [46].
The technical impact calculation method used for each feeder is presented in Fig. 2. The algorithm can be described as follows: • It defines the initial conditions (electrical grid parameters) and calculates the power of the PV systems installed at each consumer unit; • It executes the power flow for the condition without PVDG; • It randomly allocates the PV systems until the desired penetration level is achieved (S = 1); • It executes the power flow for every hour of the day over a one-year period. This is a way of considering the uncertainties related to the probabilistic feature of solar irradiance and temperature; • After a one-year simulation, it changes the location of the PV systems, thus generating a new S. Then, the simulations are started again. In order to address the uncertainties regarding PV system location, different PVDG sites must be simulated with the Monte Carlo method; • After an initial location of the PV system, we calculate the statistical variation coefficient (CV ), given by (7), to identify the number of S needed in the simulations.
To ensure that the impacts on voltages, technical losses and peak demand are statistically valid, a CV ≤ 5% needed to be achieved. However, a maximum number of 50 different PVDG sites per penetration level was established; where σ and µ are, respectively, the standard deviation and the average of the voltage magnitude, technical loss or peak demand obtained for the various simulated PVDG locations, and S is the number of simulated PVDG locations.
• It calculates the U , U , L, L, D and D; • Finally, we repeated the previous stages for each penetration level and stored the voltage, technical losses, and peak demand results. This entire procedure was applied to each feeder of the utility.

III. RESULTS OF PVDG INTEGRATION ON THE UTILITY GRID
In this section, we present the results of the application of the proposed method by way of a case study. Initially, we provide information on the utility under study and the characteristics of the simulations performed. We then present the impacts of the voltage levels, technical losses and peak demand resulting from the installation of PVDG. The analyses are then discussed in two ways: (1) considering all the feeders of the utility, regardless of their characteristics, and; (2) grouping the feeders according to the predominance -more than 60% -of the type of load (residential, commercial/industrial and rural). Lastly, the results obtained and how they are discussed may support utilities in the planning and execution of preventive grid reinforcement measures.

A. CASE STUDY
The method employed in this study was applied to 499 feeders of a distribution system located in the Brazilian Midwest. The total number of consumer units modeled was, approximately, 2.4 million, of which 2,047,909 were residential, 201,130 commercial, 6,524 industrial and 163,782 rural. The loads supplied in MV had a voltage equal to 13.8 kV or 34.5 kV. At LV, the voltage was equal to 0.22 kV. However, certain loads were fed at 0.38 kV or 0.44 kV. All loads in both MV and LV were modeled at 50% constant impedance, and 50% constant active power and reactive quadratic power.
Using data collected by measurement campaigns according to Brazilian regulations [41], several types of load profiles were determined, each representing a utility market range for weekdays, Saturdays and Sundays. Thus, the probability of each load profile occurring could be computed in function of its share in the utility market. With this information, utilities associate specific load profiles to each of their VOLUME 8, 2020 consumers [47]. The monthly energy consumption of each load and the modeling of the electric power system were performed with actual data provided by the utility for the year of 2017, under the terms of a non-disclosure agreement.
It is also worth mentioning that the solar irradiation and temperature values used in this study were obtained from measurements taken in 2017 by the National Institute of Meteorology (INMET) [48]. The Irr for the Brazilian region studied was equal to 5.422 kWh/m 2 /day.
Using the algorithm in C Sharp (C#), that controlled the OpenDSS with a COM interface, we performed simulations for ten different penetration levels (0%, 2%, 4%, 6%, 10%, 20%, 30%, 50%, 70% and 100%). In this study, pen was defined as the ratio between the sum of the installed PV system power generation and the total power in the LV feeder under analysis. The feeders have consumer units with low-voltages and medium-voltages, however, the integration of PVDG was implemented only in the LV units.
The size of each PVDG was calculated according to the Brazilian regulatory incentives [42], [43]. The values used in equation (1) were: CT equal to the monthly consumption of each feeder analyzed, k equal to 1 kW/m 2 (standard value used to compare efficiency between different PV modules), PR equal to 80% (representing the efficiency of the system as a whole, considering the joule losses, temperature losses, shading and soiling), and n days equal to 30 days.
In the computational simulations, the inverter rated power was equivalent to the installed PV system capacity and only active power was produced (power factor practically unitary). As for the connection scheme, three-phase loads received three-phase inverters and single-phase loads received single-phase inverters.
In the next topic, the impact results of PVDG integration on voltage, technical losses and peak demand are presented.  hour and penetration level, we calculated the average of the U h considering all feeders under analysis.

B. TECHNICAL IMPACTS OF PVDG INTEGRATION
It may be seen in Fig. 3 that penetration levels of up to 30% do not produce significant changes in the U h . The integration of PVDG at penetration levels greater than 30% increased U h especially between 10:00 a.m. and 3:00 p.m. (times with highest solar irradiation). These changes in voltages at the most critical periods of the day may require interventions in the electric grid. Fig. 4 displays the curves of U , U < 0.92 pu, and U > 1.05 pu in relation to the penetration levels, considering all the feeders in the analysis. In Fig. 4, it is possible to verify that for the penetration level of 0% (condition without PVDG), U is approximately 13.5%. This U is the result of the sum of 13%, value related to the U < 0.92 pu, and 0.5% associated with U > 1.05 pu.
The highest reductions in U occur for penetration levels between 10% and 30%. However, above the penetration level of 30%, the integration of new PV systems tended to increase U . Above 30%, the increase in the penetration levels resulted in a more intense increase in U > 1.05 pu than the decrease observed in U < 0.92 pu. It is possible to conclude that the magnitudes of the voltages tended to increase with the rise in the number of consumer units that receive PV systems. Fig. 5 exhibits the U boxplot graph by penetration level considering all feeders under assessment. The central mark indicates the median, and the bottom and top edges of the box express the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points which do not include the outliers. The outliers are plotted individually using the '' • '' symbol.
From Fig. 5, it can be noticed that the integration of PVDG for penetration levels up to 30% did not significantly change voltages outside the limits established as suitable. However, for penetration levels greater than 30%, for some feeders there was a reduction in the average of the voltages outside the limits established as suitable, while for others there was an increase. This occurred because, prior to the integration of PVDG, some buses were operating with voltages below 0.92 pu while others were not. Therefore, it can be concluded that, for penetration levels greater than 30%, it is not enough to only correct the nominal voltage at the substation because some feeders would benefit, while others would be negatively affected. This can imply additional costs for the utility. These discrepancies are related to the characteristics of the feeders such as topology, size, type of consumer unit, number of bars, among other aspects.
Also, in Fig. 5, there are outliers for all penetration levels. For pen 20 and 30%, approximately 4% of feeders had unusual values. Therefore, these feeders need to be studied separately regarding voltage levels, and their results must not be generalized. Fig. 6 presents the average of the U in relation to the penetration levels, considering feeders in residential, commercial/industrial, and rural areas. Most of the feeders are mixed, i.e., there are residential, commercial/industrial, and rural consumer units in the same power system. But, for example, a feeder was classified as residential if over 60% of its consumers were residential and had lower percentages of other load profile. The same rationale was used to define the feeders that were classified as commercial/industrial or rural.
In Fig. 6 it is possible to observe that for penetration levels of up to 10%, the integration of PVDG did not significantly change the U . For penetration levels greater than 10%, feeders in rural areas had negative U , i.e., the voltage levels improved as PVDG was inserted into the grid. This occurs because these feeders are generally longer and, consequently, the voltages in many buses were below 0.92 pu. For penetration levels higher than 20% in feeders in residential and commercial/industrial areas, PV generation increases voltages in the grid, and thus the amount of voltage outside the limits rises. Fig. 7 shows the histograms for the number of feeders for each U range in relation to the penetration levels, considering all the simulated feeders. It should be emphasized that a negative U represents a decrease in the average of the voltages outside the suitable limits.  In Fig. 7 it can be verified that PVDG integration improved voltage for, approximately, 75% of the feeders for penetration levels below 6%. For penetration levels of up to 20%, nearly 60% of feeders presented decreases in the out-of-range voltages. For penetration levels greater than 30%, there were more positive U values than negative ones, i.e., PVDG integration degraded voltage levels in most feeders. This occurred because most consumer units in this utility are residential. Fig. 8 presents the L boxplot graph considering all the feeders of the utility under analysis. Fig. 8 shows that PVDG integration reduced losses in certain feeders for all penetration levels under assessment. However, it is also possible to observe in Fig. 8 that, for higher penetration levels, there are feeders that exhibit a reduction in losses and others in which an increase is noted. An important observation is that there are no outliers up to the 50% penetration level. In other words, in the case of technical losses, there are no feeders with unusual values, and therefore the results found in this case study may be generalized for the entire utility. VOLUME 8, 2020   As shown in Fig. 9, feeders in rural areas presented technical loss reductions for all levels of PVDG integration. The same behavior was verified for feeders in commercial/industrial areas, except for penetration levels higher than 75%. In residential feeders, an increase in technical losses was observed for penetration levels greater than 50%. It is worth mentioning that for this type of feeder, PV generation and consumption may probably take place at different moments in time. Fig. 10 presents the histograms of the number of feeders for each L range according to the penetration level.
In Fig. 10 it may be verified that up to the penetration level of 6%, more than 90% of feeders presented a decrease in technical losses. At the 20, 30 and 50% penetration levels, many feeders displayed loss reductions at significant percentages. It should also be noted that, even at high penetration levels (70 and 100%), some feeders presented a decrease in losses because of PVDG integration. This occurred because 6.8% of feeders are rural. As shown in Fig. 9, this kind of  feeder presented lower losses as PVDG integration levels increased. Fig. 11 shows the average for D h obtained considering all the feeders of the utility under analysis.
In Fig. 11 it can be seen that penetration levels above 70% reversed the power flow between 10:00 a.m. and 2:00 p.m. The higher the penetration level, the greater the possibility of an increase in the peak demand of the feeders. This is because according to utility planning, the power available for the loads considers a coincidence factor of demands that is different from the coincidence factor of the installed PV generation. In fact, PV generation is related to the solar irradiance curve, which can affect every solar panel in a certain neighborhood, while demand regards the consumption habits of different consumers. Fig. 12 shows the D boxplot graph for all the utility feeders under analysis.
By analyzing the mean values for D in Fig. 12, it is possible to verify that up to the 50% penetration level, PVDG integration practically did not alter the peak demand. This is justified by the fact that for this utility peak demand occurs at night, i.e., when there is no solar irradiance. It should be  noted that for penetration levels above 10%, a wide variation range of D was observed (many outliers). This reveals that when PVDG is integrated, the peak demands of feeders may change in different ways. Fig. 13 presents the average of D in relation to the penetration levels, considering feeders in residential, commercial/industrial, and rural areas.
In Fig. 13, it can be seen that PVDG integration did not produce increases in the peak demand in feeders in commercial/industrial and rural areas. Feeders in residential areas presented increases in peak demand for penetration levels higher than 50%. For this kind of feeder, the probability of simultaneity occurring between PV generation and load consumption is lower. Fig. 14 presents the histograms of the number of feeders for each D range according to the penetration level, considering all utility feeders under analysis.
In Fig. 14 it can be verified that up to the 50% penetration level, most feeders exhibited a small reduction in D. However, for higher penetration levels (70 and 100%), more than 50% of feeders experienced an increase in D due to the integration of PVDG. According to Fig. 13, this increase is due to the predominance of residential units.
However, it is important to point out that with only 2% of PVDG penetration,, there was increase in the D in nearly 35% of the feeders. This means that grids may need to be expanded even for low penetration levels.

IV. CONCLUSION
In this study, we investigated the impacts of the integration of PVDG at a Brazilian utility considering a one-year simulation period, with PV system location varying based on the Monte Carlo method. Different from studies found in the literature, the behavior of the impacts on voltage levels, technical losses and peak demand arising from the integration of PVDG were analyzed, considering hundreds of feeders of a Brazilian utility. A large number of feeders were used to ensure the precision of the conclusions obtained in this study. The analysis of the impact's behavior allows, among other aspects, to identify the penetration levels at which the best benefits are derived from the integration of PVDG to the grid. Furthermore, it helps utilities plan and schedule preventive grid reinforcement measures.
From the appraisal of the results, it was possible to conclude that for up to the 20% penetration level, the integration of PVDG reduced, in over 60% of feeders, the number of voltage values outside the limits established as suitable. This is because without PVDG, several buses presented voltages below 0.92 pu. Above the 30% penetration level, PVDG increased voltages in over half of the feeders, especially between 10:00 a.m. and 3:00 p.m. (times with the highest incidence of solar irradiation). These changes in voltages may require interventions in the electric grid mainly for feeders in residential and commercial/industrial areas.
Regarding losses, our study allowed us to conclude that, in most feeders, PVDG integration reduced L. At penetration levels of up to 6%, about 90% of the feeders exhibited decreases in technical losses. For penetration levels up to 50%, significant attenuations in losses were identified for many feeders. Feeders in rural areas presented reductions in technical losses for all levels of PVDG integration. At higher penetration levels (greater than 50%), there were increases in losses in more than one-fourth of feeders in residential and commercial/industrial areas.
Through the observation of all the feeders, it was verified that the integration of PVDG did not implicate increases in VOLUME 8, 2020 peak demands at the ones located in commercial/industrial and rural areas. However, in feeders located in residential areas, for penetration levels greater than 50%, the integration of PVDG increased the peak demand. For this kind of feeder, PV generation and consumption may probably take place at different moments in time.
Based on the results obtained in the present study, it may be inferred that even for low penetration levels (2%), one-third (33.3%) of feeders presented a slight increase in peak demand, less than 1% of feeders had an increase in losses, and for approximately one-fourth (25%) of feeders the voltage levels worsened. This indicates that even for low penetration levels some grids may require reinforcement to allow PVDG integration. However, for more than 60% of feeders, PVDG integration may take place up to the 20% penetration level without significant technical impacts on voltage levels, technical losses, and peak demands.
For feeders with outliers, PVDG may be limited, for example, by way of regulation establishing penetration limits by region.
With the study of an actual distribution system, and the use of the load and PV generation data in the computational simulations of all the feeders, it was possible to identify the types of feeder that would have the most problems, and to determine when the utilities would need to carry out improvements to correct them.