Applied Energy 371 (2024) 123715

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Applied Energy
journal homepage: www.elsevier.com/locate/apenergy

A city-level assessment of residential PV hosting capacity for low-voltage
distribution systems considering rooftop data and uncertainties
Umar Hanif Ramadhani ∗, Fatemeh Johari, Oskar Lindberg, Joakim Munkhammar,
Joakim Widén
Division of Civil Engineering and Built Environment, Department of Civil and Industrial Engineering, Uppsala University, Uppsala, 75237, Sweden

ARTICLEINFO

Keywords:
PV hosting capacity
Low voltage system
Rooftop solar photovoltaic
Uncertainty modeling

ABSTRACTThe increasing trend of small-scale residential photovoltaic (PV) system installation in low-voltage (LV)
distribution networks poses challenges for power grids. To quantify these impacts, hosting capacity has become
a popular framework for analysis. However, previous studies have mostly focused on small-scale or test
feeders and overlooked uncertainties related to rooftop azimuth and tilt. This paper presents a comprehensive
evaluation of city-level PV hosting capacity using data from over 300 real LV systems in Varberg, Sweden. A
previously developed rooftop azimuth and tilt model is also applied and evaluated. The findings indicate thatthe distribution systems of the city, with a definition of PV penetration as the percentage of houses with 12
kW installed PV systems, can accommodate up to 90% PV penetration with less than 1% risk of overvoltage,and line loading is not a limiting factor. The roof facet orientation modeling proves to be suitable for city-levelapplications due to its simplicity and effectiveness. Sensitivity studies reveal that PV system size assumptions
significantly influence hosting capacity analysis. The study provides valuable insights for planning strategies
to increase PV penetration in residential buildings and offers technical input for regulators and grid operators
to facilitate and manage residential PV systems.

1. Introduction
Due to the urgency of mitigating climate change, there has been agrowing trend towards decentralized electricity generation at a small
scale within electricity distribution systems, allowing more active participation of end-users by installing power generators in their own
buildings [1]. Before 2020, residential photovoltaic (PV) system installations were increasing around the world, with a peak of morethan 16 GW of new installations in 2019 [2]. This development raises
some challenges in power grids, such as potential overvoltage andoverloading, particularly in low-voltage (LV) distribution systems [3,4].
Therefore, many studies have aimed to investigate the impacts ofintegrating PV systems in the distribution grid with varying focuses,
such as power quality [5], the impacts of several new large loads [6],probabilistic approaches [7–10], large scale assessments [11,12], andthe combination with energy management [13].
One of the key methods to quantify the impacts of PV systems on
low-voltage networks is through the so-called hosting capacity. It isa transparent framework for analysis that determines the maximum
amount of PV power generation that can be installed in a specific grid
while maintaining the operational quality of the system [14,15]. In
general, PV hosting capacity analysis requires the declaration of threeparameters: the phenomenon (e.g., over-voltage, line loading, losses),
the performance indices for the chosen phenomenon (e.g., 99% valuesof the 15-min RMS values), and the limit (e.g., 1.05 of nominal voltage).
PV hosting capacity analysis, however, has high uncertainties fromboth aleatory and epistemic uncertainty sources [16]. The tilt andazimuth of PV panels are among the most significant uncertainties in
PV system performance [17]. This is because the direct, diffuse, andreflected solar radiation components hit the surface of the panels at
different angles, depending on these two angles and on the location,
time of day, and time of year [18]. The importance of tilt and azimuth uncertainties was discussed in [19] and the significance of using
accurate rooftop data was demonstrated in [10,17].
While many studies have investigated the PV hosting capacity in
low-voltage networks, there are some important features that havenot been well-studied before. First, the majority of hosting capacity
analyses in LV networks were conducted at a small-scale level, andsome of these studies were carried out using test feeders rather than real
grids. Some exceptions include [11], which investigated the hosting
capacity for 50,000 real low-voltage networks in Brazil, and [12] which
performed such analysis for 338 low-voltage networks in the Swedishmunicipality of Herrljunga.

∗ Corresponding author.

E-mail address: uhanifr@gmail.com (U.H. Ramadhani).
https://doi.org/10.1016/j.apenergy.2024.123715
Received 17 February 2024; Received in revised form 17 May 2024; Accepted 12 June 2024
Available online 24 June 20240306-2619/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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Table 1
Characteristics of the 334 LV systems used in this study.

Second, existing studies have rarely employed real rooftop azimuth
and tilt data. Refs. [10,17] are among the studies that utilized realrooftop data for small-scale low-voltage networks. Ref. [17] also proposed a method to model a set of azimuths and tilts for multiple houses
when such data is unavailable. The method, however, has not beentested, and, importantly, has not been compared to real data in largescale LV network simulations. Third, although the method has wide
applicability, a hosting capacity study is valid only for specific grids
and for specific assumptions. Hence, an investigation with a specificlocation that has never before been studied is valuable as it adds to theaccumulated knowledge on hosting capacity in different types of grids
and locations.
Considering the aforementioned needs, a comprehensive study oncity-level PV hosting capacity considering real rooftop data at a specificlocation is required. The previously proposed method to model rooftop
azimuth and tilt uncertainties in [17] would benefit from validationand comparison to real rooftop data in a city-level hosting capacity
assessment. Additionally, the impact of specific assumptions on hosting
capacity would be valuable to evaluate
In this paper, therefore, a comprehensive evaluation of city-level PV
hosting capacity is investigated for more than 300 real LV systems in
the Swedish city of Varberg. This study utilizes an extensive data set ofrooftops model for around 37,000 buildings and historical load profiles
for around 11,800 end-customers. The hosting capacity analyses were
performed using time-series analyses for one year with a resolution of
one hour. Voltage profiles and line loading are evaluated as the chosen
phenomena. Furthermore, the previously developed rooftop azimuth
and tilt model in [17] is utilized to further validate its effectiveness bycomparing the power flow simulation results from solar irradiance profiles using the proposed method in [17] to results from solar irradianceprofiles based on LiDAR-based rooftop data.
The contributions and merits of this work can be summarized asfollows:

Parameter

AverageStandard deviation

10th and 90th percentile

Number of customers
Circuit total length (km)Average X/R ratio

36.46
3.02
0.21

40.47
2.31
0.16

3–90.6
0.57–6.29
0.09–0.37

capacity within the grid, as described in Section 3.2. Then, the resultsof this investigation were compared with two alternative methods
for representing rooftop azimuth and tilt. The first approach involves
the use of a rooftop azimuth and tilt model proposed in [17]. Thismodel enables the inclusion of rooftop azimuth and tilt uncertainties
even without explicit azimuth and tilt data, although it requires more
validation and comparison with real rooftop data in a city-level hosting
capacity assessment. The second method is based on the common
assumption that roof facet orientations are uniformly optimal. Moredetailed information on these models are provided in Section 4.2.1.
Tilted solar irradiance profiles are subsequently utilized as the
input for the power flow simulation step, along with PV array sizes
values, to generate the PV generation profiles. PV array size are varied
for sensitivity analysis purposes. The procedure for producing the PV
power generation profiles is detailed in Section 4.2.3. These PV power
generation profiles, together with grid data detailed in Section 3.1
and building load data (explained in Section 3.3 and Section 4.3), areemployed in power flow simulations to generate the simulation results.
3. Data
3.1. Grid data
The distribution grid for this study consists of four three-phase
MV (10 kV) and 334 three-phase LV (400 V) networks with 11,602
customer connection points. The grid is located in the Swedish city ofVarberg. The geographical dispersion of all 334 LV networks is shownin Fig. 2. The power grid covers both a rural area and small urban areas.
The distribution grid is connected to the transmission grid throughfour HV/MV substations. These substations have on-load tap changers
for voltage control and the values are kept constant for the MV side
voltages of the substations throughout the year and are not used forvoltage control for end-users. The MV/LV transformers, however, do
not have on-load tap changers.
General information about the LV systems is given in Table 1.
From the table one can observe that even though the LV systems arelocated in the same municipality, the characteristics of the systems
are widely diverse. This can be seen from the large standard deviationand the wide range between the 10th and 90th percentile for all threeparameters.

• Application of a comprehensive time-series hosting capacity
method utilizing actual city-level grid data, supported with realmeasurement data of power consumption and complemented witha power consumption model to address missing data.
• Inclusion of residential building rooftop tilt and azimuth values
for the entire city to improve the PV generation model.
• Consideration of roof facet conditions to determine the PV allocation for multiple penetration levels.
• Application and evaluation of a previously developed rooftop
azimuth and tilt model in [17], to further validate its effectivenessin large-scale LV network simulations.
This paper is organized as follows. Section 2 describes the overview
of this paper. Section 3 presents the data used in this study. In Section 4
the models and methods utilized are described. The results are presented in Section 5 and discussed in Section 6. Conclusions are drawn
in Section 7.

3.2. Rooftop data

2. Overview of the paper
This paper examines the potential impacts of residential rooftop PV
systems across the city of Varberg, Sweden, utilizing a LiDAR-based
rooftop facet dataset covering the entire city. The dataset includes
nearly 90,000 roof facets from approximately 37,000 buildings. The
number of roof facets exceeds the number of buildings due to the factthat many buildings have multiple roof facets. Among these buildings,
11,800 are categorized as residential buildings.
The LiDAR-based data used in this study were acquired using apreviously developed model described in Lingfors et al. [20] and validated in Lingfors et al. [21]. The general overview of this method areshown in Fig. 3. This method has been previously applied to anotherSwedish city, Uppsala, and has been utilized in various studies [17,22].
Interested readers are referred to [20] for further explanation of thismethod.

A schematic overview of the data and methodology employed inthis paper is illustrated in Fig. 1. The process can be divided into
two main steps: the solar irradiance model step and the power flow
simulation step. The solar irradiance model step aims to model solar
irradiance profiles on the tilted roofs using three distinct methods fordetermining the rooftop azimuth and tilt. Meanwhile, the power flow
simulation process generates the power flow simulation results for eachsolar irradiance profile.
For the solar irradiance model step, the required inputs include
rooftop azimuth and tilt values and horizontal solar irradiance profiles.
Three different sets of rooftop azimuth and tilt data and models were
utilized for comparison. Initially, the rooftop azimuth and tilt values
were derived from LiDAR-based data to calculate the actual hosting2

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U.H. Ramadhani et al.

Fig. 1. Schematic overview of the paper.

Fig. 2. Geographical dispersion of low voltage substations in Varberg used in the load flow simulations.

Fig. 3. Overview of method used to produce LiDAR-based rooftop data from [20].

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U.H. Ramadhani et al.
Table 2
Flat roof proportion at ten penetration levels.

The inputs to the model consist of low-resolution LiDAR data (0.5–1
pts/m2 ), with solar irradiance on the roof surfaces calculated using the
Hay and Davies transposition model [23]. Orientation and shading considerations were taken into account to determine the potential numberof PV modules that can be installed on each rooftop, specifically where
the annual irradiation exceeds 900 kWh/m2 , making PV installations
economically viable in a Swedish context [24].
The LiDAR-based rooftop data used in this study contain the following information:• Building coordinates.
• Azimuth of every roof facet.
• Tilt angle of every roof facet.
• Number of PV modules that can be fit with an annual irradiationof at least 900 kWh/m2 .

Penetration level

Proportion of flat roofs

10%
20%
30%
40%
50%
60%
70%
80%
90%
100%

0%
0%
0%
0%
16.27%
17.90%
15.34%
13.43%
11.93%
10.74%• Time-series duration and resolution. The duration is set to one year,with a one-hour resolution, for the year 2021. This choice ismotivated by the resolution of the available load consumption
data.
• Simulation tools. The grid simulations were performed using a
Python-based pandapower, an open-source tool specializing in
automated symmetric distribution system analysis [26]. This tool
is well-suited for the selected electricity distribution systems,
which include typical Swedish distribution grids featuring threephase power distribution all the way to the customer connection
points.

3.3. Load data
The electricity load data is based on real measurements spanning
the years 2020 through 2021. For most buildings, the data for the year
2021 is complete and used as is. When there are missing data points for
2021, they are filled by referring to the corresponding measurementsfrom 2020, matching the date and hour. If this is not sufficient to cover
the entire year, the electricity load models for the buildings, explainedin Section 4.3, are utilized to create simulated load and complete thedata.
4. Methods

4.2. PV system model and uncertainties

4.1. Hosting capacity analysis assessment

4.2.1. Rooftop azimuth and tilt
In this study, the rooftop azimuth and tilt values from LiDAR are
initially employed to determine the actual hosting capacity within thegrid. Then, the results of this investigation are compared with two othermethods for representing rooftop azimuth and tilt. The first approach
involves modeling rooftop azimuth and tilt using the method proposedin [17]. The second method compares the results with the commonlyused assumption that the roof facet orientations are assumed to beuniform and optimal.
The proposed method in [17] involves three simple steps, outlined
below:

As outlined in Section 1, the hosting capacity assessment involves
three main components: selecting the phenomenon, defining the performance indices, and establishing the limits. For this study, the following
elements have been chosen:• Bus voltages. Voltage profiles must conform to the following criteria: the voltage should be below 1.1 per unit (pu) for all values,
excluding only the lowest and highest 1% of values. In thiscontext, we refer to voltage profile as the phenomenon, with theindices denoting the 99% of values from the one-hour-resolution
simulations, and the limit is set at 1.1 pu.
• Line loading. Line loading must consistently remain below capacity limits at all times and in all locations. Here, the phenomenon
is the line loading, with 100% of values as indices, and the limit
is 100% line loading capacity.

1. Determine the proportion of flat roof buildings. Begin by determining the number of buildings with flat roofs at each penetrationlevel.
2. Generate azimuth and tilt distributions. Utilize the proposed equations to get the distributions of rooftop azimuth and tilt for eachpenetration level.
3. Sample non-flat roof buildings. Sample from the derived distributions to assign rooftop azimuth and tilt values to the remaining
non-flat roof buildings.

After selecting the hosting capacity parameters, several configurations are required to conduct the load flow simulations for each caseand penetration level as follows:• Penetration levels. The penetration levels range from 0% to 90%,
with an increase of 15%. The penetration level represents the percentage of houses equipped with PV systems. Note that the penetration level here is the penetration level of residential buildings,
which accounted for only 26% of all buildings.
• PV system size. Each PV system is assumed to have a rated capacityof 12 kW, based on a survey conducted in 2020 in Sweden,
which indicates that 55% of grid-connected PV systems installedon single-family buildings have a rated capacity between 10 and
20 kW, and 45% have a rated capacity between 5 and 10 kW [25].
Lower and higher values of 6 and 18 kW will be used later in asensitivity analysis.
• PV allocation. The PV allocation is based on rooftop data, assuming a building with a more suitable roof facet will have a
PV system installed earlier. The same allocation is used also forboth the case with the proposed azimuth and tilt model and theuniformly optimum roofs.

By using these three steps, the proposed method characterizes therooftop azimuth and tilt for a diverse range of buildings in the areaof interest. This approach ensures a better representation of building
types, thus enhancing the accuracy of the overall analysis.
For the first step, the proportion of flat roofs for each penetrationlevel is obtained from a reference study [17]. The specific proportions
are listed in Table 2. However, since the penetration levels consideredin this study differ slightly from those in the reference, we interpolate
the proportions for the penetration levels at 45% and 75%. The proportion for the 45% penetration level is chosen as the average between
the proportions at 40% and 50%, and similarly, the proportion for the
75% penetration level is taken as the average between the proportions
at 70% and 80%.
Then, for the second step, the azimuth and tilt distributions are
obtained from [17] and are modeled as follows.
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Fig. 4. Overview of the methodology used for replacing missing loads with simulated.

Random variables describing the roof azimuth and tilt for penetration level x can be expressed by:
𝐾𝑎𝑧𝑖𝑚𝑢𝑡ℎ = 𝐾1 𝑆 + 𝐾2 (1 − 𝑆),

4.2.2. Solar irradiance model
In this study, solar irradiance data for the Swedish city of Varberg
was produced from the STRÅNG [27] model for the year 2021 withlatitude 57.10◦ N and longitude 12.25◦ E. The STRÅNG model produces
irradiance data at hourly intervals covering most of Sweden with aresolution of 2.5 × 2.5 km [27]. The dataset provided includes solar
irradiance values for the entire year, covering the annual seasonality
and corresponding with the power consumption measurement data.
To get the in-plane irradiance, the solar irradiance data from theSTRÅNG model was processed using an irradiance model implemented
with the pvlib.irradiance.get_total_irradiance function
from pvlib python library, developed by Sandia National Laboratories
using the Hay and Davies method [28–30]. In the Hay and Davies
model, the diffuse radiation on the tilted plane 𝐼𝑑 𝑇 is calculated
as:
(
(
))
1 + cos 𝛽
𝐼𝑑 𝑇 = 𝐼𝑑 𝐴𝑅𝑏 + (1 − 𝐴)
(10)
2

(1)

for azimuth, and𝐾𝑡𝑖𝑙𝑡 = 𝐾3 𝑆 + 𝐾4 (1 − 𝑆),(2)

for tilt, where 𝐾1 and 𝐾3 are random variables for non-flat roof azimuth
and tilt, respectively, while 𝐾2 and 𝐾4 are random variables for flat roof
azimuth and tilt, respectively. S is a random variable that is either one(flat roof) or zero (tilted roof). Therefore, S has a Bernoulli distribution:
𝑆 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(𝑓 ),(3)where 𝑓 is the proportion of flat roofs at that penetration level.
Since the flat roof corresponds to 0◦ for both azimuth and tilt angles,
𝐾2 and 𝐾4 are degenerate distributions of zero and Eq. (1) and Eq. (2)can be simplified to:
𝐾𝑎𝑧𝑖𝑚𝑢𝑡ℎ = 𝐾1 𝑆

where 𝐼𝑑 is the diffuse radiation on the horizontal plane, 𝐴 is theanisotropic index, the ratio between the incident beam and the extraterrestrial radiation on the horizontal plane. 𝑅𝑏 is the geometric factor,
and 𝛽 is the plane’s inclination.
This function requires surface azimuth and tilt which were obtained
from the rooftop azimuth and tilt as explained in Section 4.2.1, and extraterrestrial radiation, calculated with the pvlib.irradiance.get_extra_radiation function from pvlib python library, which determines extraterrestrial radiation from day of year.

(4)

and
𝐾𝑡𝑖𝑙𝑡 = 𝐾3 𝑆.

(5)For the azimuth, the model was based on the hypothesis that roof
facets are uniformly distributed in all directions. Thus, the azimuths
at every penetration level 𝑥 are represented by the following uniform
distribution:
𝐾1 ∼ 𝑈 (−180𝑥, 180𝑥),4.2.3. PV power generation
The PV power generation model employed in this study was implemented using the pvlib.PVSystem class from the pvlib python
library developed by Sandia National Laboratories [30]. The model
represents an inverter and the PV modules that supply DC power tothe inverter based on the specified in-plane irradiance and moduleparameters. This particular model has been employed in various studies, including those conducted by Louwen et al. [31] and Holmgren
et al. [32].

(6)with minimum value of −180𝑥 and maximum value of 180𝑥.
For the tilt, a normal distribution is used. The non-flat roof tilt forevery penetration level 𝑥 will be represented by a normal distribution:
𝐾3 ∼ 𝑁(𝜇𝑡𝑖𝑙𝑡 (𝑥), (𝜎𝑡𝑖𝑙𝑡 (𝑥))2 ),(7)

with mean value 𝜇𝑡𝑖𝑙𝑡 (𝑥) and variance (𝜎𝑡𝑖𝑙𝑡 (𝑥))2 . 𝜇𝑡𝑖𝑙𝑡 (𝑥) and 𝜎𝑡𝑖𝑙𝑡 (𝑥) areproposed by Ref. [17] as follow:
𝜇𝑡𝑖𝑙𝑡 (𝑥) = −0.078𝑥 + 26.295,(8)

𝜎𝑡𝑖𝑙𝑡 (𝑥) = 0.028𝑥 + 6.429,(9)4.3. Missing load
In this study, missing data for hourly electricity use in residentialbuildings was filled in using a so-called urban building energy model(UBEM), developed in [33,34]. The UBEM makes use of geometrical information of buildings from GIS data and estimates the non-geometricalinformation, e.g., construction and material, occupancy, and occupantsrelated energy use as well as heating, ventilation, and air conditioning(HVAC) systems from pre-defined building archetypes. These buildingarchetypes represent the diversity of residential buildings using a few

where 𝑥 is the penetration level.
In the third step, the samples were drawn from distributions generated based on Eq. (8) and 2 using Python and the NumPy library’s
random module.
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Fig. 5. Cumulative distribution functions of voltage magnitudes at six different penetration levels for all values (a) and excluding the lowest and highest 1% of the values (b).
The vertical marks represent the maximum values of each penetration level.

5. Results and analysis

categories of buildings divided based on their type and construction
period. By importing this information to the UBEM, simplified, yet
accurate, models of residential buildings are formed and simulated under prevailing weather conditions. The simulation result represents theelectricity load in individual buildings. It includes the load for household appliances and lighting as well as space heating and domestic hotwater in case the building is electrically heated.

This section presents the results from the city-level time-series
analysis of PV hosting capacity. It consists of the results from the basecase with LiDAR-based rooftop data, rooftop azimuth and tilt model,
and sensitivity analysis.
5.1. Base case with LiDAR-based rooftop data

As regards the missing load, as illustrated in Fig. 4, after identifying the buildings with missing load, in an automated procedure,
available information on buildings was imported into the UBEM formodeling and simulation of the hourly electricity use data for the year
2021. However, due to the limitation of the UBEM in handling nonresidential buildings, the missing data from non-residential buildings
were eliminated from the simulations.

The line loading for all cases in this study remained within permissible limits and therefore, will not be shown in detail. For the voltage,
the results for all buses and times were gathered together for each penetration level and were arranged to produce the cumulative distributionfunction to show the probability of undervoltage and overvoltage. The
cumulative distribution function of the voltage in the time-series PV
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Fig. 6. Cumulative distribution functions of voltage magnitudes for all 334 LV networks at the 90% penetration level.

hosting capacity for the base case, using LiDAR-based rooftop data, isshown in Fig. 5 for six penetration levels.
The first figure displays the probability distribution for all values,
while the second one shows the distribution for values between the 1st
and 99th percentiles, effectively excluding the minimum and maximum
1% of values. The percentile used for the hosting capacity assessment isoften a matter of how much risk the distribution system operator allows
or is willing to take [6]. Previous studies used between 1% to 5% fromall values or 90% from the PV peak production times only [6,12,13,17].
From the results it can be observed that as penetration levels increase,the probability of overvoltage also increases.
The figure representing all values reveals a long tail at the minimum
and maximum values, indicating occurrences of extreme events in both
overvoltages and undervoltages. The voltage profiles sometimes exceed
the safety limit of 0.90 pu for undervoltages or 1.1 pu for overvoltages,
starting from a penetration level of 30% and above.
However, these extreme events are rare, as illustrated in Fig. 5(b)where the most extreme 1% of minimum and maximum values havebeen removed. By considering this subset of data, it becomes evident
that all values remain below 1.10 pu. Additionally, it is noticeable thatthe maximum voltages experience a significant increase with higher
penetration levels. Conversely, the minimum values remain consistentacross all penetration levels.
These voltage profiles imply that the distribution networks arecapable of accommodating solar PV systems for up to 90% of residential customers, each with a 12 kW installed capacity, without theneed for grid reinforcements, assuming a 1% risk threshold taken bystakeholders.
Each line in Fig. 5, however, is the combined value for all 334
low voltage grids. To understand the variations between low voltage
networks, Fig. 6 shows the probability distributions of voltage profiles
for each of the 334 low voltage networks for the 90% penetration level.
It can be seen that the variation is high between the networks.
One low-voltage network seems to have extremely low voltage
profiles, potentially being the main cause of undervoltage events acrossall penetration levels. It is possible that errors exist in either the grid
data or load data for this specific network, as it differs significantly
from other low-voltage networks.

It becomes evident that the probability of overvoltages varies acrossdifferent LV networks. Notably, four low voltage networks demonstrate
a probability of overvoltages exceeding 5%. On the other hand, it isnoteworthy that over 200 substations do not experience overvoltages
at all.
5.2. Rooftop azimuth and tilt model
Comparisons of the rooftop models to the actual LiDAR-based
rooftop data are given for each penetration in Fig. 7(a) for the azimuthand Fig. 7(b) for the tilt. Note that the model was fitted to building datain [17] and not fitted again in this study to evaluate the generalizabilityof the proposed model. It can be observed that, in general, the model
fits well, even though the azimuth data in this study have considerable
peaks around 0◦ and the tilt data have additional small peaks.
A comparison of probability distributions of voltages from simulations using three rooftop datasets at six penetration levels is presented
in Fig. 8. The hosting capacity simulations were performed using
LiDAR-based rooftop data, the rooftop model, and a uniformly optimal
assumption. At the lowest penetration level of 15%, the voltage distributions from the three different rooftop datasets show similarity. This
is attributed to the assumption made both for the LiDAR-based rooftop
data and for the rooftop data model, that buildings with more optimal
roof facets are prioritized for PV system adoption. Consequently, theroof facets in the lower penetration levels of both scenarios closely
resemble those in the uniformly optimal scenario.
As the penetration level increases, more significant distinctions
emerge between the results obtained from the uniformly optimal scenarios and the actual LiDAR-based rooftop data. Conversely, the results obtained from the rooftop model consistently demonstrate close
similarity to the LiDAR-based rooftop data.
At the highest penetration level of 90%, the difference becomes evenmore significant. Assuming uniformly optimal roof facets, the voltage at
the 99th percentile is 1.11 pu. As a result, when using the same chosen
index and limiting voltage values to 99%, the hosting capacity from thisdataset is restricted to 75% (or between 75% and 90%; a more exact
value would require smaller penetration level increments). Meanwhile,utilizing the rooftop azimuth and tilt model produces identical hosting
capacity results to the one using real roof facet orientation data.
7

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Fig. 7. Comparison of the distributions from the proposed models (red lines) to the histogram plot (blue bars) for roof facet azimuth (a) and tilt (b). Negative azimuth values
represent east directions and positive values represent west directions.

These findings highlight the significant disadvantages of assuming
optimal roof facets for all buildings, leading to an overestimation of
the overvoltage risk at higher penetration levels and, consequently, an
underestimation of the PV hosting capacity. Furthermore, the study
validates the applicability of the rooftop azimuth and tilt model within
the context of this city.

As anticipated, larger PV system sizes lead to notably higher voltages, the main limiting factor. Specifically, the 99th percentiles exceeded the threshold of 1.10. Consequently, in this scenario, increasing
the PV system size led to a reduction in hosting capacity, while,
conversely, decreasing the size of the PV system significantly mitigated
the risk of overvoltage. Here, 99% of voltage readings remained below
1.06. The line loading, however, still remained within permissible
limits, even for the 18 kW PV system size.

5.3. Sensitivity analysis
The sensitivity analysis aimed to assess the influence of PV systemsizes on voltage profiles as the limiting factor. For this purpose, PV
systems with sizes of 6 kW and 18 kW were tested at a 90% penetrationlevel using LiDAR-based rooftop data and compared to the base case of
12 kW also using LiDAR-based rooftop data. Fig. 9 shows a comparisonof resulting voltages for PV system sizes of 6 kW, 12 kW, and 18 kW at
90% penetration level.

6. Discussion
The main focus of this study is small-scale PV systems exclusively installed in residential buildings. However, it is essential to acknowledge
that PV systems can also be viable options for other types of buildings,
including office and commercial buildings. Expanding the scope of this8

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U.H. Ramadhani et al.

Fig. 8. Cumulative distribution functions of voltage magnitudes at six different penetration levels for the three rooftop datasets.

Fig. 9. Cumulative distribution functions of voltage magnitudes from three different PV system sizes in 90% penetration level using LiDAR-based rooftop data.

research to include these additional building types could serve as avaluable extension to the current research.
In this study, a one-hour resolution was used primarily due tothe available building power consumption measurement resolutions.
However, it is worth noting that this resolution may not be optimal.
Previous research, as cited in [35], has shown that using a 15-min
resolution instead of 10 s can lead to an overestimation of PV selfconsumption. Consequently, the results obtained in this study might
overestimate the self-consumption across all scenarios. Despite thislimitation, the comparison of results between the LiDAR-based rooftop
data, the rooftop model, and the uniformly optimal rooftop scenarios
is still expected to remain consistent.
The PV generation model employed in this study considers a varietyof rooftop tilt and azimuth configurations that affect the PV power
output. However, it utilizes the same solar irradiance data for all PV

systems. This assumption implies perfect correlation among all PV
systems, which is not necessarily realistic. A study in [36] demonstrates
significant spatial decorrelation of solar irradiance between buildings ina city slightly larger than the one examined in this study with a time
resolution of 5 min. By assuming a perfect correlation, the impact of
distributed PV systems is overestimated, leading to an underestimationof the PV hosting capacity. Nevertheless, when analyzed at an hourly
resolution, the impact of spatial decorrelation is less significant [36].
To improve the accuracy of the PV hosting capacity estimation forhigher time resolutions, it would be beneficial to account for the spatial
decorrelation of solar irradiance between buildings. However, incorporating spatial decorrelation into time-series profiles is challenging.
While the study in [36] proposes a method to model the decorrelation
for stochastic approaches, it does not directly address time-series data.
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Declaration of competing interest

Therefore, conducting a study specific specifically on this topic would
be highly valuable.
The proposed method to model roof facet orientation appears towork well for this city, and it is especially crucial for higher penetrationlevels. However, there are still some substantial assumptions in the PV
power model that simplify the complexity, which may not hold true inreality. For instance, PV system installation on flat roofs could potentially take advantage of optimal azimuth and tilt angles or increase thetilt to mitigate the impact of soiling. This issue has been raised in [17],but it remains unaddressed in the current paper.
Additionally, this study makes the assumption that the PV systemsize is uniform across all buildings and varies it during sensitivity
analysis. However, it still relies on the underlying assumption that thePV size is determined solely based on individual interests. Anotherapproach, which involves maximizing the PV system size on buildings
with better roof facets, can be an alternative. It would increase thetotal PV output efficiency and total PV electricity production. However,
it is also prone to lower self-consumption and higher losses. This approach also requires coordination within the community and may needto involve other technologies such as smart controllers and storage.
Therefore, it should be well motivated. Nevertheless, extending thisstudy in that direction could prove to be highly beneficial.
As can be seen, some assumptions and methods utilized in thisstudy may lead to an overestimated hosting capacity, while others may
underestimate it. Therefore, there is no exact final conclusion regarding
this matter. Instead, it emphasizes the existence and importance of
uncertainty modeling in hosting capacity calculations. This highlights
the need for further studies focusing on uncertainty modeling.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.
Data availability
The data that has been used is confidential.
Acknowledgments
This work was funded through SweGRIDS, by the Swedish Energy Agency and Vattenfall. This work forms part of the Swedish
strategic research program StandUp for Energy and was also partly
conducted within Solar Electricity Research Center Sweden (SOLVE).
David Lingfors is acknowledged for the help with the LiDAR-based
rooftop data.
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7. Conclusions
This paper presents a comprehensive assessment of residential PV
hosting capacity at the city level using a time-series method, incorporating massive LiDAR-based rooftop data, grid data, and power
consumption measurements. The study covers 334 LV networks withover 11,000 customer connection points and is supported by data from90,000 roof facets across approximately 37,000 buildings.
The findings reveal that the city’s distribution system can accommodate a 90% penetration level of PV with less than 1% risk ofovervoltage. However, there is significant diversity in results between
low-voltage networks, which can be attributed to the varying characteristics among them. This underscores the importance of conducting
city-level assessments for hosting capacity, as planning, regulation, andoperation of the distribution system are not done at the individual
substation level. Additionally, line loading does not present a limiting
factor for PV adoption in the studied system.
The method used to model roof facet orientation proves effective
for city-level applications, given its simplicity and accuracy compared
to LiDAR-based rooftop data. It is recommended for future studies
to employ this model. Sensitivity analyses confirm that the hosting
capacity analysis is sensitive to the PV system size.
The results from this study offer valuable insights for planning
strategies aimed at increasing PV penetration in residential buildings.
Moreover, they also serve as technical input for regulators and grid
operators to facilitate and manage PV systems in residential buildings.
CRediT authorship contribution statement
Umar Hanif Ramadhani: Writing – review & editing, Writing –original draft, Visualization, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Fatemeh Johari: Writing –review & editing, Visualization, Validation, Data curation. Oskar Lindberg: Writing – review & editing, Resources, Project administration,
Methodology, Data curation. Joakim Munkhammar: Writing – review& editing, Validation, Supervision, Conceptualization. Joakim Widén:
Writing – review & editing, Validation, Supervision, Methodology,
Funding acquisition, Conceptualization.
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