Probabilistic Adequacy and Transient Stability Analysis for Planning of Fault-initiated Islanding Distribution Networks
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Probabilistic Adequacy and Transient Stability Analysis for
Planning of Fault-initiated Islanding Distribution Networks
Citation for published version (APA):
Roos, M. H., Faizan, F., Nguyen, P. H., Morren, J., & Slootweg, J. G. H. (2021). Probabilistic Adequacy and
Transient Stability Analysis for Planning of Fault-initiated Islanding Distribution Networks. In 2021 IEEE Madrid
PowerTech, PowerTech 2021 [9495018] Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/PowerTech46648.2021.9495018
DOI:
10.1109/PowerTech46648.2021.9495018
Document status and date:
Published: 29/07/2021
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Download date: 07. Sep. 2021Probabilistic Adequacy and Transient Stability
Analysis for Planning of Fault-initiated Islanding
Distribution Networks
M.H. Roos∗ , M.F. Faizan∗ , P.H. Nguyen∗ , J. Morren∗† , J.G. Slootweg∗†
∗ Department
of Electrical Engineering
Eindhoven University of Technology, Eindhoven, the Netherlands
Email: m.h.roos@tue.nl
† Asset Management,
Enexis Netbeheer, ’s-Hertogenbosch, the Netherlands
Abstract—Fault-initiated islanding can significantly improve microgrids remains stable during the FII transient. These
the reliability of power supply in distribution networks, by properties are therefore critical to analyze during planning of
allowing (parts of) distribution networks to operate as islanded a FII distribution network. The network conditions at the fault
microgrids in case of a contingency. The probability of generation
adequacy and transient stability of these microgrids has to be instance are highly uncertain due to the uncertainty of the fault
critically evaluated during planning of fault-initiated islanding, timing, and variability of (renewable) DERs power generation
in order to compare the incurred reliability and cost. The and load in the network. This uncertainty can be taken into
analysis of the probability of transient stability is challenging, account with probabilistic planning methodologies based on
as it generally requires a very large set of detailed time-domain Monte Carlo analysis (MCA) [4].
simulations to be performed. Stability during the fault-initiated
islanding transient has therefore not been considered during The DERs generation adequacy during islanded operation
probabilistic analysis in the literature. Additionally, the beneficial of (parts of) distribution networks has been analyzed with
properties for the value of fault-initiated islanding have not MCA by [5]–[9]. The generation adequacy and expected loss
yet been identified. To address these issues, a methodology for of load of an islanded distribution network with photovoltaic
probabilistic adequacy and transient stability analysis with a low (PV) and wind turbine (WT) DERs is analyzed by [5].
computational burden is proposed in this paper, and used for
rigorous sensitivity analysis of a modified fault-initiated islanding MCA is used by [6] to analyze the adequacy and several
RBTS Bus 2 benchmark distribution network. The results show reliability indices of islanded microgrids that are formed after
that the probabilistic adequacy and transient stability analysis a contingency in a FII distribution network with WT DERs.
methodology is accurate with a relatively low computational The reactive power capacity of a distribution network which
burden, and that fault-initiated islanding is most valuable in can operate in grid-connected and islanded modes is optimally
networks with a controllable and total generation capacity of at
least 14.7% and 58.9% of the average load power respectively, planned by using MCA by [7]. MCA is used to analyze the
moderate to high fault probability, and medium to high load cost. generation adequacy of PV and battery energy storage system
(BESS) DERs, and expected energy not supplied (EENS)
Index Terms—Islanding, power system planning, power system in a permanently islanded microgrid by [8]. A planning
reliability, transient stability, microgrids. methodology for FII distribution networks based on generation
adequacy is proposed by [9]. However, two important points
I. I NTRODUCTION
have not been addressed in the literature. (i): the stability
Fault-intiated islanding (FII) has received increasing at- during the FII transient has not been taken into account, while
tention from researchers over the last decade, as it allows transient stability can significantly impact the FII capability
network operators to increase the reliability of supply, without of microgrids [3], [10], [11]. When transient stability is not
investment in redundant network components [1]–[3]. When a taken into account, the benefits of implementing FII can be
fault occurs in a distribution network, FII allows (parts of) the severely overestimated. (ii): a rigorous sensitivity analysis of
network to disconnect and operate as autonomous islanded the reliability improvement and cost reduction offered by FII
microgrids. The distributed energy resources (DERs) supply has not yet been performed in the literature. Therefore, the
the local load in the islanded microgrids, until the faulted value of FII and properties under which FII is most valuable
component is repaired and the microgrids are reconnected to have been unclear until now.
the rest of the network. The stability during the FII transient can be analyzed with
Islanded microgrids can only successfully operate when time-domain analysis using highly detailed DER and load
there is adequate DERs generation capacity and when the models [10], [12]. However, due to the high number of samples
This work has received funding from the European Union’s Horizon 2020 taken during MCA and the high computation burden of time-
research and innovation program under grant agreement N°773717. domain simulations with detailed models, it is unfeasible
978-1-6654-3597-0/21/$31.00 ©2021 IEEEto directly analyze the MCA samples. This paper addresses
the aforementioned issues by proposing a methodology for Fault, DER and
load PDFs
probabilistic adequacy and transient stability analysis, which Mad
analyzes the transient stability based on equivalent sampled
conditions and dynamic equivalent models. This allows both
probabilistic adequacy and transient stability analysis of FII Monte-Carlo conditions Clustering into N
distribution networks to be performed within reasonable time. sampling equivalent conditions
The methodology is used to perform a rigorous sensitivity
Mf N
analysis of the reliability and cost of a modified RBTS Bus 2
benchmark distribution network with and without FII. Islanding transient
Supply/demand balance
The contributions of this paper are: analysis ∀ mf ∈ Mf stability
analysis ∀ n ∈ N
1) Proposition of a methodology for probabilistic adequacy
and transient stability analysis of fault-initiated islanding Madst
distribution networks with low computational burden
EENS cost
2) Analysis of the reliability improvement and cost reduction
by implementing FII in a case study of a modified RBTS EENS and cost
calculation
Bus 2 benchmark distribution network
3) Identification of distribution network properties beneficial FII enabling costs
for FII by rigorous sensitivity analysis of the FII modified
RBTS Bus 2 benchmark distribution network System reliability
indices and cost
The adequacy and transient stability analysis methodology
and case study are proposed and described in the next section.
An analysis of the required number of equivalent conditions Fig. 1. Overview of the adequacy and transient stability analysis methodology.
for accurate transient stability analysis and the results of the
case study are described in section III. The results of the
sensitivity analysis are described in section IV and conclusions each condition mf ∈ Mf based on the total DER and
are given in section V. load power in each islanded microgrid. The conditions with
adequate generation capacity are defined as set Mad ⊆ Mf .
II. M ETHODOLOGY 2) Equivalent conditions and transient stability analysis:
Since it is unfeasible to perform time domain simulations of all
A. Adequacy and transient stability analysis
conditions mad ∈ Mad , the transient stability of all equivalent
The probabilistic adequacy and transient stability analysis conditions n ∈ N is analyzed. The conditions in the set Mad
methodology proposed in this section enables the analysis are described by numerical values e.g. DERs and load power,
of the reliability and cost of distribution networks with and the equivalent conditions can therefore be determined by
without FII over planning horizon T . The methodology ana- minimizing the squared euclidean distance between equivalent
lyzes the transient stability of the microgrids formed during conditions N and the conditions in Mad , as described by (1).
FII under a large number of different sampled conditions by A set of equivalent conditions is generated for each different
performing time-domain simulations of a set of equivalent islanded microgrid configuration that occurs according to the
conditions. As an input, the methodology requires probabil- fault conditions. The optimization problem is solved with the
ity distribution functions (PDFs) of fault occurrence, DER algorithm proposed by [13].
injected power and load absorbed power, and the cost of EENS
and enabling FII. The latter costs may vary depending on the min (mad − n)2 (1)
availability of energy storage, the installed protection relays, ∀mad ∈Mad ,n∈N
the degree of communication that is required for the control As the number of equivalent conditions are directly cor-
of DERs and the islanding options that are considered. An related with the computational burden, the required size of
overview of the methodology is shown in Fig. 1. set N should be minimized while allowing accurate transient
1) Sampling and adequacy analysis: The methodology is stability of the microgrids. In this paper, the required size
initialized by generating a large set of M sampled conditions of set N is determined by analyzing the transient stability
with MCA of the fault, DER and load PDFs. The sampled while increasing the size of set N . The required size of set
fault conditions determine where and when a fault occurs, and N is reached when the stability results no longer significantly
thus what islanded microgrids are formed. The set Mf ⊆ M change. The results of this analysis are given in section III-A.
contains all sampled conditions where the fault occurs within In order to perform transient stability analysis, a time-
the planning horizon T . The sampled DER and load conditions domain simulation model is developed for each different
determine the power injected by DERs and absorbed by loads islanded microgrid configuration that occurs according to the
when the faults occur and FII is performed. The generation fault conditions. To reduce the computational burden while
adequacy of each formed islanded microgrid is analyzed for maintaining accuracy, dynamic equivalent microgrid modelsare developed with the methodology proposed by [14]. The F1 MG1
transient stability of the equivalent conditions is analyzed LP1,2 LP3,4 LP5,6 LP7
by performing time-domain simulations ∀n ∈ N . FII is External 33/11kV MG2
F2
Network
considered to be stable when the voltage and the frequency LP8 LP9
in each microgrid converges to an equilibrium point within F3 MG3
predefined margins of their nominal values δV and δf after
LP10 LP11,12 LP13,14 LP15
FII. The adequate and stable microgrids are defined as set F4 MG4
Madst .
LP16,17 LP18,19 LP20 LP21,22
3) Loss of load and cost calculation: In case of a fault, all
load is considered to be lost in: faulted parts of the network Fig. 2. Modified RBTS Bus 2 network with possible islanded microgrid
which cannot be islanded, islanded microgrids with inadequate formations after a fault occurs in the 11kV busbar, both 33/11kV transformers,
generation capacity and unstable islanded microgrids. Since the 33kV busbar or the external network. MG: microgrid, LP: load point.
the set Madst contains the microgrids which are successfully Load point
formed, the EENS over all sampled conditions is equal to
L(Mf )−L(Madst )
M , where L(x) is the sum of the load in set x.
11/0.4kV
Similarly, the EENS difference between a distribution network
with FII and without FII is determined by L(MMadst ) . In this
paper, the EENS is the main considered reliability index.
However, other reliability indices can be directly calculated
from the results if required. Z
The cost reduction offered by implementing FII is deter- CFL P CZ
mined with (2), where C(EEN Sw ), C(EEN Swo ), C(F II)
DER SMPS
are the annual EENS cost with and without islanding, and the M
cost to implement FII respectively. The payback time can be
VFD
calculated with (3).
Fig. 3. Connection of DER and load devices to load points. DER: distributed
energy resource. CFL: compact fluorescent lighting. VFD: variable frequency
∆C = T C(EEN Swo ) − C(EEN Sw ) − C(F II) (2) drive. SMPS: switched-mode power supply. CZ: constant impedance load.
C(F II) 2) Fault-initiated islanding: When a fault occurs in the
Tpb = (3) main 11kV busbar, both 33/11kV transformers, the 33kV
C(EEN Swo ) − C(EEN Sw )
busbar or the external network, the circuit breakers at F1-F4
B. Case study open after a protection relay operating time of 100ms to create
1) Network description: To demonstrate the effectiveness four microgrids. The DERs are normally operating in grid-
of the methodology proposed in the last subsection, and feeding control mode and switch to grid-supporting control
analyze the benefits and cost of implementing FII in distri- mode 50ms after islanding occurs [18]. The DERs in grid-
bution networks, a case study of a FII distribution network is supporting control mode will regulate the voltage and fre-
proposed in this subsection. The network is modified from the quency in the microgrids and supply the load for the duration
RBTS Bus 2 network described by [15] and shown in Fig. of the repair time. After the fault is repaired, the microgrids
2. Multiple inverter-based DERs are integrated in the network are resynchronized and reconnected to the main network. The
and the simple loads are replaced by detailed load models as resynchronization and reconnection are not considered in this
shown in Fig. 3 to allow FII and detailed transient stability paper, as the generation adequacy and transient stability are
analysis. PVs are situated at load points (LP) LP7, LP9, LP15 not threatened during this stage [19].
and LP18, WTs are situated at LP3, LP13 and LP21, and 3) Probability distribution functions: The case study is an-
BESSs are situated at LP7, LP15 and LP21. The different types alyzed over a planning horizon of T = 30 years with a sample
of load in distribution networks can be classified as lighting, size of M = 100000 and N = 25 equivalent conditions. The
motor drive, power electronic and resistive load [16], which fault probability of different components is taken from [15]
in this paper are represented by compact fluorescent lighting and an average repair time of 5 hours is considered. Faults
(CFL), variable frequency drive (VFD), switched-mode power are assumed to be independent and the fault probability is
supply (SMPS) and constant impedance (CZ) load devices constant over the planning horizon. The PDFs of wind speed,
respectively. The time-domain simulation models for DERs PV irradiation and loads are described by Weibull, Beta and
and different types of loads are described by [12]. The load Lognormal PDFs respectively. The Weibull shape and scale
points in the network are classified into residential, small parameters are determined to be kw = 2.15 and λw = 4.39
commercial, large commercial and industrial load. The share respectively, by fitting the PDF over hourly historical wind
of different types of load devices at each load point class is speed data of Eindhoven, the Netherlands provided by [20].
based on [17] and shown in table I. Since the probability of PV irradiation strongly varies overTABLE I TABLE II
C ONTRIBUTION OF LOAD DEVICES AT LOAD POINT CLASSES (%). CFL: PARAMETER VARIATIONS DURING SENSITIVITY ANALYSIS , DEFAULT
COMPACT FLUORESCENT LIGHTING . VFD: VARIABLE FREQUENCY DRIVE . VALUES ARE INDICATED IN BOLD . V X : VALUE X . FPM: FAULT
SMPS: SWITCHED - MODE POWER SUPPLY. CZ: CONSTANT IMPEDANCE PROBABILITY MULTIPIER . ENFP: EXTERNAL NETWORK FAULT
C
LOAD . PROBABILITY. cyc : COST PER BESS CHARGE / DISCHARGE CYCLE .
Class Load points CFL VFD SMPS CZ
Parameter Val1 Val2 Val3 Val4 Val5
Residential 1, 2, 3, 10, 11, 2.12 61.2 29.6 7.10
PV,WT rating (MVA) 1 2 3 4 5
12, 17, 18, 19
BESS rating (MVA) 0 1 2 3 4
Small comm. 6, 7, 15, 16, 22 16.5 79.6 3.93 0
FPM 0.5 0.75 1 1.25 1.5
Large comm. 4, 5, 13, 14, 20, 21 20.5 70.4 9.05 0
Industrial 8, 9 7.36 92.4 0.22 0 ENFP ( %
y
) 0 0.25 0.50 0.75 1.0
C
EENS cost ( kW h
) 11.47 17.21 22.94 28.68 34.41
BESS cost ( kW C∗cyc ) 0 0.2660 0.5319 0.7979 1.064
time, 288 different Beta distribution parameters are determined
for each hour of the day and each month. The parameters are 20 1
determined by fitting the distribution over hourly historical
Relative error (%)
0
irradiation data of Eindhoven, the Netherlands provided by 10
[20]. The load is described by a lognormal PDF with mean -1
25 50 100
factor and standard deviation factor of µln = 0 and σln = 0.69 0
respectively [21], where the mean load values are described
by [15]. To include seasonal and hourly changes in load
-10
probability, the each value sampled from the load PDF mL 1 5 10 15 20 25 50 100
is multiplied by hourly fh (t) and monthly fm (t) factors as Size of set N
shown in (4). The hourly and monthly factors are determined
Fig. 4. Relative transient stability analysis error for different sizes of N
by the the normalized hourly and monthly mean of the E1A compared to N = 250.
load profile described by [22].
III. R ESULTS
P (t) = fh (t) ∗ fm (t) ∗ mL , ∀ mL ∈ M (4)
A. Required number of equivalent conditions and computa-
4) Cost: The cost of EENS of C
22.94 kW
is equal to the tional burden
h
annual average domestic cost of EENS in the Netherlands [23]. As discussed in section II-A2, the required number of
To implement FII, synchronization relays have to be placed at equivalent conditions N can be determined by increasing the
points F1-F4 and the BESS in the network are utilized as size of set N until the stability results no longer significantly
controllable generation source. Therefore, the synchronization change. The transient stability of samples Mad is analyzed for
relay cost, relay programming cost, BESS usage cost and soft N = [1, 5, 10, 25, 50, 100, 250] with the default parameters
costs are considered as FII implementation costs C(F II). shown in table II, and a power rating of PV and WT of
BESS can be used for multiple applications in distribution 2MVA. The evolution of the error with increasing N is
networks such as peak shaving and voltage control, the cost determined by comparing the number of stable samples for
of BESS is therefore be divided over different applications. To N = [1, 5, 10, 25, 50, 100] to the number of stable samples for
determine a generic cost of BESS applied for FII, the BESS N = 250, as shown in Fig. 4.
usage cost is expressed in the cost per cycle by dividing the With a small size of set N , the methodology can overes-
cost of energy storage by the number of lifetime cycles. Based timate (e.g. N = 1 or N = 10), or underestimate (N = 5)
on the 50kW BESS data described by [24], the cost of using the transient stability. Underestimation of the transient stability
a Li-Ion BESS is equal to 0.5319 kW C∗cyc . For every islanding occurs when some of the stable conditions are represented by
event, the BESS is assumed to perform one charge/discharge unstable equivalent conditions, while overestimation occurs
cycle within the repair time. The cost of a relay capable of when some of the unstable conditions are represented by
resynchronization is C3851 per relay [25], while the total stable equivalent conditions. When N ≥ 25 the result of
cost of programming the relays and soft cost is estimated at the transient stability analysis of the case study does not
C20000 [26]. significantly change with increasing size of N , which indicates
5) Sensitivity analysis: To analyze the sensitivity of the that N = 25 provides accurate transient stability analysis
reliability improvement and cost reduction offered by FII to results. By analyzing the transient stability of only N = 25
different network properties, the EENS and cost of the case equivalent conditions as opposed to M = 100000 samples,
study are analyzed with the different input parameters shown the computational burden of the transient stability analysis is
in table II. During the sensitivity analysis, the PV and WT dramatically reduced. With N = 25 and M = 100000, a
power rating, BESS power rating, fault probability, external PC with an Intel Xeon E5 processor is able to analyze the
network fault probability, value of EENS and BESS usage cost adequacy and transient stability of the case study, and calculate
are all individually varied, while the other parameters remain the EENS and cost of the system in 56 minutes by using the
at the default values. methodology proposed in section II-A. This enables network15
Val1 Val2 Val3 Val4 Val5
EENS (MWh) 15 Val1 Val2 Val3 Val4 Val5
Payback time (y)
10
10
5 5
0 0
PV,WT rat. BESS rat. FPM ENFP PV,WT rat. BESS rat. FPM ENFP EENS cost BESS cost
Fig. 5. EENS reduction over the planning horizon by implementing FII in Fig. 7. Payback time of implementing FII in the case study network under
the case study network under the different parameters shown in table II. the different parameters shown in table II.
Probability of stable islanding (%)
4 Val1 Val2 Val3 Val4 Val5
Val1 Val2 Val3 Val4 Val5 80
3
60
2
40
1
20
0
0
PV,WT rat. BESS rat. FPM ENFP EENS cost BESS cost PV,WT rat. BESS rat.
Fig. 6. Cost reduction over the planning horizon by implementing FII in the Fig. 8. Probability of stable FII in the case study network under the different
case study network under the different parameters shown in table II. parameters shown in table II.
operators to analyze the reliability and cost of different FII IV. D ISCUSSION
configurations and allows iterative optimization of the network Even though the probability of a fault is relatively low,
design. implementing FII in the case study network is beneficial in
most cases due to the large impact of faults and the relatively
B. Case study results low cost of implementing FII in the case study.
1) Default parameters: With the default parameters from The results of the BESS rating variations in Figs. 5, 6, 7
table II, the total probability of stable FII of the four mi- and 8 indicate that FII should only be implemented when the
crogrids is 69.30%. This leads to a EENS reduction of controllable generation capacity e.g. energy storage capacity
10.82MWh over the duration of the planning horizon when is at least 14.7% of the average load power in the network.
FII is implemented compared to the network without FII. The BESS in the case study provides this controllable gen-
The expected cost reduction over the duration of the planning eration capacity, and can both inject and absorb power. This
horizon when FII is implemented is C211790 compared to the significantly increases the probability of adequate generation
network without FII, which results in a payback time of 4.41 capacity and improves the transient stability of the microgrids.
years. The results of the PV,WT rating variations in Figs. 5, 6, 7
2) Sensitivity analysis: The EENS reduction by implement- and 8 show that implementation of FII is most interesting in
ing FII in the case study network for different parameter networks which have a total DERs generation capacity of at
variations is shown in Fig. 5. The cost difference between least 58.9% of the average load capacity, moderate to high
the case study network with and without FII, and payback fault probability and medium to high EENS costs. Higher
time of implementing FII for different parameter variations DERs power rating allows more load to be supplied, increases
are shown in Figs. 6 and 7 respectively. The probability of the probability of adequate generation capacity and improves
stable islanding for different PV, WT and BESS power ratings the transient stability of microgrids. Higher fault probability
is shown in Fig. 8. allows FII to be utilized more often, while higher EENS costs
The implementation of FII in the case study network reduces increases the impact of FII per fault occurrence, both of which
the EENS by between 186.7kWh and 12.57MWh over the increase the benefits gained by implementing FII.
planning horizon. The reduction in system costs is positive in As shown in Figs. 6 and 7, the value of implementing FII
all but one parameter variation i.e. when there is no BESS in is only slightly impacted by BESS usage costs. As previously
the network. In the positive cases the system costs are reduced discussed, the BESS is already available in the network.
between C41471 and C335920, while the cost with FII is However, if energy storage has to be implemented solely
C3112 higher when there is no BESS in the network. The for FII, the cost of implementing FII increases significantly.
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14.0 years, with a probability of successful FII between 28.9% costs with and without FII are equal if the BESS usage costs
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