Introduction

Since the beginning of the 21st century, power systems are faced with an increasing integration of distributed energy resources (DERs). In the broadest sense, DERs include generation capacities of relatively low rated power connected to the distribution network in close proximity of the end consumers.

From the perspective of end consumers, owning DERs reduces the need to purchase electricity from the grid, decreases sensitivity to electricity price fluctuations, and ultimately enhances their energy independence. In addition, using DERs based on renewable energy sources leads to significant financial savings due to minimal operation and maintenance costs throughout their entire lifespan.

From the perspective of distribution system operators (DSOs), connecting generation capacities near consumption centers in general alleviates stress on network elements, resulting in reduced total power and energy losses, as well as an improved voltage profile in the network. This also significantly delays the need for expanding and developing new network capacities, while still meeting consumer demand and maintaining reliability and power quality standards. Moreover, DERs can provide ancillary services such as voltage and frequency regulation, thereby contributing to the overall security and stability of the power system.

Despite numerous technical and socio-economic benefits, excessive DER integration presents several technical challenges due to the specific configuration and operating characteristics of distribution networks. Some of these challenges include feeder and transformer overloading, occurrence of unacceptably high voltages, flickers and voltage fluctuations, increased current and voltage harmonics, higher short-circuit currents, and negative impacts on the operation of protective devices, among others. Therefore, it is essential to determine the maximum level of installed power of DERs that can be connected to the distribution network without compromising its normal operation. This maximum level is referred to as the distribution network hosting capacity.

In this article, we conducted a hosting capacity assessment on six low-voltage distribution networks, examining the factors that limit further expansion of photoltaic-based DERs. The study focused on how the hosting capacities of these specific networks align with international DSO guidelines, particularly in managing feeder and transformer overloading, as well as overvoltage concerns. While the results offer valuable insights into how hosting capacities correspond with established rules of thumb, the intention was not to generalize these findings across all distribution networks. Instead, the goal was to evaluate the accuracy of these empirical capacities in the context of international experiences. To draw broader, more generalized conclusions, it would be necessary to perform hosting capacity assessments on a wider range of real-world networks, considering the diverse conditions and configurations that exist globally. This article serves as the first in a series aimed at exploring the complex dynamics of distributed generation and its impact on distribution networks.

International DSO Experience

DSOs often receive a large number of applications for DER integration on a daily basis. Evaluating each application through detailed studies can be time-consuming and delay the integration process. Rules of thumb allow DSOs to make quick, preliminary assessments of whether a DER can be connected, streamlining the process and reducing delays. A CIGRE C6.24 working group collected some practical rules of thumb employed by DSOs where hosting capacity is limited primarily by feeder and transformer overloading, as well as overvoltage concerns [1]:

• Belgium: The aggregate power of DER should not exceed the MV/LV transformer power rating.
• Canada: The reverse power flow must not exceed 60% of the station capacity (calculated as the sum of 60% of the maximum MVA rating of the MV/LV transformer and the minimum substation load).
• Italy: The aggregate rated power of all DER must not exceed 65% of the rated power of the MV/LV transformer.
• Portugal: The aggregate DER nominal power connected to an MV/LV transformer should not exceed 25% of the rated power of the transformer.
• South Africa: For shared LV feeders, the aggregate DER rated power connected should not exceed 25% of the rated power of the transformer. For dedicated LV feeders, the aggregate DER rated power should not exceed 75% of the rated power of the transformer.
• Spain and South Korea: The aggregate rated power of all DER connected to an MV/LV transformer must not exceed 25% of the transformer's rated power for shared LV feeders, or 50% for dedicated LV feeders.

As can be seen, the LV network hosting capacity rules of thumb vary in a wide range from 25 to 100% of the MV/LV transformer rating based on the country. In this context, it is interesting to assess how these rules of thumb estimate the hosting capacity of realistic low voltage networks.

Hosting Capacity Assessment Methodology

Extensive literature in the field offers various methods for hosting capacity assessment. These methods can be placed in one of the three categories, namely deterministic, stochastic and optimization-based methods. Since the integration of distributed generators is essentially a stochastic process in nature, a stochastic assessment approach is employed in this article. The employed assessment methodology consists of three steps:

1. In the first step, 10000 DER deployment scenarios are generated. Each scenario represents different number of DERs with different locations and different rated powers. While potential DER locations correspond to load locations in the network, their rated powers are randomly generated from the probability density function describing the occurrence frequency of different DER sizes in low-voltage networks.
2. In the second step, hourly power flow analysis throughout the entire year is performed for each scenario to evaluate whether the deployment scenario violates the normal operating limits of the distribution network. Operating limits considered in this analysis include transformer and line overloading, as well as ±10% voltage limits in the entire network, in line with the EN 50160 standard for voltage characteristics of public distribution systems.
3. In the third step, network hosting capacity is determined with respect to the selected network criteria. Two values can be identified: first and last hosting capacity. The first hosting capacity represents the lowest value of the total installed DER capacity which leads to the violation of normal operating limits for one of the deployment scenarios. On the other hand, the last hosting capacity represents the value of the total installed DER capacity after which no feasible deployment scenarios exist. The first, more conservative approach is employed in this analysis.

While this methodology can be easily adapted to other network criteria, overloading and overvoltage are recognized as the two primary hosting capacity limiting factors for low-voltage networks.

Low-Voltage Test Distribution Networks

Test networks are crucial for R&D activities in the field of power systems because they provide a safe and controlled environment to study and simulate grid behavior, plan future expansions, and develop new technologies. While most available test networks focus on high and medium-voltage levels, there are significantly fewer resources for low-voltage networks. In our opinion, one of the best low-voltage test network datasets is provided by the SimBench project [2]. SimBench offers a comprehensive approach to creating realistic and representative low-voltage network models that reflect the diverse characteristics of German distribution grids.

The methodology employed by SimBench involves a data-driven approach using clustering techniques, specifically the k-means algorithm, to group similar supply tasks based on publicly available demographic and geographical data. This clustering process ensures that the generated models accurately represent the variety of conditions found in real-world low-voltage grids. Under this methodology, six distinct low-voltage test networks were generated, each designed to reflect different types of supply environments:

1. Urban (U) Network: High-density areas with compact grids, typical of city centers. Rated MV/LV transformer capacity is 630 kVA.
2. Semi-Urban 1 (SU1) Network: Moderately dense areas with intermediate levels of urban infrastructure. Rated MV/LV transformer capacity is 630 kVA.
3. Semi-Urban 2 (SU2) Network: Suburban areas with lower population density and more dispersed infrastructure. Rated MV/LV transformer capacity is 400 kVA.
4. Rural 1 (R1) Network: Sparsely populated rural areas with small municipal areas. Rated MV/LV transformer capacity is 400 kVA.
5. Rural 2 (R2) Network: Rural areas with larger municipal spaces, indicating a more spread-out population. Rated MV/LV transformer capacity is 250 kVA.
6. Rural 3 (R3) Network: The most rural settings, with vast areas and very low population densities, requiring extensive grid coverage. Rated MV/LV transformer capacity is 160 kVA.

It is important to note that while these test networks are representative of German DSOs, they also encompass a wide range of scenarios and operating conditions typical to European design standards.

Hosting Capacity Assessment Results

The stochastic hosting capacity assessment methodology has been applied to each of the six low-voltage test networks detailed in the previous section. Before presenting the specific values of the hosting capacities, detailed assessment results are presented in the case of an urban network below. Maximum MV/LV transformer and feeder loading, as well as maximum bus voltages have been presented for each PV deployment scenario. Feeder and transformer loading, as well as maximum bus voltages increase with the total installed PV capacity. However, the first constraint being violated concerns the allowed feeder loading. Thus, the limiting factor for the further increase of the installed PV capacity in the case of the studied urban network is feeder overloading. The MV/LV transformer is overloaded at a much higher installed capacity. On the other hand, bus voltages remain within the 90-110% limits for each of the simulated PV deployment scenarios.

Specific hosting capacity values along with their limiting factors for each network are given in the table below.

Network	Hosting capacity [% of MV/LV transformer rating]	Limiting factor
U	76.39	Feeder overloading
SU1	64.26	Feeder overloading
SU2	64.15	Feeder overloading
R1	115.96	Transformer overloading
R2	115.28	Transformer overloading
R3	110.31	Transformer overloading

Urban and suburban networks are characterized by high population density, compact infrastructure, and short feeder lines. The high density of loads and relatively short distances mean that feeder lines are quickly loaded as more PVs are integrated. As such, feeder overloading is the primary limiting factor in these networks, with hosting capacities in a relatively small range between 64.15% and 76.39% of the MV/LV transformer rating.

On the other hand, rural networks supply areas with low population density, where feeders are generally long and less densely loaded. As a consequence, transformer overloading occurs much sooner than the overloading of feeder lines. The hosting capacities of the three rural networks range between 110.31% and 115.96% of the MV/LV transformer rating. In particular, the hosting capacity can be approximated as a sum of the transformer rating and the minimum network load during peak PV generation hours.

Previous analysis has been performed under the assumption that substation voltage can be held at its nominal value by means of an on-load tap-changer. However, in practice, most MV/LV transformers don’t have on-load tap-changing capabilities. As such, the substation voltage can vary significantly. Repeating the previous analysis with substation voltage at 105% during the critical hours yields the results given in the table below.

Network	Hosting capacity [% of MV/LV transformer rating]	Limiting factor
U	64.26	Overvoltage
SU1	81.15	Feeder overloading
SU2	77.37	Feeder overloading
R1	28.94	Overvoltage
R2	58.72	Overvoltage
R3	115.22	Transformer overloading

In the critical scenario, overvoltage becomes the main limiting factor for the further integration of PVs in urban networks. Feeder overloading is still a concern; however, reverse power flows due to extensive PV integration in densely populated areas lead to unacceptable voltages faster than they lead to feeder overloading. This is not the case with suburban networks, where the increased substation voltage led to an increase in the hosting capacity due to a decrease in power losses and line currents.

Rural networks R1 and R2 supply sparsely populated areas with small municipalities. Extensive PV integration in these municipalities, which are supplied over long overhead distribution lines, leads to a significant voltage rise close to the end customers, which limits further PV integration. In the case of both networks, the hosting capacity is significantly reduced compared to the baseline scenario. On the other hand, in the case of the rural network R3, the hosting capacity limiting factor remains transformer overloading. The reason for the deviation from the other two rural networks is that the feeder branches supply just several individual customers or smaller municipalities, so extensive PV integration close to the end consumers doesn’t lead to a significant voltage rise. As such, transformer overloading remains the primary limiting factor.

Conclusions

In conclusion, the integration of distributed energy resources (DERs) into low-voltage networks requires careful consideration of various factors to ensure reliable operation. The hosting capacity assessment across different network types highlights the importance of context-specific strategies, and these findings can be directly related to the international DSO experiences discussed earlier.

If the substation voltage can be controlled effectively, Italy's rule of thumb, which limits the aggregate rated power of all DERs to 65% of the MV/LV transformer rating, is well-suited for urban and suburban networks where feeder overloading is the primary limiting factor. In these networks, the presented results show hosting capacities ranging from 64.15% to 76.39% of the transformer rating, aligning closely with Italy's guidelines. However, in rural networks, where transformer overloading is the main concern, the results correspond more closely with Belgium's rule of thumb, which allows the aggregate power of DERs to match the MV/LV transformer rating. The hosting capacities in rural networks, ranging from 110.31% to 115.96%, support this approach.

Varying substation voltage during critical hours can significantly impact the PV hosting capacity, particularly in terms of overvoltage risks. In urban and relatively rural areas where overvoltage becomes the primary concern, the hosting capacity estimations employed by Spain's and Portugal's DSOs, which limit DER integration to 25-50% of the transformer's rated power, seem reasonable. The presented results show a significant reduction in hosting capacity in these areas when substation voltage is not maintained at nominal levels. On the other hand, for suburban networks, Italy's DSO recommendations, which allow up to 65% of the transformer rating, remain the most accurate. In extremely rural networks, where transformer overloading remains the main limiting factor even with varying substation voltage, Belgium's rule of thumb, which matches the transformer rating with the DER capacity, proves to be the best fit.

These conclusions highlight how the hosting capacities obtained from the six test networks align with international DSO experiences, but it’s important to clarify that the intention was not to generalize these results across all distribution networks. Instead, the focus was to evaluate how well the hosting capacities derived from this study correspond with the established rules of thumb used by various DSOs globally. To draw broader, more general conclusions, hosting capacity assessments would need to be conducted on a much wider range of real-world networks, reflecting diverse conditions and configurations. Only through such comprehensive studies can we develop more universally applicable guidelines for integrating DERs into low-voltage networks while ensuring reliable operation.

References

1. S. Papathanassiou, N. Hatziargyriou, P. Anagnostopoulos, L. Aleixo, B. Buchholz, C. Carter-Brown, et al., Capacity of Distribution Feeders for Hosting DER, vol. 24, 2014. Working Group C6.
2. S. Meinecke et al., ‘SimBench—A Benchmark Dataset of Electric Power Systems to Compare Innovative Solutions Based on Power Flow Analysis’, Energies, vol. 13, no. 12, 2020.