Development of a Self-Healing Strategy for Future Smart ...

School of Engineering and Information Technology

Development of a Self-Healing Strategy for

Future Smart Microgrids

Soheil Bourbour

32948493

This thesis is presented for the Degree of

Master of Philosophy

of

Murdoch University

September 2016

ii

Declaration

I declare that this thesis is my own account of my research and contains as its

main content work which has not previously been submitted for a degree at any

tertiary education institution.

Soheil Bourbour

16/09/2016

iii

Abstract

Microgrid is expected to supply its local loads independently. But, due to

intermittency of wind and solar-based energy resources as well as the load

uncertainty, it is probable that a microgrid experiences power deficiency. This

problem can be mitigated by coupling the overloaded microgrid to another

neighbouring microgrid that has surplus power. Considering a distribution network

composed of several islanded microgrids, defining the suitable microgrids to be

coupled to the overloaded microgrid is a challenge. A microgrid overload

management technique is developed in this thesis which first identifies the

overloaded microgrid(s) and then selects the most suitable neighbouring microgrids.

The alternative selection is based on different criteria such as available surplus

power, reliability, supply security, power loss, electricity cost and emissions in the

selected microgrids. Moreover, the frequency and voltage deviation in the system of

coupled microgrids are considered in the selection. In addition, the thesis evaluates

the impact of the weightings of each criterion on the outcome of the alternative

selection strategy and presents the sensitivity of the selection procedure on the

weightings of each criterion since each criterion weighting has the potential to vary

the outcome of the alternative selection therefore the impact of every criteria is found

to be crucial. Therefore, a dynamic multi-criteria decision-making algorithm is

iv

developed for this purpose. To contemplate the uncertainties in the considered

distribution network, a cloud theory-based probabilistic analysis is deployed as the

research framework and the performance of the developed technique is evaluated in

MATLAB. Once a selection is identified, the interconnection should take place, but

before that, a synchronisation between selected microgrids is required for a safe and

appropriate interconnection between them and thereby in this thesis, the transition

stage forming a system of coupled microgrids is also discussed, and a suitable and

practically applicable strategy is developed which facilitates their synchronisation

before interconnection. The performance of the developed strategy is evaluated by

time-domain simulation studies in PSCAD/EMTDC.

v

Table of Contents

Chapter 1 Introduction ............................................................................................ 1

1.1 Introduction ............................................................................................................ 1

1.2 Aims and objectives of the thesis ........................................................................... 5

1.3 Significance of research ......................................................................................... 6

1.4 Structure of the thesis ............................................................................................. 6

Chapter 2 Coupling of Neighbouring Microgrids ................................................. 8

2.1 Necessity and Complexity of Coupling Microgrids............................................... 8

2.2 Proposed Overload Management Technique (OMT) ........................................... 11

2.3 Dynamic Multi-Criteria DMA ............................................................................. 16

2.3.1 Risk Index ......................................................................................................... 19

2.3.2 Dynamic DMA .................................................................................................. 20

2.3.3 Criteria Weightings ........................................................................................... 20

2.3.4 Qualifying Criteria ............................................................................................ 21

2.3.5 Other Criteria .................................................................................................... 22

2.3.6 Power Loss in Interconnecting Lines ................................................................ 23

2.3.7 Electricity Price ................................................................................................. 24

2.3.8 Reliability .......................................................................................................... 25

2.3.9 Supply Security ................................................................................................. 26

2.3.10 CO2 Emissions ................................................................................................ 26

2.4 Power Flow Analysis (PFA) for Microgrids ........................................................ 29

2.5 Cloud Theory-Based Stochastic Analysis ............................................................ 34

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2.6 Performance Evaluation ....................................................................................... 37

2.7 Conclusion ............................................................................................................ 48

Chapter 3 Impact of the Criteria Weighting ....................................................... 50

3.1 Performance Evaluation of the Alternative Selection Strategy ............................ 50

3.2 Sensitivity Analysis Results of the Weightings ................................................... 57

3.3 Conclusion ............................................................................................................ 62

Chapter 4 Synchronisation Strategy for Coupling Microgrids .......................... 64

4.1 Considered Structure and Control of ISS ............................................................. 64

4.2 Synchronisation Strategy of Multiple Microgrids ................................................ 72

4.3 Communication System Considerations .............................................................. 82

4.4 Performance Evaluation ....................................................................................... 82

4.4.1 Scenario-A ......................................................................................................... 83

4.4.2 Scenario-B ......................................................................................................... 84

4.4.3 Scenario-C ......................................................................................................... 84

4.5 Conclusion ............................................................................................................ 94

Chapter 5 Conclusions and Recommendations ................................................... 95

5.1 Conclusions .......................................................................................................... 95

5.2 Recommendations for future research .................................................................. 96

5.2.1 Consideration of reactive power capacities and limits of microgrids ............... 96

5.2.2 Possibility of interconnection of a microgrids through multiple links .............. 97

5.2.3 Synchronisation method for microgrids with different topologies ................... 97

5.2.4 Protection Issues of the system of coupled microgrids ..................................... 97

5.2.5 Communication network and data transfer delay effect .................................... 97

References ................................................................................................................ 99

Publications arising from this Thesis ................................................................... 105

vii

List of Figures

Figure ‎1.1. A distribution network consisting of several isolated microgrids with

normally-open ISSes among them ............................................................................... 2

Figure ‎1.2. A distribution network consisting of several isolated microgrids with

normally-open ISSes among them. .............................................................................. 4

Figure ‎2.1. A remote-area distribution network composed of three islanded

microgrids with all three alternative CMGs when MG-1 is overloaded. ..................... 9

Figure ‎2.2. Schematic diagram of the communication links between the developed

OMT (located within the network tertiary controller) and the central controller of

each microgrid as well as the ISSes. .......................................................................... 11

Figure ‎2.3. Flowchart of the developed multi-criteria dynamic DMA. ..................... 18

Figure ‎2.4. Assumed power system topology for the microgrids in the distribution

network under consideration. ..................................................................................... 32

Figure ‎3.1 Sensitivity analysis plot of the selected alternative versus different

weightings of cost and distance.................................................................................. 60

Figure ‎4.1. Two sample structures of normally-open ISSes among the microgrids. . 65

Figure ‎4.2. Developed local controller for the ISSes. ................................................ 66

Figure ‎4.3. Required communication links and the transferred data. ........................ 66

Figure ‎4.4. (a) Phase-a voltage at two sides of the ISS when the synchronisation

command is initiated, (b) Phase-a voltage at two sides of the ISS when two MGs are

viii

synchronized, (c) The difference of phase-a voltages at two sides of the ISS at the

synchronisation. .......................................................................................................... 69

Figure ‎4.5. Required time for interconnection of microgrids for different and f. 70

Figure ‎4.6. Different interconnections of neighbouring microgrids: (a) Scheme-1, (b)

Scheme-2: radial line, (c) Scheme-2: loop line, (d) Scheme-3, (e) Scheme-4. .......... 73

Figure ‎4.7. Developed operation sequences of coupling multiple neighbouring

microgrids during the interconnection transition. ...................................................... 77

Figure ‎4.8. Case-1 simulation results. ........................................................................ 91

Figure ‎4.9. Case-2 simulation results. ........................................................................ 91

Figure ‎4.10. Case-3 simulation results. ...................................................................... 92




ix

List of Tables

Table ‎2.1. Assumed Line Parameters of the Microgrid System of Figure ‎2.4 at

Fundamental Frequency ............................................................................................. 33

Table ‎2.2. Assumed Uncertainties in the Generation Capacity and Demand for the

Microgrids. ................................................................................................................. 35

Table ‎2.3. Assumed Uncertainties in the Parameters of the Criteria in DMA. .......... 35

Table ‎2.4. Assumed Cloud Theory-Based Probabilistic Power Data and the

Calculated UPC and PDL for the Distribution Network [kW] (Example-1) ............. 38

Table ‎2.5. Assumed Cloud Theory-Based Probabilistic Data for Each Microgrid of

the Distribution Network Used in DMA (Example-1) ............................................... 39

Table ‎2.6. Comparison among the Parameters of Available Alternatives to Support

Overloaded MG-1 (Example-1) ................................................................................. 39

Table ‎2.7. Calculated Decision Making Matrix (Example-1) .................................... 39

Table ‎2.8. Assumed Weightings for the Criteria in DMA ......................................... 39

Table ‎2.9. Calculated Weighted Decision Making Matrix (Example-1) ................... 40

Table ‎2.10. Normalized Weighted Decision Making Matrix (Example-1) ............... 40

Table ‎2.11. Selected Alternative and Evaluation Results from Different Aggregators

(Example-1)................................................................................................................ 40

Table ‎2.12. Decision Making Matrix (Example-2) .................................................... 41

Table ‎2.13. Normalized Weighted Decision Making Matrix (Example-3) ............... 41

x


and Risk Matrix (Example-3) ..................................................................................... 42

Table ‎2.15. Risk Matrix (Example-3) ........................................................................ 42

Table ‎2.16. Assumed Cloud Theory-Based Probabilistic Power Data and the

Calculated UPC and PDL for the Network [kW] (Example-4) ................................. 43

Table ‎2.17. Assumed Cloud Theory-Based Probabilistic Data for Each Microgrid of

the Distribution Network Used in DMA (Example-4) ............................................... 43

Table ‎2.18. Comparison among the Parameters of Available Alternatives to Support

Overloaded MG-1 (Example-4) ................................................................................. 44

Table ‎2.19. Decision Making Matrix (Example-4) .................................................... 45


(Example-4) ................................................................................................................ 46

Table ‎2.21. Stochastic Analysis Results Demonstrating the Flags Generated by the

OMT and Decision-making and Load-shedding Functions for a Network Composed

of 3 Microgrids under two Considered Study Cases. ................................................. 48

Table ‎3.1. Considered Nominal Values for a Network Composed of 6 microgrids. . 51

Table ‎3.2 Random Values for the Assumed Network at the Time of Study. ............. 51

Table ‎3.3. Assumed Normalized Weightings for the Criteria. ................................... 52

Table ‎3.4. Decision Making Matrix for the Network with the Assumptions of the

Data of Table ‎3.1 and Table ‎3.2. ................................................................................ 53

Table ‎3.5 Normalized Weighted Decision Making Matrix Assuming the Weighting

Matrix of Table ‎3.3. .................................................................................................... 55

Table ‎3.6. Corresponding Column of the Normalized Weighted Decision Making

Matrix When Only One Criterion is Considered. ...................................................... 58

xi

Table ‎4.1. The overloaded and selected non-overloaded microgrids of the distribution

network as well as their UPC and PDL in the considered study cases. ..................... 86

Table ‎4.2. Time-sequence of the events in the considered study cases. .................... 87

xiii

List of Abbreviations

ALS Amount of load to be shed

APC Available power capacity

CMG Coupled microgrids

DER Distributed energy resources

DMA Decision-making algorithm

ISS Interconnecting static switch

MAIFI Momentary average interruption frequency index

MG Microgrid

OMT Overload management technique

PDF Probability density function

PDL Power deficiency level

PFA Power flow analysis

SAIDI System average interruption duration index

SAIFI System average interruption frequency index

SLSA Selective load-shedding algorithm

UPC Unused power capacity

Chapter 1 - Introduction

1

Chapter 1 Introduction

1.1 Introduction

Electrification of remote and rural areas has been always a major challenge due

to a variety of constraints such as the area accessibility and economic factors [1-2].

The electricity demand in these areas can be supplied by the help of distributed

energy resources (DERs) in an islanded scheme. Thus, the power system of remote

areas can be considered as a microgrid that operates in islanded mode [3]. The

microgrids should be formed such that there is enough generation capacity in their

embedded DERs to meet their local demands [4-6]. It is to be noted that a remote

area/town can be supplied by several independent microgrids, where each may have

a different owner (operator) and each is responsible for supplying the loads of a

specific region. Thus, the distribution network of a remote area can resemble the

system of Figure ‎1.1. These types of islanded microgrids are conventionally supplied

by diesel generators. The fuel transportation difficulties and the fuel cost adversely

affect the profits for the owners of each microgrid. If these areas are rich in

renewable energies, renewable-energy-based DERs can be utilized for electricity

generation to meet the local electrical demand [7].


2

MG-2MG-1

MG-k

DERMG-N–1

MG-N

D1

DN–1

DN–2

Load

Figure ‎1.1. A distribution network consisting of several isolated microgrids with normally-open

ISSes among them

The intermittency of non-dispatchable (e.g. solar and wind- based) DERs in

addition to load uncertainties can lead to imbalance between the instantaneous power

generation and demand in a microgrid. Any generation deficiency (overloading) will

lead to voltage/frequency drop. To address power imbalance problems in microgrids,

several solutions can be considered such as:

under frequency/voltage load-shedding [9]

utilization and control of battery energy storages [10],

optimal capacity design of dispatchable DERs (e.g. diesel generators) [11-

12],

interconnection of the microgrid to utility [13],

coupling of one microgrid to one/more neighbouring microgrid(s) [14].

Microgrids coupling is introduced in [14] as a solution to proliferate the

number of DERs in distribution networks. Each microgrid in Figure ‎1.1 may be

supported by one/more of its neighbouring microgrid(s) during power deficiency.


3

This can be achieved by closing the normally-open interconnecting static switch

(ISS) which is located between every two adjunct microgrids.

References [16-17] have proposed a transformative architecture for coupling

the neighbouring microgrids as a technique for improving the self-healing of the

distribution system in case of short-circuit faults in the network. The trade of power

among microgrids in the system of coupled microgrids (CMG) is addressed in [18].

Optimal control of a distribution network composed of utility-connected microgrids

forming a CMG is also studied in [19]. Dynamic operation of DERs within CMGs is

investigated in [20] and the dynamic security of the CMGs is examined in [21]. The

conditions under which two microgrids are interconnected are addressed in [22]. The

stability analysis of a CMG prior to the interconnection of the microgrids is

discussed in [23], as a preliminary step to prevent any interconnection that may lead

to system instability. Selection of the suitable microgrid(s) among the available

neighbouring microgrids when interconnecting them during overloading has not been

addressed in previous literature and is the main focus of this research.

This research proposes an overload management technique (OMT), based on

coupling the neighbouring islanded microgrids, and utilizes a dynamic multi-criteria

decision-making algorithm. The proposed OMT assumes a data communication

system is available to receive the power generation of all DERs and consumption of

essential/non-essential loads in all microgrids. The communication system also

transmits the command (output) of the OMT to the relevant ISS(es) to couple the

microgrids. Under such a case, the power flow control in the considered system is

based on the proper operation of the ISS; i.e. if the OMT decides that some

microgrids should be interconnected, the ISS of each of those microgrids will be

closed and thereby, the power flow will occur between the interconnected microgrids


4

automatically based on the dynamic operation of the DERs in each microgrid and no

further power control is required.

Load

MG-N

Load

MG-1DER

Load

MG-2DER

Load

MG-N-1DER

DER

Figure ‎1.2. A distribution network consisting of several isolated microgrids with normally-open

ISSes among them.

Based on the above assumptions, considering the distribution network of

Figure ‎1.2 with N islanded microgrids among which MG-1 is assumed to be

overloaded. Each of the other existing microgrids may be able to support MG-1

individually or in combination. In general, assuming N overloaded microgrids within

a distribution network composed of N microgrids, 2N–N′

–1 alternatives are available.

Thus, selecting the suitable microgrids to couple with the overloaded microgrid is

challenging due to the high number of alternatives. In addition, different criteria can

be considered for the selection, each with a different weighting which can further

complicate the selection process. Weighting of criteria is another area of research

which is also mentioned in this research. Because a criteria with higher weighting

than others can easily vary the outcome of OMT, different weighting are applied to

the criteria and the result of the outcomes are compared for assessment.


5

An important stage of forming a CMG is the synchronisation of the

interconnecting microgrids. This transition stage has not been investigated in details

in literature and it is another main research gap that is addressed in this thesis.

Conventionally, synchronisation will take place by using either a forced

technique to achieve quicker synchronisation or a non-forced technique in which

every two microgrids are synchronized over some time. In this research, a suitable

and effective, non-forced technique is considered in which the selected microgrids

are interconnected safely and promptly. To this end, a generalized algorithm is

developed and validated by time-domain simulation studies in PSCAD/EMTDC.

This developed algorithm is able to synchronize any number of microgrids, and

depending on how large the selected group is, this method can manage to

continuously check the voltage and frequency levels of every microgrid and

depending on their voltage and frequency difference, the algorithm decides which

two microgrids can be synchronized first. In large group of microgrids, for example,

when there are ten microgrids to be interconnected, the developed method can

synchronize two, three or even more pairs of microgrids at the same time so then the

final interconnection can be achieved quicker.

1.2 Aims and objectives of the thesis

The main objective of this thesis is to develop an OMT for islanded microgrids

to support a microgrid when a power deficiency occurs in an microgrid. The

proposed technique enables the overloaded microgrid to connect to one or more

neighbouring microgrids depending on some defined criteria. In addition, a

synchronisation strategy is developed for interconnection of the microgrids. To

achieve this goal, the specific objectives of the research are identified as:


6

to develop a dynamic multi-criteria decision making algorithm (DMA) to

select the suitable microgrids,

to define the different criteria required for DMA,

to qualify the selected microgrid(s) based on the deviations in voltage and

frequency after coupling the microgrids,

to define the portion of the non-essential loads to be shed from each

microgrid based on the proposed DMA such that all essential loads of all

microgrids are always supplied,

to develop a suitable and practically applicable strategy for coupling

neighbouring microgrids,

to develop a suitable local control system for the ISSes.

1.3 Significance of research

It is expected that the future distribution networks will be in the form of

multiple islanded microgrids, distributed over a close proximity. This research will

help to improve the operation, control and management of those microgrids during

power deficiencies. A proper technique is developed which detects the overloading

and aims to interconnect the microgrids to mitigate this problem. Also, proper

synchronisation technique is developed which facilitates the suitable connection of

the microgrids.

1.4 Structure of the thesis

This thesis is organized in five chapters: ‎Chapter 1 outlines the research aims

and objectives along with the need and the justification through a literature review


7

for the research topic. ‎Chapter 2 discusses the necessity of coupling the microgrids

and the complexity of decision-making in details. The proposed OMT consisting of a

dynamic multi-criteria DMA is introduced in this chapter. The performance of the

developed technique is evaluated within a MATLAB-based stochastic analysis.

‎Chapter 3 focuses on the impact of the weightings considered for each criterion as it

is expected that these weightings can significantly modify the selected alternative.

‎Chapter 4 describes the developed synchronisation strategy in details. The required

data communication system for this technique is highlighted in this chapter. The

performance evaluation results of a distribution network with the developed

technique are also presented here. Finally, the conclusions drawn from this research

and the recommendations for future research are highlighted in ‎Chapter 5.

Chapter 2 – Coupling of Neighbouring Microgrids

8

Chapter 2 Coupling of Neighbouring

Microgrids

This chapter discusses the interconnection of microgrids when the generation

in one or more microgrids cannot meet the demand. An algorithm is developed and

presented in this chapter that first detects any overloading in a microgrid and then

aims to interconnect the overloaded microgrid with a suitable neighbouring

microgrid, using the dynamic multi criteria decision making technique. Any decision

is made by considering several criteria in which each criterion has a specific

weighting. The outcome of the decision identifies whether an interconnection will be

able to rectify the overloaded microgrid or not, and if so, identifies the selected

microgrids for interconnection.

2.1 Necessity and Complexity of Coupling Microgrids

This research focuses on remote area networks where a utility connection is not

available. Thus, the loads are supplied by small microgrid networks. Each of these

microgrids may have a different owner, that has invested in the installation of the

DERs in that microgrid and charges the loads based on their electricity consumption.

Thereby, it is assumed that these microgrids operate in islanded mode and

independently from each other.


9

Due to load and generation uncertainty, it is highly probable to expect power

generation deficiency or overloading at some portions of the operation stage. Under

such conditions, except load-shedding, the other possible option to control a

microgrid is external support in the form of importing power from one or a group of

neighbouring microgrids. Thereby, an OMT is proposed and developed in this

research to overcome the overloading issues of the microgrids that operate in remote

areas.

DER

Load

MG-3

D1

D3

MG-1

MG-2

D2

DER

Load

MG-3

MG-2

CMG

(b)(a)

MG-1

DER

Load

MG-3

MG-1

MG-2

CMG

(d)(c)

DER

Load

MG-3

MG-1

MG-2

CMG

Figure ‎2.1. A remote-area distribution network composed of three islanded microgrids with all three

alternative CMGs when MG-1 is overloaded.

Consider the distribution network of Figure ‎1.1 with N islanded microgrids,

among which MG-1 is assumed to be overloaded. Each of the other existing


10

microgrids may be able to support MG-1 individually or in combination with others.

As an example, for N = 3, the alternative microgrids are [{2}, {3}, {2,3}] (see Figure

‎2.1) and for N = 4, the alternative microgrids are [{2}, {3}, {4}, {2,3}, {2,4}, {3,4},

{2,3,4}] while for N = 5, the alternative microgrids are [{2}, {3}, {4}, {5}, {2,3},

{2,4}, {2,5}, {3,4}, {3,5}, {4,5}, {2,3,4}, {2,3,5}, {2,4,5}, {3,4,5}, {2,3,4,5}]. In

general, assuming N microgrids are overloaded, the alternatives are combinations of

any‎single‎microgrids,‎any‎ two‎microgrids,‎ any‎ three‎microgrids…,‎and‎any‎N– N

microgrids out of the available N– N microgrids. Hence, the total number of

alternatives, denoted by NA, is

NN

NN

NNNNNNNN

i

NN

iA CCCCCN

...3211 (‎2.1)

where b

aC = b!/[(b–a)!a!] and a! = a (a – 1) …1. Equation (‎2.1) can be

simplified as

12 NN

AN (‎2.2)

Thus, selecting the suitable microgrid(s) to couple with the overloaded microgrid

among all alternatives is challenging due to the high number of alternatives. In

addition, different criteria can be considered for the selection, each with a different

weighting, which can further complicate the selection process.

To overcome the problem of proper alternative selection among a large number

of alternatives, while considering several criteria with different weighting, the

developed OMT utilizes a decision-making algorithm to assess the alternatives and

select the suitable one.

It is worth mentioning that Figure ‎1.1 depicts only one of the many possible

topologies that the neighbouring microgrids can be connected. The proposed OMT in

this research does not depend on neither the interconnection topologies of the


11

microgrids, nor the topology of an individual microgrid. Thus, other interconnection

topologies are also acceptable.

2.2 Proposed Overload Management Technique (OMT)

The developed OMT will be located as a module (agent) within the network

tertiary controller and will continuously communicate with the central controller of

each microgrid as well as the ISSes (see Figure ‎2.2). It is to be noted that the

communication system, data bandwidth and topology is beyond the scope of this

research and is not discussed in this thesis.

MG-2MG-1

MG-k

MG Central

Controller

MG Central

Controller

MG Central

Controller

MG Central

Controller

MG Central

Controller

Network

Tertiary

Controller

Figure ‎2.2. Schematic diagram of the communication links between the developed OMT (located

within the network tertiary controller) and the central controller of each microgrid as well as the

ISSes.

The proposed OMT is composed of one main function and three sub-functions,

namely decision-making function, load-shedding function, and PFA function. Two

algorithms, namely DMA and selective load-shedding algorithm (SLSA) are used

respectively within the decision-making and load-shedding functions. The proposed


12

OMT and its sub-functions are described in details below while the algorithms are

described in the next Section. The PFA function is discussed in Section ‎2.4.

The OMT continuously communicates with the central controller of each

microgrid to receive the information about the total active power generation of the

dispatchable DERs as well as the total active power consumed by all loads. For MG-

i, let us denote these quantities respectively as Pdisp-DER (MG-i) and Pload (MG-i). The

OMT will first identify the overloaded microgrid(s) and then will take action

depending on the network conditions such as the number of overloaded microgrids

and the unused power capacity (UPC) that is available in the other microgrids. The

OMT calculates the UPC for MG-i as

max

)-(MGDER-disp1

ii PUPC (‎2.3)

It is desired to maintain the UPC of every microgrid higher than a threshold as

}...,,1{ A)-(MGload)-(MGDER-dispNiPPUPC

iii (‎2.4)

where‎∑max

)-(MGDER-disp

iP

is the total capacity of dispatchable DERs in MG-i and 0 < 1 < 1

(e.g. 1 = 0.1) imposes a safety margin. In the rest of this thesis, (‎2.4) is assumed as

the overloading condition of a microgrid.

If condition (2.4) is valid for all microgrids of the distribution network, no

action needs to be taken by the OMT. However, if it is invalid for one or more

microgrids, the OMT evaluates the availability of surplus power in the network as

N

i

i

N

i i PUPC1

max

)-(MGDER-disp11 (‎2.5)

In the rest of this thesis, (2.5) is considered as the constraint for coupling the

microgrids.

If condition (2.4) flags that one or more microgrids are overloaded and

constraint (2.5) flags the availability of surplus power in the distribution network, the


13

OMT proceeds to support the overloaded microgrids by coupling one or more of the

non-overloaded microgrids to the overloaded one(s).

If condition (2.4) is invalid for n1 = N – 1 microgrids but constraint (2.5) is

valid, the OMT flags that the only alternative is coupling all microgrids. It then calls

the PFA function to verify that coupling all microgrids will not cause non-standard

voltage and frequency deviation in the CMG system. From the PFA, which is

discussed in Section ‎2.4, the maximum voltage deviation in the buses of the system

and the maximum frequency deviation in the system, respectively denoted by V and

F, are calculated as

||Δ

|)(|maxΔ

nom

1,...,nom bus

ffF

VVV Nii

(‎2.6)

where Vi is the per-unit (pu) voltage of bus-i, i 1,‎2,‎…,‎Nbus and f is frequency of

the system and Nbus is the number of buses in the system of CMG while it is assumed

that Vnom = 1 pu and fnom = 50 Hz. These two parameters are then evaluated in

V 0.1 and F 0.5 (‎2.7)

to verify the possibility of microgrids interconnection, assuming that the maximum

acceptable voltage deviation is 10% and the maximum acceptable frequency

deviation is 0.5 Hz.

If condition (2.4) is invalid for 1 < n1 < N microgrids, the OMT flags that

several alternatives are available and decision-making is required. It then calls the

decision-making function to formulate all alternatives and to define the suitable

alternative using the DMA. The proposed DMA is discussed in details in the next

Section. If an alternative is selected by the DMA, the OMT initiates the proper

command for the relevant ISS(es) to close. However, if no suitable alternative is


14

chosen, the decision-making function flags that load-shedding is inevitable and

requests the main function of the OMT to call the load-shedding function.

If the OMT calls the load-shedding function, it first seeks the possibility of

shedding a portion of the non-essential loads in one or more microgrids such that the

essential loads of all microgrids are not interrupted. For this, it first identifies the

available power capacity (APC) of each microgrid as

)-(MGDER-nondisp)-(MGDER-disp ii

PPAPC i (‎2.8)

where‎ ∑Pnondisp-DER (MG-i) denotes the total active power generation by non-

dispatchable DERs in MG-i at that moment. It is to be noted that APC represents the

maximum power that can be supplied in MG-i to its loads plus the power loss in the

lines. Based on (2.8), the load-shedding function defines the amount of loads to be

shed (ALS) from each microgrid as

))(1()-(MGLoad2 ii APCPALS

i (‎2.9)

where 0 < 2 < 1 (e.g. 2 = 0.1) imposes a safety margin to compensate for line

losses. For successful load-shedding in each microgrid, the ALS should be equal or

smaller than the total of non-essential loads in each microgrid at that moment,

denoted‎by‎∑Pnon-ess Load, i.e.

)-(MGLoad ess-non i

PALS i (‎2.10)

If the load-shedding function defines that condition (2.10) is valid for all

microgrids, it flags that load-shedding is successful and sends the ALS level of each

microgrid to their central controllers. And if condition (2.10) is invalid for all

microgrids, it flags that load-shedding is not viable.

If condition (2.10) is invalid for 1 n2 < N microgrids, the load-shedding

function first sends the ALS level to the microgrid(s) which satisfy (2.10) to shed the

defined portion of their non-essential loads. Then, it evaluates whether the sum of


15

ALSes in all microgrids of the distribution network is less than the sum of non-

essential loads in all microgrids i.e.

N

i

N

i i iPALS

11 )-(MGLoad ess-non (‎2.11)

If (2.11) is satisfied, the load-shedding function seeks the possibility of

interconnecting the microgrid(s) which do not satisfy (2.10) with the one(s) that still

have some non-essential loads. For this, it defines a second ALS level to compensate

for the microgrids who did not satisfy (2.10). In the rest of this thesis, (2.11) is

considered as another constraint for coupling microgrids, which is used only when

load-shedding is accompanying coupling. The second ASL level, denoted by ALS 2

,

is defined as

}...,,1{)( 21

2 2

)-(MGLoad ess-nonniPALSALS

n

i i i

(‎2.12)

The load-shedding function then formulates the alternatives which their total

remaining non-essential loads are higher than ALS 2

, i.e.

}...,,1{)( 2

)-(MGLoad ess-non Ak i NkALSALSPi

(‎2.13)

where NA is the number of the formulated alternatives. The alternatives qualified in

(2.13) are then assessed by the SLSA to select a suitable alternative. If a suitable

alternative is selected by the SLSA, the load-shedding function flags that a suitable

alternative is selected. It then defines the portion of ALS 2

for each microgrid of the

selected alternative based on the ratios of their non-essential loads and sends the

amount of the second load-shedding level to the central controller of each microgrid

as well as the proper command to the relevant ISS(es) to close. However, if the

SLSA does not select an alternative, the load-shedding function flags that microgrids

coupling with further load-shedding is not viable.

In this research, the microgrids are coupled to prevent overloading of a

microgrid. The proposed method can be further expanded to facilitate coupling of


16

microgrids so that the surplus power of the DERs of a microgrid can be exported to

other microgrids with a lower electricity price (as an incentive technique) [18] to be

stored in the energy storage [24], or to be consumed by the controllable loads of the

other microgrids under the demand dispatch concept [25].

It is worth mentioning that the proposed OMT solely focuses on the situations

that at least one of the microgrids are overloaded and tries to select a suitable

alternative to which the overloaded microgrid(s) will be interconnected, such that an

acceptable power balance is achieved. The proposed OMT does not lead to an

optimum generation in the DERs but tries to reduce the load-shedding rate and

prevent instability due to power generation-demand imbalance. To achieve optimum

generation in the DERs of a CMG, an economic dispatch-type method can be

utilized.

It is also noteworthy that in this research, overloading is defined based on the

balance of generation and consumption of active power solely. Reactive power was

not considered in this approach assuming that reactive power support (in the form of

fixed or switched capacitors) are available in the network. The proposed OMT can be

further modified to consider the interconnection of microgrids for reactive power

support, after a detailed techno-economic analysis.

2.3 Dynamic Multi-Criteria DMA

The multi-criteria decision-making model prescribes a method for prioritizing

and selecting the most favourable alternative from a set of alternatives, denoted by A

{A1, A2,‎…, ANA}, based on a set of criteria, denoted by c {c1, c2,‎…, cNc .}, Nc being

the number of criteria. Each criterion may have a different weighting. The

corresponding normalized weightings for the criteria are denoted by w {w1, w2,‎…,


17

cNw .}‎where‎∑j wj = 1. These weightings are defined by the help of the experts, as

discussed later in this Section.

The multi-criteria decision-making problem can be modelled in the form of a

matrix as [26]

CAAA

C

C

A

CC

NNNN

N

N

N

NN

xxx

xxx

xxx

A

A

A

wcwcwc

21

22221

11211

2

1

2211 )()()(

(‎2.14)

where xuv represents the performance of alternative Au from the perspective of

criterion cv. The matrix of (2.14) will then be modified to include the weighting of

each criterion as

ANCNANCNANAN

CNCN

CNCN

AN

CN

X

X

X

xwxwxw

xwxwxw

xwxwxw

A

A

A

ccc

2

1

2211

2222211

1122111

2

1

21

(‎2.15)

The evaluation results for the alternatives, denoted by X {X 1, X 2,…,‎ANX }, are

calculated as

)(agg uvvu xwX (‎2.16)

where agg(.) is an aggregating function such as average, product, max-min and

Hurwitz in the form of [27-29]


18

Selecting Criteria

{c1, c2,…, c }

Formulating Alternatives

{A1, A2,…, A }

Requesting the

Weightings from ExpertsFirst iteration

k = 1 ?

Acceptable data

dispersion v e ?

Yes

No

Weighting the Criteria

{w1, w2,…, w }

Yes

},...,,{21

iii

CNwww

No

Start

Evaluating Alternatives

with different aggregators

{X1, X2,…, X }

Defining Dynamic Evaluations

},...,,{21

dN

dd

CXXX

Memory

1-k

uX

Qualifying Alternatives

based on Qualifying Criteria

{xu1, xu2, xu3, xu4}

Calculating Performance of

Alternatives for other Criteria

{xu4, xu5,…, xu }

Retrieving previous iteration

evaluation results

kd

uuXX

Storing new evaluation results

for next iteration

Constitu

ting D

ecis

ion

Ma

kin

g M

atr

ix

Same Alternative Selected

by All Aggregators?

Yes

Selecting the Alternative(s) with

Highest Dynamic Evaluation

from each Aggregator

end

Defining the Risk Index

of Each Alternative

{ru1, ru2,…. ru }

Defining the Risk Index

of Selected Alternative

{R1, R2, R3, R4}

Risk Matrix

No

Choosing the Selected Alternative

with minimum Risk Index {Ru}

Applying the Effect of Different Criteria

Weighting in the Performance Values

{w1xu1, w2xu2,…., w x }

CN

AN

CN

CN

CN CANN

AN

AN

Defining the Criteria Weightings

Figure ‎2.3. Flowchart of the developed multi-criteria dynamic DMA.

where min(.) and max(.) are respectively the minimum and maximum functions and

3 [0,1] (e.g. 3 = 0.75) is the optimist coefficient used in the Hurwitz method.

Each of these aggregators has advantages and disadvantages as discussed in [27-29].

The alterative with the highest X has the highest priority and is selected by the DMA.

The flowchart of the developed multi-criteria dynamic DMA is shown in

Figure ‎2.3.


19

2.3.1 Risk Index

)max().1()min(.)(Hurwitz

)(min

)(product

)(average

33

,...,1

1

1

uvvuvvuvvu

CNvuvvu

CN

u uvvuvvu

C

CN

u uvvuvvu

xwxwxwX

xwX

xwxwX

NxwxwX

(‎2.17)

All of the aggregators given in (2.17) may not necessarily select the same

alternative. To overcome this problem, the risk index, denoted by R {R1, R2, …,

ANR }, is defined for each alternative in the form of a matrix as [26-27]

ANMNANANAN

MN

MN

AN

MNM

R

R

R

rrr

rrr

rrr

A

A

A

xcxcxc

2

1

21

22221

11211

2

1

maxmax

22

max

11 )()()(

(‎2.18)

where ruv for criterion cv is the deviation of the performance of each alternative

versus the alternative with the highest performance and is calculated from

max

vuvvuv xxwr (‎2.19)

where max

vx is the maximum of wvxuv for criterion cv among all alternatives. From

(2.18), the risk index for alternative Au, denoted by Ru, is selected as the maximum of

ruv.

In case of difference among the selections by aggregators of (2.17), the risk

index of the alternatives selected by the aggregators are analyzed only to speed up

the process and the selected alternative with a lower risk index is chosen by the

DMA as the suitable alternative.


20

2.3.2 Dynamic DMA

DMA carries out dynamically. However, overtime the available alternatives

can be modified e.g. newer alternatives get added or previously existing alternatives

vanish depending on the overloaded microgrids. Furthermore, the criteria and their

weightings can dynamically change due to the preference of the network operator.

Hence, a dynamic DMA is utilized in which the historical decision-making results

are considered in future decision-makings. In dynamic DMA, first the evaluation

result of each alternative is defined from (2.15). Then, a new dynamic evaluation

result, denoted by X d {X

d1, X

d2,‎ …, X

dNA}, is defined at iteration k based on

previous iteration as [28].

11 k

u

k

u

k

u

k

u

d

u XXXXX (‎2.20)

Note that in case an alternative appears for the first time, its current evaluation

result is used instead of (2.20) In addition, if an alternative vanishes in a new

decision-making iteration but it was available in the previous iteration, its evaluation

result is stored in memory and retrieved in the first decision-making iteration that the

alternative appears again.

2.3.3 Criteria Weightings

The outcome of the DMA highly depends on the assumed weightings for each

criterion. Therefore, these weightings should be selected carefully. In complex

systems such as power systems, there is not a systematic method to define these

weightings. An acceptable method is a census from the experts. For this purpose, a

group of experts are required to be asked to participate in defining the weightings for

these criteria. They will evaluate the weightings for each criterion based on their

experience and outlook in either form of linguistic (extremely big/small, very


21

big/small, big/small, a little big/small, and neutral) or number (between 0-100%).

After this, the linguistic and numerical values will be first mapped into a number in

[0, 1] range and then normalized. The weighting for each criterion will be defined as

the average of all normalized values as

e

eN

i

i

uu Nww

1 (‎2.21)

where Ne is the number of the experts. To achieve a high confidence in the

weightings, the variation coefficient for data dispersion (v ) of criterion cv is

calculated as

ue

N

i u

i

v wNwwe

u

1

2)(

(‎2.22)

If v is smaller than a pre-defined small threshold (e.g. e), it can be concluded that

wv represents the true weighting for criterion cv based on experiences and outlooks

of all participated experts. If v is not smaller than the pre-defined threshold, more

experts should be invited to participate in the census so that the weightings fulfill the

desired dispersion.

2.3.4 Qualifying Criteria

All possible alternatives may not be qualified to couple with the overloaded

microgrid(s) due to reasons such as lack of enough surplus power in microgrids of an

alternative, non-standard voltage and frequency deviation in the system after an

alternative is coupled with the overloaded microgrid(s) or when one microgrid vetoes

supporting another microgrid.

Hence, the DMA first qualifies the alternatives based on these conditions. The

first 4 criteria are defined as:

criterion-1: microgrid consent/veto for coupling,


22

criterion-2: availability of surplus power in microgrids,

criterion-3: voltage deviation, and

criterion-4: frequency deviation.

The performance of alternative Au versus these criteria is expressed as

0..orΔ0.5if0

0Δ0.5 if1 Δ2

5.0Δ0 if1Δ2

0.orΔ0.1if0

0Δ0.1 if1 Δ10

1.0Δ0 if1Δ10

0or1 if0

31 if)1(5.0

3 if1

coupling consentsMG if1

coupling MG vetoes if0

321

4

21

3

1

2

1

uuuu

uu

uu

u

uuu

uu

uu

u

uu

uu

u

u

u

xxxF

FF

FF

x

xxV

VV

VV

x

x

x

x

(‎2.23)

where u is the ratio of the UPC in microgrid(s) of alternative Au versus the power

deficiency level (PDL) of overloaded MG-j (i.e. u = UPCu / PDLMG-j).

If any of the above 4 criteria define an alternative unqualified, the performance

of that alternative versus the remaining criteria is neglected i.e.

}...,,5{0...if

0...if0

4321

4321

C

uuuuuv

uuuu

uv Nvxxxx x

xxxx x

(‎2.24)

2.3.5 Other Criteria

Six other criteria are considered for alternative selection other than the 4

qualifying criteria. These criteria consider the line loss, electricity price, reliability

indices, supply security and CO2 emission when selecting a suitable alternative. It is

to be noted that defining and calculating these indices for each of the microgrids is

beyond the scope of this research. Assuming these parameters are known and


23

revealed to the OMT, the performance of each alternative for criterion 5-10 will be

calculated, as discussed below:

2.3.6 Power Loss in Interconnecting Lines

One important criterion in the selection of an alternative is the power loss in

the interconnecting lines (tie-lines) which depends on the distance between the

overloaded microgrid and the selected microgrid(s) and the impedance of these lines.

The power loss can be calculated from PFA for each alternative. Then, it is

normalized in the range of [0, 1] where 0 and 1 are respectively for the alternative

with maximum and minimum power loss.

To reduce the required computation time, a second method is utilized in this

research in which the distance and impedance of the line(s) among the overloaded

microgrid and the microgrid(s) of each alternative is considered. These values are

pre-defined for the DMA and the only unknown parameters are the power flow from

each microgrid to the overloaded microgrid. However, based on droop characteristic,

each DER in the microgrid shares the load based on a pre-defined ratio (i.e. droop

curve coefficients). Based on this concept, each microgrid shares a portion of the

power deficiency level of the overloaded microgrid according to the maximum

capacities of its dispatchable DERs. Hence, assuming p microgrids in alternative Au,

coefficient i represents the ratio of power supplied from MG-i to overloaded MG-j

as

}...,,1{1

max

)-(MGDER-disp

max

)-(MGDER-disppiPP

p

i iiui, (‎2.25)

where‎∑max

)-(MGDER-disp iP

shows the maximum power capacity of all dispatchable DERs in

MG-i. Coefficient i,u is calculated once only and is not repeated in each iteration.


24

Thus, the computation time is significantly improved compared to the PFA. After i

is calculated, the total power loss parameter of alternative Au is calculated as

p

i iiui,u DZP1loss, )( (‎2.26)

Note that (2.26) is not equal to the power loss of each alternative (in kVA) but

represents a relationship among different alternatives from line loss prospective.

From (2.26), the performance of each alternative is calculated for this criterion as

ANuuuu PPx 1,...,loss,loss,5 )max(1 (‎2.27)

Although the second method is not as accurate as considering PFA but it highly

improves the speed of decision-making and is therefore, preferred and used in this

research.

2.3.7 Electricity Price

Another important criterion in selecting an alternative is the price of electricity

offered by the owner of each microgrid. A microgrid owner may sell electricity to

neighbouring microgrids with a different price with respect to its own costumers. The

price can also dynamically change over time due to different reasons (e.g. the

variations in the price of fuel consumed in diesel generators or the availability of

power from intermittent non-dispatchable DERs). Assuming Ei as the electricity unit

price offered by MG-i (in $/kWh), the total equivalent electricity cost to be paid by

the owner of the overloaded microgrid to the owners of microgrid(s) in alternative Au

is defined as

p

i iui,u EE1cost, (‎2.28)

From (‎2.28), the performance of alternative Au is calculated for this criterion as

ANuuuu EEx 1,...,cost,cost,6 )(max1 (‎2.29)


25

2.3.8 Reliability

It is highly probable that each microgrid may have a different reliability level.

In addition, the failure rate of CMG is the sum of the failure rates of each

participating individual microgrid. Therefore, as the number of microgrids increases

in an alternative, the failure rate of the alternative increases (i.e. the reliability

decreases). It is highly desirable for the overloaded microgrid to couple with

microgrid(s) in an alternative which have higher reliability to reduce the possibility

of interruption to the essential load of the overloaded microgrid. Different reliability

indices can be considered such as system average interruption frequency index

(SAIFI), momentary average interruption frequency index (MAIFI) and system

average interruption duration index (SAIDI). SAIFI and MAIFI represent the

frequency of supply interruptions whereas SAIDI represents the duration of

interruptions (in minutes). RBfu and RB

du indices are defined for alternative Au

composed of p microgrids as

p

i ui,u

p

i ui,ui,u

SAIDIRB

.MAIFI.SAIFIRB

1

d

1 21

f (‎2.30)

where {1, 2} [0, 1] and 1 +2 = 1 are the assumed weightings for SAIFI and

MAIFI, respectively. In this research, it is assumed that 1 =2. From (2.30), the

performance of alternative Au is calculated for these criteria as

ANuuuu

ANuuuu

RBRBx

RBRBx

1,...,

dd

8

1,...,

ff

7

)(max1

)(max1

(‎2.31)

Alternatively, these criteria can be combined together with different weightings to

constitute one criterion only. However, since the performance of each alternative is

easily compared when they are separate (due to dimension difference), reliability is

considered as two criteria but with the same weightings in this research.


26

2.3.9 Supply Security

If a microgrid has high power generation by its non-dispatchable DERs, it may

have a higher UPC in its dispatchable DERs. Once this microgrid is coupled with an

overloaded microgrid, the overloaded microgrid does not have a high supply security

as any unexpected drop in the power of the non-dispatchable DERs (due to

environmental conditions) may cause overloading of the CMG. Hence, it is important

to consider the security of supply when selecting an alternative. Supply security

index SSu is defined for alternative Au composed of p microgrids as

p

i i

p

i iu PPSS1 )-load(MG1 )-DER(MG-disp (‎2.32)

where‎∑Pload(MG-i) shows the average active power consumed by all loads in MG-i.

From (2.32), the performance of alternative Au is calculated for this criterion as

ANuuuu SSSSx 1,...,9 )(max/1 (‎2.33)

2.3.10 CO2 Emissions

Consider a distribution network in which the distribution network operator

penalizes the microgrid owners based on their level of CO2 emission [30]. Hence,

each microgrid owner may charge CO2 emission penalties from customers in the

form of carbon tax, based on the supplied electricity to each customer. When

selecting an alternative, it is desired to select an alternative with less CO2 emissions

to minimize the penalties imposed to the overloaded microgrid. Therefore, the level

of CO2 emissions by each microgrid can be considered as a criterion. Assuming the

total CO2 emission for MG-i as Emi, CO2 emission index is defined for alternative Au

composed of p microgrids as

p

i iui,uEmCO

12 (‎2.34)


27

From (2.34), the performance of alternative Au is calculated for this criterion as

ANuuuu CoCox 1,...,10 )2(max21 (‎2.35)

The developed OMT with its main, load-shedding and decision-making

functions is shown Algorithm 2.1 and has a time-complexity of O(N).


28

Algorithm 2.1. Overload Management Technique (OMT)

Pre-defined Inputs: max

)-(MGDER-disp

iP

Dynamic Inputs: ∑Pload (MG-i),‎∑Pnon-ess load (MG-i),‎∑Pdisp-DER (MG-i),‎∑Pnon-disp-DER (MG-i)

Dynamic Outputs: Flag, command to ISSes, ALSi, ALSi2

Main Function:

1 Calculate UPCi from (2.3) for each microgrid;

2 if condition (2.4) is satisfied for all microgrids then

3 | Flag: No interconnection is required;

4 else

5 | Calculate‎∑UPCi i=1,…,N from (2.3);

6 | if constraint (2.5) is not satisfied then

7 | | Flag: Coupling microgrids is not helpful and load-shedding is

| | inevitable;

8 | | Call Load-shedding Function to evaluate the possibility of load-shedding;

9 | else

10 | | if N – 1 microgrids are overloaded based on condition (2.4) then

11 | | | Flag: The only alternative is coupling all N microgrids;

12 | | | Call PFA Function;

13 | | | if constraint (2.7) is satisfied then

14 | | | | Flag: All N microgrids can be coupled;

15 | | | | Send the command to relevant ISS(es) to close;

16 | | | else

17 | | | | Flag: Coupling all N microgrids is not viable and load-

| | | | shedding is inevitable;

18 | | | | Call Load-shedding Function to evaluate the possibility of

load-shedding;

19 | | | end

20 | | else

21 | | | Flag: Several alternatives are possible; hence, decision-making

| | is required;

22 | | | Call Decision-making Function to assess the alternatives;

23 | | | if an alternative is selected by Decision-making Function then

24 | | | | Flag: A suitable alternative is selected;

25 | | | | Send the command to relevant ISS(es) to close;

26 | | | else

27 | | | | Flag: A suitable alternative is not available and load-

| | | shedding is inevitable;

28 | | | | Call Load-shedding Function to evaluate the possibility of

| | | load-shedding;

29 | | | end

30 | | end

31 | end

32 end


29

Decision-Making Function:

1 Formulate the alternatives;

2. Call DMA;

3 if an alternative is selected by DMA then

4 | Flag: A suitable alternative is selected for coupling the microgrids;

5 | Send the command to relevant ISS(es) to close;

6 else

7 | Flag: A suitable alternative is not available and load-shedding is inevitable;

|

8 | Call Load-shedding Function to evaluate the possibility of load- shedding;

|

9 end

Load-shedding Function:

1 Calculate ALSi from (2.9);

2 if condition (2.10) is satisfied for all microgrids then

3 | Flag: Load-shedding is successful;

4 | Send ALS to each microgrid to shed its loads accordingly;

5 else

6 | Send the ALS level to those microgrid(s) that satisfy condition (2.10);

7 | if constraint (2.11) is satisfied then

8 | | Calculate ALS 2 from (2.12) & formulate alternatives satisfying (2.13);

9 | | Call SLSA;

10 | | if an alternative is selected by SLSA then

11 | | | Flag: Coupling of microgrids accompanied by further load- shedding is selected;

12 | | | Send ALS 2 to relevant microgrid(s) to shed their loads;

13 | | | Send the command to relevant ISS(es) to close;

14 | | else

15 | | | Flag: Coupling of microgrids accompanied by further load- shedding is not viable;

16 | | end

17 | else

18 | | Flag: Coupling of microgrids accompanied by further load- shedding is not viable;

19 | end

20 end

2.4 Power Flow Analysis (PFA) for Microgrids

Standard PFAs have one slack bus with known voltage magnitude and angle

and regulated buses with known voltage magnitudes and active powers. It also

assumes that frequency is constant. The microgrids operating in islanded mode do

not have slack bus. For a microgrid operating in islanded mode, the DERs modify

their output voltage magnitude and frequency, using the droop control, based on the


30

network loading conditions, as discussed in [31-32]. Hence, the PFA for an islanded

microgrid needs to consider these characteristics, as highlighted in [33]. It is also to

be noted that as the voltage and frequency are not constant in the microgrid under

different loading conditions, the dependency of the load and line parameters on

voltage and frequency should also be considered in the PFA.

A Gauss-Seidel-based PFA is developed in this research and used within the

OMT to compute the maximum voltage and frequency deviation for the considered

CMG systems. Consider a microgrid with Nbus buses, Ndisp DER dispatchable DERs

and Nnon-disp DER non-dispatchable DERs (which may have a radial or mesh structure)

and an admittance matrix of Ybus

(in pu). Assume that a bus is connected to either a

load or a DER. Bus-i when connected to a load (referred to as load-bus in the rest of

this section) has a power consumption of Siload

= Piload

+ j Qiload

(in pu) whereas when

connected to a non-dispatchable DER (referred to as non-dispatchable DER-bus) has

a power consumption of Sinon-disp DER

= –Pinon-disp DER

(in pu). Assuming a set of initial

values for the voltages of all buses (e.g. 1 0.01 pu), the PFA first calculates the

current drawn by each load in iteration kp as

}...,,1{)(conj load

1NiVSI pk

ii

pk

i

(‎2.36)

where conj(.) is the conjugate function. In a similar way, the current injected by each

non-dispatchable DER is calculated for i {1,…,Nnon-disp DER}. Then, the voltages of

all load and non-dispatchable DER-buses are calculated similar to classic PFA as

busbus

1

1bus

i

N

k

pk

kki,

pk

i

pk

iYVYIV

(‎2.37)

Once the voltages for all load-buses and non-dispatchable DER-buses are

updated from (2.37) at each iteration, the voltages of the buses are slightly modified

based on classic Gauss-Seidel method with a correction/acceleration factor of 4 as


31

)(1

4

1 pk

i

pk

i

pk

i

pk

iVVVV

(‎2.38)

then, the pu total power loss in the lines of microgrid, denoted by Sloss

, is calculated

as

bus

1

bus 2busloss )()(N

i

N

ik

pk

k

pk

iki,

pkVVYS (‎2.39)

Hence, the required power to be generated by the dispatchable DERs is

DER disp-nonlossloadDER disp )()( SSSS pkpk (‎2.40)

The active and reactive power part‎ of‎∑Sdisp DER

is shared among the dispatchable

DERs of the microgrid based on their pre-defined droop ratios, denoted by mD and

nD, as

)(Im1

1)(

)(Re1

1)(

DER disp

DERdisp

1

D

D

DER disp

DER disp

DERdisp

1

D

D

DER disp

Sn

nQ

Sm

mP

N

i i

ipk

i

N

i i

ipk

i

(‎2.41)

where i {1,…,‎ Ndisp DER} while Re(.) and Im(.) are respectively the real and

imaginary functions.

Once the active powers generated by the dispatchable DER-buses are defined

from (2.41), the microgrid frequency is calculated from the droop curve of either of

the dispatchable DERs as

pk

ii

pkPmff )( DER disp

max (‎2.42)

In addition, the voltage magnitude of each dispatchable DER-bus is calculated

from the reactive power-voltage droop coefficient of each DER as

pk

ii

pk

i QnVV| )(| DER disp

max (‎2.43)

Due to lack of slack bus, the bus connected to one of the dispatchable DERs

(e.g. the first dispatchable DER) needs to be assumed as the reference bus. The angle


32

of the reference bus is always zero and all other angles in the microgrid are

considered with respect to this bus. Thus, the voltages of the dispatchable DER-buses

are updated at each iteration based on the voltage magnitudes calculated in (A8) and

the angles of the voltages in the previous iteration as

}...,,2{)(angle||

10||

DER disp

1NiVV

iVV

pk

i

pk

i

pk

ipk

i (‎2.44)

where angle(.) is the function to derive the angle.

The considered loads in this research are assumed to be a voltage and

frequency-dependent constant impedance-type. Thus, all loads are updated in each

iteration of the PFA based on the voltage magnitude and frequency of the buses to

which they are connected at the previous iteration as [34]

)Δ(1)||()(

)Δ(1)||()(

0

1load

0

1load

pk

qvkpk

i

pk

i

pk

pvkpk

i

pk

i

FkVQQ

FkVPP

(‎2.45)

where P0 and Q0 are respectively the assumed nominal active and reactive power of

the load (in pu) while k′v = 2, k′p = 0.1 and k′q = 0.1.

Load

Bus-1Bus-2

Bus-3

Bus-4

Bus-5

Tie-lineISS

Figure ‎2.4. Assumed power system topology for the microgrids in the distribution network under

consideration.


33

Table ‎2.1. Assumed Line Parameters of the Microgrid System of Figure ‎2.4 at Fundamental

Frequency

From To Line Impedance

Bus-1 Bus-2 0.3 + 3.0i []

Bus-1 Bus-3 0.2 + 2.0i []

Bus-2 Bus-5 0.1 + 1.0i []

Bus-3 Bus-4 0.3 + 3.0i []

Bus-4 Bus-5 0.2 + 2.0i []

Bus-5 External loop* 0.1 + 1.0i [/km]

* The distance between Bus-5 of each microgrid and the external loop is a probabilistic data, as

given in Table ‎2.2.

The assumed line parameters for the microgrid power system of Figure ‎2.4 are

provided in Table ‎2.20 at fundamental frequency (i.e. 50 Hz). It is to be emphasized

that the impedance of the lines and thus the Ybus

of the system is updated in each

iteration to consider the effect of the frequency changes in the microgrid.

At every iteration, the mismatch value is calculated as the maximum of

differences between all bus voltages of the microgrid with their values in the

previous iteration along with the differences between the active/reactive power of all

dispatchable DERs with the values in the previous iteration, as

),,max(Δ || QPV eee (‎2.46)

where

DER disp1

1DER dispDER disp

DER disp1

1DER dispDER disp

bus1

1

||

)()(max

)()(max

||||max

N,...,i

pk

i

pk

iQ

N,...,i

pk

i

pk

iP

N,...,i

pk

i

pk

iV

QQ

PP

VV

e

e

e

Once is smaller than a pre-defined value (e.g. 10–10

), the PFA is deemed to be


34

converged.

Through the observations in this research, it is revealed that the developed PFA

converges as far as the assumed demand is within the power generation capacity of

the DERs. It is to be noted that since the size of the considered network is small, the

number of iterations are limited and no convergence problems were observed.

However, analysing the convergence property, rate and regions of the developed

PFA is beyond the scope of this research and can be a future research topic.

2.5 Cloud Theory-Based Stochastic Analysis

To consider the uncertainties in the wind and solar generation, load, capacity of

dispatchable DERs, reliability indices, CO2 emissions and electricity price in each

microgrid, a stochastic framework is developed in this research. Monte Carlo is an

approach for modelling uncertainties in power system studies in which the

uncertainties are modelled with an appropriate probability density function (PDF).

Although the mean of the PDF for the above- mentioned uncertainties can be

compromised by the historical statistics, the standard deviation is another uncertain

parameter [35-36]. This issue can be solved by considering a stochastic framework

based on cloud theory in which the standard deviation for each uncertainty is defined

as a hyper entropy index. Hence, the uncertainty of parameter x is defined by a cloud

theory-based model, denoted by CL (Ex, En, He) where Ex is the expected (mean)

value, En is the entropy (variation range) and He is the hyper entropy (divergence of

variation range) [35-36]. He uses a normal distribution to model the entropy of En

and CL uses a normal distribution to model uncertainty x with the assumed mean of

Ex and standard deviation of En. Thus, the cloud theory-based stochastic framework

captures the uncertainty that exists in the determination of standard deviation. The


35

values for cloud theory-based models of load demand and its essential and non-

essential portion, maximum (capacity) of power generated by wind and solar-based

and dispatchable DERs, electricity price, CO2 emissions, SAIFI, SAIDI and MAIFI

in each microgrid are listed in Table ‎2.2 and Table ‎2.3 where floor(.) is the floor

function.

Table ‎2.2. Assumed Uncertainties in the Generation Capacity and Demand for the Microgrids.

load ess

max

loadload ess-non

max

loadload ess

maxwind

maxsolar

maxload

maxDERdisp

maxload

))01.0,05.0,75.0(normrnd

kW))5.0,315,((floor

kW))5.0,210,((floor

kW}3.0,6.0{

kW))3,15100,((floor

PPP

PP

CP

CP

PP

CP

L

L

L

Table ‎2.3. Assumed Uncertainties in the Parameters of the Criteria in DMA.

m/s))1,514,((floor

C))1,530,((floor

km))1,2,5((floorDistance

min))5,20,001((floor

))5.0,25,((floor

))5.0,25,((floor

kg/kW)01.0,1,5.3(

/kWh$)02.0,05.0,03.0(

nominalwind L

LA

L

L

L

L

L

L

Cv

CT

C

CSAIDI

CMAIFI

CSAIFI

CEm

CE

The probabilistic load of network is chosen from a uniform distribution over [0,

max

loadP ] range. The random output power of a solar-based DER in each microgrid

depends on the random solar irradiance parameter, denoted by s, and derived from a

Beta PDF as [37-38] where 5 and 5 are the shape parameters of the beta

distribution (e.g. 5 =2 and 5 = 2).


36

1515

55

55 )1()Γ()Γ(

)Γ()(

sssfbeta

(‎2.47)

The probabilistic output power of a solar-based DER, denoted by PPV, is then

calculated from [37-38]

))25(()8.0

20(PV

ci

scop

Av

oc TkIsT

sTkVNc.FF.P (‎2.48)

where Nc is the number of cells; FF = 0.7 is the fill factor; Tc = 25 °C and Top = 25

°C are respectively the assumed cell and normal operational temperatures; TA is

ambient temperature, Voc

= 22 V and Isc

= 3.7 A are the assumed open-circuit voltage

and short-circuit current of the PV cells and kv = –2.3 and ki = 6E-5 are respectively

the assumed voltage and current coefficients.

The random value for the nominal (rated) wind speed of wind-based DERs is

chosen from a normal PDF where the value for the wind speed (vwind) is chosen

randomly from a Rayleigh PDF as [37-38]

2)wind(wind

windrayleigh e2

)( v/cv

vc

vvf

(‎2.49)

where cv 1.128 vm and vm is the average wind speed. Thus, the probabilistic output

power of a wind-based DER, denoted by Pwind, is [37-38]

co

ci

ci

ci

coci

vvvP

vvvvv

vvP

vvvv

P

wind

nominal

windmax

wind

nominal

windwindnominal

wind

maxwind

windwind

wind

or0

(‎2.50)

where vci = 3.5 m/s and v

co = 25 m/s are respectively the assumed cut-in and cut-out

speeds for the wind turbine.


37

2.6 Performance Evaluation

To evaluate the performance of the developed OMT based on the proposed

DMA, first the network of Figure ‎2.1, composed of 3 isolated microgrids, is

considered. Later, a larger distribution network composed of 6 microgrids is focused.

It is to be noted that although in theory a network with infinite number of microgrids

can be assumed, in reality, the number of microgrids in a remote-area network will

be limited.

In the carried out analysis, all microgrids are assumed to have the power

system topology of Figure ‎2.4. In this topology, it is assumed that the non-

dispatchable solar and wind- based DERs are connected to bus-1 and 2 respectively

whereas the dispatchable DER (i.e. diesel-generator) is connected to bus-4. The

essential and non-essential loads are assumed to be connected to bus-3 while bus-5 is

the assumed interconnection point of the microgrid to its neighbouring microgrids.

The assumed line parameters are provided in Table ‎2.1 in Section ‎2.4.

It is worth mentioning that in reality, the microgrids will have different

topologies; however for simplicity, the same structure is considered for all of the

microgrids in this Section. It is to be highlighted that the developed OMT does not

depend on neither the microgrid topology nor the line parameters.

A cloud theory-based stochastic analysis is carried out in this research which

defines randomly the microgrid essential and non-essential loads, capacity of the

dispatchable and non-dispatchable DERs, nominal and actual wind speed for wind

turbines, sun radiation for solar-based DERs, electricity price, CO2 emission and the

reliability indices for each microgrid. The cloud theory-based stochastic analysis is

discussed in details in Section ‎2.5 and all uncertainty values are provided in Table

‎2.5 and Table ‎2.6.


38

First, let us consider the network of Figure ‎2.1 with three microgrids. Examples

1 to 3 demonstrate three examples in which the OMT flags that one microgrid is

overloaded while there is surplus power in the other microgrids of the network (i.e.

condition (2.4) is invalid for one of the microgrids while constraint (2.5) is valid for

the distribution network). Table ‎2.4 provides the assumed cloud theory-based

probabilistic power data for all 3 microgrids as well as the calculated UPC and PDL

for Example-1. This table illustrates that MG-1 is overloaded while MG-2 and MG-3

have surplus power. Thus, several alternatives (i.e. A1 = {MG-2}, A2 = {MG-3} and

A3 = {MG-2, MG-3}) are available for microgrids interconnection and thereby the

OMT calls the decision-making function. Table ‎2.5 lists the assumed cloud theory-

based probabilistic data for each microgrid of the alternatives for this example. These

data are utilized in DMA to define the performance of each alternative for each

criterion, as seen from Table ‎2.6. Table ‎2.7 demonstrates the calculated decision-

making matrix of (14).

Let the normalized weightings for the considered criteria based on the experts

comments, defined from (2.21), be as listed in Table ‎2.8. From the data of Table ‎2.7

and Table ‎2.8, the weighted decision-making matrix is calculated from (2.15).

Table ‎2.4. Assumed Cloud Theory-Based Probabilistic Power Data and the Calculated UPC and PDL

for the Distribution Network [kW] (Example-1)

∑Pload ∑ max

DER-dispP ∑Pdisp-DER Pwind Ppv UPC PDL

MG-1 63 58 61.4424 1.3985 0.1591 - 9.2424 -

MG-2 55 63 37.4820 17 0.5180 25.52 - 0.562

MG-3 34 49 16.8372 17 0.1628 32.16 - 0.437


39

Table ‎2.5. Assumed Cloud Theory-Based Probabilistic Data for Each Microgrid of the Distribution

Network Used in DMA (Example-1)

Z.D E SAIFI MAIFI SAIDI Em

MG-2 6 0.2748 5.1883 6.2373 56.4762 3.5261

MG-3 5 0.3158 4.1663 11.2216 43.4203 4.4508

Table ‎2.6. Comparison among the Parameters of Available Alternatives to Support Overloaded MG-1

(Example-1)

Consent u |Vu| |Fu| Ploss,u Ecost,u RBfu RB

du SSu CO2,u

A 1 1 2.76 0.080 0.383 6 0.275 11 56 0.681 3.526

A 2 1 3.48 0.071 0.136 5 0.316 15 43 0.495 4.451

A 3 1 6.24 0.014 0.151 5.562 0.293 27 99 0.610 3.931

Table ‎2.7. Calculated Decision Making Matrix (Example-1)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 1 0.880 0.197 0.234 0 0.130 0.706 0.668 0.681 0.208

A 2 1 1 0.294 0.728 0.166 0 0.604 0.744 0.495 0

A 3 1 1 0.858 0.699 0.073 0.073 0.311 0.412 0.610 0.117

Table ‎2.8. Assumed Weightings for the Criteria in DMA

w 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 w 9 w 10

0.133 0.120 0.120 0.120 0.093 0.106 0.080 0.080 0.080 0.006

As given in Table ‎2.9 and then normalized as given in Table ‎2.10, the

normalized weighted decision-making matrix is then used to define the evaluation

result of each alternative, using the aggregators of (2.17), as given in Table ‎2.11. For

Example-1, MG-1 is overloaded and alternative A3 is the preferred choice of all

aggregators and is selected to couple to MG-1. To investigate the reasons behind the

selection of A3 and its superiorities over the two other alternatives, the numerical


40

values of Table ‎2.6 should be investigated. From this table, it can be seen that A3

presents the best performance from the perspective of criterion 2 and 3 while it has

an average performance from the perspective of criterion 4, 5, 6, 9 and 10. A3 also

illustrates the worst performance from the perspective of criterion 7 and 8. Finally,

the DMA has selected this alternative since criterion 2, 3, 4 and 6 had larger

weightings versus criterion 7 and 8, based on the experts.

Table ‎2.9. Calculated Weighted Decision Making Matrix (Example-1)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 0.133 0.106 0.024 0.028 0 0.014 0.056 0.053 0.054 0.014

A 2 0.133 0.120 0.035 0.087 0.015 0 0.049 0.060 0.040 0

A 3 0.133 0.120 0.103 0.084 0.007 0.008 0.025 0.033 0.049 0.008

Table ‎2.10. Normalized Weighted Decision Making Matrix (Example-1)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 0.333 0.306 0.146 0.414 0 0.640 0.435 0.366 0.381 0.640

A 2 0.333 0.347 0.218 0.438 0.696 0 0.373 0.408 0.278 0

A 3 0.333 0.347 0.636 0.421 0.304 0.360 0.192 0.226 0.341 0.360

Table ‎2.11. Selected Alternative and Evaluation Results from Different Aggregators (Example-1)

Alternatives Average Min Product Hurwitz

A 1 3.3890 0 0 0.1600

A 2 3.0903 0 0 0.1739

A 3 3.5207 0.1917 0.0000 0.3027

Selected Alternative A 3 A 3 A 3 A 3

Example-2 demonstrates another scenario in which MG-2 is overloaded and

alternative A1 (i.e. {MG-1}) fails to satisfy one of the qualifying criteria (i.e.


41

criterion-4) as seen from Table ‎2.12. Hence, the performances of this alternative for

all other criteria are neglected based on (2.24) and are discarded from the

alternatives.

Example-3 demonstrates another case in which MG-3 is overloaded. The

normalized weighted decision-making matrix is as given in Table ‎2.13 and the

evaluation results of each alternative, based on the aggregators of (2.17), are given in

Table ‎2.14. From this Table, it is seen that alternatives A1 and A3 are selected by the

aggregators. Hence, a risk matrix is defined for these alternatives from (2.18)-(2.19),

as given in Table ‎2.15. From this table, alternative A3 (i.e. {MG-1, MG-2}) is

selected as it demonstrates a lower risk index.

Table ‎2.12. Decision Making Matrix (Example-2)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 1 0.402 0.320 0 0 0 0 0 0 0

A 2 1 0.967 0.628 0.222 0.500 0.177 0.602 0.659 0.707 0

A 3 1 1 0.883 0.302 0.641 0.095 0.384 0.360 0.820 0.065

Table ‎2.13. Normalized Weighted Decision Making Matrix (Example-3)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 0.333 0.333 0.304 0.343 0 0.381 0.428 0.400 0.571 0.633

A 2 0.333 0.333 0.114 0.348 0.243 0.279 0.419 0.412 0.069 0

A 3 0.333 0.333 0.581 0.308 0.756 0.338 0.151 0.187 0.358 0.366


42

Table ‎2.14. Selected Alternative and Evaluation Results from Different Aggregators and Risk

Matrix (Example-3)


A 1 0.373 0 0 0.158

A 2 0.255 0 0 0.104

A 3 0.371 0.151 0.000 0.302


Risk Index 0.756 0.277 0.277 0.277

Preferred Alternative A 3

Table ‎2.15. Risk Matrix (Example-3)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 0 0 0.277 0.005 0.756 0 0 0.012 0 0

A 3 0 0 0 0.040 0 0.043 0.277 0.225 0.213 0.267

To illustrate the performance of the developed OMT for a distribution network

with larger number of microgrids, and thus a larger number of alternatives, another

study is carried out which assumes the network of Figure ‎2.1 with 6 microgrids.

Thus, the OMT may evaluate up to 31 alternatives to define the suitable one.

Example-4 illustrates one of such scenarios. Table ‎2.16 provides the assumed cloud

theory- based probabilistic power data for all 6 microgrids as well as the calculated

UPC and PDL for Example-4. This table illustrates that MG-2 and MG-6 are

overloaded simultaneously. Thus, the OMT calls the decision-making function to

formulate the possible alternatives to select the suitable one. Table ‎2.17 provides the

assumed cloud theory-based probabilistic data for each of the microgrids of the

distribution network for this example which are utilized to define the performance of

each alternative for each criterion, as seen from Table ‎2.18. For this example, a total


43

of 15 alternatives are possible, as listed in Table ‎2.18. The calculated decision-

making matrix for this example is provided in Table ‎2.19. Table ‎2.20 illustrates the

results of different aggregators for each of the alternatives. Two alternatives (i.e. A6

and A7) are selected by the aggregators. Thus, their risk index is calculated by the

DMA. The risk index of both of these alternatives are the same (i.e. 0.47). So, the

DMA selects one of them randomly. In this example, alternative A6 is selected.

Hence, the OMT sends a command to the ISSes of MG-1, 3, 5 and 6 to close and

form a CMG.

Table ‎2.16. Assumed Cloud Theory-Based Probabilistic Power Data and the Calculated UPC and

PDL for the Network [kW] (Example-4)

∑Pload ∑ max

DER-dispP ∑Pdisp-DER Pwind Ppv UPC PDL

MG-1 12 58 0 14 0.58 58 -

MG-2 72 49 66.87 4.79 0.33 - 24.55

MG-3 35 63 21.98 12.61 0.40 41.02 -

MG-4 25 70 20.35 4.31 0.33 49.65 -

MG-5 20 62 0.63 19 0.37 61.37 -

MG-6 75 64 63.27 10.99 0.73 - 5.67

Table ‎2.17. Assumed Cloud Theory-Based Probabilistic Data for Each Microgrid of the

Distribution Network Used in DMA (Example-4)

Z.D E SAIFI MAIFI SAIDI Em

MG-1 9 0.2867 5.18 3.237 72.504 2.312

MG-2 4 0.2869 3.60 3.670 86.561 4.307

MG-3 7 0.2608 5.62 4.521 91.440 3.437

MG-4 6 0.3328 4.59 2.036 85.1244 2.697

MG-5 5 0.2752 5.27 2.938 128.403 2.277

MG-6 7 0.2902 5.13 2.849 100.830 3.646


44

Table ‎2.18. Comparison among the Parameters of Available Alternatives to Support Overloaded MG-1 (Example-4)

Composed of Consent u |Vu| |Fu| Ploss,u Ecost,u RBfu RB

du SSu CO2,u

A 1 {MG-1} 1 2.0392 0.0108 0.1652 9 0.2867 8.4175 72.5047 0 2.3126

A 2 {MG-3} 1 1.4422 0.0192 0.1052 7 0.2608 10.1435 91.4408 0.6280 3.4377

A 3 {MG-4} 1 1.7455 0.0073 0.1169 6 0.3328 6.6334 85.1244 0.8141 2.6970

A 4 {MG-5} 1 2.1577 0.0147 0.1719 5 0.2752 8.2127 128.4030 0.0315 2.2770

A 5 {MG-4, MG-5} 1 3.9032 0.0006 0.2175 6 0.3328 6.6334 85.1244 0.8141 2.6970

A 6 {MG-3, MG-5} 1 3.5999 0.0088 0.2117 7 0.2608 10.1435 91.4408 0.6280 3.4377

A 7 {MG-3, MG-4} 1 3.1877 0.0031 0.1695 7 0.2608 10.1435 91.4408 0.6280 3.4377

A 8 {MG-1, MG-5} 1 4.1969 0.0014 0.2580 9 0.2867 8.4175 72.5047 0 2.3126

A 9 {MG-1, MG-4} 1 3.7847 0.0040 0.2134 9 0.2867 8.4175 72.5047 0 2.3126

A 10 {MG-1, MG-3} 1 3.4814 0.0048 0.2073 9 0.2867 8.4175 72.5047 0 2.3126

A 11 {MG-1, MG-3, MG-4} 1 5.2269 0.0062 0.2357 9 0.2867 8.4175 72.5047 0 2.3126

A 12 {MG-1, MG-3, MG-5} 1 5.6391 0.0017 0.2715 9 0.2867 8.4175 72.5047 0 2.3126

A 13 {MG-1, MG-4, MG-5} 1 5.9424 0.0082 0.2748 9 0.2867 8.4175 72.5047 0 2.3126

A 14 {MG-3, MG-4, MG-5} 1 5.3454 0.0020 0.2388 7 0.2608 10.1435 91.4408 0.6280 3.4377

A 15 {MG-1, MG-3, MG-4, MG-5} 1 7.3846 0.0095 0.2828 9 0.2867 8.4175 72.5047 0 2.3126


45

Table ‎2.19. Decision Making Matrix (Example-4)

c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 1 0.5196 0.8920 0.6696 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 2 1 0.2211 0.8075 0.7896 0.8158 0.2163 0.7915 0.8381 0.6280 0.2019

A 3 1 0.3728 0.9268 0.7662 0.8421 0 0.8637 0.8493 0.8141 0.3739

A 4 1 0.5788 0.8527 0.6562 0.8684 0.1731 0.8312 0.7727 0.0315 0.4714

A 5 1 1 0.9938 0.5650 0.8421 0 0.8637 0.8493 0.8141 0.3739

A 6 1 1 0.9117 0.5766 0.8158 0.2163 0.7915 0.8381 0.6280 0.2019

A 7 1 1 0.9687 0.6611 0.7632 0.2163 0.7915 0.8381 0.6280 0.2019

A 8 1 1 0.9859 0.4840 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 9 1 1 0.9595 0.5731 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 10 1 1 0.9521 0.5853 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 11 1 1 0.9380 0.5285 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 12 1 1 0.9828 0.4571 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 13 1 1 0.9175 0.4503 0.7632 0.1385 0.8270 0.8716 0 0.4631

A 14 1 1 0.9804 0.5225 0.8158 0.2163 0.7915 0.8381 0.6280 0.2019

A 15 1 1 0.9053 0.4345 0.7632 0.1385 0.8270 0.8716 0 0.4631


46

Table ‎2.20. Selected Alternative and Evaluation Results from Different Aggregators (Example-4)


A 1 0.5927 0 0 0.0202

A 2 0.7170 0.0174 0.0000 0.0507

A 3 0.7176 0 0 0.0488

A 4 0.6196 0.0076 0.0000 0.0262

A 5 0.4787 0 0 0.0488

A 6 0.7614 0.0352 0.0000 0.0641

A 7 0.7752 0.0352 0.0000 0.0641

A 8 0.6160 0 0 0.0202

A 9 0.6243 0 0 0.0202

A 10 0.6252 0 0 0.0202

A 11 0.6177 0 0 0.0202

A 12 0.6127 0 0 0.0202

A 13 0.6072 0 0 0.0202

A 14 0.7601 0.0352 0.0000 0.0641

A 15 0.6045 0 0 0.0202


Risk Index 0.47 0.47 0.47 0.47

Preferred Alternative A 6

The stochastic analysis results of the network of Figure ‎2.1 with three

microgrids are summarized in Table ‎2.21 which demonstrates the flags pointed out

by the OMT and its embedded decision-making and load-shedding functions. The

table shows the results of two sets of stochastic analyses:

case-1 with the assumption that the dispatchable DERs have a capacity of

60% nominal load demand based on [11-12], and

case-2 with the assumption that the dispatchable DERs have a capacity of


47

30% of the nominal load demand. From this table, it is seen that for the

considered uncertainties of case-1, no coupling of the microgrids is required

for 25.69% of the cases, as interconnection condition (2.4) is satisfied for all

3 microgrids. In 9.29% of the cases, interconnection of all 3 microgrids is

required among which 6.45% satisfy PFA constraint (2.6) and

interconnection is possible whereas in 2.84% PFA constraint (2.6) is not

satisfied. In 41.54% of the cases, several alternatives are possible and the

OMT calls the decision-making function where in all of them, a suitable

alternative is selected. In 4.45% of the selected alternatives, the DMA selects

an alternative which is composed of one microgrid while in 37.09% an

alternative composed of two microgrids is selected. In 23.48% of the cases,

the OMT calls the load-shedding function where load-shedding is found to be

successful in all microgrids.

From Table ‎2.21, it can also be seen that in 80.66% of the cases, the OMT calls

the load-shedding function where load-shedding is found to be unsuccessful in

0.01% and successful in 65.18% of them. Coupling of microgrids accompanied by

load-shedding counts for 14.59% of the load-shedding section, among which in

7.59% of them the selected alternative is composed of one microgrid and in 7% of

them the selected alternative is composed of two microgrids. In 0.88% of the total

cases, it is found that coupling of microgrids by further load-shedding is not viable.

Note that the utilized stochastic analysis has a minimum of 10,000 trials to

prevent any immature results. The stopping rule is defined to achieve a confidence

level of 95% in the mean and standard deviation of the results.


48

Table ‎2.21. Stochastic Analysis Results Demonstrating the Flags Generated by the OMT and

Decision-making and Load-shedding Functions for a Network Composed of 3 Microgrids under two

Considered Study Cases.

Flags Pdisp DER / Pload = 60% 30%

No interconnection is required. 25.69 4.60

The only alternative is coupling all N microgrids. 9.29 1.83

All N microgrids can be coupled 6.45 0.9

Coupling all N microgrids is not viable and load-shedding is inevitable 2.84 0.93

Several alternatives are possible; hence, decision-making is required. 41.54 12.91

A suitable alternative is selected for coupling microgrids. 41.54 12.91

Selected alternative is composed of one microgrid. 4.45 1

Selected alternative is composed of two microgrids. 37.09 11.91

A suitable alternative is not available and load-shedding is inevitable. 0 0

A suitable alternative is not available and load-shedding is inevitable. 23.48 80.66

Load-shedding is not successful. 0 0.01

Load-shedding is successful. 23.48 65.18

Coupling of microgrids accompanied by load-shedding is selected. 0 14.59

Selected alternative is composed of one microgrid. 0 7.59

Selected alternative is composed of two microgrids. 0 7.00

Coupling of microgrids accompanied by further load-shedding is not

viable.

0 0.88

2.7 Conclusion

An overload management technique is developed in this chapter to reduce the

load-shedding rate of a remote-area microgrid, during overloading conditions, by

interconnecting it with suitable neighbouring microgrid(s). A dynamic multi-criteria

DMA is presented to formulate the possible alternatives, qualify them based on 4

proposed criteria and then assess and select the most suitable one to achieve the


49

highest satisfaction and minimum risk considering another 6 criteria. All criteria

have different weightings. In case, surplus power is not available in the other

microgrids, the developed OMT proceeds to define the required amount of load to be

shed from each microgrid. If this level is less than the non-essential part of the loads

of a microgrid, the developed technique defines which neighbouring microgrid(s)

have extra non-essential loads. It then proceeds to identify those microgrids, defines

the portion of non-essential load to be disconnected from them and then

interconnects those microgrids. The successful performance of the developed

algorithms is validated in a stochastic frame in MATLAB for a small network

composed of 3 microgrids as well as a large network, composed of 6 microgrids.

Chapter 3 - Impact of the Criteria Weighting

50

Chapter 3 Impact of the Criteria Weighting

As it was mentioned in previous chapter, ten criteria are considered for the

decision-making. Each criterion has a contribution to the final decision. However,

depending on weighting of each criterion, the final decision can lean towards the

criterion that has a higher weighting. Thus, the weightings of criteria have a crucial

influence on the decision-making outcome. In this chapter, the effect of changes in

the weighting of any criterion is investigated and its results are presented.

3.1 Performance Evaluation of the Alternative Selection Strategy

To evaluate the performance of the developed alternative selection strategy, let

us consider the network of Figure ‎2.2, composed of 6 isolated microgrids. Let us

presume the aggregated generation capacity for the diesel generators (DG), wind

turbines and solar cells, and the nominal demand of each microgrid as listed in Table

‎3.1This table also lists the assumed electricity price offered by each microgrid, the

distance of each microgrid to the central node of all microgrids, the SAIFI and

SAIDI indices for each microgrid as well as the corresponding CO2 emissions of the

DGs of each microgrid. Now, let us assume that at a specific time of a day, the

aggregated actual electricity generation from the DGs, wind turbines and solar cells

of each microgrid are as listed in Table ‎3.2.This table also lists the aggregated

amount of the (essential and non-essential) demand of each microgrid and the


51

expected generation level from the DGs to satisfy the power balance in every

microgrid.

Table ‎3.1. Considered Nominal Values for a Network Composed of 6 microgrids.

MG No. 1 2 3 4 5 6

Generation

Capacity of

Diesel Generators 46 48 62 63 67 55

Wind Turbines 15 16 17 17 10 12

Solar Cells 10 9 12 11 8 10

Nominal Demand 77 80 104 105 112 105

Electricity Cost 29.95 27.52 33.01 24.76 32.98 31.73

Distance 5 6 1 5 6 2

SAIFI 10.06 7.27 8.37 9.07 13.16 7.70

SAIDI 100.9 100.7 53.5 124.9 103.7 89.3

CO2 Emissions 4.61 4.25 4.21 4.78 5.79 3.64

Table ‎3.2 Random Values for the Assumed Network at the Time of Study.

MG No. 1 2 3 4 5 6

Actual Solar Generation 0.40 0.49 0.71 0.85 0.40 0.28

Actual Wind Generation 1.74 16 9.13 0 2.43 0

Actual Essential Demand 7.33 18.14 8.74 2.88 12.89 19.57

Actual Non-essential Demand 22.66 34.85 36.25 10.11 36.10 37.42

Actual Aggregated Demand 30 53 45 13 49 57

Expected DG Generation 27.85 36.50 35.15 12.14 46.16 56.70

From Table ‎3.2, it can be seen that the expected power generation from the

DGs in all microgrids, except MG-6, is well below their respective capacities.

Thereby, condition (2.3) is only valid for MG-6 and thereby, it will be flagged as

overloaded. On the other hand, constraint (2.4) is valid which illustrates that there is


52

enough extra generation capacity in the neighbouring microgrids to support the

overloaded one. Thereby, in total there will be 31 alternatives available from which

the alternative selection strategy needs to choose the most suitable one.

The decision-making matrix of (2.14) is then formed based on the formulas

provided in chapter 2 for the CMG system, composed of MG-6 and each of the 31

alternatives. This matrix is provided in Table ‎3.3.

Now, let us assume the weighting for each criterion as listed in Table ‎3.4.

Based on these weightings, it is assumed that criterion-1 to 4 are the utmost

important criteria and criterion-6 is the second utmost one. Other criteria have lower

importance. With this assumption, the weighted decision-making, after being

normalized will be as given in Table ‎3.5. From this table and using the aggregators of

(2.17), the alternative selection strategy selects alternative A4 as the most suitable

one.

Table ‎3.3. Assumed Normalized Weightings for the Criteria.

w 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 w 9 w 10

0.133 0.120 0.120 0.120 0.093 0.106 0.080 0.080 0.080 0.066


53

Table ‎3.4. Decision Making Matrix for the Network with the Assumptions of the Data of Table ‎3.1 and Table ‎3.2.

Alternative Participating microgrids c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10

A 1 {MG-1} 1 1 0.915 0.866 0.800 0.093 0.819 0.824 0.928 0.204

A 2 {MG-2} 1 1 0.897 0.845 0.760 0.166 0.869 0.824 0.689 0.266

A 3 {MG-3} 1 1 0.914 0.888 0.960 0.000 0.850 0.907 0.781 0.271

A 4 {MG-4} 1 1 0.870 0.975 0.800 0.250 0.837 0.782 0.934 0.173

A 5 {MG-5} 1 1 0.917 0.861 0.760 0.001 0.763 0.819 0.942 0.000

A 6 {MG-4, MG-5} 1 1 0.880 0.951 0.889 0.121 0.600 0.601 0.940 0.084

A 7 {MG-3, MG-5} 1 1 0.907 0.895 0.926 0.000 0.613 0.726 0.865 0.130

A 8 {MG-3, MG-4} 1 1 0.875 0.972 0.939 0.126 0.686 0.689 0.815 0.222

A 9 {MG-2, MG-5} 1 1 0.915 0.868 0.877 0.070 0.633 0.643 0.810 0.111

A 10 {MG-2, MG-4} 1 1 0.898 0.949 0.891 0.214 0.706 0.606 0.737 0.213

A 11 {MG-2, MG-3} 1 1 0.917 0.888 0.942 0.073 0.719 0.731 0.731 0.269

A 12 {MG-1, MG-5} 1 1 0.909 0.882 0.882 0.038 0.583 0.643 0.937 0.083

A 13 {MG-1, MG-4} 1 1 0.874 0.966 0.898 0.183 0.656 0.606 0.930 0.186

A 14 {MG-1, MG-3} 1 1 0.907 0.902 0.951 0.039 0.669 0.731 0.840 0.243

A 15 {MG-1, MG-2} 1 1 0.916 0.872 0.890 0.130 0.688 0.648 0.775 0.235

A 16 {MG-3, MG-4, MG-5} 1 1 0.879 0.955 0.945 0.082 0.450 0.508 0.873 0.145

A 17 {MG-2, MG-4, MG-5} 1 1 0.897 0.938 0.923 0.134 0.470 0.425 0.824 0.133


54

A 18 {MG-2, MG-3, MG-5} 1 1 0.921 0.893 0.943 0.045 0.482 0.550 0.801 0.167

A 19 {MG-2, MG-3, MG-4} 1 1 0.896 0.954 0.950 0.137 0.556 0.513 0.755 0.234

A 20 {MG-1, MG-4, MG-5} 1 1 0.880 0.949 0.926 0.114 0.420 0.425 0.936 0.115

A 21 {MG-1, MG-3, MG-5} 1 1 0.904 0.904 0.946 0.025 0.432 0.550 0.880 0.150

A 22 {MG-1, MG-3, MG-4} 1 1 0.878 0.966 0.953 0.117 0.506 0.513 0.854 0.217

A 23 {MG-1, MG-2, MG-5} 1 1 0.921 0.883 0.921 0.076 0.452 0.467 0.837 0.137

A 24 {MG-1, MG-2, MG-4} 1 1 0.894 0.948 0.928 0.178 0.525 0.430 0.797 0.210

A 25 {MG-1, MG-2, MG-3} 1 1 0.920 0.899 0.954 0.079 0.538 0.555 0.777 0.250

A 26 {MG-1, MG-2, MG-3, MG-4} 1 1 0.893 0.952 0.960 0.128 0.375 0.337 0.792 0.228

A 27 {MG-1, MG-2, MG-3, MG-5} 1 1 0.914 0.901 0.956 0.055 0.301 0.374 0.823 0.175

A 28 {MG-1, MG-2, MG-4, MG-5} 1 1 0.893 0.938 0.943 0.125 0.289 0.249 0.846 0.148

A 29 {MG-1, MG-3, MG-4, MG-5} 1 1 0.882 0.953 0.957 0.084 0.269 0.332 0.885 0.156

A 30 {MG-2, MG-3, MG-4, MG-5} 1 1 0.895 0.944 0.955 0.099 0.319 0.332 0.812 0.169

A 31 {MG-1, MG-2, MG-3, MG-4, MG-5} 1 1 0.892 0.943 0.963 0.098 0.138 0.156 0.831 0.174


55

Table ‎3.5 Normalized Weighted Decision Making Matrix Assuming the Weighting Matrix of Table ‎3.3.


A 1 {MG-1} 0.173 0.158 0.141 0.131 0.101 0.013 0.088 0.086 0.102 0.018

A 2 {MG-2} 0.173 0.158 0.138 0.128 0.096 0.024 0.094 0.086 0.075 0.023

A 3 {MG-3} 0.173 0.158 0.141 0.135 0.121 0.000 0.092 0.095 0.085 0.024

A 4 {MG-4} 0.173 0.158 0.134 0.148 0.101 0.036 0.090 0.082 0.102 0.015

A 5 {MG-5} 0.173 0.158 0.141 0.130 0.096 0.000 0.082 0.086 0.103 0.000

A 6 {MG-4, MG-5} 0.173 0.158 0.135 0.144 0.112 0.017 0.065 0.063 0.103 0.007

A 7 {MG-3, MG-5} 0.173 0.158 0.140 0.136 0.117 0.000 0.066 0.076 0.095 0.011

A 8 {MG-3, MG-4} 0.173 0.158 0.135 0.147 0.119 0.018 0.074 0.072 0.089 0.019

A 9 {MG-2, MG-5} 0.173 0.158 0.141 0.132 0.111 0.010 0.068 0.067 0.089 0.010

A 10 {MG-2, MG-4} 0.173 0.158 0.138 0.144 0.112 0.031 0.076 0.063 0.081 0.019

A 11 {MG-2, MG-3} 0.173 0.158 0.141 0.135 0.119 0.010 0.078 0.076 0.080 0.024

A 12 {MG-1, MG-5} 0.173 0.158 0.140 0.134 0.111 0.005 0.063 0.067 0.103 0.007

A 13 {MG-1, MG-4} 0.173 0.158 0.134 0.146 0.113 0.026 0.071 0.063 0.102 0.016

A 14 {MG-1, MG-3} 0.173 0.158 0.140 0.137 0.120 0.006 0.072 0.076 0.092 0.021

A 15 {MG-1, MG-2} 0.173 0.158 0.141 0.132 0.112 0.019 0.074 0.068 0.085 0.021

A 16 {MG-3, MG-4, MG-5} 0.173 0.158 0.135 0.145 0.119 0.012 0.049 0.053 0.096 0.013

A 17 {MG-2, MG-4, MG-5} 0.173 0.158 0.138 0.142 0.117 0.019 0.051 0.044 0.090 0.012


56

A 18 {MG-2, MG-3, MG-5} 0.173 0.158 0.142 0.135 0.119 0.006 0.052 0.057 0.088 0.015

A 19 {MG-2, MG-3, MG-4} 0.173 0.158 0.138 0.145 0.120 0.020 0.060 0.054 0.083 0.021

A 20 {MG-1, MG-4, MG-5} 0.173 0.158 0.135 0.144 0.117 0.016 0.045 0.044 0.102 0.010

A 21 {MG-1, MG-3, MG-5} 0.173 0.158 0.139 0.137 0.119 0.004 0.047 0.057 0.096 0.013

A 22 {MG-1, MG-3, MG-4} 0.173 0.158 0.135 0.146 0.120 0.017 0.055 0.054 0.093 0.019

A 23 {MG-1, MG-2, MG-5} 0.173 0.158 0.142 0.134 0.116 0.011 0.049 0.049 0.092 0.012

A 24 {MG-1, MG-2, MG-4} 0.173 0.158 0.137 0.144 0.117 0.025 0.057 0.045 0.087 0.018

A 25 {MG-1, MG-2, MG-3} 0.173 0.158 0.141 0.136 0.120 0.011 0.058 0.058 0.085 0.022

A 26 {MG-1, MG-2, MG-3, MG-4} 0.173 0.158 0.137 0.144 0.121 0.018 0.040 0.035 0.087 0.020

A 27 {MG-1, MG-2, MG-3, MG-5} 0.173 0.158 0.141 0.136 0.121 0.008 0.033 0.039 0.090 0.015

A 28 {MG-1, MG-2, MG-4, MG-5} 0.173 0.158 0.137 0.142 0.119 0.018 0.031 0.026 0.093 0.013

A 29 {MG-1, MG-3, MG-4, MG-5} 0.173 0.158 0.136 0.144 0.121 0.012 0.029 0.035 0.097 0.014

A 30 {MG-2, MG-3, MG-4, MG-5} 0.173 0.158 0.138 0.143 0.121 0.014 0.034 0.035 0.089 0.015

A 31 {MG-1, MG-2, MG-3, MG-4, MG-5} 0.173 0.158 0.137 0.143 0.122 0.014 0.015 0.016 0.091 0.015


57

3.2 Sensitivity Analysis Results of the Weightings

It is desired to investigate the impact of each criterion on the outcome of

the alternative selection strategy. For this, it is assumed that the weighting of

only one criterion is 1 at a time while the weighting of all other criteria is

assumed to be zero. Considering the 10 criteria listed in the previous Section,

this analysis is repeated 10 times. In each analysis, the weighted decision-making

matrix will have only one non-zero column, which corresponds to the criterion

with a weighting of 1. The results of the corresponding column in the weighted

decision-making matrix of each analysis, after being normalized, are provided in

Table ‎3.6. Considering criterion-1 and 2, all alternatives have the same priority

and thus the alternative selection strategy fails to select one while considering

criterion-3 to 10, a different alternative is selected in each case (i.e., respectively

A18, A4, A31, A4, A2, A3, A5, and A3), as highlighted in Table ‎3.6.

Now, let us analyse the sensitivity of the selected alternative versus the

ratio of the weightings of the criteria. As the electricity cost is a very important

factor, the sensitivity analyses are conducted versus this criterion.

Figure ‎3.1a illustrates the variation in the outcome of the alternative

selection strategy (i.e., the most suitable alternative) when only criterion-3

(voltage deviation) and criterion-6 (electricity cost) are considered. From this

Figure, it can be seen that A4 is the preferred alternative since the weighting of

criterion-3 is low; however, A10 can become the preferred alternative if its

weighting is high.


58

Table ‎3.6. Corresponding Column of the Normalized Weighted Decision Making Matrix When Only One Criterion is Considered.


A 1 {MG-1} 1 1 1.001 0.888 1.053 0.763 1.337 1.196 1.146 0.956

A 2 {MG-2} 1 1 0.982 0.867 1.000 1.369 1.418 1.197 0.850 1.246

A 3 {MG-3} 1 1 1 0.911 1.263 0.000 1.386 1.316 0.964 1.273

A 4 {MG-4} 1 1 0.951 1 1.053 2.056 1.366 1.136 1.152 0.813

A 5 {MG-5} 1 1 1.004 0.883 1 0.007 1.246 1.189 1.162 0.000

A 6 {MG-4, MG-5} 1 1 0.963 0.976 1.170 1 0.980 0.873 1.160 0.394

A 7 {MG-3, MG-5} 1 1 0.993 0.918 1.218 0.003 1 1.054 1.067 0.612

A 8 {MG-3, MG-4} 1 1 0.957 0.997 1.236 1.036 1.120 1 1.006 1.041

A 9 {MG-2, MG-5} 1 1 1.002 0.891 1.154 0.575 1.032 0.934 1 0.520

A 10 {MG-2, MG-4} 1 1 0.983 0.974 1.172 1.759 1.152 0.880 0.910 1

A 11 {MG-2, MG-3} 1 1 1.003 0.911 1.239 0.598 1.173 1.061 0.902 1.261

A 12 {MG-1, MG-5} 1 1 0.995 0.905 1.161 0.315 0.951 0.934 1.156 0.389

A 13 {MG-1, MG-4} 1 1 0.956 0.991 1.181 1.511 1.071 0.880 1.148 0.873

A 14 {MG-1, MG-3} 1 1 0.993 0.926 1.251 0.325 1.091 1.061 1.036 1.138

A 15 {MG-1, MG-2} 1 1 1.002 0.895 1.170 1.073 1.123 0.941 0.957 1.104

A 16 {MG-3, MG-4, MG-5} 1 1 0.962 0.980 1.244 0.677 0.734 0.737 1.078 0.678

A 17 {MG-2, MG-4, MG-5} 1 1 0.982 0.962 1.215 1.100 0.766 0.618 1.017 0.624


59

A 18 {MG-2, MG-3, MG-5} 1 1 1.008 0.916 1.241 0.374 0.787 0.798 0.989 0.784

A 19 {MG-2, MG-3, MG-4} 1 1 0.980 0.979 1.250 1.129 0.907 0.745 0.932 1.098

A 20 {MG-1, MG-4, MG-5} 1 1 0.963 0.974 1.218 0.938 0.685 0.617 1.155 0.541

A 21 {MG-1, MG-3, MG-5} 1 1 0.989 0.927 1.245 0.203 0.705 0.798 1.086 0.702

A 22 {MG-1, MG-3, MG-4} 1 1 0.961 0.991 1.254 0.963 0.825 0.744 1.054 1.018

A 23 {MG-1, MG-2, MG-5} 1 1 1.007 0.906 1.212 0.629 0.737 0.678 1.033 0.644

A 24 {MG-1, MG-2, MG-4} 1 1 0.978 0.972 1.221 1.468 0.857 0.625 0.983 0.987

A 25 {MG-1, MG-2, MG-3} 1 1 1.007 0.922 1.255 0.646 0.878 0.806 0.959 1.171

A 26 {MG-1, MG-2, MG-3, MG-4} 1 1 0.977 0.976 1.263 1.052 0.612 0.489 0.977 1.068

A 27 {MG-1, MG-2, MG-3, MG-5} 1 1 1.000 0.924 1.257 0.454 0.492 0.543 1.015 0.819

A 28 {MG-1, MG-2, MG-4, MG-5} 1 1 0.978 0.963 1.241 1.031 0.471 0.362 1.044 0.692

A 29 {MG-1, MG-3, MG-4, MG-5} 1 1 0.965 0.978 1.259 0.694 0.439 0.482 1.092 0.731

A 30 {MG-2, MG-3, MG-4, MG-5} 1 1 0.980 0.968 1.257 0.816 0.521 0.482 1.002 0.791

A 31 {MG-1, MG-2, MG-3, MG-4, MG-5} 1 1 0.977 0.968 1.268 0.807 0.226 0.226 1.025 0.818


60

A26

A24

A10

A4

0.1 0.2 0.4 0.6 10.1

Loss Weighting

0.2

0.4

1

A2

A4

0.1 0.8 1

0.1

SAIFI Weighting

1

Cost

Wei

ghti

ng

A1A

4

0.1 0.8 10.1

SAIDI Weighting

1

A3 A

2A

4

0.1 0.8 10.1

CO2 Weighting

1

A4

0.1 10.1

Frequency Deviation Weighting

1

A4

0.1 0.6 1

0.1

Voltage Deviation

Weighting

1

A10

(a) (b)

(c) (d)

(e) (f)

Cost

Wei

ghti

ng

Cost

Wei

ghti

ng

Cost

Wei

ghti

ng

Cost

Wei

ghti

ng

Cost

Wei

ghti

ng

Figure ‎3.1 Sensitivity analysis plot of the selected alternative versus different weightings of cost

and distance.


61

Figure ‎3.1b illustrates the most suitable alternative when only criterion-4

(frequency deviation) and the electricity cost are considered. From this Figure, it

can be seen that A4 is always the preferred alternative irrespective of the

weighting of criterion-4, for the studied network.

Figure ‎3.1c illustrates the variation in the outcome of the alternative

selection strategy when only criterion-5 (power loss) and the electricity cost are

considered. From this Figure, it can be seen that A4 is the preferred alternative

when the weighting of criterion-5 is very low and the weighting of criterion-6 is

high; however, A10 becomes the preference when the weighting of criterion-5 is

in the range of low to medium or when the weighting of both criterion-5 and 6

are low. Alternatively, A24 becomes the preferred alternative when its weighting

is in the medium range while A26 can become the preference if criterion-5

weighting is high.

Figure ‎3.1d illustrates the variation in the outcome of the alternative

selection strategy when only criterion-7 (SAIFI) and the electricity cost are


since the weighting of criterion-7 is low; however, alternative A2 can become the

preferred alternative if the weighting is high.

Figure ‎3.1e illustrates the variation in the outcome of the alternative

selection strategy when only criterion-8 (SAIDI) and the electricity cost are


when the weighting of criterion-8 is low. It can also be seen that alternative A1

becomes the preferred alternative since its weighting is in the range of medium

to high, while alternative A3 can become the preferred alternative if the

weighting is very high.


62

The most suitable alternative is A4 when only criterion-9 (renewable energy

dependency) and the electricity cost are considered for the studied network,

similar to Figure ‎3.1b, irrespective of the weighting of criterion-9.

Figure ‎3.1f illustrates the variation in the outcome of the alternative

selection strategy when only criterion-10 (CO2 emissions) and the electricity cost

are considered. From this Figure, it can be seen that A4 is the preferred

alternative since the weighting of criterion-10 is low; however, A2 can become

the preferred alternative if its weighting is high.

3.3 Conclusion

An overloaded microgrid can be temporarily relieved by the imported

power from its neighbouring microgrids. To this end, suitable neighbouring

microgrids should be defined and then coupled to the overloaded one(s). This

selection can be based on different criteria including the level of the available

surplus power in the neighbouring microgrids, their reliability, dependency on

the renewable energies, electricity costs and CO2 emissions as well as the power

losses in the interconnecting lines. Some technical criteria such as the voltage

and frequency deviation in the CMG system can also be considered in the

selection. Each criterion may have a different weighting; however, it is not

possible to ignore a criterion when selecting the most suitable neighbouring

microgrid. Through the analyses carried out in the chapter for a sample

distribution network, it was found out that these weightings have a strong impact

on the outcome of the alternative selection strategy. Among these criteria, power

loss and electricity cost are the two major criteria for the considered network and

they strongly affect the outcome of the alternative selection strategy. In contrary,


63

frequency deviation and dependency on the renewable energies criteria have the

minimum impact on the outcome.

Chapter 4 – Synchronization Strategy for Coupling Microgrids

64

Chapter 4 Synchronisation Strategy for

Coupling Microgrids

Coupling of neighbouring Microgrids requires synchronisation. The

synchronisation needs to be effective and quick so that abnormal conditions in

the microgrid are mitigated before the operation of the protective devices. Hence

an algorithm is developed and presented in this chapter to assess the

synchronisation criteria between every microgrid and to decide which microgrids

should interconnect first. The algorithm also defines the sequence of

synchronisation among the microgrids in a group of microgrids.

4.1 Considered Structure and Control of ISS

The microgrids will be coupled by the help of ISSes, with the per-phase

structures of Figure ‎4.1. The structure of Figure ‎4.1a, composed of an insulated

gate bipolar transistor (IGBT) within a diode bridge, is used in this research. It is

to be highlighted that Figure ‎4.1a illustrates the structure of the ISS, and

obviously, depending on the current and voltage capacity of each IGBT and

diode and the system requirements, more IGBTs and diodes may need to be

connected in series and/or in parallel.

In the structure of Figure ‎4.1a, when the IGBT is turned on, a bi-directional

sinusoidal current can flow from the ISS where only two forward-biased diodes


65

conduct in each half-cycle. The microgrids will be isolated as soon as the IGBT

is turned off. Therefore, this ISS has a less complicated switching control system

versus the structure of Figure ‎4.1b which needs a continuous turn on/off signals

for each IGBT in each half-cycle. Moreover, the IGBT in the structure of Figure

‎4.1a has only conduction losses and no continuous switching losses. However,

the diodes have conduction as well as switching losses. A detailed economic

analysis on these two structures can yield the most suitable economic structure

for the ISSes in a future research.

(b)(a)

Figure ‎4.1. Two sample structures of normally-open ISSes among the microgrids.

Each considered ISS in this research has a local controller, illustrated

schematically in Figure ‎4.2. It turns on the IGBT based on the closing and

synchronisation commands that it receives from the synchronisation module, an

agent located within the distribution network controller which facilitates the

synchronisation and interconnection of the microgrids, and turns it off when

receiving the opening command from the OMT. The controller also observes the

status of the ISS and sends a closing confirmation (CC) signal to the

synchronisation module, whenever it closes. It is to be highlighted that the ISS

controller receives and transmits these information through the central controller

of the relevant MG and does not directly communicate with the distribution

network controller in order to obey the system hierarchical control aspects.


66

Figure ‎4.3 illustrates the schematic diagram of the communication links that are

required for data communication among the distribution network controller (i.e.,

the OMT and synchronisation module), the central controller of each microgrid,

and the local controller of each ISS.

if |Δδ| < ε

output = 1

else

output = 0

δ

if |Δv| < ε

output = 1

else

output = 0

v

+

_

+_

Synchronize

Signal

AND

v (t)in v (t)out

PLL

PLL

Mono-

stableReceiver

IGBT

Driver

ISS

Reset

ISS

Observer

Close Signal

Transmitter-1

CC Signal

if |Δf | < ε

output = 1

else

output = 0

f

OR

Transmitter-2

if |Δv| = v

output = 1

else

output = 0

in

AND

AND

MG-k

Open Signal

Failure Flag

if f < f

output = 1

else

output = 0

ANDCMG CMG

min

AND

Figure ‎4.2. Developed local controller for the ISSes.

MG Central

Controller

Network

Controller

OMT

Synchronization

Module

ISS

ISS

Controller

UPC, PDL

Selected

MGs

On/Off

Synchronize,

Close, DR

CC, DR

Synchronize,

Close, Open, DR

CC, DR

Open, DR

Figure ‎4.3. Required communication links and the transferred data.


67

Before the interconnection of any two microgrids, each microgrid may

have a different voltage and frequency. Thereby, an important stage of forming a

CMG is the synchronisation of the interconnecting microgrids. In this research,

synchronisation is referred to as the connection process of an microgrid to a

neighbouring microgrid through an ISS. Connection should only take place once

the voltage magnitude difference and the voltage phase difference across the ISS

are zero (or lower than a very small specified value) [42]. Inappropriate

connection may cause high current fluctuations which can damage the network

assets or result in system instability. The ISS closing consists of a

synchronisation process, after which a CMG is formed. Different

synchronisation methods are proposed in [15-17]. Additionally, some other

techniques such as the ones presented in [18-19] can be used to speed up the

synchronisation process. In this research, a normal (non-forced) synchronisation

procedure is utilized. Therefore, the ISS closes once the voltage magnitude

difference across the ISS (|v|) becomes smaller than ev (e.g., ev = 0.001), and the

voltage phase difference across ISS (| |) becomes smaller than e (e.g., e =

0.001) [48], only if its local controller has received the synchronisation

command. This is schematically shown in the logic diagram of the local

controller of the ISS in Figure ‎4.2.

Let us assume that the local controller of the ISS receives the closing

command at t = 0. The voltages at either sides of the ISS are assumed to be

synchronized at tsync if

ktftf )2()2( 2sync1sync 2-MG1-MG (‎4.1)

where fMG-1 and fMG-2 are respectively the frequency of MG-1 and MG-2 while θ1

and θ2 are the phase of the voltage of MG-1 and MG-2 side of the ISS, when it


68

has received the synchronisation command. From (4.4), the required

synchronisation time can be expressed as

fkt 2sync (‎4.2)

where Δθ = θ1 – θ2,‎Δf = fMG-1 – fMG-2 and k = 0, 2 is determined based on the

different‎ values‎ of‎Δθ and‎Δf. It is to be noted that the actual synchronisation

time may be slightly (i.e., less than half a cycle) larger than tsync so that |v| also

becomes smaller than ev. As an example, let us consider the interconnection of

two neighbouring microgrids, i.e. MG-1 and MG-2, in which fMG-1 = 50.4 Hz and

fMG-2 = 49.6 Hz when a synchronisation command is received at t = 1 s. Figure

‎4.4a shows the instantaneous phase-a voltage at either sides of the ISS at this

time. From this Figure, considering the time difference between the command

reception time (i.e. t = 1 s) and the previous zero-crossing of each phase (i.e. t1 =

0.992 s and t2 = 0.982 s), the voltage phase at either side of the ISS are defined

respectively as θ1 = 2.513 rad and θ2 = 5.340 rad. Therefore, the required

synchronisation time becomes tsync = 0.562 s from (4.5). Hence, the

synchronisation is expected to occur at t = 1.562 s. Figure ‎4.4b-c show that the

synchronisation is fulfilled and the ISS closes at t = 1.57 s (due to the voltage

magnitude difference).


69

Figure ‎4.4. (a) Phase-a voltage at two sides of the ISS when the synchronisation command is

initiated, (b) Phase-a voltage at two sides of the ISS when two MGs are synchronized, (c) The

difference of phase-a voltages at two sides of the ISS at the synchronisation.

Figure ‎4.5a shows the required synchronization time as a function of for

0.2 f 1 Hz. It can be seen from this Figure that for each f, the

synchronization time increases linearly as increases. Figure ‎4.5b shows the

required synchronisation time as a function of f for /4 . It can be seen

from this Figure that for each , the required synchronisation time increases as

f decreases. Figure ‎4.5c-d illustrate a 3D diagram of the required

synchronisation time versus different positive and negative values of f and .


70

Figure ‎4.5. Required time for interconnection of microgrids for different and f.


71

The main limitation of the considered normal synchronisation procedure is

that it will take a long time if the frequency difference of two microgrids is very

small. As an example, from (4.5), assuming angle difference of 1 rad, the

required synchronisation time increases from 1.591 s to 15.915 s, 159.155 s (i.e.,

2.65 min), and 1,591.5 s (i.e., 26.53 min) if f reduces from 0.1 to respectively

0.01, 0.001 and 0.0001 Hz. In such cases, a forced synchronisation is

unavoidable. To this end, the local controller of an ISS sends a notification signal

(via transmitter-2 of Figure ‎4.2) to the central controller of the microgrid when it

detects a frequency difference (|f |) of less than ef (e.g., ef = 0.01). The central

controller of the microgrid then enables an activation signal to one of its non-

dispatchable DERs to slightly and temporarily reduce the set-point of its

frequency (fset-point) as

old

pointset

new

pointset ff (‎4.3)

where 0 < < 1 (e.g. = 0.02) such that |f | becomes larger than ef. If so, the

ISS closes after synchronisation and the set-point resets to the initial value,

immediately after the closing of the ISS. As this stage falls into the local

controller of a DER, it is not elaborated more here.

It is to be reminded that the ISS opening signal is directly issued by the

OMT and the ISS opens immediately after receiving this signal. To enable the

safe operation of a CMG, each ISS is suggested to be equipped with a back-up

control system which forces an ISS to open only if the data communication

system failure is detected, while the frequency of the CMG (fCMG) falls below

minCMGf where


72

min

min

CMG )1( ff (‎4.4)

in which 0 < < 0.02 (e.g., = 0.001) and fmin is the minimum acceptable

frequency in the distribution network (e.g., fmin = 49.5 Hz in a system with a

nominal frequency of 50 Hz). This back-up control is also seen in Figure ‎4.2.

4.2 Synchronisation Strategy of Multiple Microgrids

In general, synchronisation of the neighbouring microgrids highly depends

on the existing physical links (distribution lines) between the microgrids. Let us

assume 4 general schemes of

Scheme-1: all microgrids are connected physically to a central node (bus)

through individual links (see Figure ‎4.6a),

Scheme-2: all microgrids are connected to a common distribution line,

spread among the microgrids. This line can be in the form of a radial or

loop one (see Figure ‎4.6b-c),

Scheme-3: a physical link is available between every two microgrids (see

Figure ‎4.6d),

Scheme-4: a physical link is available among some of the microgrids (see

Figure ‎4.6e).


73

MG-N-1

MG-N

(a) MG-2

MG-k

MG-1

T

e

s

t

S

e

t

t

i

n

g

s

G e n e r a l

N o . o f r a m p s t a t e s : 2

T o t a l s t e p s p e r t e s t : 4 2

T o t a l t im e p e r t e s t : 4 . 2 0 0 s

N o . o f t e s t e x e c u t i o n s : 1

In p u t M o d e : D i r e c t

F a u l t T y p e :

RampedQuantities

MG-N-

1

(b) MG-2

MG-k

MG-1

MG-N

MG-N-1

(c) MG-2

MG-k

MG-1

MG-NMG-N-1

(d) MG-2

MG-k

MG-1

MG-N

MG-N-1

(e) MG-2

MG-k

MG-1

MG-N

Figure ‎4.6. Different interconnections of neighbouring microgrids: (a) Scheme-1, (b) Scheme-2:

radial line, (c) Scheme-2: loop line, (d) Scheme-3, (e) Scheme-4.

It is to be noted that this research does not aim to define the best scheme

among the above schemes, as it is a planning stage research. Depending on each

of the above schemes, a suitable synchronisation procedure should be employed.

Among the above schemes, scheme-1 and 2 do not have any difference from the

synchronisation point of view and are treated equally. This study only focuses on

these two schemes. It is noteworthy that scheme-3 has numerous options for


74

synchronisation while forming a CMG. In general, since it is desired to form the

CMG as soon as possible to limit the duration of non-standard voltage/frequency

drop in the overloaded microgrid(s), an optimization-based technique can be

developed to determine which microgrids should be connected first (in the

transition stage) so that the overloaded microgrid is relieved quicker. However,

development of a suitable optimization technique for this purpose is a technical

challenge and can be the scope of a future publication. Scheme-4 has limited

options and probably, depending on the physical links of the overloaded

microgrid with the other microgrids, one or more options may be available

during the synchronisation procedure.

Now let us consider either of the distribution networks of Figure ‎4.6a-c.

The developed synchronisation strategy is in the form of an autonomous agent,

referred to as the synchronisation module, which only gets activated when the

OMT has selected the suitable microgrids to be coupled with the overloaded

ones. Let us assume that the OMT selects M microgrids to be coupled with K

overloaded microgrids.

Considering the fact that it is desired to minimize the appearance of non-

standard voltage/frequency in the overloaded microgrid(s), the objective of the

developed synchronisation strategy is to interconnect one of the selected

microgrids with the overloaded microgrid(s) as soon as practically possible. This

will be followed by the connection of the other selected microgrids to them. To

this end, there must be at least one microgrid among the selected microgrids that

can solely supply the PDL of one or more overloaded microgrids without being

overloaded. For this, the synchronisation module first compares the PDL of the


75

overloaded microgrid(s) with the UPC of the selected microgrids and shortlists

those selected microgrids that satisfy

P

j

PDL

or

PDL

UPC

j

j

ss

)1(

)1(

-MG

(‎4.5)

where 0 < β < 1 (e.g., β = 0.05) is a small deadband to compensate for any losses

in the interconnecting lines between the microgrids. Let us call these microgrids

as‎the‎‘self-sufficient microgrids’.‎The‎synchronisation module lists them under a

vector called SS. After this evaluation, the synchronisation module selects the

shortlisted microgrid with the highest UPC. Let us call this microgrid as MG-ss.

It then lists the overloaded microgrid(s) that can be fully supplied by MG-ss

within vector P. It is to be highlighted that all overloaded microgrids within P

should be able to be supplied by MG-ss, if they all form a temporary CMG. The

synchronisation module then sends an instantaneous closing command to the ISS

of the first overloaded microgrid within P. Closing of this ISS occurs

immediately since the outgoing side of the ISS is not energized (To prevent an

instantaneous closing if the outgoing side the ISS is energized, the local

controller of the ISS checks the voltage difference across the ISS when receiving

a closing command, as seen from Figure ‎4.2). When the ISS is closed, it sends a

CC signal back to the synchronisation module. As soon as the synchronisation

module receives the CC signal, it sends a command to the ISSes of other

overloaded microgrids within P as well as the other non-overloaded selected

microgrids to synchronize with the current CMG. As soon as their ISSes receive

the command, they initiate the synchronisation procedure. The ISS of each of

these microgrids close and they couple with the existing CMG as soon as they

are synchronized. Whenever the synchronisation module receives a CC signal


76

from the ISS of a non-overloaded selected microgrid, it evaluates the possibility

of interconnecting the existing temporary CMG with one or more overloaded

microgrids (MG-l), which are not within P, that satisfy

P

l

PDLPDL

or

PDLPDL

UPC

l

CMGExisting

j

l

CMGExisting

j

CMGExisting

i

)1(

)1(

(‎4.6)

If the synchronisation module detects that one or more overloaded microgrids

satisfy (4.9), it will send a synchronisation command to their ISSes. This process

continues until all overloaded microgrids are connected to the selected

microgrids. As an example, let us assume that the OMT has selected 5

microgrids to connect to an overloaded microgrid. Let us also assume that 3 of

them are defined to be self-sufficient from (4.8).


77

Figure ‎4.7. Developed operation sequences of coupling multiple neighbouring microgrids during

the interconnection transition.

Figure ‎4.7a illustrates schematically the operation sequence of the developed

synchronisation module for this case. As a second example, let us assume the


78

OMT has selected 4 microgrids to connect to 4 overloaded microgrids. Let us

also assume one of these microgrids can solely supply two of the overloaded

microgrids. It is also assumed that any three non-overloaded microgrids can

supply all overloaded microgrids. Figure ‎4.7b illustrates schematically the

operation sequence of the developed synchronisation module for this case.

The synchronisation module may define that no selected microgrids can

solely supply the PDL of the overloaded microgrid(s). In such a case, it defines

the two-MG combinations from the list of the selected microgrids that can satisfy

(4.8)‎ together.‎ Let‎ us‎ call‎ those‎ as‎ the‎ ‘self-sufficient two-MG combinations’.‎

The synchronisation module then aims to select one of those self-sufficient two-

MG combinations. It is desired that the selection of a suitable two-MG

combination takes place based on either of the below objectives:

Objective-1: selecting a two-MG combination which synchronizes

quicker than other two-MG combinations,

Objective-2: selecting a two-MG combination where the total

synchronisation time (i.e., between the two microgrids, and between the

overloaded microgrid with them) is minimum,

Objective-3: selecting a two-MG combination which has the highest

combined UPC versus other two-MG combinations.

Objective-1 guarantees that the selected two-MG combination will be

formed quicker than the other two-MG combinations; however, there is no

guarantee that the total synchronisation time with the overloaded microgrid will

be the minimum (as it is possible that another two-MG combination with a larger

synchronisation time may synchronize with the overloaded microgrid quicker).

Although objective-2 is the most desired one, development of a fast and accurate


79

calculation technique is very challenging. This is due to the fact that the

synchronisation module needs to exactly calculate the synchronisation time of

the microgrids in every two-MG combinations and define the angle of voltage at

that time. It then needs to recalculate the synchronisation time of the overloaded

microgrid with that two-MG combination. This fast and exact time calculation

and the calculation of the corresponding voltage angles at that time is the main

technical barrier in deploying an optimization-based technique. Thereby, in this

research, it is assumed that objective-3 is the most practical option and thus, it

has been utilized in the developed strategy.

When a two-MG combination is selected, the synchronisation module lists

the microgrids that constitute the selected two-MG combination under vector SS.

It also lists the overloaded microgrid(s) that can be fully supplied by the selected

two-MG combination, within a temporary CMG, under vector P. Then, the

synchronisation module sends a command to the ISS of the first microgrid listed

within SS to close instantly. As soon as the synchronisation module receives the

CC signal from that ISS, it sends a command to the ISS of the other microgrid

listed within SS to synchronize with that. Upon receiving the CC signal, the

synchronisation module initiates a synchronisation command to the ISS of all

overloaded microgrids listed within P. It also sends a synchronisation command

to the ISSes of all remaining non-overloaded selected microgrids. As soon as the

synchronisation module receives the CC signal from one of the remaining non-

overloaded selected microgrids, it conducts the evaluation of (4.9) to detect

whether any overloaded microgrids that are not listed under P can be supplied in

the existing temporary CMG. If so, it sends a synchronisation command to those

overloaded microgrids. This procedure continues until all overloaded microgrids


80

are connected to the selected microgrids. As an example, let us assume the OMT

has selected 4 microgrids to be connected to an overloaded microgrid. It is also

assumed that neither of them is capable to supply the overloaded microgrid

solely based on (4.8) while a two-MG combination can supply it. Figure ‎4.7c

illustrates schematically the operation sequence of the developed synchronisation

module for this case.

If the synchronisation module fails to define two-MG combinations, it

looks for defining x (i.e., respectively 3, 4 and more) microgrid combinations

that together satisfy (4.8). The same procedure discussed above will continue

until all selected microgrids by the OMT are coupled with the overloaded

microgrids. As an example, Figure ‎4.7d illustrates schematically the operation

sequence of the developed synchronisation module when a 4-MG combination

can satisfy (4.8) for a CMG of 5 microgrids. The algorithm of the developed

strategy is shown in Algorithm 4.1.


81

Algorithm 4.1. Algorithm of the developed synchronisation module

1. Fetch the selected MGs from the OMT,

2. Call the number of overloaded MGs as K ,

3. Call the number of non-overloaded MGs as M,

4. Define the self-sufficient MGs and the relevant overloaded MGs by comparing

their UPCs and PDLs,

5. If there is at least one self-sufficient MG that can solely supply one or more

overloaded MGs then6. Select the self-sufficient MG with the highest UPC and Call this MG as MG-ss,

7. List the overloaded MGs that MG-ss can supply solely within a temporary CMG

under vector P,

8. Call the number of MGs in vector P as R,

9. Send an instantaneous closing command to the ISS of the first overloaded MG

of P,

10. If the CC signal is received then

11. Send a synchronization command to the ISS of MG-ss,

12. If the CC signal is received then

13. If R > 1 then

14. Send a synchronization command to the ISS of other overloaded

MGs in P,15. End-if

16. Send a synchronization command to the ISS of M1 remaining

non-overloaded selected MGs,17. x = 1

18. While x K-R

19. If a CC signal is received from the ISS of a non-overloaded

selected MG then

20. Define the MGs coupled together based on the received CC

signals and list them under CMG,

21. Define the un-coupled overloaded MGs that can be supplied

by the existing MGs in CMG and list them in vector P,

22. If an MG is listed under P then

23. Send a synchronization command to the ISS of the MGs

listed under P,

24. End-if

25. End-if

26. End-while

27. End-if

28. End-if

29.Else

30. y = 1; j = 2; x = 1

31. While y M-K

32. y = y + 1

33. Define the self-sufficient y-MG combinations,

34. If there is at least one self-sufficient y-MG combination then

35. Select the self-sufficient y-MG combination with the highest UPC,

36. List these MGs under vector SS,

37. List the overloaded MGs that the MGs of SS can supply solely

within a temporary CMG under vector P,

38. Call the number of MGs in vector P as R,

38. Send an instantaneous closing command to the ISS of the first MG

of SS,

39. Send a synchronization command to the ISSes of all MGs in the

selected y-MG combination,

40. If y CC signals are received then

41. Send a synchronization command to the ISSes of all MGs in P,

42. Send a synchronization command to the ISS of My remaining

non-overloaded MGs,

43. While x K-R

44. If a CC signal is received from the ISS of a

non-overloaded selected MG then

45. Define the MGs coupled together based on the

received CC signals and list them under CMG,

46. Define the un-coupled overloaded MGs that can be

supplied by the existing MGs in CMG and list them in

vector P,

47. If an MG is listed under P then

48. Send a synchronization command to the ISS of

the MGs listed under P,

49. End-if

50. End-if

51. End-while

52. End-if

53. End-if

54. End-while55.End-if


82

4.3 Communication System Considerations

The proposed synchronisation strategy, similar to all communication

technology-based strategies and systems, is vulnerable to the communication link

failure. A global communication link failure (i.e., the failure of all

communication links illustrated in Figure ‎4.3) can prevent the proper operation of

the OMT and the CMG formation following the overloading of an microgrid. On

the other hand, if the communication failure is limited to data transmission

failure of the closing and synchronisation commands and the CC signals (either

between the local controller of the ISS and the central controller of an microgrid,

or between the central controller of an microgrid and the distribution network

controller), the formation of the CMG will not be possible. It is however, to be

noted that both above failures will only result in load-shedding in the overloaded

microgrid and will not impose any system instability issues.

It is also possible to assume that a data communication mismatch occurs

when any of the above signals are transmitted. To rectify this issue, it is

suggested that the transmitter continues to transmit the signal in periods of T

(e.g., T = 300 ms) until a data receipt signal is received from the relevant receiver

[51]. If the transmitters fail to receive a data receipt signal after a few (e.g. 30)

transmissions, a communication system failure flag turns on.

4.4 Performance Evaluation

To evaluate the feasibility of the developed synchronisation strategy, the

distribution network of Figure ‎4.6a is modelled with N = 6 microgrids in

PSCAD/EMTDC where the technical data of the microgrids, DERs and voltage

source converter models are provided in [6, 8]. The aggregated maximum


83

capacity of the dispatchable DERs of each microgrid is assumed to be 300 kVA

(i.e. 1 pu), while their demands and generations of non-dispatchable DERs are

different. Several study cases are considered, six of which (i.e., case-1 to case-6)

discussed below. Table ‎4.1 summarizes the UPC and PDL of each microgrid and

highlights the overloaded microgrid(s), selected microgrids, and the self-

sufficient microgrid(s). Different CMGs are desired in each study case, as

provided in Table ‎4.1. In the below studies, the demand variation in an

microgrid, which has resulted in its overloading, is not illustrated. Thus, t = 0

shows the time that the OMT has detected the overloading in the microgrid(s)

and has decided on the suitable microgrids to form a CMG. At this time, the

frequency of the overloaded microgrid in each case (except Case-5) is assumed

to be 49.65 Hz; however, after the formation of the desired CMG, their

frequency rises up, as listed in Table ‎4.1. Furthermore, neither communication

delay nor any communication data mismatches are considered in these studies.

Frequency of the participating microgrids in the CMGs of Case-1 to Case-6 as

well as the open/close status of their ISSes are shown in Figure ‎4.8 to Figure

‎4.13, respectively. Table ‎4.2 summarizes the time-sequence of the events in each

study case.

4.4.1 Scenario-A

First, let us assume that MG-3 is overloaded and MG-1 and 2 are the

selected microgrids by the OMT to support MG-3.

Case-1: The UPC of MG-1 is higher than the PDL of MG-3 while this is not

valid for MG-2. Thus, the synchronisation module couples MG-1 with MG-3

before connecting MG-2.


84

Case-2: The UPC of neither MG-1 nor MG-2 is higher than the PDL of MG-3

while their combined UPC is higher than that. Thus, the synchronisation module

selects a two-MG combination (i.e., MG-1 and MG-2) and couples them before

connecting MG-3.

4.4.2 Scenario-B

Now, let us assume that MG-5 is overloaded and MG-1 to MG-4 are

selected by the OMT to form a CMG.

Case-3: The UPC of MG-1 is higher than that of MG-2 and the UPC of

both of them is higher than the PDL of MG-5. However, the UPC of MG-3 and 4

is less than the PDL of MG-5. Thus, the synchronisation module couples MG-1

with the MG-5 and then initiates a synchronisation command to MG-2, MG-3

and MG-4.

Case-4: The UPC of all selected microgrids is less than the PDL of MG-5.

Thereby, the synchronisation module lists the two-MG combinations that can

supply MG-5. Among them, the synchronisation module recognizes that the two-

MG combination of MG-1 and MG-2 has the highest UPC. Thereby, the

synchronisation module couples MG-1 with MG-2 first and then initiates a

synchronisation command to MG-3, MG-4 and MG-5.

4.4.3 Scenario-C

Now, let us assume that two overloaded microgrids are detected.

Case-5: MG-4 and MG-5 are overloaded and MG-1 to MG-3 are selected

by the OMT to support them. The UPC of MG-1 is higher than the PDL of both

MG-4 and MG-5 and the UPC of MG-2 is higher than the PDL of MG-4.


85

Thereby, the synchronisation module selects MG-1 (the self-sufficient MG with

the highest UPC) to be coupled with MG-5 (the overloaded MG with the highest

PDL). It then initiates a synchronisation command to MG-2 and MG-3 (the

remaining selected microgrids). If either of them are coupled and the existing

temporary CMG can supply MG-4 (the remaining overloaded MG), it initiates a

synchronisation command to that.

Case-6: MG-5 and MG-6 are overloaded and MG-1 to MG-4 are selected

by the OMT to form a CMG. Neither of the selected microgrids can solely

support the overloaded microgrids. Thereby, the synchronisation module lists the

self-sufficient two-MG combinations and selects the combination composed of

MG-1 and MG-2, as it has the highest UPC. It then sends a synchronisation

command to MG-6 (the overloaded with the highest PDL) as well as MG-3 and

MG-4 (the remaining selected microgrids). If either of MG-3 or MG-4 are

coupled and the existing temporary CMG can supply MG-5 (the remaining

overloaded MG), it initiates a synchronisation command to that.


86

Table ‎4.1. The overloaded and selected non-overloaded microgrids of the distribution network as well as their UPC and PDL in the considered study cases.

Overloaded MG(s) Selected Alternative by OMT

Self-sufficient

microgrids P UPC [pu] f [Hz]

Number PDL [pu] SS MG-1 MG-2 MG-3 MG-4 MG-5 MG-6 Overloaded MG(s) CMG

Case-1 MG-3 0.60 {MG-1, MG-2} {MG-1} 0.84 0.57 0 - - - 49.65 50.0

Case-2 MG-3 0.62 {MG-1, MG-2} {MG-1, MG-2} 0.56 0.22 0 - - - 49.65 49.95

Case-3 MG-5 0.65 {MG-1, MG-2, MG-3, MG-4} {MG-1}, {MG-2} 0.84 0.76 0.43 0.32 0 - 49.65 50.05

Case-4 MG-5 0.70 {MG-1, MG-2, MG-3, MG-4} {MG-1, MG-2} 0.35 0.56 0.17 0.09 0 - 49.65 49.95

Case-5 MG-4, MG-5 0.35, 0.64 {MG-1, MG-2, MG-3} {MG-1} {MG-5} 0.84 0.62 0.43 0 0 - 49.65, 49.80 49.98

Case-6 MG-5, MG-6 0.65, 0.68 {MG-1, MG-2, MG-3, MG-4} {MG-1, MG-2} {MG-6} 0.56 0.43 0.34 0.18 0 0 49.65, 49.65 49.90


87

Table ‎4.2. Time-sequence of the events in the considered study cases.

t [s] Case-1

0.1 Synchronisation module sends an instant closing command to ISS of overloaded MG (MG-3).

0.1+ Synchronisation module sends a synchronisation command to ISS of self-sufficient MG (MG-1).

0.95 ISS of MG-1 synchronizes with MG-3 and closes.

0.95+ Synchronisation module sends a synchronisation command to ISS of the remaining selected MG (MG-2).

1.54 ISS of MG-2 synchronizes with existing temporary CMG and closes. At this time, desired CMG is formed.

Case-2

0.1 Synchronisation module sends an instant closing command to ISS of the first MG of selected two-MG combination (MG-1).

0.1+ Synchronisation module sends a synchronisation command to ISS of the remaining MG of two-MG combination (MG-2).


6.25+ Synchronisation module sends a synchronisation command to ISS of the overloaded MG that can be supplied by this two-MG combination (MG-3).


Case-3

0.1 Synchronisation module sends an instant closing command to ISS of overloaded MG (MG-5).

0.1+ Synchronisation module sends a synchronisation command to ISS of the self-sufficient MG with highest UPC (MG-1).


88


1.04+ Synchronisation module sends a synchronisation command to ISS of the remaining selected microgrids (MG-2, MG-3, MG-4).

1.19 ISS of MG-2 synchronizes with existing temporary CMG and closes.



Case-4


0.1+ Synchronisation module sends a synchronisation command to ISS of the remaining MG of two-MG combination (MG-2).


2.17+ Synchronisation module sends a synchronisation command to ISS of the overloaded MG that can be supplied by this two-MG combination (MG-5) and the

remaining selected microgrids (MG-3 and MG-4).




Case-5


89

0.1 Synchronisation module sends an instant closing command to ISS of the overloaded MG with highest PDL (MG-5) that can be supplied by the self-sufficient

MG which has highest UPC (MG-1).

0.1+ Synchronisation module sends a synchronisation command to ISS of MG-1.


1.04+ Synchronisation module sends a synchronisation command to ISS of remaining selected microgrids (MG-2, MG-3).


1.38+ Synchronisation module evaluates the possibility of connecting remaining overloaded MG (MG-4) with the existing temporary CMG. Since the

Synchronisation module detects sufficient UPC, it sends a synchronisation command to ISS of MG-4.



Case-6


0.1+ Synchronisation module sends a synchronisation command to ISS of MG-2.


2.06+ Synchronisation module sends a synchronisation command to ISS of the overloaded MG with highest PDL that can be supplied by this two-MG combination

(MG-6) and remaining selected microgrids (MG-3 and MG-4).


90

2.16 ISS of MG-4 synchronizes with the existing temporary CMG and closes.

2.16+ Synchronisation module evaluates the possibility of connecting remaining overloaded MG (MG-5) with the existing temporary CMG. Since the

synchronisation module detects sufficient UPC, it sends a synchronisation command to ISS of MG-5.




91

Figure ‎4.8. Case-1 simulation results.



92




93




94

4.5 Conclusion

Connection of multiple neighbouring microgrids needs a suitable

synchronisation technique. This connection depends on the topology of the existing

physical links among the microgrids. This chapter presented a suitable

synchronisation strategy which can be used at the transition stage of forming a CMG

system, when they are coupled through a central bus or line. The developed

algorithm, used as an agent within the distribution network controller, manages the

connection of the microgrids. In this strategy, normal synchronisation of any two

microgrids is the preferred technique and forced-synchronisation is limited to

conditions in which the frequency difference between the two interconnecting

microgrids is very small. The developed strategy aims to reduce the duration of non-

standard voltage/frequency in the overloaded microgrid(s) while preventing

temporary overloading of the participating microgrids in the transition stage. The

main limitation of this strategy is the dependency on communication systems.

Chapter 5 - Conclusions and Recommendations

95

Chapter 5 Conclusions and Recommendations

This chapter summarizes the general findings of the thesis. Some

recommendations for future researches in the areas of the thesis are also introduced

here.

5.1 Conclusions

The general conclusions of the thesis are:

(1) A new self-healing technique has been developed and validated to

support an overloaded microgrid during power deficiency conditions.

Based on the developed approach, the power deficiency of the

overloaded microgrid is compensated by external power support from

its neighbouring microgrids, after the temporary interconnection of the

overloaded microgrid to one or more suitable neighbouring microgrids.

The developed self-healing agent is identifies the overloaded microgrid

and defines the suitable neighbouring microgrids using a dynamic

multi-criteria decision-making approach.

(2) Once a microgrid is overloaded, the developed technique is able to

support the microgrid by making interconnections between microgrids.

However, if neighbouring microgrids cannot support the level of the

power deficiency in the overloaded microgrid, the developed algorithm

utilizes a load-shedding technique merged with coupling the microgrids

Chapter 7: Conclusions and Recommendations

96

for disconnecting some of the non-essential loads such that all essential

loads of all microgrids remain energized.

(3) The outcome of the decision-making approach is based on the defined

criteria and their weightings. Hence, microgrid owners (operators) may

adjust the weightings of these criteria to suit their needs. According to

the investigation in this thesis, it is discovered that electricity cost

offered by each neighbouring microgrid mostly is the main criterion

that influences the outcome of the decision-making approach.

(4) Coupling of microgrids requires synchronisation in order to provide

their safe and proper interconnection. A suitable synchronisation

method is developed and validated in this thesis. The developed

synchronisation method aims to interconnect the neighbouring

microgrids to the overloaded microgrid as quick as possible but while

avoiding a forced-synchronisation technique.

5.2 Recommendations for future research

Some future research topics in the area of this thesis are presented below:

5.2.1 Consideration of reactive power capacities and limits of microgrids

In the studies of this thesis, only the active power of DERs and loads were used

for the calculation of UPC. The developed technique does not consider the reactive

power capacities of the DERs and their limits. Evaluating the impact of the capacities

and limits of the reactive power of the DERs and microgrids on defining the level of

UPC in each microgrid and expanding the overloading condition definition of a

microgrid based on that can be a topic for future research.


97

5.2.2 Possibility of interconnection of a microgrids through multiple links

In the studies of this thesis, it was assumed that the microgrids are

interconnected through one bus only. However, in general, it is possible to consider

the interconnection of one microgrid through different buses to one or multiple

microgrids. This can be a future research topic and the power flow control under

such conditions needs to be investigated further.

5.2.3 Synchronisation method for microgrids with different topologies

As discussed in Section ‎4.2, in the studies of this thesis, it is assumed that all

microgrids are connected physically to a central node or a common distribution line.

However, it can be also assumed that the microgrids can be interconnected in a radial

or loop configuration or a physical link is available between every two microgrids.

Development of a suitable synchronization method for each of these topologies can

be the topic of a future research.

5.2.4 Protection Issues of the system of coupled microgrids

One of the main important issues that need further investigation is development

of proper protection systems for the CMG system. Suitable protection schemes

should be developed and validated that can isolate a CMG system, immediately after

a short-circuit fault in the CMG system.

5.2.5 Communication network and data transfer delay effect

In this research, it was assumed that the data transfer in the network (among

the DERs and the microgrid central controller) is carried out immediately. However,

depending on the communication network type and the number of DERs in the


98

microgrid, the data transfer may experience large delays and/or data packet loss may

be observed. The proper communication network for the microgrid, data coding

characteristics and the effect of the data transfer delay and data packet loss can be

another topic for a future research.

99

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Every reasonable effort has been made to acknowledge the owners of copyright

materials. I would be pleased to hear from any copyright owner who has been

omitted or incorrectly acknowledged.

105

Publications arising from this Thesis

Journal papers

1) F. Shahnia, S. Bourbour,‎ and‎A.‎Ghosh,‎“Coupling‎neighbouring microgrids

for overload management based on dynamic multicriteria decision-making,”‎

IEEE Trans. Smart Grid (in-press), doi:10.1109/TSG.2015.2477845, 2016.

Conference papers

2) S. Bourbour,‎F.‎Shahnia,‎and‎A.‎Ghosh,‎“Selection‎of‎a‎suitable‎microgrid to

couple with an overloaded neighbouring microgrid based on decision‎making,”‎

IEEE 47th

North American Power Symposium (NAPS), pp. 1-6, Charlotte,

North Carolina, USA, Oct. 2015.

3) S. Bourbour, F. Shahnia‎“A‎suitable‎mechanism‎for‎the‎interconnection‎phase‎

of‎ temporary‎ coupling‎ of‎ adjacent‎microgrids,”‎ IEEE‎ PES‎ Innovative‎ Smart‎

Grid Technologies Conference (ISGT-Asia), Melbourne, Australia, Nov. 2016.

4) S. Bourbour,‎and‎F.‎Shahnia,‎“Impact‎of‎the‎weightings‎of‎different‎criteria‎in‎

selecting the suitable microgrids when forming a system of coupled

microgrids,”‎IEEE‎PES‎Innovative‎Smart‎Grid Technologies Asian Conference

(ISGT-Asia), Melbourne, Australia, Nov./Dec. 2016.

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