Photovoltaic Integration in Smart City Power Distribution

A Probabilistic Photovoltaic Hosting Capacity Assessment based on

Smart Metering Data

Vasiliki Klonari

, Jean-François Toubeau

, Jacques Lobry

and

François Vallée

Electrical Engineering Department, University of Mons, 31 Boulevard Dolez 7000, Mons, Belgium

General Physics Department, University of Mons, 9 Rue de Houdain 7000, Mons, Belgium

Keywords: Smart Cities Power Distribution, Low Voltage, Hosting Capacity, Smart Meters, Photovoltaic, Probabilistic

Analysis.

Abstract: Maximizing the share of renewable resources in the electric energy supply is a major challenge in the design

of smart cities. Concerning the smart city power distribution, the main focus is on the Low Voltage (LV) level

in which distributed Photovoltaic (PV) units are the mostly met renewable energy systems. This paper

demonstrates the usefulness of smart metering (SM) data in determining the maximum photovoltaic (PV)

hosting capacity of an LV distribution feeder. Basically, the paper introduces a probabilistic tool that estimates

PV hosting capacity by using user-specific energy flow data, recorded by SM devices. The probabilistic

evaluation and the use of historical SM data yield a reliable estimation that considers the volatile character of

distributed generation and loads as well as technical constraints of the network (voltage magnitude, phase

unbalance, congestion risk, line losses). As a case study, an existing LV feeder in Belgium is analysed. The

feeder is located in an area with high PV penetration and large deployment of SM devices. The estimated PV

hosting capacity is proved to be much higher than the one obtained with a deterministic worst case approach,

considering voltage margin (magnitude and unbalance).

Table 1: Abbreviations.

MV/LV Medium Volta

e/Low Volta

PV Photovoltaic

DER Distributed Energy Resource

DSO Distribution System Operator

SM Smart Meter

CDF Cumulative Distribution Function

HC Hosting Capacity

overvoltage

Probability of exceeding upper voltage limit

undervoltage

Probability of exceeding lower voltage limit

unbalance

Probability of exceeding voltage unbalance

limit

i,j

Grid voltage at node i, phase j

nom

Nominal voltage in the feeder

rated,l,i

Installed PV power at node i, considered in

iteration l in case it is a future PV node

rated,tot

Installed PV power in whole feeder

step

Increase step of the installed PV power at a

node

Reference factor

1 INTRODUCTION

A major challenge in the design of smart cities is to

maximize the share of renewable resources in their

electric energy supply. The principal objective is to

increase the self-sufficiency of a city, based on local

resources, while responding to the climate change.

The smart city power distribution mainly concerns the

Low Voltage (LV) electric network. Photovoltaic

(PV) generation is the mostly met Distributed Energy

Resource (DER) in such systems.

So far, the biggest share of distributed PV units

came with no strategic design or reinforcement of the

network while monitoring data in the small-usage

(residential or small business) sector were absent

almost everywhere in Europe. Given the lack of

controllability in common LV networks, the

uncoordinated integration of PV units often leads to

distinct power quality issues. Moreover, it slows

down the increase of renewable energy share. Thus,

the growing volatility of electricity consumption and

generation in the distribution network urges the

166

Klonari, V., Toubeau, J-F., Lobry, J. and Vallee, F.

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart Metering Data.

In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 166-178

ISBN: 978-989-758-184-7

adoption of a streamlined planning approach for the

future smart cities.

In this evolving framework, Distribution System

Operators (DSOs) are called to safeguard a stable and

secure power supply in all possible demand

conditions while fostering the massive integration of

DER generation. In cost-efficiency terms, this fact

highlights the necessity of leaving behind

deterministic worst case planning approach. This

traditionally applied approach focuses on the least

favourable network operation states, which are very

rare. Naturally, it leads to very restrictive decisions in

terms of PV hosting capacity or to costly network

reinforcements.

Given the current uncertainty of DSO costs and

revenues, new planning tools are required for

considering the constant variability of the energy

network (EDSO, 2015). In a smart city vision, this

argument becomes even more solid in view of the

upcoming integration of electric vehicles and the

development of flexibility services. As a matter of

fact, both are seen as basic components of the future

smart cities. The large deployment of smart metering

(SM) devices in the residential and commercial sector

will drastically enlarge the potential of cost-effective

planning approach. Indeed, user-specific data will

result in a better insight of the smart city power

distribution system.

Considering the above facts and the probabilistic

character of the EN 50160 technical standard

(EN50160, 2012; Antoni Klajn, 2013) (which

addresses the LV network) this paper presents a

feeder- and user- specific probabilistic methodology

that estimates the DER hosting capacity of an LV

feeder. Practically it introduces a probabilistic tool

that uses user-specific energy flow data recorded by

SM devices, installed in the studied feeder. The

probabilistic evaluation and the use of historical SM

data yield a reliable estimation that considers the

volatile character of distributed generation and loads

as well as network operational criteria.

Section 2 of this paper presents literature review

regarding this subject and the drivers for developing

the proposed analysis tool. Section 3 presents the

overall structure of the developed algorithm and

Section 4 thoroughly describes the important role of

user-specific SM measurements in this development.

Section 5 explains the computation process of the

maximum acceptable PV hosting capacity.

In Section 6, a real LV feeder in Belgium is

analysed. The feeder is located in an area with high

PV penetration and large deployment of SM devices.

When the probabilistic character of EN 50160

standard’s voltage limits is considered, the estimated

PV hosting capacity is proved to be much higher than

the one obtained with a deterministic approach, based

on worst case energy flow profiles. Moreover, the use

of long term SM measurements verifies the

computation of technical metrics that can only be

considered with a deterministic approach (violation

of the maximum current capacity of the lines).

2 CURRENT FRAMEWORK

Slow or over rigid hosting capacity review processes

hamper DER integration in many regions worldwide.

Very often, users who want to invest and play an

active role in managing their energy usage are

increasingly unable, in expediency and cost-

efficiency terms, to do so. In this context, a stream-

lined approach together with the expansion of

allowable DER integration approvals seem to be a

necessity (Solar City Grid Engineering, 2015).

For increasing penetration levels while shortening

the application review timeline, DSOs should

incorporate automated DER hosting capacity

analyses. A process flow for incorporating such

analysis into the DER integration review process is

outlined in Figure1.

Figure 1: Process flow for incorporating hosting capacity

analysis into the DER integration process.

Recently, many energy utilities are adapting their

DER hosting capacity review so as to remove or

update restrictive maximum allowable limits (Noone,

2013). As far as the fast track analysis part is

concerned (second step in Figure 1), the Electric

Power Research Institute (EPRI) presents a set of

models that could be used by DSOs or electric utilities

(Smith, 2015; Electric Power Research Institute,

2012). These feeder-based methodologies are very

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart

Metering Data

167

solid computation examples that take account of all

steady state operational criteria.

Focusing on PV hosting capacity, EPRI

recommends stochastic analysis as a highly

appropriate tool for determining PV hosting capacity

in distribution feeders (Smith, 2015; Electric Power

Research Institute, 2012). The stochastic deployment

concerns the position and size of future PV units

while the steady state estimation of the feeder is done

with deterministic approach.

In the same vein, a set of studies addressing the

European framework and the EN 50160 standard

highlight the efficiency of stochastic and probabilistic

analysis in determining hosting capacity or otherwise

the impact of PV generation in LV feeders (Bollen

and Hassan, 2011; Conti and Raiti, 2007; Conti et al.,

2003; Hernandez et al., 2013; Ruiz-Rodriguez et al.,

2012; Billinton and Bagen, 2006; Billinton and Karki,

2003). Meanwhile, the European Photovoltaic

Industry Association (EPIA) and the technical

standard EN 50160 suggest that distribution networks

should be designed on a probabilistic basis. For

example, EN 50160 standard deals with the voltage

characteristics of LV feeders in probabilistic terms. It

gives recommendations that, for a percentage of

measurements (e.g. 95%) over a given time, the

voltage value must be within specified limits.

Most of the existing methodologies deploy the

stochastic analysis regarding the size and position of

PV units and not the load/generation profiles of users.

However, the ongoing integration of SM devices in

LV networks enlarges the potential of using feeder-

specific or even user-specific data for modelling

energy flows. According to (Bollen and Hassan,

2011) , deploying long-term measurements in the LV

network is highly valuable, not only for estimating the

maximum PV hosting capacity, but also for voltage

coordination of the network in general.

The EPRI’s report (Electric Power Research

Institute, 2012) estimates PV hosting capacity using

feeder-specific data to create either absolute worst

case scenarios (maximum recorded generation-

minimum recorded load) or load/PV time-of-day

coincident worst case scenarios. As previously

mentioned, although feeder-specific data are used, the

steady state estimation of the feeder is still done with

a deterministic approach. Indeed, this approach does

not consider the fact that the time-of-day in which

worst case values apply for a specific user does not

necessarily coincide with the one of other users

connected to the same feeder. Nevertheless, the

operational criteria of the feeder are determined both

by the individual user’s demand and by the

simultaneous demands of other network users. Since

the demands of every user and the degree of

coincidence between them constantly varies, so does

the operation of the feeder (Antoni Klajn, 2013).

The above argument demonstrates that although

user-specific SM data are primordial for creating

reliable network models, there is another challenge

that needs to be addressed. The latter lies in the fact

that users follow volume-wise (kWh) or capacity-

wise (kW) an almost stable daily pattern. However,

this pattern does not necessarily remain the same on

the time axis. In long term decision making, profiles

should be based on the recorded ones considering all

possible deviations. Those deviations could be

inserted either as random statistical errors or by

making random possible combinations of the

recorded values or by combining both approaches.

Therefore, reliable models that take into account

load/PV time- and user-variability are necessary for a

less conservative and more cost-effective hosting

capacity review. Probabilistic and particularly Monte

Carlo approach are very suitable to address this

modelling challenge.

3 THE PV HOSTING CAPACITY

COMPUTATION TOOL

This paper presents a tool that uses probabilistic state

estimation (Vallee et al., 2013; Klonari et al., 2015),

15-min user-specific SM data and feeder-specific

technical parameters to estimate the PV hosting

capacity of a given LV feeder. Hosting capacity is

defined as the maximum amount of PV that can be

accommodated in the feeder without impacting

system operation (reliability, power quality, etc.)

under existing control and infrastructure

configurations (Electric Power Research Institute,

2012).

The proposed methodology aims to address the

central block of Figure 1 by providing a detailed

feeder- and user-specific DER hosting capacity

analysis. The analysis takes into account the EN

50160 standard operational criteria (EN 50160, 2012;

Antoni Klajn, 2013). The focus is on voltage

magnitude and unbalance which are the primary

technical concerns in LV feeders with distributed PV

generation. The maximum line capacity is also

considered so as to address important reverse power

flows due to high PV injection.

Apart from steady state constraint management,

there are other considerations that could be accounted

for, such as transformer aging factor, grid losses, etc.

Such criteria are included in cost-benefit analysis

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168

(CBA) but they are not addressed by the EN 50160

standard. Depending on the country and the applied

DSO tariff methodology (“cost-plus”, “revenue cap”,

etc.), DSOs are incentivised to reduce certain

operation costs that can or cannot be integrated in

their tariffs. Thus, the impact of such criteria on

decision making, varies in function of the distribution

utility. Consequently, this paper determines PV

hosting capacity based on commonly adopted EN

50160 standard criteria and line capacity issues,

however line losses are also determined by the

probabilistic analysis.

3.1 Overview of the Simulation Tool

As previously said, this chapter presents a

probabilistic algorithm that determines the PV

hosting capacity of an LV feeder by elaborating

feeder-specific SM measurements. The SM

measurements are the necessary input for performing

a reliable steady-state analysis of various possible

energy flow scenarios in the studied feeder. The

flowchart in Figure 2 presents the structure of the

simulation algorithm, which is entirely developed in

MATLAB®.

Figure 2: Flowchart of the PV hosting capacity computation

tool.

The energy exchange scenarios are generated by a

Monte Carlo algorithm sampling from the historic

SM data of the feeder (Vallee et al., 2013; Klonari et

al., 2015). The power flow analysis is performed with

the three-phase algorithm that is presented in

Appendix A. Both balanced and unbalanced

situations can be considered in this study.

3.2 Feeder Model

The feeder model is constructed based on the

technical parameters of the lines, the position of the

users, the installed PV power per node, the voltage at

the MV/LV transformer secondary output and the

respective set points and bandwidths in case voltage

control algorithms are integrated. The feeder model

also assigns the load/PV generation SM datasets to

the respective users. This necessary information is

directly available to the DSO.

Regarding the PV hosting capacity computation,

the possible future locations of the PV units have to

be specified in the feeder model. This analysis is not

based on stochastic random distribution of PV units

along the feeder. A set of scenarios regarding the

positions of future PV nodes is specified and each one

of them is studied separately so as to focus on its

specific impact on the feeder.

The technical constraints that must be respected

for the current situation and for future scenarios are

the ones specified in local, regional or national

directives. However, these operational constraints

can be determined in a more restrictive manner,

depending on the case. In the EU framework, the

steady-state constraints are set by the EN 50160

standard. Regarding voltage magnitude and

unbalance, 95-percentile limits are suggested. Based

on this standard, the simulation tool verifies that the

following criteria apply for the whole system (in

current and future installed PV power scenarios):







,

1.10∙



  0.05

(1.a)







,

0.90∙



0.05

(1.b)











2%



0.05



(1.c)

where





,



and



represent

respectively the probability of having an

overvoltage, an undervoltage or exceeding the phase

voltage unbalance limit at any node over a number M

of simulated network states. In 

,

, i stands for nodes

1 to N (total number of nodes in the feeder) and j

stands for phase a, b or c.

The thermal limits of the cables are also

considered in the computation. The current carrying

capacities of the lines should not exceed the DSO

requirements or the recommended values in technical

standards such as (IEC).

The load flow analysis of each system state is

performed with the three-phase algorithm that is

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart

Metering Data

169

presented in (Klonari et al., 2016).

4 THE USE OF SM

MEASUREMENTS

4.1 User Profiles and Feeder State

Modelling based on Historic SM

Datasets

The load/ PV profiles of existing users are created by

using their respective SM recorded datasets. The

generation of the system states is practically based on

a very large number of random combinations of

users’ energy flow values. The methodology for

creating the energy flow profiles and for generating

the system states under analysis are thoroughly

explained in (Vallee et al., 2013; Klonari et al., 2015).

Longer recording periods of SM readings result in

more reliable estimation of the PV impact on the

feeder.

The probabilistic deployment of this simulation

tool relies on the principle that load/PV generation

profiles of users are highly time-varying. This time-

variability induces another variability that concerns

the time coincidence of the load profiles of various

users. Both arguments are very important when

assessing the impact of PV generation on a LV

network. Indeed, the consideration of this variability,

both in the time axis and regarding users coincidence,

makes more realistic the simulation of the network

operation. Such an approach can lead to less

restrictive and more cost-effective decisions that do

not rely on rare extreme cases but on the most

frequent ones.

4.2 Generation Profiles of Future PV

Nodes

A key component in accurately assessing the impact

of future PV units is reliably representing their

generation profiles. Based on the findings of several

studies, geographically close customers are entirely

correlated as far as their PV generation profiles are

concerned (Shedd et al., 2012; Vallée et al., 2015).

For this reason, this study considers that the

generation profiles of future PV customers will be

very similar, along the time axis, to the ones of the

existing PV units.

As previously explained, the load/PV generation

profiles of customers with SM devices are made of 96

Cumulative Distribution Functions (CDFs) of

probability built with the 15-min recorded datasets.

Concerning PV generation, such CDFs are apparently

not available for the future PV units. For this reason,

the available SM datasets are used in this case to

create a reference CDF, based on the 15-min

generation SM datasets of the existing PV owners

(Lefebvre, 2015), which is used to simulate the time-

variability of PV generation at the future PV nodes.

In reality, customers that are connected to the

same LV feeder can have different PV units’ sizes.

Assuming an equivalent statistical distribution of

their PV power profiles due to geographical

proximity, the principle is to create a standardized

reference CDF for PV generation in the specific

feeder, based on the measurements of the available

SM devices (Rousseaux et al., 2015). Initially, the

CDF for the 15-min PV energy generation E

inj,pv,j,q

each existing PV node j is normalized by applying the

following relation, for each time step q:



,,,





,,,







,, for j = 1:N

(2)

where N

is the number of users in the feeder that

are equipped with an SM device, 

,,,

values are

the normalized 15-min energy generation values of

customer j during time step q, 

,,,

values are the

recorded 15-min energy generation values of

customer j during time step q and 

,

is the total

yearly PV energy generation of customer j.

Once this is done, the 15-min CDFs of every user

are aggregated in order to create one reference CDF

that can represent all PV owners in the specific

feeder. For creating the CDF of each particular future

PV owner, this reference CDF should be normalised

in function of his annual PV generation. For existing

PV owners, such information is usually available to

the DSO even if the customer is not monitored by an

SM device. In case of future PV nodes, such

information is apparently not available since no PV

unit is connected. Consequently, the reference CDF is

normalised with the annual PV generation of an

existing PV unit (in the feeder or in proximity)

multiplied by a reference factor f, as explained in the

following section.

5 PV HOSTING CAPACITY

COMPUTATION

Practically, the algorithm starts with the probabilistic

analysis of the current situation (existing PV units),

by simulating a large number M of possible system

states. One should note that although system states are

based on 15-min resolution data, each one of them is

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170

considered as a possible instantaneous state of the

system. Thus, the accuracy and reliability of the

computation increases with the number of treated

system states.

The probabilities P

overvoltage

, P

undervoltage

and

unbalance

are computed at every node, based on the

analysis results. Compliance with the conditions set

by (1.a, 1.b, 1.c) is verified for the whole feeder. In

case the conditions are respected, the algorithm

increases the installed PV power at the future

(specified by the user) PV nodes by the defined

increase step. Therefore, an LV feeder is simulated

considering a total number N of PV nodes. Some of

the simulated N nodes may be currently existing PV

nodes while the rest of them are the considered future

PV nodes. If the total number of future PV nodes is

equal to K (K ≤ N), the new installed power at each

future PV node i is computed as follows:



,,



,,



,

,

 1:nodes

(3)

where 

,

is the new installed PV power at node

i in the current configuration l that will be analysed

by the algorithm (in step 5, Figure2), 

,,

is the

installed PV power at node i that was analysed (and

accepted in terms of impact on the technical

constraints) in configuration l-1 and 



is the

increase step (defined by the user). A small





value (≈ 0.5-1kVA for residential or small

commercial users) is recommended so as to make a

more precise computation. In several countries, the

maximum admissible installed power per distributed

PV unit in the LV network, concerning residential and

small-business users, is equal to 10kVA. In such

cases, the condition 

,,

 10kVAshould be

integrated in step 5 of the algorithm.

Once relation (2) is applied, the new installed PV

power 

,,

is defined at every new PV node

before the algorithm performs the next “hosting

capacity review” iteration (step 5, Figure2). However,

the reference CDF that represents the time-variability

of generation at the new PV nodes needs to be scaled

in function of 

,

at each node. As previously

highlighted, since the annual PV generation of new

PV units cannot be available, the reference CDF is

normalised with the annual PV generation of an

existing PV unit (in the feeder or in proximity). Then,

a reference factor f is introduced for scaling the

normalised CDF in function of 

,

. The factor f

is computed as follows:









,,



,



, i=1: K

(4)

where 

,

is the installed PV power of the

existing PV unit that has been used to normalize the

reference CDF.

Once the generation profiles have been set up for

the future PV nodes, the algorithm repeats steps 2 and

3 for analyzing the current configuration l. At this

point, it is important to clarify that each “hosting

capacity review” iteration l practically performs the

power flow analysis of configuration l by applying a

full MC simulation, similar to the one of step 2. This

means that each “hosting capacity review” iteration l

runs the same large number of MC iterations M that

was analysed in step 2. Thus, in every iteration l, a

very large number of system states is analysed

(=M·96) so that the values of P

overvoltage

, P

undervoltage

and P

unbalance

converge. Thanks to this procedure, the

verification of compliance with equations (1.a, 1.b,

1.c) for each configuration l is assumed to be reliable.

If the analysis of M system states, in configuration l,

demonstrates that the operational constraints are not

violated, the installed PV power is again increased at

each future node. Then, the algorithm passes again to

steps 4 and 5.

The described iterations stop as soon as the

operational constraints are for the first time exceeded

at least at one of the nodes. Therefore, the PV size of

some units could probably increase even more, given

that the operational constraints at their PCC are not

violated. However, this study treats the LV feeder as

a whole since the violation of limits at one node is

always affected by the energy flow at all nodes. The



,,

that is applied in the last iteration l, which led

to a violation of acceptable limits, is the one

considered as the maximum admissible hosting

capacity per node.

The aggregated PV hosting capacity of the feeder

is computed by adding 

,,

(existing and new)

along the feeder:



,



,,







(5)

where N is the total number of PV nodes in the feeder.

In order to make a more detailed computation,

different increase steps could be applied per node in

function of its position in the feeder. The voltage

limits are usually more easily violated at the end of

the line. Consequently, the PV power steps could be

bigger for the nodes at the head of the line. However,

this strategy could eventually result to an earlier (in

terms of PV size) violation of the limits at the last

nodes, which does not tally with a common welfare

among end-users.

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart

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171

6 CASE STUDY: AN LV FEEDER

IN BELGIUM

6.1 Description of the Simulation

This section describes the application of the

previously described analysis tool for computing the

PV hosting capacity of an LV feeder in Flobecq.

Flobecq is a municipal area in Belgium with high

penetration of distributed PV generation (≈25% of

Flobecq LV grid users) and large deployment of SM

devices. Thanks to an official research fellowship

between the local DSO and the authors’ affiliation,

the technical parameters of the feeder and SM

datasets of the respective users have been

communicated strictly for research purposes. The

datasets cover a total period of one year (2013).

The topology of the simulated three-phase feeder

is presented in Figure 3. Currently, four PV units are

installed in the feeder which supplies a total of 19

residential users. These PV units are located at nodes

4,5,12 and 14, by means of single-phase inverters,

and their installed PV power is respectively 5kVA,

10kVA, 2.63kVA and 5kVA.

Figure 3: The simulated LV feeder of the power distribution

network of Flobecq (conductors colour code as in IEC

60446 standard).

A spatial correlation study had already been

performed for the specific feeder and the generation

profiles of the users were proved to be entirely

correlated (Vallée et al., 2015). This consideration is

taken into account in this analysis, regarding also

future PV nodes. Practically, this means that for every

simulated system state, the randomly sampled

probability for defining the respective PV generation

value is common for all PV units.

Concerning operational constraints, the ones of

EN 50160 standard have been considered in the

simulation. Therefore, compliance with the group of

equations (1.a, 1.b, 1.c) has been verified for each

system state, as far as voltage magnitude and

unbalance are concerned. The maximum current

capacity of the lines has been determined based on

table (IEC). The PV size increase step is defined

equal to 1kVA and the power factor of all PV

inverters is considered equal to 1, unless reactive

power control is considered in the simulation.

A set of different scenarios have been simulated

regarding the position and phase connection of future

PV units as well as the action of voltage control

schemes. The analysed scenarios are listed in Table 2.

Concerning the scenarios A-D, only the on-off

control scheme is considered, which is currently

implemented by most DSOs in Europe. This control

scheme enables a total cut-off of the PV unit (in most

cases during 3 minutes) as soon as the voltage limit

has been locally exceeded for a period longer than 10

minutes. This analysis considers each simulated state

as instantaneous. Therefore each violation of the 95-

percentile limit of EN 50160 standard is counted in

the probabilities even though in reality it might had

lasted less than 10 minutes. This means that the

computed maximum PV hosting capacity is possibly

slightly lower than the one that the feeder can really

support, considering voltage margin.

Table 2: The simulated PV hosting capacity scenarios.

No Description

12 new PV units at nodes 2, 3, 6, 7, 8, 10, 11, 13, 15,

16, 17, 18, 19. The PV units at nodes 8, 11, 17, 18, 19

are connected to phase A, the PV unit at node 3 is

connected to phase B and the PV units at nodes 2, 6,

7, 10, 13, 15 are connected to phase C.

B

12 new PV units at nodes 2, 3, 6, 7, 8, 10, 11, 13, 15,

17, 18, 19. All new PV units connected to phase B,

except from PV unit at node 15 (phase A).

C

12 new PV units at nodes 1, 2, 3, 6, 8, 10, 11, 13, 15,

16, 17, 18. The PV units at nodes 1, 8, 11, 15, 16 are

connected to phase A, the PV units at nodes 3, 17 and

18 are connected to phase B and the PV units at nodes

2, 6, 10, 13 are connected to phase C.

1 new PV unit connected to node 16 (phase A).

Similarly to scenario A but considering 100-

percentile limits. Practically the PV hosting capacity

is not increased as soon as voltage and VUF limits are

exceeded at least once in the feeder.

Similarly to scenario A but considering the action of

three-phase damping control integrated in the new PV

inverters. In this case, the new PV units need to be

connected b

means of three-

hase PV inverters.

Similarly to scenario A but considering the action of

reactive power control of (CEI, 2012)

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The control scheme applied in scenario F is the

three-phase damping control scheme which behaves

resistively towards the negative- and zero-sequence

voltage component, without modifying the injected

power, so as to eliminate phase voltage unbalance

(Meersman et al., 2011). This control scheme requires

a three-phase PV inverter, it is very promising in

terms of voltage magnitude and unbalance mitigation.

It is actually implemented in a EU pilot program (FP7

INCREASE Project). The third control scheme is

reactive power control in the way it is implemented

in the Italian distribution system (CEI, 2012)

concerning new PV units in the LV network. These

voltage control schemes are integrated in the

simulation tool as explained in (Klonari et al., 2016).

6.2 Comparing with a Deterministic

Approach

One of the main purposes of this study is to

investigate, up to which extent, a probabilistic method

based on user specific data leads to a less restrictive

computation of PV hosting capacity, compared to a

deterministic approach. For this purpose, a

deterministic approach has been implemented

simulating worst case energy flow profiles. The load

profiles of all users and the PV generation profiles of

existing PV units have been also based on SM

recorded data. The deterministic steady state analysis

has been conducted for scenarios A-D, F, G. Scenario

E is not mentioned because, in a deterministic

framework, it coincides with deterministic scenario

A. The following load/ PV generation profiles have

been considered:

I. Maximum PV power per node (installed PV

power) – Minimum recorded load per node;

absolute values, irrespective of time

coincidence among users

II. Maximum PV power recorded in the feeder –

Coincident PV generation/load values for the

other nodes.

III. Minimum recorded load in the feeder during PV

injection hours – Coincident PV

generation/load values for the other nodes.

6.3 Results and Discussion

The probabilistic hosting capacity review results are

illustrated in Figure 4 and analytically listed in Table

3. The aggregated maximum admissible PV hosting

capacity in the feeder, considering only voltage

margins (magnitude and unbalance), is presented in

the second column for each individual scenario. The

third column presents the violation due to which PV

hosting capacity could not be further increased for the

respective scenario. The aggregated PV hosting

capacity obtained with deterministic analysis is

presented in Figure 5 and Table 4 for all scenarios and

worst case load/ PV generation profiles (§6.2).

Figure 4: The computed aggregated PV hosting capacity of

the feeder for scenarios A-G. The number of new PV units

is also indicated.

Table 3: Aggregated maximum PV hosting capacity

considering only EN 50160 voltage margins (Probabilistic

Simulation).

No Voltage margin consideration (EN 50160 standard)



Aggregated

HC 

Violation

A

154.63kVA

(11kVA per

new PV)

-- P

overvoltage

at nodes 18 and 19

(phase (B)) resulted 5.7% and

6.4% respectively (> 5%, which is

the value accepted by the EN

50160 standard)

B 144.63kVA 

-- P

overvoltage

at nodes 13,14,15

(phase (C), resulted 5.4%, 6.16%

and 6.18% respectively 

C 178.63kVA 

-- P

overvoltage

at nodes 13, 14

resulted 6.78% and 6.77%

ti l

D 65.63kVA 

-- P

overvoltage

at node 19

(phase (B)) resulted 5.15% 

E 94.63kVA 

-- P

overvoltage

at nodes 13,14,

(phase (C)), resulted 0.0001% in

both cases (> 0%, which is the

condition in scenario E)

F 202.63kVA 

-- P

overvoltage

at nodes 2-19 (at all

three phases) resulted from 5.5%

to 28% 

G 154.63kVA 

-- P

overvoltage

at node 19 (phase

(B)) resulted 5.17% 

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart

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173

Figure 5: Aggregated PV hosting capacity of the feeder for

probabilistic & deterministic scenarios (A to D).

Table 4: Aggregated maximum PV hosting capacity for

each simulated scenario (Deterministic Approach).

No Aggregated PV Hosting Capacity (kVA)

A 70.63kVA 82.63kVA 82.63kVA

OV at all new

PV nodes

B 58.63kVA 58.63kVA 58.63kVA

OV at all new

PV new PV

nodes

C 94.63kVA 94.63kVA 106.63kVA

OV at all new

PV nodes

D 43.63kVA 49.63kVA 52.63kVA

OV at all new

PV new PV

nodes

Considering only voltage margin as a constraint (both

magnitude and unbalance), one should note that the

result of scenario E (applying 100-percentile limits)

is close to the ones of the deterministic scenarios A.I,

A.II and A.III which analyse the same topology as

scenario A but with a deterministic approach. Based

on this remark, it can be reasonably assumed that the

probabilistic computation covers (samples and

analyses) almost the whole range of possible system

states, including the ones recorded in reality (the

combination of coincidently recorded values) which

are treated in the deterministic scenarios A.II and

A.III.

However, accounting for voltage margins, the

restrictive condition of scenario E according to which

voltage limits must never be exceeded (in none of the

simulated states), results in a quite lower admissible

PV hosting capacity compared to scenario A (same

topology as scenario E). Basically, in scenario E, PV

hosting capacity could not further increase because

the computed P

overvoltage

resulted equal to 99.99%

(>95% is the condition in EN 50160). Therefore, if

the admissible PV hosting capacity does not exceed

94.63kVA, the operational limits will most probably

never be violated in the feeder, based on the

elaboration of the available historic data. Otherwise,

if the admissible PV hosting capacity increases up to

154.63kVA, as in scenario A, voltage limits’

violation will only take place in less than 5% of total

system states. Even with such an increase of the

aggregated PV hosting capacity, the temporary cut-

offs of the PV units due to overvoltage will be very

rare. Scenario A takes advantage of the probabilistic

character of EN 50160 standard (limits violation

allowed during 5% of week time), which is not the

case in scenario E or in the deterministic approach.

Investigating congestion risk for all scenarios, PV

hosting capacity results much lower than in case only

voltage margins are considered. For a more rigorous

view, statistical distributions of current values of all

line segments have been constructed based on the

total number of simulated states. In all cases, the

violation of maximum line capacity took place in

segment 6-7 (Table 5). For this reason, the

configuration in scenario A was reordered in order to

address this remark by examining scenario C.

Table 5: Aggregated maximum PV hosting capacity

considering both EN 50160 voltage margins and maximum

line capacity.

No

Maximum current capacity and voltage margins

consideration



Aggregated HC Violation

A

70.63kVA (4kVA/

per new PV) 

max

of line 6-7: 13% deviation

(13% higher than the maximum

current capacity of the lines)

B

58.63kVA (3kVA/

per new PV)

max

of line 6-7: 50% deviation

(50% higher than the maximum

current capacity of the lines)

C

94.63kVA (6kVA/

per new PV)

max

of line 6-7: 0.18% deviation

(10.5% higher than the

maximum current capacity of

the lines)

D

37.63kVA (15kVA/

per new PV)

max

of line 6-7: 6.2% deviation

(6.2% higher than the

maximum current capacity of

the lines)

E

70.63kVA (4kVA/

per new PV)

max

of line 6-7: 13% deviation 

F

70.63kVA (4kVA/

per new PV)

max

of line 6-7: 11% deviation 

G

70.63kVA (4kVA/

per new PV)

max

of line 6-7: 11% deviation 

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Practically, scenario C considers the same number

and phase configuration of scenario A but new PV

units are distributed at different nodes aiming to

reduce current flows in line segment 6-7. Indeed, the

analysis of scenario C, taking into account congestion

risk, resulted in an improved hosting capacity

compared to scenario A (94.63kVA > 70.63kVA).

Considering voltage margin, scenario C also led to

higher hosting capacity (178,63kVA > 154.63kVA).

In Figure 6 the probabilistic consideration of

overvoltage is illustrated with the evolution of the

CDF of probability of phase voltage (B) at node 19

while the total installed PV power increases (scenario

A). If total installed PV power increases by 144kVA

(12kVA per new PV unit), phase voltage (B) at node

19 respects the defined limits in 94.6% of the

simulated states (< 95% is the EN 50160 limit). Thus,

the maximum PV power that can be added to the

feeder, considering this configuration, is 132kVA

(11kVA per new PV unit).

Figure 6: CDFs of probability for phase voltage (B) at node

19, for each increase step of the total installed PV power in

the feeder (scenario A).

The above arguments should be considered in a cost-

benefit analysis (CBA) that compares network

operational costs, eventual penalties for low DER

integration, and potential revenue loss for users and

energy utilities. For highlighting the cost-

effectiveness of deploying long-term measurements

in the LV network and analysing it with a

probabilistic approach, a more detailed computation

of line losses in the feeder was performed. Assuming

that the computed maximum admissible PV power is

installed (=154,63kVA if one considers only voltage

margin in scenario A), the study focuses on the total

energy losses along the lines of the feeder during

hours of high PV injection in a typical day (this period

varies with the month).

The worst case approach considers only one

system state which will more likely take place during

hours with the highest PV injection. Based on the

available historic data for the feeder, this period is

between 12:00AM and 18:30PM on a typical July

day. The sum of energy losses has been computed

Figure 7: CDF of probability of total energy losses in the

feeder during high PV injection hours in a typical July day,

considering the maximum admissible installed PV power

(scenario A).

along the feeder for the considered period, for each

simulated day. Figure 7 illustrates the statistical

distribution (CDF of probability) of the computed

daily line losses, obtained with the probabilistic

approach.

The probabilistic approach and the consideration

of the SM measurements demonstrated that total

energy losses in the feeder vary significantly,

depending on the system state. Consequently, in 95%

of the simulated days, total energy losses during high

PV injection hours (12:00AM to 18:30PM) do not

exceed 35kWh in a day. In the deterministic approach

which assumes the worst case scenario taking place

all along the high PV injection period, the respective

energy losses result equal to 148kWh. This important

difference highlights that the probabilistic approach

considers the extremely low frequency of worst case

scenarios to take place simultaneously for all feeder

users. Considering such probabilities, the DSO could

manage a less conservative and more cost-effective

long-term strategy.

Undoubtedly, the computed PV hosting capacity

values depend on the load profiles of the customers

that are located in the feeder. However, the results

clearly indicate in relative terms, that smaller

distributed PV units have a much smoother impact

than the bigger ones concentrated in one small area of

the feeder. This fact is demonstrated by the

comparison of scenario A to scenario D. Moreover,

as previously mentioned, in certain countries the

maximum admissible installed power per PV unit

connected to the LV network is equal to 10kVA. In

such cases, scenario D might not be appropriate based

on the probabilistic simulation results. As a matter of

fact, the admissible total installed power would have

to limit to 32.63kVA although the network would be

able to support 37.63kVA. The difference between

the PV hosting capacity computed with the

probabilistic and the deterministic approach for these

cases (considering only voltage margin) is not as big

as for scenarios A and B. Indeed, in scenarios A and

Photovoltaic Integration in Smart City Power Distribution - A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart

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175

B, the volatile character and the extremely rare

coincidence of worst case values for 12 units cannot

be reliably represented by a deterministic model.

Regarding the distribution of units among phases,

the comparison of scenarios A and B shows that the

existing phase unbalance affected the computation.

Indeed, the violated parameter in this case is voltage

magnitude of phase (C) although all new PV units are

connected to phase (B). Therefore, the unfair

distribution of new PV units among phases did not

directly affect P

unbalance

but it had an impact on the

voltage magnitude of phase (C). Considering voltage

limits, the aggregated PV hosting capacity for

scenario B resulted equal to 144.63kVA, if one

considers only voltage constraints. However, the

connection of most new PV units at phase (B) resulted

in very high current values so that the maximum

current capacity was exceeded by 50%.

In scenario F, the connection of new PV units by

means of three-phase inverters integrating three-

phase damping control can increase the aggregated

hosting capacity by 36%, considering voltage margin.

Thanks to the resistive behaviour of this control

scheme towards the zero- and negative-sequence

voltage component, the deviation of voltage

magnitude and unbalance becomes much smoother

compared to the currently applied on-off control.

Thus, the risk of exceeding the defined limits is

reduced and a bigger share of PV generation can be

integrated. Applying this control in scenario C would

definitely lead to even higher PV hosting capacity.

Based on the results of scenario G, reactive power

control does not result in higher PV hosting capacity

compared to scenario A (on-off control). Voltage

profile in the feeder is however improved compared

to scenario A. As a matter of fact, voltage limits are

not violated in scenario G whereas the maximum

current capacity limit is exceeded for the same

amount of PV integration compared to scenario A.

In the first two cases (scenarios A and B),

comparing the probabilistic simulation results to the

respective ones of the deterministic approach, an

important difference in the aggregated admissible

hosting capacity is observed. One should notice that

the violated parameter in the deterministic

approaches is mainly the voltage magnitude and

secondly the maximum current capacity of the lines.

The deterministic approach led to 58-146% lower

aggregated PV hosting capacity (compared to the one

computed with the probabilistic approach) due to a

violation that according to the probabilistic

elaboration of the historic SM dataset took place for

much less than 6% of the simulated system states.

Indeed, based on figure 8, the addition of 12 new PV

units of 4kVA each (deterministic scenario A.I)

generated an overvoltage risk that is lower than 1%.

The studied feeder currently hosts 22.63kVA of

distributed PV generation and supplies 19 residential

customers. The analysis of the current conditions

(based on the historic SM datasets) demonstrated that

both voltage violation risk and congestion risk are

very low. Moreover, the above probabilistic load-

flow analysis proved that congestion and voltage

problems will only appear if 48kVA and 132kVA

respectively of distributed PV generation (scenario

A) are further integrated. This remark highlights the

cost-efficiency of designing distribution networks

based on the most frequent system states and on well-

studied future scenarios. Such probabilistic approach

can lead to customised solutions and help to avoid

over-dimensioning and costly initial investments for

the DSO.

Finally, a general remark concerns the self-

sufficiency potential of the feeder. Based on the

available user specific data, the annual generated PV

energy in the feeder is in the range of 22400kWh

corresponding to 22.63kVA of currently installed PV

generation. The annual aggregated load for all users

is in the range of 87200kWh. Given that PV users are

entirely correlated regarding their PV profiles, the

potential annual PV generation in the whole feeder

has been roughly estimated for each analysed

scenario s as follows:



,,,





,

∙



(6)

where 

,

isthe reference factor introduced in (3)

applied for the total installed PV generation in

scenario s and 



is the total annual generated PV

energy in the feeder at present (≈22400kWh). The

estimation demonstrated that the annual potential PV

generation in scenarios A, C, F and E would

correspond to 80 to 107% of the annual load in the

feeder (with hosting capacity considering both

voltage margin and line capacity). This is only an

orders of magnitude observation. For determining the

self-sufficiency of the feeder, further studies should

be deployed, including congestion risk or other

technical and economic issues that would have to be

encountered for storing the generated PV power

(Thirugnanam et al., 2015).

However, based on this rough estimation, certain

renewable integration scenarios could potentially

increase to an important extent the self-sufficiency of

feeders like the studied one. As a result, their

dependency on big conventional power plants,

connected at the transmission level, could be

efficiently reduced. However, big conventional plants

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are important for maintaining grid stability. In a high

DER integration scenario, without large and reactive

storage facilities and/or flexibility services, the

amount of RES should be carefully reviewed. To this

end, costs induced by the use of grid services,

including insurance against periods when it is not

possible to consume own generated electricity, should

be considered and reflected in the bill of generator

owners (EDSO 2015). Reliable feasibility studies and

comprehensive CBAs are necessary for evaluating

various strategies in the decision making process.

7 CONCLUSIONS

This paper addresses the problem of determining the

maximum PV hosting capacity that can be

accommodated in a LV distribution feeder, while

respecting local technical standards. To this purpose,

a probabilistic simulation tool that uses as input user-

specific SM energy flow data and feeder-specific

parameters is presented. A PV hosting capacity

review for a municipal area in Belgium is used as a

case study for evaluating the usefulness and reliability

of the proposed tool. The study outcome

demonstrates that it is to the interest of the DSO and

of the grid users to deploy probabilistic analysis that

considers the time-variability of load/PV generation,

both in the time axis and between different users’

profiles. This variability of network state can be taken

into account thanks to the deployment of long-term

SM measurements. Consequently, the further

deployment of SM devices is strongly recommended

for a more cost effective long-term planning and

coordination of the LV network.

ACKNOWLEDGEMENTS

The authors of this chapter acknowledge the support

of ORES, the DSO who manages the electricity and

natural gas distribution grids in 193 communes in

Wallonia (Belgium), in terms of funding and SM data

supply, both indispensable elements for conducting

this research work.

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