# A Tool for Reliability Assessment of Smart and Active Distribution Systems -
RELSAD

Stine Fleischer Myhre1, Olav Bjarte Fosso1, Poul Einar Heegaard2, Oddbjørn
Gjerde3  1Department of Electric Power Engineering, NTNU
2Dept. of Information Security and Communication Technology, NTNU
3SINTEF Energy Research
Trondheim, Norway
{stine.f.myhre, olav.fosso<EMAIL_ADDRESS><EMAIL_ADDRESS>
(February 2020)

###### Abstract

With increased penetration of new technology in the distribution systems such
as renewable energy resources, flexible resources, and information and
communication technology, the distribution systems become more complex and
dynamic. The traditional reliability analysis methods do not consider the new
components and technology and new considerations need to be taken to address
these new changes in the distribution system. This paper presents an open-
source reliability assessment tool for smart and active distribution systems
(RELSAD). The tool aims to function as a foundation for reliability
calculation in the smart and active distribution systems, where these new
components and technologies are included. The tool is made as a Python package
built up based on an object-oriented programming approach. The method will be
illustrated on the IEEE 33-bus system with the inclusion of generation,
battery, and ICT.

###### Keywords:

Distribution systems, ICT, Object-oriented programming, Python, Reliability
assessment, Smart-grid

##  I Introduction

The electrical power system is under constant change, and some of these
changes are observed at the distribution system level. With higher integration
of renewable energy resources, flexible end-users, energy storage, and ICT
components, the system becomes more complex with bidirectional power and
communication flow [1, 2]. However, even though the distribution system is
moving towards an active system with more similar behavior as the transmission
system, the distribution systems are still operated as radial or weakly meshed
systems.

The traditional reliability analysis methods for distribution systems do not
consider the new components and technologies in the distribution system [3].
Typically, only passive operation of the distribution systems, often systems
without any generation, is considered. If generation units are present, they
will be disconnected during the whole outage period of the faulted line and
not participate in an active way to restore supply to isolated system parts.

Reliability evaluation of radially operated distribution systems is conducted
mainly through analytical approaches or simulation. The common goal is to
evaluate the impact on the distribution system and the system customers of the
possible outage scenarios in the system. The basic calculated reliability
parameters are the average failure rate, $\lambda_{s}$, average outage time,
$r_{s}$, and average annual outage time, $U_{s}$ for the system. In addition,
it is common to calculate interruption indices to give a better representation
of the system behavior.

In [4], multiple analytical approaches for evaluating the reliability in
distribution systems are described. A mathematical representation of the
distribution system is constructed by evaluating the components and the
relation between them. To capture the dynamics in the system behavior, Markov
models can be applied. From the state models, both transient and stationary
properties can be extracted, such as the availability and the reliability of
the system. To capture the structure and the interrelation between the system
components, Markov models are not scalable. Alternatively, the system can be
represented by a structural model (such as Reliability Block Diagrams and
Fault trees), from which minimal cut sets can be defined and stationary system
properties can determined. Another analytical approach, RELRAD, uses the fault
contribution from all the network components to calculate the individual load
point reliability in the system [5]. However, these methods consider the
passive operation of the network and are therefore not optimal when analyzing
modern distribution systems.

Through simulation, a more accurate representation of a modern distribution
system is possible. In a simulation, information about the variability of the
reliability indices is included. Monte Carlo simulation is the approach most
frequently used for studying combined ICT-power system [6]. Multiple studies
have used Monte Carlo simulation as an approach to evaluate reliability in
modern distribution systems with ICT and active components such as distributed
generators (DG). In [7], a comprehensive study is conducted on modeling smart
distribution networks with ICT and DGs. The reliability of a distribution
system with the possibility of creating intentional islands with DGs is
evaluated in [8] where a sequential Monte Carlo method is used to evaluate the
reliability. Whereas in [9], an overview of reliability models and methods for
distribution systems with renewable DGs is presented with the focus on the
impact from the DGs. Here, Monte Carlo is often the preferred method. However,
even though the studies illustrate comprehensive methods, they do not bring
forward a general tool for the reliability assessment of modern distribution
systems. In [3], a survey of reliability assessment techniques for modern
distribution systems is conducted. The research points out Monte Carlo
simulation as a commonly used strategy. This is mostly due to its stochastic
nature which allows for more accurate modeling of the system where the
complexity and uncertainty of the system are considered. The paper also points
out the need for new reliability assessment tools for active distribution
systems.

This paper aims to introduce a tool for reliability assessment in a smart and
active power system. The tool, RELSAD (RELiability tool for Smart and Active
Distribution networks), offers the following features:

  * •

A foundation for calculating the reliability of modern distribution systems
with smart and active components.

  * •

A simulation tool that includes active participation of different power
sources such as distributed generation, microgrids, and batteries.

  * •

A simulation tool that includes ICT components and the dependency between the
ICT components and the power system.

The tool is made as a Python package openly available at Github with package
documentation [10]. The use of the tool is demonstrated by examples performed
on the IEEE 33-bus network [11] including active and smart components.

The rest of this paper is organized as follows; In Section II, the package
structure is described, and the system components are presented. Section III
aims to describe the core functionality of the method. A case study is
illustrated in Section V before the results are presented and discussed in
Section VI. The conclusions are presented in Section VII with future work.

##  II Package Structure

The structure of the program is divided into an electrical power system part
and an ICT system part. This chapter aims to describe both system structures.

###  II-A Electrical power system

The modeling of the electrical power system is divided into two categories, 1)
Systems and 2) Electrical components. Fig. 1(a) and 1(b) illustrates the
structure of the systems and electrical components respectively.

The systems are based on a parent power system - $P_{s}$, which further is
built upon a combination of one or more transmission systems - $T_{s}$,
distribution systems - $D_{s}$, and microgrids - $M_{s}$. The transmission
network is not yet implemented and is therefore not discussed in this paper.

Furthermore, the power systems are built up of different electrical components
such as lines - $l$, buses - $b$, disconnectors - $d$, circuit breakers -
$cb$, loads - $p_{d}$, production units - $p_{u}$, and batteries - $p_{b}$.
Together, both the implemented systems and the electrical components in the
systems constitute the power system. The load is an attribute of a bus.

(a) The system structure of the power system networks

(b) The components structure of the power system components

Figure 1: The electrical power system structure

###  II-B ICT system

The ICT system, $I_{s}$, is built up of three different communication
components;

  1. 1.

Controller, $dc$: The software containing the algorithm such as SCADA system.
The data center is responsible for monitoring and computations in the system.
Functions as the controller of the system.

  2. 2.

Sensor, $s$: Such as intelligent electronic device (IED) placed on the system
lines. Sensors can send line data information to the controller. The data can
be used to, e.g., find out which line is faulty.

  3. 3.

Intelligent switch, $d_{i}$: An Intelligent switch that can receive commands
about the switch position from the controller and automatically open/close the
breaker.

The ICT components are placed inside the given power system the component
belongs to ($D_{s}$ or $M_{s}$), e.g., an intelligent switch is connected to a
disconnector in a distribution system. Fig. 2 illustrates the setup and
communication between the different ICT components. The sensor can send
information about the line to the controller whereas the controller can
command the intelligent switch to open or close a switch automatically
remotely.

Figure 2: The communication component structure

###  II-C Class structure

The reliability assessment tool is constructed based on an object-oriented
programming approach with a class structure for the different network
components. The class structure is divided between an electrical power network
structure and an ICT network structure, where the logic inside and between the
different network structures are implemented in the program. Fig. 3
illustrates the class structure based on the layers in the system as well as
the connection between the different classes. The electrical power system
classes are illustrated in blue, while the ICT component classes are
illustrated in green. First, a $P_{s}$ is created before a combination of one
or multiple $D_{s}$ and $M_{s}$. After that, all the different components,
both electrical and ICT, can be created and added to the associated parts of
the system.

Figure 3: The component structure

##  III Core functionality

###  III-A Monte Carlo simulation and incremental procedure

RELSAD calculates the reliability of a power system through Monte Carlo
simulations. The Monte Carlo method is a stochastic simulation approach based
on a random sampling of input variables to solve numerical problems such as
stochastic problems. Monte Carlo uses randomness to compute the statistical
distributions of parameters of interest. In the simulation, time steps are
used to comprehend the behavior of the power system to give a better
representation of the actual system. In RELSAD, a sequential simulation model
is developed with a user-chosen increment interval.

First, $P_{s}$ is created and initialized with all the systems and components
in the $P_{s}$. Algorithm 1 illustrates the incremental procedure of the
model. The algorithm will first set the load and the production at the nodes
in the system before it will draw the status of the components in the $P_{s}$.
The algorithm will then check for failures in the $P_{s}$. If there are any
failures, the $D_{s}$ and/or $M_{s}$ with failed components will be divided
into sub-systems and a load flow and minimization problem will be solved for
each sub-system (see section III-C). After this, the systems and components’
history variables are updated. The history variables are further used to
evaluate the reliability for the whole system, $P_{s}$, the individual $D_{s}$
and $M_{s}$, and the individual load points. The rest of this section will
explain the different procedures of the reliability evaluation in greater
detail.

1Set bus $p_{d}$ and $p_{u}$;

2 Draw component fail status;

3 if  _Failure in $P_{s}$ (in systems, $D_{s}$ and $M_{s}$)_ then

4 Find sub-systems;

5 foreach  _sub-system_ do

6 Update $p_{b}$ demand (charge or discharge rate);

7 Run load flow;

8 Run optimization problem;

9

10 end foreach

11 Update history variables;

12

13 end if

Algorithm 1 Increment procedure

###  III-B Failure mode

The system is constructed with a user-specified failure rate and repair time
for the different system components. Fig 4 illustrates a simple Markov model
of the system components. The system components are, at the moment,
implemented with three different possible states, a working state when the
component is up and running, a failed state where the component is down and
not working, and a repair state where the component is under repair. The
failed state for the controller is further divided into two different failure
modes, hardware failures, and software failures. The repair state is a sub-
state of the failed state, but the difference is that the failed component is
acknowledged and is under repair.

Figure 4: A simple Markov model of the system components. $\lambda_{c}$ is the
failure rate of component $c$, $\mu_{c}$ is the repair rate of component $c$,
and $t_{c}$ is the time from component failure until the component is under
repair.

The transition between the working state and the failed state is decided based
on the failure rate of the component and is drawn by the simulator for each
increment. If the component is in a failed state, a new state for the
component will not be drawn until the component is repaired.

1if  _Failure on $s$ or software failure on $dc$_ then

2 repair_time = new_signal_time;

3 Draw signal success;

4 if  _Component new signal received_ then

5 return _repair_time_ ;

6

7 else

8 repair_time += reboot_time;

9 Draw reboot success;

10 if  _Reboot successful_ then

11 return _repair_time_ ;

12

13 else

14 Start manual repair;

15 return _repair_time_ ;

16

17 end if

18

19 end if

20

21 end if

Algorithm 2 Repair procedure

The transition between the failed state and the repair state can vary based on
the time it takes for the system to discover the failure on the failed
component. E.g., for an intelligent switch, the failure will not be discovered
until the switch is requested to open or close. The same applies to the
sensor, where the failure is not discovered until the sensor is called upon.
For a failure on a line, the $t_{c}$ is decided by the sectioning time of the
system, i.e., the time it takes for the system to find and isolate the failed
section in the power system, and the sectioning time is initialized by the
opening of the circuit breaker.

The transition between the repair state and the working state is determined by
the outage or repair time of the component. For the sensor and the controller
during software failures, the repair time follows a multi-phase recovery as
seen in Algorithm 2. This will result in three different possible outcomes
related to the time it takes for the system to address the failure in the
power system. First, a new signal is searched for. If that fails, the
component is rebooted. If the reboot fails to fix the problem, the component
needs manual repair.

###  III-C Load flow

To consider the behavior of the system, the state of the system at the
simulated time-step needs to be calculated. This can be done by adding load
flow calculations into the simulation, calculating the condition and behavior
of the system at all the specified time steps. In addition, the behavior of
the battery, the DGs and the other flexible resources are included and an
accurate calculation of the impact these sources have on the $P_{s}$ can be
evaluated. The electrical consequence of a failure can be calculated and
changed load and production can be simulated.

A load flow solver is implemented in the tool to capture the behavior of the
system. Since the system includes smart and active components, which can
restore some parts of the network, load flow calculations are added to
determine the electrical consequence of an outage in the system. Since the
model currently only considers radially operated networks, the chosen load
flow solver is based on a Forward-Backward Sweep (FBS) approach. The FBS will
calculate the load flow parameters of the network iteratively in a backward
and forward sweep order until convergence is achieved [12, 13]. The FBS is
preferred as the load flow solver for radially operated networks since the FBS
approach does not go through the Jacobian matrix, as the Newton-Raphson
method, which for some weak networks can cause an ill-conditioned matrix and
result in convergence problems for the load flow calculation. The FBS approach
is based on PyDSAL [14].

In addition to the load flow solver, a optimization problem is implemented
with the objective to determine the amount of shedded load in the network that
will minimize the Cost of Energy not Supplied (CENS). This is subjected to
load flow balance and limitations in the network. The minimization problem can
be seen in eq. 1. Here $C_{n}$ is the cost of shedding load at node n while
$P_{n}^{s}$ is the amount of shedded power at node n. $P_{j}^{g}$ is the
production from generator $j$. $P_{k}^{d}$ is the load demand at node $k$
while $P_{i}^{l}$ is the power transferred over line $i$. $\gamma_{i}=1$ if
line $i$ is the starting point, -1 if line $i$ is the ending point of the
line. $\lambda_{j}=1$ if there is a generation unit at node $j$, 0 else.
$\mu_{k}=1$ if there is a load on node $k$, and $\mu_{k}=0$, otherwise.

$\displaystyle\underset{P^{s}_{n}}{\text{minimize}}\quad\mathcal{P}_{s}=\sum_{n=1}^{N_{n}}C_{n}\cdot
P^{s}_{n}$ (1) subject to: $\displaystyle\begin{aligned}
\sum_{i=1}^{N_{l}}\gamma_{i}\cdot
P^{l}_{i}&=\sum_{j=1}^{N_{g}}\lambda_{j}\cdot
P^{g}_{j}-\sum_{k=1}^{N_{n}}&\mu_{k}&\cdot(P^{d}_{k}-P^{s}_{k})\\\ \min
P_{j}^{g}&\leq P_{j}^{g}\leq\max P_{j}^{g}&\forall j&=1,\dots,N_{g}\\\ 0&\leq
P_{k}^{s}\leq P_{k}^{d}&\forall k&=1,\dots,N_{n}\\\
\left|P_{i}^{l}\right|&\leq\max P_{i}^{l}&\forall i&=1,\dots,N_{l}\\\
\end{aligned}$

###  III-D Reliability indices

To evaluate the reliability of the $P_{s}$ and the systems contained in
$P_{s}$, some reliability indices are calculated during the increment
procedure. These are updated in the history variables of the different
components and systems in $P_{s}$.

The considered reliability indices calculated in RELSAD are divided into two
different indices groups, 1) Load- and generation-oriented indices and 2)
Customer-oriented indices.

#### Load- and generation-oriented indices

The load- and generation-oriented indices aim to indicate the electrical
consequence of failures in the system. The energy not supplied in eq. 2
indicates how much power is not being able to be served where $U_{s}$ is the
outage time of load point $i$ and $P_{i}$ is the load at load point $i$.

${\tt ENS}_{s}=\sum{U_{i}P_{i}}$ (2)

The interruption cost for the system can be calculated as seen in eq. 3 [15],
where $c_{i}$ is the specific interruption cost for each customer category at
load point $i$.

${\tt CENS_{s}}=\sum{\tt ENS}_{i}c_{i}$ (3)

#### Customer-oriented indices

The customer-oriented indices aim to indicate the reliability of the
distribution system by the interruption experienced by the customers. There
are multiple different types of indices, but in this paper, only three
important indices are investigated,

  1. 1.

System Average Interruption Frequency Index

${\tt SAIFI}=\frac{\sum_{\forall i}\lambda_{i}N_{i}}{\sum N_{i}}$ (4)

where $N_{i}$ is the total number of customers served, and $\sum_{\forall
i}\lambda_{i}N_{i}$ is the total number of customer interruptions. ${\tt
SAIFI}$ is a measure of the frequency of interruptions the customers in the
system expect to experience.

  2. 2.

System Average Interruption Duration Index

${\tt SAIDI}=\frac{\sum U_{i}N_{i}}{\sum N_{i}}$ (5)

where $\sum_{\forall i}U_{i}N_{i}$ is total number of customer interruption
durations. ${\tt SAIDI}$ is a measure of the expected duration of
interruptions a customer is expected to experience.

  3. 3.

Customer Average Interruption Duration Index

${\tt CAIDI}=\frac{\sum U_{i}N_{i}}{\sum_{\forall
i}\lambda_{i}N_{i}}=\frac{\tt SAIDI}{\tt SAIFI}$ (6)

${\tt CAIDI}$ is the ratio between ${\tt SAIDI}$ and ${\tt SAIFI}$ and
measures the average duration each given customer in the system is expected to
experience.

##  IV User interface

###  IV-A Networks

The user will have the opportunity to create the network(s) to be
investigated. The network should be made in Python as a .py file. The user
creates a $P_{s}$ before the different system components. The network is
created by connecting all the elements. For more detailed information, see the
documentation in the package repository at Github [10].

###  IV-B Data input

After the $P_{s}$ is created, a run file with the Monte Carlo commands needs
to be established. Here, the load and generation at the buses are set. Data
input such as system load and production should be collected through a self-
made Python file (.py file), that can read and fetch the system data. In the
run file, the data is included and connected to the right bus and generation
element. The load and production data are included through Python dictionaries
made in the run file. To include cost function related to the different load
types, these should be included in the run file as a part of the load
dictionary.

Since the simulator allows for user-chosen time steps, a function is included
in the tool to interpolate the data for the specified time step.

###  IV-C Simulation increment

RELSAD has a user-defined time interval, meaning that the user can specify the
simulation increment. The system is built with a TIME utils class which will
convert all the time units used in the system to a common time unit. Be aware
that the reliability evaluation will be less accurate with coarser time steps,
but with lower simulation time compared to a higher resolved time step. In
addition, the tool is implemented with the possibility of parallel processing,
which will speed up the simulation time.

##  V Case Study

###  V-A Test network

The model is applied on the IEEE 33-bus system seen in Fig. 5. The
distribution system includes the discussed ICT components, a battery placed on
B30, and a wind power plant placed on B15.

Figure 5: System topology with ICT

The network data and the reliability data can be seen in Tab. I and Tab. II
respectively. The increment is set to one hour. The load data is generated
based on the FASIT requirement specification which has hourly load increments
and different load types [16]. The weather data for the load profiles and the
wind turbine are collected from a location east in Norway.

Table I: Distribution system specifications Component | Specification
---|---
Battery |  Max capacity: 1 MWh Inverter capacity: 500 kW Min SOC: 0.1
Wind power | Max power: $\sim$ 5 MW
Load distribution system | Peak load $\sim$ 6.3 MWh
Table II: Failure rate and repair time of the system components. The failure
rate and repair time for the power system components are based on interruption
statistic from the Norwegian power system, while the failure and repair rates
for the ICT components are based on [17].

Component |  Failure rate [failure/year] |  Outage time/repair time [h/failure]
---|---|---
Line |  0.07 |  4
Transformer |  0.007 |  8
Intelligent switch |  0.03 |  2
Sensor |  0.023 |  New signal: 2 sec Reboot: 5 min Manual repair: 2
Controller (hardware failure) |  0.2 |  2.5
Controller (software failure) |  12 |  New signal: 2 sec Reboot: 5 min Manual repair: 0.3

####  V-A1 Battery strategy

The battery is assumed to follow the electrical market in the system, meaning
that the batteries will sell and store energy based on market prices. This
will be simulated by predicting the SOC level of the battery following a
uniform distribution between max and min SOC.

###  V-B Scenario description

The case study aims to illustrate how the presented model is working and how
it calculates the reliability in a more advanced power system. The case study
consists of four different scenarios seen below:

  1. 1.

No ICT, storage, and generation in the distribution network: The network is
operated traditionally without any ICT and production units present.

  2. 2.

Distribution system with storage and generation, no ICT: Including the
production units, a battery, and wind turbines, in the system. The system can
now restore supply to some parts of the system.

  3. 3.

Distribution system with ICT, no storage and generation: Including the ICT
components, sensor, controller, and intelligent switch. No production units
are present. Fast sectioning time in the system when the ICT components are
working.

  4. 4.

Distribution system with ICT, storage and generation: The distribution system
includes ICT components, storage, and generation.

By using hourly increments in the simulation, some information will be
inaccurate. The time step is set to one hour to follow the manual sectioning
time of the system. However, if there are ICT components in the system, the
sectioning time will in most of the cases be very small (seconds or minutes
during some failure events), the shedded electrical power in these time
intervals will therefore not be accounted for in an hourly increment
simulation and the result is, therefore, a little optimistic for the cases
with ICT.

##  VI Result and discussion

###  VI-A Result

The network is simulated for the different cases with a time interval of 1
hour. The result for the simulations is illustrated in Tab. III. As expected,
the $\tt ENS$ will decrease for the cases with ICT and generation units
compared to the base case. The largest difference can be seen for the cases
with ICT since the sectioning time is very low compared to the no-ICT cases.
This will lead to fewer load points experiencing shedding and will also result
in a lower $\tt SAIFI$. The case with only generation and battery will give
lower $\tt ENS$ compared to base cases since some parts of the network will
gain supply.

In addition, $\tt SAIDI$ is decreased for all the cases compared to the base
case since the load points will experience a decreased period of shedded load.
However, $\tt CAIDI$, the expected outage duration for the customer, will
increase. In the cases without ICT, all the load points will experience an
outage during the sectioning time of the system forcing $\tt CAIDI$ closer to
one which is the period of the sectioning time. For the cases with ICT
however, only the customers that are directly affected by the failure will
experience an outage in most of the cases. This will result in a much lower
$\tt SAIFI$, but $\tt SAIDI$ will not decrease that much since most of the
outage time in the system is related to the outage time of the system
components and not the sectioning time.

Another factor to consider is the simulation interval. Since the simulation
interval is set to 1 hour, the small periods where the ICT system is searching
for a new signal and rebooting are neglected. This means that the result for
the ICT cases is a bit optimistic compared to a real situation. In addition,
the result for $\tt CAIDI$ will be off since the small sectioning time that
will occur in the cases with ICT is not considered. It is therefore important
to consider simulation time up against the measure of the accuracy of the
result. A higher time resolution on the simulation will give longer simulation
time, but will also give a more accurate result. In this paper, the aim is to
introduce RELSAD, and a simulation time of 1 hour is acceptable for this
analysis. However, this is an important factor to address and consider when
building simulation tools. A possible solution is to have a function that can
create a higher time resolution on the simulation interval when this is needed
during outages in the system. The simulation interval during the outage will
then be set based on the situation of the components in the system, but this
is not yet implemented.

Table III: Reliability indices of the four cases

Case 1: No ICT, storage and generation in the distribution network
---
ENS |  SAIDI |  SAIFI |  CAIDI
39.8309 |  9.9317 |  5.4205 |  1.8322
Case 2: Distribution system with storage and generation, no ICT
ENS |  SAIDI |  SAIFI |  CAIDI
34.8709 |  9.8626 |  5.3633 |  1.8389
Case 3: Distribution system with ICT, no storage and generation
ENS |  SAIDI |  SAIFI |  CAIDI
16.6798 |  7.6166 |  1.0915 |  6.9781
Case 4: Distribution system with ICT, storage, and generation
ENS |  SAIDI |  SAIFI |  CAIDI
14.6094 |  7.5903 |  1.0894 |  6.9674

##  VII Conclusion and future work

This paper has introduced RELSAD as a reliability assessment tool for the
future smart and active distribution system. RELSAD is built up as a Python
package based on object-oriented programming and will be published as open-
source for public use upon publication of the paper. RELSAD introduce a
simulation method that includes DGs, batteries, microgrids, and ICT components
into the reliability evaluation of modern distribution network. By this, it
can comprehend the new components and technology and evaluate the reliability
of a modern distribution system.

One important factor to consider when using a simulation tool is the time-step
of the simulation. A higher time resolution on the time-step gives a more
accurate result, but the simulation time will increase. Therefore, it is
important to determine the required accuracy of a given problem.

###  VII-A Future work

The tool will be further developed, tested, documented, and made more robust.
In addition, some features will be addressed in more detail

  1. 1.

Further development of the ICT components by including more failure modes.

  2. 2.

Investigate possible solutions for more precise analysis of the result by
having more resolved time intervals or a more precise increment timeline.

  3. 3.

Include additional features such as the inclusion of more ICT components and
the ICT network.

##  VIII Acknowledgement

This work is funded by CINELDI - Centre for intelligent electricity
distribution, an 8-year Research Centre under the FME-scheme (Centre for
Environment-friendly Energy Research, 257626/E20). The authors gratefully
acknowledge the financial support from the Research Council of Norway and the
CINELDI partners. The authors would like to thank Jonas Rudshaug for his great
technical support.

## References

  * [1] G. Prettico, M. Flammini, N. Andreadou, S. Vitiello, G. Fulli, and M. Masera, “Distribution system operators observatory 2018,” _Publications Office of the European Union_ , 2019.
  * [2] A. Ipakchi and F. Albuyeh, “Grid of the future,” _IEEE power and energy magazine_ , vol. 7, no. 2, pp. 52–62, 2009. [Online]. Available: http://doi.org/10.1109/MPE.2008.931384
  * [3] A. Escalera, B. Hayes, and M. Prodanović, “A survey of reliability assessment techniques for modern distribution networks,” _Renewable and Sustainable Energy Reviews_ , vol. 91, pp. 344–357, 2018. [Online]. Available: https://doi.org/10.1016/j.rser.2018.02.031
  * [4] R. Billinton and R. N. Allan, _Reliability evaluation of engineering systems_. Springer, 1992.
  * [5] G. Kjolle and K. Sand, “Relrad-an analytical approach for distribution system reliability assessment,” _IEEE Transactions on Power Delivery_ , vol. 7, no. 2, pp. 809–814, 1992. [Online]. Available: http://doi.org/10.1109/61.127084
  * [6] T. Chaudonneret, H. Decroix, and J. D. F. McDonald, “Representation of the influence of telecommunications on electrical distribution network reliability,” in _2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm)_ , Nov. 2012, pp. 258–263. [Online]. Available: http://doi.org/10.1109/SmartGridComm.2012.6485993
  * [7] G. Celli, E. Ghiani, F. Pilo, and G. G. Soma, “Reliability assessment in smart distribution networks,” _Electric Power Systems Research_ , vol. 104, pp. 164–175, 2013. [Online]. Available: https://doi.org/10.1016/j.epsr.2013.07.001
  * [8] P. M. de Quevedo, J. Contreras, A. Mazza, G. Chicco, and R. Porumb, “Reliability assessment of microgrids with local and mobile generation, time-dependent profiles, and intraday reconfiguration,” _IEEE Transactions on Industry Applications_ , vol. 54, no. 1, pp. 61–72, 2017. [Online]. Available: https://doi.org/10.1109/TIA.2017.2752685
  * [9] C. L. T. Borges, “An overview of reliability models and methods for distribution systems with renewable energy distributed generation,” _Renewable and sustainable energy reviews_ , vol. 16, no. 6, pp. 4008–4015, 2012. [Online]. Available: https://doi.org/10.1016/j.rser.2012.03.055
  * [10] S. F. Myhre, “RELSAD,” https://github.com/stinefm/relsad, 2021.
  * [11] M. E. Baran and F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” _IEEE Power Engineering Review_ , vol. 9, no. 4, pp. 101–102, 1989. [Online]. Available: http://doi.org/10.1109/61.25627
  * [12] D. Shirmohammadi, H. W. Hong, A. Semlyen, and G. Luo, “A compensation-based power flow method for weakly meshed distribution and transmission networks,” _IEEE Transactions on power systems_ , vol. 3, no. 2, pp. 753–762, 1988. [Online]. Available: http://doi.org/10.1109/59.192932
  * [13] M. Haque, “Load flow solution of distribution systems with voltage dependent load models,” _Electric Power Systems Research_ , vol. 36, no. 3, pp. 151–156, 1996. [Online]. Available: https://doi.org/10.1016/0378-7796(95)01025-4
  * [14] O. B. Fosso, “Pydsal-python distribution system analysis library,” in _2020 IEEE International Conference on Power Systems Technology (POWERCON)_. IEEE, 2020, pp. 1–6. [Online]. Available: http://doi.org/10.1109/POWERCON48463.2020.9230554
  * [15] T. Langset, F. Trengereid, K. Samdal, and J. Heggset, “Quality dependent revenue caps-a model for quality of supply regulation,” in _16th International Conference and Exhibition on Electricity Distribution, 2001. Part 1: Contributions. CIRED. (IEE Conf. Publ No. 482)_ , vol. 6, 2001, p. 5 pp. vol.6. [Online]. Available: https://doi.org/10.1049/cp:20010906
  * [16] A. O. Eggen, “Fasit kravspesifikasjon,” Sintef Energy AS., Tech. Rep., 2016.
  * [17] T. Amare, B. E. Helvik, and P. E. Heegaard, “A modeling approach for dependability analysis of smart distribution grids,” in _2018 21st Conference on Innovation in Clouds, Internet and Networks and Workshops (ICIN)_. IEEE, 2018, pp. 1–8. [Online]. Available: http://doi.org/10.1109/ICIN.2018.8401634