About 15 000-customers are connected to the individual secondary distribution networks supplied through 48-medium voltage 10 kV radial feeders. The hosting capacity assessment uses the end-customer voltage magnitude rise and transformer thermal overload. The hosting capacity is estimated by applying the “stochastic mixed aleatory-epistemic method” to determine the voltage magnitude rise and load flow with solar PV. The minimum power consumption is compared with the solar PV power infeed through the individual transformers. The hosting capacity estimation is done for three-phase connected solar PV sizes from 3 to 18 kW. At moderate PV penetration (25%–50%), the results showed that overvoltage would limit the hosting capacity more often than overload, but it becomes an issue only for LV networks studied with more than 8-customers. Considering all LV networks, most of the customers could install 6 kWp. Even when installing PV systems of 18 kWp (about twice the average size today and about the maximum area of a typical residential roof), two-thirds of houses would not need an upgrade to withstand SS-EN 50160 voltage limits. The latter customers can connect solar PV units with 18 kWp size without overvoltage or overload issues.

This paper proposes a deterministic and stochastic approach to quantify the hosting capacity that is often limited by the loadability limit of the cable cabinet or transformers due to customers with solar photovoltaics (PV) units. Distribution networks from two areas in Sweden supplying 309 MV/LV distribution transformers with 12,000 customers downstream have been studied. Using a deterministic model, a method is proposed and applied to assess the cable overvoltage against the loadability while considering the voltage rise margin. In addition, measurements have been applied to the methods and the loadability limits assessed. Illustrations for the concepts and important results for the guide to DSOs decision-making guide has been obtained. It is shown in the paper the hosting capacity anticipated at the end of a distribution network cable with a particular size is determined more often by the loadability at larger voltage rise margin and by overvoltage at smaller voltage rise margins. The results obtained for the data used show that the overload limit is exceeded more often for transformers than for cable supplying the cable cabinets at smaller solar PV sizes. For larger solar PV sizes, the feeder cable loadability limit is likely to be exceeded first before that of the transformers. The stochastic approach applied to the yields a small probability to exceed the hosting capacity and depend on the two epistemic uncertainties.

This paper presents a stochastic approach to single-phase and three-phase EV charge hosting capacity for distribution networks. The method includes the two types of uncertainties, aleatory and epistemic, and is developed from an equivalent method that was applied to solar PV hosting capacity estimation. The method is applied to two existing low-voltage networks in Northern Sweden, with six and 83 customers. The lowest background voltage and highest consumption per customer are obtained from measurements. It is shown that both have a big impact on the hosting capacity. The hosting capacity also depends strongly on the charging size, within the range of charging size expected in the near future. The large range in hosting capacity found from this study—between 0% and 100% of customers can simultaneously charge their EV car—means that such hosting capacity studies are needed for each individual distribution network. The highest hosting capacity for the illustrative distribution networks was obtained for the 3.7 kW single-phase and 11 kW three-phase EV charging power. 

Solar photovoltaics in electricity distribution networks is often limited by the rise in voltage magnitude. The pre-connection voltage magnitude is an important factor that determines the hosting capacity.

This paper studies to which extent details of the pre-connection voltage magnitude impact the hosting capacity. Extensive measurements of voltage magnitude and solar power production were obtained for a number of distribution networks with 10-minute resolution. The measured background voltage during the sunny-hours from the two-year measurements was used to obtain representative probability distribution functions. A guide for selecting the time-of-day (ToD) used is presented.

The obtained probability distribution functions are applied to estimate the stochastic hosting capacity for a low-voltage distribution network with 83 customers. The impact of various details on the hosting capacity are studied.

The results show that general knowledge about the range of the pre-connection voltage are essential for the hosting capacity estimation. Measurements over one year were shown to be sufficient to estimate the hosting capacity. The hosting capacity considering the entire day was underestimated by 11 % when compared to the 10 am – 2 pm sunny-hours. The proposed method is general and can be applied to other aleatory uncertainties and other types of hosting capacity studies.

This paper applies a deterministic and stochastic approach to estimate the hosting capacity and likelihood of an overload at the cable cabinet or transformer due customers with solar PV. Distribution networks at 10 kV, suppling feeders with 1300 MV/LV transformers, have been studied. The paper also quantifies whether overvoltage or overload limits the hosting capacity first. Voltage and current measurements from a Northern Sweden distribution network have been applied in the paper. Illustrations are used to show the concept and important results are obtained. It is shown in the paper the hosting capacity is determined more often by overload than by overvoltage. In this paper, only the hosting capacity with reference to the overload limit is considered. The results obtained for the data used show that the overload limit is exceeded more often for transformers than for cable cabinets. The stochastic approach applied to the cable cabinets yields a small probability to exceed the hosting capacity.

This paper proposes a stochastic method, ''mixed aleatory-epistemic“, for estimating solar PV hosting capacity (HC) of low-voltage (LV) distribution networks. The approach treats the aleatory and epistemic uncertainties in a different way. The HC is estimated by applying the transfer impedance matrix, 'which is only calculated once', and the superposition principle to determine the voltage magnitude rise due to solar PV. By distinguishing between aleatory and epistemic uncertainties, the calculations are limited to the relevant hours (time-of-day or time-of-year) during which high solar PV production is expected. In this way, the random aleatory uncertainties (background voltage, solar PV production, local consumption) are modelled by their probability distributions during the selected time period. The distributions for the epistemic uncertainties (installed capacity per customer, number of customers with solar PV, phase to which single-phase units are connected) are created with simple models involving the interval value and possible occurrence. The stochastic approach proposed is applied to three LV distribution networks to illustrate the method. The results show that both types of uncertainties affect the HC. The need for distribution network planners to identify and distinguish between the types of uncertainties is emphasised.

A literature review is presented in this paper of the methods for quantifying the solar PV hosting capacity of low-voltage distribution grids. Three fundamentally different methods are considered: i) deterministic ii) stochastic iii) time series. The methods’ outline of applications, merits and shortfalls are summarized. The methods differ in the input data, accuracy, accuracy, computation time, consideration of uncertainties, consideration of the time-related influence and the models used. Two types of uncertainties need to be considered: certain (aleatory) uncertainties and uncertain (epistemic) uncertainties. The latter ones are only included in some of the stochastic methods.

In most of the reviewed publications, the voltage magnitude rise and increased loading with increased risk of overvoltage and overloading (for lines, cables and transformers) were the main phenomena considered in the hosting capacity study.

This review offers guidelines for distribution system planners on which hosting-capacity method to be used and to researchers on research gaps.

The rapid expansion of photovoltaic (PV) systems has raised voltage concerns. This paper investigates voltage variations measured at four hundred on-line PV installations in Sweden. Small (<10 kW inverter size) three phase residential PV systems had the least impact whereas single phase systems had the most impact for the same amount of power injected per phase. PV systems were grouped based on post code location into urban and rural areas. Urban areas were found to be more resilient to PV induced  voltage fluctuations with a narrower back-ground voltage band in comparison to rural areas, indicating that PV inverter measurements can be an efficient method to empirically determine grid strength.

This paper presents the overvoltage caused by single and three-phase connected PV to a low-voltage distribution grid. Statistics are obtained based on source-impedance data for 40 000 customers. A stochastic approach is applied to a 28-customer low-voltage network and the probability of overvoltage is assessed. It is shown that the voltage rise due to single-phase connected PV is six times the rise for three-phase connected PV.To mitigate the overvoltage, grid-reinforcement, reactive power compensation, curtailment and coordinated connection of PV can be used. It is shown that reactive compensation is not effective in LV grids due to high R/X ratio. Coordinated connection helps in reducing the overvoltages caused by single-phase PV.Policy suggestions towards three-phase PV installations and coordinated single-phase PV connections are included in the paper.

This paper introduces the terms aleatory and epistemic uncertainties for use in a stochastic hosting capacity method. The role these uncertainties play in the hosting capacity determination is illustrated. It is shown that distinction between aleatory (statistical) and epistemic (systematic) uncertainties is helpful to characterize the probability distributions correctly. For epistemic uncertainties, it is often challenging to obtain information on the probability distribution function. For aleatory uncertainties, a method for characterizing the probability distribution is presented. Aleatory uncertainties’ data measurements are used to obtain a distribution best-fit. The background voltage measurement for a customer in a low-voltage distribution network is used to illustrate the method. Values were obtained for the distribution functions of the three-phase voltages. The used distribution functions are found to influence the resulting hosting capacity. This entails that there is need for measurements and data collection. A research challenge remaining concerns the stochastic model of epistemic uncertainty.