Planeamento de redes de distribuição com incerteza na produção distribuída

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F

ACULDADE DE

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NGENHARIA DA

U

NIVERSIDADE DO

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ORTO

Power Distribution Planning Under

Distributed Generation Uncertainty

João Pedro Gomes Pina Marques

Dissertation conducted under the

Integrated Master in Electrical and Computers Engineering Major Energy

Supervisor: Professor Doutor Manuel António Cerqueira da Costa Matos

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Resumo

O planeamento de redes de distribuição consiste, de um modo geral, em determinar quais os in-vestimentos a realizar garantindo a satisfação de consumos previstos, de acordo com os critérios aplicados, obedecendo a restrições técnicas. A atividade de planeamento apresenta um elevado grau de complexidade, tanto pela sua natureza de problema de decisão, como pelas característica combinatória e incerteza relacionada com previsões dos consumos futuros e conexão de produção dispersa.

Com o crescente desenvolvimento de recursos de energia descentralizados, como a produção dis-persa, que se tem assistido nos últimos anos, motivados por questões de natureza técnica, regu-latória, mas acima de tudo ambiental, o paradigma dos sistemas elétricos de energia alterou-se. Será por isso de grande importância introduzir novas perspetivas nos tradicionais estudos levados a cabo para o setor elétrico.

Neste contexto, esta dissertação apresenta uma metodologia para planeamento de redes de dis-tribuição em ambiente de grande incerteza quanto à localização e volume da produção dispersa. Numa primeira fase, é desenvolvida uma metodologia para modelização da incerteza relativa à localização e volume de produção dispersa ao nível da baixa tensão. Neste processo propõem-se descrever a incerteza por via de cenários a gerar aleatoriamente com base numa estimativa da ca-pacidade global de produção dispersa no sistema, prevista em estudos externos, para o horizonte do planeamento. Cada cenário será avaliado em regime normal de operação em dias típicos de carga e produção em sistemas de geração distribuída. Segue-se, um processo de análise multicritério onde se identificarão soluções eficientes para reforço de rede, tendo por base a minimização do risco de corte de produção dispersa e dos custos de investimento e operação da rede de distribuição. As principais contribuições desta tese são: (1) metodologia para modelização de incertezas até então desconsideradas na literatura; (2) modelo de planeamento de redes de distribuição sensível a cenários extremos de integração produção dispersa; (3) desenvolvimento de uma metodologia de suporte à decisão de reforço de redes de distribuição de dimensões reais.

Palavras-chave: Planemanto, Redes de Distribuição, Produção Dispersa, Incerteza, Análise Mul-ticritério

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Abstract

The power distribution planning consists of determining what investments to be made, supplying the expected demand, according to some criteria, subjected to technical constraints. The planning activity presents a high level of complexity, both by its nature of decision problem and by the combinatorial characteristic as well as because of uncertainty related to the forecast of future con-sumption and distributed generation connection.

In the last years, the increasing development of decentralized energy resources, such as distributed generation motivated by technical, regulatory, but above all environmental issues, has changed the paradigm of power systems. Therefore, it is of great importance to also change the perspectives of traditional studies carried out for the electric power sector.

Within this context, this thesis presents a methodology for power distribution planning under high levels of uncertainty regarding size and location of distributed generation units at the secondary substations.

Firstly, a methodology is developed for uncertainty modelling. In this method, it is proposed a representation of uncertainties through scenarios randomly generated based on an estimate of the global installed capacity scattered throughout the system, forecasted in external studies, for the planning horizon. Each scenario will be evaluated under normal operating conditions on typical days. Then, a multicriteria analysis will be performed, where efficient reinforcement plans will be generated, based on the minimization of risk of distributed generation curtailment and on opti-mization of investment and operation costs.

The main contributions of this thesis are: (1) methodology for modelling uncertainties not consid-ered so far in the literature; (2) power distribution planning strategy that takes into consideration extreme scenarios of distributed generation integration; (3) development of a decision aid method to reinforce real-dimension distribution networks.

Key words: Power Distribution Planning, Distributed Generation, Uncertainty, Multicriteria anal-ysis

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Acknowledgement

First of all, I would like to start by thanking Professor Manuel Matos, Full Professor at the Faculty of Engineering of the University of Porto (FEUP) for accepting me under his supervision. His creative and rigorous thinking opened my mind to new perspectives in different subjects. Without his guidance and advices this thesis would be a very hard journey.

To all my colleagues and friends, specially Hugo, Bruna, Tiago and Zé for their friendship and support, a big thank.

I also must to express my profound gratitude to my family, specially my parents and my sister, for who words are not enough to describe their outstanding love, patient and guidance to light my path in all ups and downs.

Finally, I would like to thank my beloved Melanie, for being alongside me enriching this journey, supporting me whenever I needed and for the absolute trust in my capacities.

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“If do you wanna succeed as bad as you wanna breathe, than you’ll be successful”. - Eric Thomas

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List of Figures

1.1 Shares of power generation worldwide: 1970-2050. . . 2

1.2 Evolution of global annual solar PV installed capacity 2000-2016. . . 2

1.3 European solar PV total capacity until 2016 for selected countries. . . 3

1.4 Scenarios for global PV rooftop segment development 2017-2022. . . 4

2.1 Duck Curve phenomenon evolution in California power systems due to PV solar systems integration. . . 11

2.2 PDP problem characteristics. . . 13

2.3 Uncertainty modelling methods [1]. . . 16

3.1 Operational scheme of PDP. . . 20

3.2 Scenarios Generation flowchart. . . 27

3.3 Generation strategy scheme for MO problems. . . 28

3.4 Fast Nondominated Sorting algorithm [2]. . . 29

3.5 Crowded Distance Assignment structure [2]. . . 30

3.6 Crowded-Comparison Operator implementation [2]. . . 31

3.7 NSGA-II procedure [2]. . . 31

3.8 Trade-off graphical interpretation [3]. . . 32

4.1 Urban MV Network. . . 36

4.2 Load profiles of typical days. . . 40

4.3 PV generation profiles of typical days. . . 40

4.4 After reinforcement of branch B, PV generation is curtailed due to branch A con-gestion. Thus, a new case of reinforcement need is identified. . . 42

4.5 Pareto Frontier Graph. . . 46

A.1 Alternative one-line diagram for the MV network illustrated in figure 4.1. . . 61

B.4 Thermal constraints by feeder in all MCS scenarios. . . 70

B.8 Bus voltage constraints by feeder in all MCS scenarios. . . 71

B.12 DG curtailment by feeder in all MCS scenarios. . . 72

B.13 DG curtailment by period of the selected typical days. . . 73

C.1 Pareto Frontier - NSGA II. . . 75

C.2 Plans enumeration. . . 75

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List of Tables

4.1 Results of base case PF. . . 37

4.2 MV network branches load in base case, without DG integration. . . 37

4.3 MV network buses voltage in base case, without DG integration. . . 38

4.4 Typical Days. . . 39

4.5 Weight of each load class profile. . . 39

4.6 Weight of each PV generation class profile. . . 40

4.7 MCS test functions. . . 41

4.8 MCS overview. . . 41

4.9 Maximum DG curtailment scenario. . . 42

4.10 NSGA-II parameters. . . 43

4.11 Cost of reinforcing a given branch in test MV network. . . 44

4.12 Operation Costs Data. . . 44

4.13 Bound solution and Pareto Frontier. . . 45

4.14 Trade-off analysis and equivalent cost for each alternative [α1= 10 000 C/MW; α2= 10 000 C/MW]. . . 47

4.15 Trade-off analysis and equivalent cost for each alternative [α1= 200 000 C/MW; α2= 0 C/MW]. . . 47

4.16 Trade-off analysis and equivalent cost for each alternative [α1= 10 000 C/MW; α2= 70 000 C/MW]. . . 47

4.17 Possible combinations of ranges of values for α1 and for α2so that plan 1 is the preferred one. . . 48

C.1 Maximum DG curtailment scenario. . . 76

D.1 Reinforcement plan 1. . . 77

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List of Acronyms and Abbreviations

DER Distributed Energy Resources DM Decision Maker

DG Distributed Generation DMS Demand Side Management DN Distribution Network

DSO Distribution System Operator

EPSO Evolutionary Particle Swarm Optimization GA Genetic Algorithm

GDP Gross Domestic Product GHG Green House Gas HV High Voltage LP Linear Programming LV Low Voltage

MCDA Multicriteria Decision Aid MSC Monte Carlo Simulation

MILP Mixed-Integer Linear Programming MO Multiobjective

MV Medium Voltage

NSGA-II Non-dominated Sorting Genetic Algorithm II OPF Optimal Power Flow

PDP Power Distribution Planning PES Power Electric System PF Power Flow

PSO Particle Swarm Optimization PV Photovoltaic

RO Robust optimization

T&D Transmission and Distribution TS Tabu Search

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Chapter 1

Introduction

In this Chapter, a brief overview about the addressed problem will be discussed. Initially, the general context and motivation to the development of this thesis will be presented, referring the change of Power Systems paradigm and the importance of new approaches to the Power Distribu-tion Planning problem in order to cope with new challenges. Then, the purpose of this work will be detailed and the objectives explained. Finally, the organization of this thesis will be exposed.

1.1 General Context and Motivation

Since the beginning of World electrification, one of the main indices to measure countries eco-nomic growth is the rate of energy consumption, as there are a bi-directional causal relation be-tween them [4]. In a moderate economic growth scenario, it is expected that by 2040, world GDP more than doubles, driven by increasing prosperity in fast-growing developing economies, like China and India, as more than 2 billion people are lifted from low incomes. At the same time, in mature economies, the share of vehicles kilometers powered by electricity will rise from negligi-ble to almost 40% of total world expected kilometers made by 2040. These trends will lead to an increase in global power demand by one third over the next 25 years [5].

In the last few decades, the concerns of industrialized countries and World organizations have been the toxic impact of human being activities on the environment. Thus, the need of maintaining eco-nomic growth with environmental sustainability has changed the way commodities, as electric power, are generated and consumed, leading to a new power systems paradigm.

The new power systems paradigm is this: high levels of distributed generation penetration, with intermittent and unpredictable nature, throughout all voltage levels of an unidirectional-flow-based network. It means big challenges in order to improve grid flexibility, at the same time, more am-bitious quality service is required.

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In the last 20 years, the bet on this kind of distributed generation systems has gradually increased, worldwide. It has been pushed forward by several reasons, including deregulation of electricity markets, technology development and incentive policies, encouraging the use of renewable energy sources in a supporting action to a growing environmental awareness [6]. The trend for the next decades is a faster-growing in energy production based on renewable and decentralised sources such as wind and sun, figure 1.1.

Source: Bloomberg NEF, IEA.

Figure 1.1: Shares of power generation worldwide: 1970-2050.

The first revolution on decentralized renewable energy integration, started in the nineties and was led by wind harnessing. Wind farms, whether onshore or offshore, are essentially connected to the transmission or distribution grid at high voltages. The second renewable energy revolution started ten years ago, with the development of solar PV technology driven by European Union’s new poli-cies about consumer side production and feed-in tariffs. Recently, countries in fast development like China and India are heading the 50% annual growth of total solar PV installed capacity, figure 1.2.

Source: Solar Power Europe 2017

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1.2 Objectives and Contributions 3 Regarding LV distribution networks, the transition has been shaped by integration of consumer-side rooftop solar PV systems. Despite of the fact that the global solar market remains driven by utility-scale solar power systems, the established ones are now controlling deployment of ground-mounted PV by switching fed-in tariffs to tenders. If along with this trend, attractive incentive schemes are launched, it will draw new opportunities towards rooftop solar PV installations. In Europe, figure 1.3, relevant work has been made, specially in countries like Germany and Italy, as well as in US, where California is leading the harnessing of sun power.

Figure 1.3: European solar PV total capacity until 2016 for selected countries.

The concept of prosumers have a huge potential. Price decreasing of PV solar technology and storage devices, more competition in deregulated markets and incentive programs are important factor to harness their potential, figure 1.4. In Europe, it has been estimated that 264 million peo-ple could be producing their own electricity by 2050 [7]. Over the next 5 years, China, India, US and Japan will continue to absorb the bulk of the solar power system capacity. India, for example, targets a 40% solar rooftop share for its 100 GW program by 2022 [6].

Thus, the development of innovative work in power distribution planning (PDP) is required in the near future to accommodate all the expected amount of distributed generation. The stochastic nature of distributed generators based on renewable sources and the unpredictable behaviour of private initiatives to invest in assets like these, in a deregulated market, will require the exploration of new approaches to the PDP exercise.

1.2 Objectives and Contributions

The main objective of this work is to develop a methodology to PDP under extreme scenarios of non-dispatchable DG systems connection on secondary substations of MV networks. The main expected contribution is to propose a methodology that generates flexible reinforcement plans

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Figure 1.4: Scenarios for global PV rooftop segment development 2017-2022.

suitable to as much scenarios of DG integration as possible, which would not be predicted by a typically PDP approach. This methodology aims to deal with a increasingly-significant uncertainty faced by DSOs in developed and deregulated power systems: the freedom of private investors to decide the location and capacity of their grid-connected DG units. Unlike classic PDP, where de-mand evolution was the main issue, in this new approach it has a secondary role.

One key point of this thesis is the assumption that, by no means, does DSO influence the location and size of any distributed generator in LV network. It is a demand side resource driven by private investors. This is, indeed the environment of many markets.

Only PV solar systems will be considered either for self-consumption or small production, as it is the most common technology used in renewable based decentralised generation at LV level. In order to cope with DG installation uncertainty, a broad range of scenarios of DG size and location will be generated and tested in typical days. The scenarios generation is based on an estimate of global PV installed capacity foreseen by external studies. Although, there is uncertainty related to this estimate (several values could be tested), the developed work starts from this value as a given information.

Thereafter, a set of non-dominated reinforcement plans is generated taking into consideration the forecasted scenarios. Then, a decision aid method based on multicriteria analysis will be

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imple-1.3 Structure 5 mented to help DSO in choosing the preferred plan according to its preferences and obligations. In summing up, from the DSO point of view this work introduce a new reducing-risk tool to take in consideration in modern PDP exercise. In addition, it has a potentially beneficial impact to prosumers as it can reduce substantially DG units generation spillage during peak periods.

1.3 Structure

This thesis is organized on five main chapters. The first one presents the purpose of this thesis and its contribution to PDP new perspectives.

The second chapter includes three main topics, presenting what is already developed in each con-cept related to this work. The first one is about Distribution Generation: concon-cepts related to it, main drivers of DG development and big challenges regarding its integration. The second topic is Power Distribution Planning: the existing methodologies, the consideration of renewable distri-bution generation in PDP problems and types of uncertainty consideration as well as methods to uncertainty modelling. the third is about multicriteria decision-aid methods.

The third chapter depicts the formulation of PDP exercise approached and tools for resolution. Firstly, the general problem statement of PDP is made. Then, the adoption of Monte Carlo Simula-tion combined with OPF for uncertainty modelling is explained. the third topic is about the strategy of reinforcement plans generation as a multiobjective problem through a meta-heuristic: NSGA-II. Finally, a multicriteria decision-aid method is formulated completing the purposed methodology. The fourth chapter applies the methodology depicted in chapter 3 to a realistic Portuguese 150-buses power distribution network. There, important comments are made about this strategy and the most relevant results about uncertainty modelling and plans generation are shown. Finally, it is performed a simulation about decision maker (i.e. DSO) preferences in order to illustrate the multicriteria decision-aid method.

The fifth chapter presents the main conclusions of this work about PDP problems considering DG integration, along with future complementary perspectives.

Finally, an appendix is added to the work with complementary information about test system and results.

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Chapter 2

State of the Art

This chapter presents important aspects related to the main topics of this thesis, namely: distributed generation, power distribution planning, uncertainty modelling tools and multicriteria decision-aid methods.

2.1 Distributed Generation

DG has increased substantially during the past few years. Fast technological developments, dereg-ulation of energy markets and incentive policies motivated by economic, environmental and so-cietal drivers have paved the way for it growth [8]. Until few years ago, the connection of DG was essentially confined to MV and HV levels due to technical, safety and economic reasons. However,because of energy policies objectives, developments in generators and respective elec-tronic interfaces, the interest in microgeneration units, connected to the LV networks, has rapidly increased. However, DG integration imposes several challenges to power delivery. These chal-lenges arise since the distribution systems infrastructure was designed assuming that the electric energy would be carried unidirectional from HV/MV substations downstream to customers. This assumption influences protection and control, and as a consequence, the distribution systems reli-ability [8]. Hence, the complexity of planning the distribution systems as a whole increases with the integration of DG.

2.1.1 Concepts

DG is part of a plan to change electric power system paradigm. There are different concepts of DG in the existing literature and therefore there is no consistent definition [9]. Countries has defined DG based on different characteristics, namely: voltage connection level; electricity production source or technology (e.g. renewable energy, co-generation); not dispatched or centrally planned generation plants; direct connection with demand, among others. However, some common char-acteristics can be found: Regarding to location, DG can be defined as electric power sources directly connected to distribution network (or it can be connected to the transmission network, by depending on the size) or on the demand side; DG is based on small scale generators compared to

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centrally dispatched power plants. It can be from few tens of kW to thousands of MW [10].

2.1.2 Main Drivers for DG growth

DG deployment and its integration into power electric system (PES) operation and planning have been pushed forward by many drivers that can be of four categories: environmental, technical, economic and regulatory/national [1, 11, 10, 12, 13].

• Environmental

Limiting greenhouse gas (GHG) emissions: One of the main drivers of DG growth is its po-tential contribution for the reduction of global greenhouse gas emission. It can be reached by, on one hand, a high level of DG penetration which may reduce the generation in con-ventional fossil-fuel power plants and consequentially leads to power transmission and dis-tribution losses reduction. On the other hand, the adoption of DG technologies based on renewable energy sources (e.g. PV solar systems, wind turbines, mini-hydros) or at least with high efficiency level (e.g. CHP) reduces the impact of power systems on the environ-ment.

Deferral of new infrastructures construction: Another key driver for DG deployment from the environmental perspective is it contributes to deferring construction of new transmission lines and conventional power plants.

• Technical

Load peak shaving: low capacity DG, e.g. PV solar systems or thermal units, can be in-stalled to mitigate peak loads. They can be seen as supplementary systems.

Reliability: due to decentralized characteristic of DG the number of consumers affected by an out of service generator is less then compared with a failure in conventional power plants.

• Economic

Less risk taken on initial investment: the promotion of competitiveness in deregulated en-ergy markets with an open access to the distribution network has increased the risk faced by players in the electricity supply chain. Hence, investors may search for smaller capacity projects with less capital outlay required, which is expected to favor the development of DG applications.

Low operation and maintenance costs: wind and solar power come with no cost and even in CHP due to its symbiotic nature, the operation costs are commensurately small. The modularity and compact characteristics of DG technologies make it easier and faster to replace and maintain.

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2.1 Distributed Generation 9 Power quality and reliability improvement: In addition to losses reduction and grid invest-ments deferral, DG is also a cost effective way to improve power quality and reliability levels, which helps DSO achieving goals imposed by regulator.

• Regulatory/National

Energy mix diversification: In a highly-energy dependent society as observed nowadays, relying generation in few energy sources and small number of power plants is totally in-appropriate regarding energy security and sustainability. A disruption in resources supply would imply serious consequences in economic, social and political terms. DG complies with many aspects to mitigate this issue: It uses diverse energy sources and technologies reducing nations external dependency on fossil fuel of unstable regions and contributes to the control over nation’s energy portfolio; it distributed nature around the network and on the demand side, contributes to reliability improvement as said before.

Contribution for market competition: The low initial investments required to DG imple-mentation will attract many new players to the electricity market. Along with costumer flexibility, it can improve competitiveness, reducing market prices.

2.1.3 Main Challenges Towards DG Integration

Enhance DG integration means overtake some challenges. However, it is not always easy to iden-tify the main impacts, because it strongly depends on the local characteristics of the distribution network, on the energy source and connection interface properties. There are some potential chal-lenges with different natures widely reported in the literature.

• Commercial

Loss Allocation: The costs of electricity transmission and distribution activities need to be allocated to the network users, trough tariffs that fairly depict their impact in these costs [14]. DG integration adds complexity to this already nonlinear problem. In [15], P. M. Costa and M. A. Matos addressed the loss allocation problem in distribution networks with DG, in a liberalized environment. An AC power flow based method was adopted to study the impact of DG in the avoidance and increase of distribution losses. This methodology can be used to design DG incentive schemes or to define tariffs to subside network operator activity. Active distribution network management: As mentioned above, the deployment of DG may have a profitable consequence to DSO, regarding their daily operation and grid investments. In [16], Van Werven and Scheepers identified a lack in DSO business model that threaten the exploitation of full potential offered by DG. For DG to flourish, DSOs have to undertake substantial upfront investments in grid infrastructures, to make it actively manageable. J. P. Lopes et al [10] enumerated three possible approaches: Recovering the cost of imple-menting active management through increased charges for the use of the grid; Establishing

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incentive schemes that would reward DSOs for integrating DG; Creating a commercial en-vironment where DSOs would offer active management services to generators for a charge. • Technical

Power quality: Power quality is essentially assessed by two important factors: harmonic distortion of the network voltage and transient voltage. The influence of DG integration depends on several network characteristics. DG can either improve or deteriorate the quality of network voltage [10].

Overvoltage: The voltage rise effect due to DG plants generation, particularly, at remote parts of distribution feeders can lead to overvoltage scenarios. It’s an important limitation regarding DG deployment at low voltage distribution network and it will be taken into con-sideration during this thesis PDP approach.

Overload & Losses: In general, DG production has a beneficial effect on overloading and losses, as it is connected closer to the consumption, reducing power flow in T&D network [6]. However, during periods with high levels of DG penetration and low consumption, there are a risk of components overload and additional losses. These issues will be assessed in the PDP methodology developed in this work.

Protection: DG impacts the protection of DN in different ways: protection of the DG equip-ment from internal faults, noncontrolled island DG operation or its impact on existing distri-bution system protection [10]. Most of these failures are consequence of inadequate system protection settings for this new DG penetration paradigm. In order to allow more DG con-nections, in the long term, occasional protection failure might be accepted. However, it will represent a disadvantageous for costumers.

TSO operation: DG units could supply total or partially the demand needs, reducing the power flow through the transmission network. The advantageous effects of it are risk of overload reduction and losses curtailment. Nevertheless, there are some concerns to take into consideration. TSO will face high slope power ramps, which means they will face strict conditions to offset the fluctuation of DG generation. A related well-known phenomenon is the "Duck curve", as shown in figure 2.1. It is a consequence of high level of decen-tralised PV solar systems integration. A risk of overgeneration will be faced in periods where nondispatchable production overtakes the demand. Another impact at the transmis-sion system is the degradation of frequency and voltage control because, shutting down controllable power plants to accommodate nondispatchable power generation from noncon-trollable DG will reduce the number of available resources to provide ancillary services. • Regulatory

A clear policy and efficient modifications to the regulatory framework are a key factor for DG to thrive. New market rules have to be implemented to fairly reflect the impact of DG in DSO activities and to incentive DSO investment in order to improve DG integration. It is

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2.2 Power Distribution Planning 11 also important to reward DG owners by providing them access to the market and remuner-ating them for the benefits their assets represent to the system. In [17], Harrison et al., using a multiobjective OPF, shown that, in U.K. as many European countries, DG investors and DSOs would tend to connect DG in significantly different locations and capacities. They concluded that implemented incentive schemes are the reason for this difference.

Ancillary Services: the provision of ancillary services required for safe and reliable opera-tion of the electric power system is still essentially based on convenopera-tionally power plants. As the share of DG is growing, it is necessary launching mechanisms in order to include its participation on ancillary service provision [10].

Source: California Independent System Operator (CAISO).

Figure 2.1: Duck Curve phenomenon evolution in California power systems due to PV solar sys-tems integration.

2.2 Power Distribution Planning

2.2.1 Introduction

The PDP consists on deciding the construction and location of new substations and feeders, as well as the reinforcement of existing ones, in order to supply future demand. In general, this task is restricted by three conflicting types of factors: technical (e.g. voltage variation, thermal limits), economical (e.g. minimization of investment and operational costs) and regulatory obligation (e.g. reliability index, GHG effect reduction).

Demo-geographic aspects of a region, like population growth or geographic barriers have a huge influence on power distribution investment and operational costs.

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The purpose of PDP has changed over the years: Electrification

At the beginning, the fundamental issue was the electrification paradigm. The goal was to encour-age consumption. At that time, investments in expansion led the power distribution costs.

Power quality

As the goal of connecting all consumers was being met, the electrification rate decreased. On the other hand, the power quality became an important aspect to take in consideration in PDP. As distribution network (DN) failures had economic consequences for consumers, they became more aware of their legal rights and of the need to improve the quality of energy supply. A new era has arise with emergence of regulatory instruments to improve DSOs’ power quality. Quality became the main purpose of PDP.

Distributed Generation

In the last two decades, a new paradigm has emerged with de power sector deregulation. One of the main consequences was the connection of independent generation to DN. Although, there was already a high level of uncertainty in the existing power system, the introduction of nondispatch-able DG based on intermittent primary energy sources will introduce new types of uncertainties. This new paradigm has motivated the development of new approaches to the PDP as the one that will be presented in this thesis. To satisfy the power demand as much economically as possible with an adequate level of quality and reliability is a complex task due to the uncertainties, system dimension, constraints and objectives taken in consideration. Any planning strategy has important economic risks associated, so the role of PDP methodologies is to mitigate that risks.

2.2.2 Methodologies

Over the years, the PDP subject has been studied from diverse perspectives, which differ by several aspects, figure 2.2.

Initially, the PDP problem used to be solved with linear programming (LP) and Mixed-Integer Linear Programming (MILP). However, with the substantially growth of power system, these ap-proaches did not cope efficiently with requirements.

In the 80s and 90s, the contributions of Merrill et al. [18, 19] and Merrill and Wood [20], among others introduced a new philosophy that shaped the modern era of power systems planning: Least Cost Planning. This conceptualization is based on three fundamental elements:

Options: consideration of a broad range of options, e.g. Demand Side Management (DMS), DG integration, Storage.

Uncertainty: modelling different types of uncertainties related with loads, generation or economic factors.

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2.2 Power Distribution Planning 13

Figure 2.2: PDP problem characteristics.

Objective: reconciliation of conflicting technical, regulatory or economic objectives.

The evolution of computing processing speed and the development of algorithms, capable of mod-elling power systems with precision, have boosted PDP studies. Considering the PDP problem nature - nonlinear, typically multiobjective, combinatorial and uncertain with a huge number of binary, continuous and discrete variables - new methods with different contents and formulations have shown up.

2.2.3 PDP considering Renewable Distributed Generation

The PDP problem has been intensively studied in the last decades and therefore the literature about this subject is quite extensive. In this subsection, the focus goes to approaches that consider re-newable distributed generation in their formulation.

Two main types of methods can be adopted to generate solutions for PDP: numerical and heuristic methods.

Numerical methods

It includes linear programming (LP), nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP), among others.

Linear programming can only deal with optimization of linear objective functions and linear con-straints [21]. Keane and O’Malley implemented LP to solve optimal DG placement to achieve maximum DG penetration in [22, 23].

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Nonlinear programming refers to methods capable of dealing with nonlinear problems. This meth-ods are based on derivatives, e.g. Newton Raphson. In [24], Newton Raphson method was chosen to find optimal size and placement of DG in order to obtain the optimization of both cost and power losses.

Mixed-integer nonlinear programming can be introduced in PDP problems to deal with integer or binary variables. The proposed model in [25] formulates the optimal planning problem as MINLP, with the objective of minimizing the energy losses and for optimally allocation of DG in the dis-tribution network. Porkar S, et al. [26] have employed a MINLP method to find the optimal size and location for diverse types of DG by considering the electricity market price volatility.

Heuristic methods

Methods based on intelligent searches that have no guarantee of finding optimal solution, but can have satisfactory results near the optimal one. It have been implemented in PDP problems to cope with local optimum solutions and uncertainties.

Authors in [27] have implemented Simulated Annealing method (SA) to find optimal location and sizing of DG to minimize the total losses and to improve voltage profile in a large distribution net-work. Also in [28] SA is implemented as an optimization tool to determine the optimum location and size of DG in order to minimize a multi-objective function.

After it’s deployment in 1986, Tabu Search (TS) has been used as an optimization tool in PDP problems. In [29], TS was applied to find optimal location and capacity of DG in parallel with tap position of voltage regulators and distribution network configurations. The objective function was to minimize the cost of power losses.

Evolutionary computation is a group of heuristics based on populations natural selection. In the last decades it has been widely adopted in power systems studies. Borges and Falcão have pro-posed Genetic Algorithm (GA) method to solve optimal DG placement and capacity in order to minimize the power loss and maximize benefit/cost ratio [30]. On the other hand, Harrison et al. combined GA and OPF to find optimal location and size of DG to respectively maximize DG capacity and profit [31, 32]. Authors in [33], adopted a Balanced GA (BGA) to improve the in-tensification of the solution search procedure by trading-off diversification ability in a multistage PDP under uncertainty.

In [34], a multi-objective programming method based on the non-dominated sorting genetic algo-rithm (NSGA) is proposed to find maximum sets of distributed wind power generation in order to minimize the power losses and short-circuit levels.

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2.2 Power Distribution Planning 15 Later, an improved NSGA was developed: NSGA-II. In [35] it was implemented to perform a multiobjective optimal placement of switching devices considering DG unavailability, network re-liability and equipment cost, with no island network operation. Pires et al. [36] adapted NSGA-II to compute solutions to a multiobjective reactive power compensation model. They claimed an enhancement of the algorithm by applying a local search within it. On the other hand, in [37], NSGA-II was proposed to solve the multiobjective planning problem by optimal placement and sizing of DG.

A social behaviour fish schooling optimization tool, named Particle Swarm Optimization (PSO), has been applied to different areas of electric system problems. Wong et al. has combined PSO and Newton-Raphson methods to determine the optimal location and size of DG to reduce total power losses [38]. In [39], the authors proposed a multi-objective PSO to find the best DG location and capacity along with shunt capacitor banks in order to minimize overall costs.

In 2002, Miranda and Fonseca introduced Evolutionary Particle Swarm Optimization (EPSO). It is a general-purpose algorithm, whose roots are in Evolutions Strategies and in Particle Swarm Optimization concepts [40]. This method has been adopted in [41] to find the optimal size of DG in a PDP study. The objective of this paper is to gain the lowest result of real power losses. Other methods, like Ant Colony Optimization (ACO), Artificial Bee Colony (ABC) or Cockoo Search Algorithm (CSA), are used in PDP considering DG, essentially to determine optimal DG placement and capacity to enhance a specific objective, [42, 43, 44].

2.2.4 Uncertainty Consideration

Uncertainty consideration in power systems studies is a necessary approach to deal with its un-certain nature. There are several technical and economic parameters whose behaviour is unpre-dictable:

Technical parameters: Load, generation, forced outage, faults;

Economic parameters: Market price, economic growth, fuel price and supply;

Different methods are been adopted to handle with aforementioned uncertainties. Approaches from robust optimization, interval based analysis, probabilistic methods to possibilistic methods are implemented in PDP problems, figure 2.3. [45, 46].

Robust optimization (RO) is adopted for multi-period economic dispatch under high levels of wind energy penetration, in [47]. Authors in [48] are handling with uncertainties in variable renewable sources, forecasted load values and market prices, for scheduling of multi-micro grid systems by using RO.

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Figure 2.3: Uncertainty modelling methods [1].

In [49], Zio et al. address the problem of DG penetration in MV distribution networks, with a Monte Carlo technique that accounts for the intrinsic variability of electric power consumption. MCS has been used to cope with uncertainties related with DG generated power, load profiles and electricity market prices, in [50]. Mokryani et al. adopted MCS to handle with uncertainties re-lated to intermittent generation of PV systems and load demands [51]. To deal with uncertainties related to output power of a plug-in electric vehicle (PEV) due to its stochastic charging and dis-charging schedule, wind generation unit due to the stochastic wind speed, solar generating source due to the stochastic illumination intensity, volatile fuel prices and future uncertain load growth, a MCS has been proposed in [52], to find the optimal sitting and sizing of distributed generators in distribution system planning. To preserve the time series characteristics of fluctuating primary energy sources and variable load, a sequential MCS has been introduced in [53].

After Leite da Silva has proposed the Pseudo-sequential MCS, for the first time, in 1994, it has been used to cope with uncertainties in studies with specific requirements. In [54], this MCS vari-ation has been implemented to evaluate the impact of high PV power penetrvari-ation on customers’ nodal reliability and system energy and reserve deployment.

Regarding analytical methods, Point Estimate Method (PEM) was introduced to handle with un-certainties related to electricity market prices and wind power outputs, in competitive markets, [55]. A new probabilistic framework based on 2m Point Estimate Method (2m PEM) has been in-troduced to consider the uncertainties in the optimal energy management of micro grids including renewable power sources like PV, wind turbine, micro turbine, fuel cells as well as storage devices [56].

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2.3 Multicriteria Decision-aid Methods 17 Zadeh proposed, in 1965, a novel possibilistic approach, where parameters are described by using membership functions: fuzzy sets. Since then, this concept has been adopted in power systems studies to handle with DG uncertainties. In [57], Ponce de Leão and Matos have modelled loads profile and DG uncertainties with fuzzy sets in a PDP problem. Later, a fuzzy evaluation tool has been proposed for analysing the effect of renewable DG on active power losses and the capacity of distribution network in load supply at presence of uncertainties, [58].

Another approach adopted to model uncertainty in power systems studies is the Information Gap Decision Theory (IGDT). It measures the difference between parameters and their estimation. IGDT has been proposed for DSO when it faces several loads and renewable DG uncertainties [59, 60].

2.3 Multicriteria Decision-aid Methods

The PDP problem may bring up a set of important consequences to the future. Such consequences can be evaluated from economical, technical and environmental points of view and attributed to different interest stakeholders, like the DSO, DG owners, consumers, among others. Therefore, the consideration of DG integration in PDP leads to multiple, potentially conflicting criteria. For that reason, the adoption of these concepts presents a problem with multicriteria nature.

The Multicriteria Decision Aid (MCDA) subject is devoted to the development and implementa-tion of decision support tools and methodologies for aiding decision in problems involving con-flicting multiple criteria, goals, objectives, and points of view [61].

Hwang and Yoon [62] separated multicriteria problems in two types:

• Multiattribute problems, with discrete, usually limited number of pre-specified alternatives, requiring attribute comparisons and involving explicit or implicit trade-offs;

• Multiobjective problems, with decision variable values to be determined in a continuous or integer domain, of infinite or large number of choices, to best satisfy the decision maker constraints, preferences or priorities.

In literature, there are several MCDA techniques which differ by required information to the De-cision Maker (DM) and by the attribute type (e.g. qualitative, numeric, ordinal, among others). Several authors act as a reference source for describing the main MCDA methods, which have proven useful in different types of decision-making problems and the approaches taken to resolve them, among others [63, 64, 65, 66, 67, 68], Robert T. Clemen in [69] and Roy et al. [70], have already demonstrate systematic approaches to the MCDA.

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Bellow, it will be presented some of the most common methods adopted in existing literature about the PDP exercise.

Weighted sum methods

These are methods based on multi-attribute additive value functions. The alternatives evaluation is performed by a value function built through attributes aggregation. Among others, Trade-off Analysis is an easy weighted sum method. Due to its suitability to the multicriteria problem pre-sented in this work, it will be the MCDA technique performed.

Preliminary analysis methods

These methods perform a preliminary analysis of alternatives based on specific thresholds for all criteria [71]. They require communication with the DM as the threshold reflects his preferences. Among others, Domination (based on principle of dominance between alternatives), Conjunctive (reject alternatives with at least one attribute worst then the specified threshold), and Disjunctive (rejects alternatives by comparing some attributes with outstanding values in one or more alterna-tives). Methods which belong to this category are considered screening methods. A disadvantage is the need of posterior analysis for helping the DM decision.

Categoric Procedures methods

Methods like these do not require interaction with the DM. The elimination of alternatives are made based on DM attitude, e.g. the Lexicographic method performs a comparison between al-ternatives regarding the most important attribute; the Linear Assignment is an ordinal partiality method where alternatives are order based on each criteria and then the one with best global performance are selected; or Maximin and Maximax methods, where the alternatives are deleted according with their worst attributes. The adoption of these methods depends on if DM attitude is, respectively pessimist or optimist as the best (Maximin) or the worst (Maximax) alternatives are deleted.

Other techniques, like ELECTRE, MACBETH or the ones used to handle with fuzzy sets could be highlighted, but the detailing of all techniques is not part of this thesis.

Summing up, several tools and methods could be adopted in this thesis. Some are more suitable the others to the PDP exercise proposed, but all of them have their advantageous and disadvantageous.

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Chapter 3

Tools and Modelling

In this chapter, the modelling of PDP problem will be presented. Firstly, it will be exposed and ex-plained the proposed PDP approach, regarding decision variables, objective functions, constraints and planning period. Then, the tool adopted to handle with uncertainties is depicted. Finally, the implemented technique to seek for non-dominant reinforcement alternatives is presented along with a MCDA method to help DSO decision about what plan to adopt.

3.1 Power Distribution Planning

In deregulated power systems, DSOs are not responsible for investing in demand-side DG systems. The only concern of the DSO must be finding the best way of ensuring a good service quality to costumers, at the lowest cost as possible. In fact, the investment in DG units, under unbundling rules, are taken by private investors. Thus, DSO is exposed to a risk associated to investors de-cisions. Despite some connection rules (e.g. grid codes) which vary by country, DG owners can decide about the size and location of their assets. In scenarios with high levels of DG penetration or in case of weak network, e.g. rural networks, it kind of risks can lead to an undesirable grid malfunction. Preventing this consequences by assuming the possibility of such scenarios is the basilar philosophy of the PDP methodology developed in this work.

As seen in chapter 1, the next decades will be synonymous of PV solar systems fast deployment, which means that demand side generation will become more and more a reality of power distri-bution systems. For that reason, it seems of great importance to develop PDP studies considering high levels of uncertainty regarding capacity and location of DG units to predict possible inconve-nient phenomenons and to enhance DG integration.

3.1.1 General problem statement

The proposed PDP model is applied to the reinforcement of existing MV distribution networks to accommodate future growth of PV solar systems penetration. The PDP problem proposed is classified as single-stage concerning reinforcement periods. The evaluation of the alternative plans

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will be performed with a multiobjective formulation and it will consider economic and technical objectives.

Regardless of aforementioned characteristics, this study will follow a classical structure of PDP approaches, as presented in figure 3.1.

Figure 3.1: Operational scheme of PDP.

3.1.1.1 Decision Variables

It is assumed a reinforcement exercise, i.e. network expansion is not expect. Thus, the topology and technical characteristics of MV distribution network are known, i.e. all branches and nodes are problem data.

all information about peak load and location are also problem data. Regarding distributed PV solar systems, the information about sizing and siting is acquired from the uncertainty modelling process, whereas the global estimative of DG total installed capacity and PV generation profile are data got from external studies. As the main purpose of this thesis is the assessment of DG grid inte-gration at LV level, it will be considered no evolution of power demand during the planning period. The only decision variables of the problem are related to the reinforcement (or not) of MV net-work branches. They only admit integer numbers and a finite number of possibilities, (e.g. 0 - no

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3.1 Power Distribution Planning 21 reinforcement; 1 - reinforcement with a 120mm2-section cable; 2 - reinforcement with a 240mm2 -section cable, and so on).

Below, it is presented all variables that will be used in mathematical formulation.

n total number of nodes PGε total active power of global PV without

cur-tailments consideration [MW]

m total number of branches PGcε total active power of global PV after

curtail-ment [MW]

w total number of nodes with DG connection PC_ε vector of active power generation curtailment

of global PV generation by scenario [MW] t planning horizon [years] Ui voltage on node i [p.u.]

s Number of OPFs (performed to assess each DG scenario) with DG curtailment flag

Umax maximum admissible voltage [p.u.]

Pk active power flow on branch k [MW] ek reinforcement of branch k; ek ∈ N0

Qk reactive power flow on branch k [Mvar] ε reinforcement plan; set of branches

reinforce-ment: ε = [e1, ...,em]

Ik current on branch k [A] ψε average of total PV generation curtailment

as-sociated to reinforcement plan ε [MW] rk resistance of branch k cable [Ω] crk investment cost of reinforcing branch k [e]

pk active power losses on branch k [MW] Crε investment costs of reinforcement plan ε [e]

PDi active power demand on node i [MW] Coε1 annual operation costs associated to

rein-forcement plan ε adoption [e]

QDi reactive power demand on node i [Mvar] Coεt operation costs associated to reinforcement

plan ε considering an exploration period of t years [e]

PGi active power generation on node i [MW] cp cost coefficient of power losses [e/MWh]

QGi reactive power generation on node i [Mvar] Cε investment and operation costs of

reinforce-ment plan ε [e]

3.1.2 Objective Functions and Constraints

As discussed in chapter 2, in a PDP exercise, many objectives of different natures could be con-sidered, (e.g. environmental, economic or technical), with potentially conflicting interests among different stakeholders involved in electricity supply, such as system operators, DG owners, DG operators, energy suppliers, consumers and regulatory entities. However, in the proposed model,

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the choice fell on three fundamental objectives to take in consideration the DSO and DG owners interests (it will be seen that consumers will not take any risks with this approach):

Minimization of PV solar generation curtailment Minimization of investment costs

Minimization of exploration costs

Other objectives has been adopted in literature, e.g. minimization of environmental impact, but due to its subjectivity, it is not always easy to measure. Nevertheless, the environmental impact is indirectly minimized with the maximization of renewable DG penetration since it reduces the dispatched capacity of conventional thermal power plants. On the other hand, it must be defined a limited number of objective functions, otherwise operational and computational requirements grow substantially.

Following the traditional formulation, multiobjective (MO) problems are generally formulated as: (3.1) min f(x) =            f1(x) f₂(x) ... fj(x) subject to: g(x) = 0 (3.2) h(x) ≤ 0 (3.3) x≥ 0 where:

x- vector of decision variables f(x)- vector of objective functions g(x)- set of equality constraints h(x)- set of inequality constraints

3.1.2.1 Objective Functions PV solar generation curtailment

In PDP studies, the maximization of DG integration is a recent concern. It inclusion started mak-ing sense since a prosperous environment to DG deployment was created, either by technological development or by economic and regulatory incentives, and consequently a significant amount of

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3.1 Power Distribution Planning 23 distributed generators are been connected to the grid.

Energy sector is in the renewable energy era and the next revolution lays on an active demand side role in activities of power systems, like power generation or providing ancillary services. Thus, it is important to evaluate both the influence of DG integration in DSO investments and, on the other hand, the impact of DSO investment decisions in DG owners costs. The last mentioned conse-quence will be assessed in this work by the objective function (3.4), which represents the expected average PV generation curtailment if plan ε is considered:

min ψε(ε) = mean(PC_ε) (3.4)

Investment costs

The investment costs are related to reinforcement of MV network branches. As the reinforcement is made at the year zero and it is a single-stage exercise, the total investment cost of plan ε is given by equation 3.5. Crε(ε) = m

∑

k=1 crk(ek) (3.5)

In this case costs actualization is not needed. Operation costs

The exploration costs are related to network active power losses. Power losses of a network branch are directly proportional to the current flow in that element, where the proportional coefficient is defined by the cable resistance. The annual operation cost of plan ε based on the average losses at the s scenarios () is given by the following equation

Coε1(ε) = s ∑ z=1 m ∑ k=1 cp· rk,z· Ik,z2 · 8760 s (3.6)

where cpis the cost coefficient of power losses.

For solutions analysis the annual exploration costs of all years considered in the planning horizon must be updated. Considering the same annual average of power losses for each operation year, the present value of these future costs can be calculated by expression (3.7).

Coεt(ε) = Coε1(ε) ·

1 − (1 + τ)−t

τ (3.7)

where τ is the pre-defined discount rate.

As can be seen in the expressions (3.6) and (3.7), the operation costs are deterministically calcu-lated thereby, no uncertainties are considered.

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In order to simplify problem computation, the minimization of investment and explorations costs will be merged, leading to a two-objective MO PDP problem. Therefore, the aggregated objective is as follow:

min C_ε = Crε(ε) +Coεt(ε) (3.8)

3.1.2.2 Constraints

Constraints are of two categories, as seen before: equality constraints, generally formulated in (3.2) and inequality constraints (3.3).

The equality constraints are simply the verification of kirchhoff laws with nonlinear active and reactive power balance equations by node, 3.9 and 3.10.

Pi= PDi+ PGi, i= 1, ..., n (3.9)

Qi= QDi+ QGi, i= 1, ..., n (3.10)

The inequality constraints consist of technical limitations together with decision variables limits: Two sets of m branch power flow limits as nonlinear functions of the bus voltage angles and magnitudes, equation (3.11).

|Sk| ≤ Skmax, k= 1, ..., m (3.11)

Where |Sk| is the absolute apparent power flow in branch k and Smax is the maximum admissible

apparent power flow in branch k.

It also include an equality constraint on any reference bus angle and upper and lower limits on all bus voltage magnitudes and active and reactive distributed generators injections:

θre f = 0 (3.12)

Ui,min≤ Ui≤ Ui,max, i= 1, ..., n (3.13)

PGj,min≤ PGj ≤ PGj,max, j= 1, ..., w (3.14)

QGj,min≤ QGj ≤ QGj,max, j= 1, ..., w (3.15)

As mentioned before, the decision variables represent reinforcement levels of each branch. e.g. 0 - no reinforcement; 1, 2 and 3 consist of reinforcement acts with a cable of, respectively, 120 mm2, 240 mm2and 400 mm2, and so on. Thus, another constraint is added to problem formulation:

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3.2 Uncertainty Modelling 25

3.2 Uncertainty Modelling

As mentioned in chapter 2, there are several types of uncertainties in power systems behaviour. To handle with it, many approaches has been proposed in literature. This works aims to introduce the uncertainty faced by DSOs related to capacity and location of future privately held DG units in secondary substations, which have not been studied so far.

3.2.1 Combined Monte Carlo and OPF Method

To lead with the uncertainties a Non-Sequential Monte Carlo Simulation will be performed. MCS is one of the most common and accurate stochastic approaches adopted in PDP exercises. It is based on sampling theory and on the law of large numbers. The idea behind MCS is to pre-dict the global behaviour of the system by analysing the average value of a significant sample [72]. With the advances in power computation and adoption of convergence acceleration techniques, the MCS became widely employed since, unlike analytical and deterministic methods, it is suitable for large scale systems. Another advantage over other methods is its relatively easy implementa-tion.

The non-sequential approach generates system scenarios which are characterized by its elements state at that point. These scenarios are temporal independent of each other. It is like taking a picture of the system.

The evaluation process of a power system, through a MCS, can be outlined as follow [72]: Initialize system data

Do

NScen = 0;

REPEAT (Until the coefficient of variation βSP is reached)

NScen=NScen+1;

Simulate a new scenario xi ∈ X using P(x) distribution;

Calculate test function F(xi) for the scenario xi;

Estimate the expected value ˆE(F);

Evaluate the uncertainty of the estimator V ( ˆE(F)); End

where NScen is the number of scenarios that are evaluated, xi is a simulated system scenario that

belongs to the system possible scenarios vector X, P(x) is the associated probability distribution and F(x) is the test function (can be more than one) that evaluates power system performance. F(x) can represent, for example, average DG curtailment.

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3.2.1.1 Scenarios

In this work, the scenarios are characterized by the siting and sizing of rooftop PV solar systems on the demand side at LV level. The scenarios generation is based on a global estimate of DG installed capacity in the considered distribution network (e.g. 50MW) Since the study is about MV network, the DG generation surplus is seen as opposite power flow coming from secondary substation.

The scenarios generation process has two different phases: firstly, the network secondary substa-tions with possible DG penetration will be randomly sorted; then, the capacity of DG units in each substation is randomly defined based on an uniform probability distribution. This process obeys to some rules mentioned below:

1º PV generation is only connected to secondary substations;

2º In each substation, the total installed capacity of PV systems is directly proportional to the value of the active power peak load (MW) in that node, i.e. the PV generation capacity is considered to be a multiple of the annual peak load.

The first rule intends to reflect the reality about most of the DG systems privately held: they are demand side installations. The second one has the purpose of avoiding unreal concentration of DG penetration and do it by linking the installed capacity to load values.

The load growth rate was not considered throughout the planning horizon (no load growth at all) so as to create the most severe conditions for the massive integration of DG units.

3.2.1.2 Test Functions

In order to assess the suitability of DG integration at the MV distribution network in each scenario, two test functions will be considered:

• Average DG curtailment; • DG curtailment probability.

The first one reveals the average level of global PV generation curtailment. The second mentioned function shows the number of periods wherein PV solar generation must be reduced to guarantee that all network technical constraints are satisfied.

The MCS performed in this thesis must estimate the expected value of aforementioned test func-tions. The process ends only when the coefficients of variation related to these two indexes take values lower than a pre-defined number between 0 and 1 , e.g. 0.05.

In order to calculate the test functions, OPFs will be carried out. Each scenario of DG integration will be performed with load and PV solar generation profiles of four typical days. These days were selected according to the following criteria:

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3.2 Uncertainty Modelling 27 • Season: Winter, Spring/Autumn and Summer;

• Weekday: weekend, holiday and weekday;

• Worst-case scenario: minimum load and maximum PV generation; maximum load and minimum PV generation.

The process philosophy is to generate scenarios with the lowest DG curtail as possible, while no technical constraints are violated. Since the objective function of an OPF is to minimize system operation costs, in order to accomplish the above-mentioned optimization, it is associated a near zero cost for DG generators dispatch.

The assessment performed in each scenario is made up of: DG curtailment data by node and system

voltage active constraints thermal active constraints power losses

HV/MV substation power flow

Figure 3.2 depicts the algorithm of scenarios generation.

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3.3 Reinforcement Plans Generation

3.3.1 Generation Strategy

As referred above, a strategy for generation of efficient alternative plans was followed. In this strategy, there is no inclusion of DM preferences. The preferences are considered a posteriori. Hence, the decision process is constituted of two phases, figure 3.3.

Figure 3.3: Generation strategy scheme for MO problems.

The first phase consists of seeking for the Pareto Frontier: a list of efficient decision for further DM analysis. The second one is a decision-aid method to help the DM based on its preferences, which will be formulated later.

3.3.1.1 Multiobjective GA: NSGA-II

The PDP considered in this thesis is a multiobjective combinatorial problem, with nonlinear con-straints and nonlinear objective functions. In cases like this, heuristic search algorithms are the proper way to approach the generation of efficient solutions.

To implement this strategy, a fast and elitist multiobjective Genetic Algorithm was adopted: NSGA-II - Non-dominated Sorting Genetic Algorithm NSGA-II, proposed by Deb et al. in [2]. Like others GA’s, this variant is based on a population of individuals. Each one represents a position in the universe of feasible solutions for the optimization problem, i.e. a possible solution.

In typically GAs, population converges to a problem optimum through sequential applications, at each iteration, of the following genetic operators:

Mutation: Some individuals are randomly modified, in order to reach other solutions of the universe of feasible solutions.

Crossover: The individuals, randomly organized pairwise, have their space locations com-bined, in such a way that each former pair of individuals gives rise to a new pair.

Selection: The individuals, after mutation and crossover, are evaluated. They are chosen or not chosen for being inserted in the new population through a probabilistic rule that gives a greater probability of selection to the better individuals (the ones with smaller objective function evaluation).

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3.3 Reinforcement Plans Generation 29 Elitism: A subset of the former population that contains the best individuals is deterministi-cally inserted in the new population.

In order to implement the pareto frontier search, the selection and the elitism operators should be structured in order to correctly identify the non-dominant individuals. Mutation and crossover operators do not depend on the mono or multiobjective problem nature, [73].

It should be noticed that a multiobjective GA evolves a whole population toward the Pareto fron-tier. In a single run, the whole pareto frontier or, at least, a large portion of it will be found. This means that the ratio of the computational effort of executing a GA by the computational cost of executing a deterministic algorithm or transforming a multiobjective problems in a set of single-objective problems (e.g. ε-Constraint or Parametric Variation) becomes much smaller in the case of multiobjective optimization problems since the second ones would have to run once a time for finding each Pareto point.

Each operator can be implemented in several alternative ways: a specific combination of specific realizations of the aforementioned operators constitutes an instance of GA. One of these combi-nations is the NSGA-II which will be adopted in this work.

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The main contributions delivered by NSGA-II laid on selection and elitism operators. In the first one, an optimized version of non-dominated sorting scheme was used: Fast Nondominated Sort-ing(figure 3.4), [74]. This process sorts and separates the population in subsets (F1,F2,...), where

F1is the non-dominated subset. All the other subsets are dominated by the preceding ones. Thus,

it is established a ranking where the individuals in the first subset (F1) are the best classified. With

this approach the computational complexity of non-dominated sorting is O(MN2)(where M is the number of objectives and N is the population size), unlike the O(MN3)complexity of other GAs, [2]. Therefore, the above mentioned optimization is a critical aspect specially when big population sizes are required.

Another key factor to take in consideration in MO GAs is the diversity-preservation mechanism to get a good spread of solution in the obtained Pareto frontier. The process introduced in NSGA-II is: Crowding Distance Assignment. This approach, unlike others (e.g. Sharing Function), does not require external parameters for maintaining the diversity. It also presents a better performance regarding computational complexity when compared with other MO GAs [74]. The proposed method is divided in two phases:

Density Estimation: The density of solutions in a particular solution surrounds is estimated by using the distance to nearest neighbours (crowding distance). The exception of this estimation goes to boundary solutions which are assigned an infinite crowding distance.

Figure 3.5: Crowded Distance Assignment structure [2].

Crowded-Comparison Operator (_{≺k): This operator guides the selection process, at} differ-ent stages of the algorithm, based on two attributes of population individuals: Nondomina-tion rank (irank)and crowding distance (idistance). The definition of a partial order according

to ≺k operator is has follow: Between two solutions with differing non-domination ranks, the solution with the lower rank is chosen. Otherwise, if both solutions belong to the same front (Fi), then it is selected the solution that is located in a lesser crowded region.

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3.4 Multicriteria Decision Aid 31

Figure 3.6: Crowded-Comparison Operator implementation [2].

The overall NSGA-II procedure is depicted below, figure 3.7.

Figure 3.7: NSGA-II procedure [2].

3.4 Multicriteria Decision Aid

The aim of Multicriteria Decision Aid techniques (MCDA) is to perform a multicriteria evaluation able to deal with different DM’s preferences and helping him/her, in that way, to better understand the influence of each potential solution in the final decision. The potential solution is defined as preferred alternative (among others solutions of Pareto Frontier) evaluated over the set of estab-lished criteria. This approach requires a close communication with the DM, which increases the robustness of final solution in regard of DM’s preferences. [75].

In the process of alternative reinforcement plans evaluation, DM can have different preferences over the range of performance measures of each criterion. In order to simulate these preferences a trade-off analysis will be implemented.

Planeamento de redes de distribuição com incerteza na produção distribuída

F

E

U

P

Power Distribution Planning Under

Distributed Generation Uncertainty

João Pedro Gomes Pina Marques

Resumo

Abstract

Acknowledgement

Contents

List of Figures

List of Tables

List of Acronyms and Abbreviations

Chapter 1

Introduction

1.1

General Context and Motivation

1.2

Objectives and Contributions

1.3

Structure

Chapter 2

State of the Art

2.1

Distributed Generation

2.2

Power Distribution Planning

2.3

Multicriteria Decision-aid Methods

Chapter 3

Tools and Modelling

3.1

Power Distribution Planning

∑

3.2

Uncertainty Modelling

3.3

Reinforcement Plans Generation

3.4

Multicriteria Decision Aid