Study of a generation capacity expansion on an island

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DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2020,

Study of a generation

capacity expansion on an island

JUSTINE VALÉRIE MAGALI GUILMINEAU

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

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Study of a generation capacity expansion on an island

Justine GUILMINEAU April 2020

Examiner:

Mikael AMELIN Supervised by:

Egill TÓMASSON (KTH)

Eckehard TRÖSTER (Energynautics GmbH)

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Abstract

The study carried out in this master thesis is part of a larger project led by Energynautics GmbH focusing on renewable energy development in the Caribbean. One of the Caribbean states, consisting of multiple islands, has set a target of 30 % of renewable energy in the power sector by 2030. The first objective of the thesis is to develop optimal generation capacity expansion plans for two different islands of this country, utilizing solar PV generation, which is the only available renewable energy resource. To achieve this objective, three main tasks are identified. The first is the development of an optimal generation capacity expansion plan for the next three years using the optimization tool HOMER Energy. At the beginning only diesel generation is present on the islands. For each study case year, the installed capacity of PV and BESS is optimized and enabling technologies such as curtailment (controllability of PV) and grid-forming inverters are deployed. The second task focuses on the development of a new dispatch strategy, improving on the black box dispatch algorithms built into HOMER. The dispatch strategy minimises the cost of electricity generation and is based on a rolling 48 hours forecasts of the load and PV. It is implemented in MATLAB and linked to HOMER via the built-in MATLAB interface. As HOMER is focused on generation expansion and dispatch and inherently neglects the grid, a grid study is required to assess the stability of the network. This study is the last task of the thesis and is limited to determined steady-state voltage and the asset loading on one of the studied islands through load flow simulations in DIgSILENT PowerFactory. It is shown that there are no major issues even at high PV shares, however, grid performance can be improved if the PV unit is equipped with reactive power capability to control the voltage. A study on the impact of the Q(U)- control and the PQ-capability of the PV and BESS inverters is performed.

Keywords: Generation capacity expansion, optimisation, dispatch strategy, load flow calculation, grid- forming, grid-following, HOMER Energy, PowerFactory

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Sammanfattning

Studien som genomförts i detta examensarbete är en del av ett större projekt vilket leds av Energynautics GmbH med fokus på utveckling av förnybar energi i Karibien. En av de Karibiska staterna, bestående av flera öar, har ett mål på 30 % förnybar energi i elkraftssektorn innan 2030.

Första syftet med examensarbetet är att utveckla optimala utbyggnadsplaner för produktionskapaciteten för två olika öar i detta land, med användning av solcellsproduktion, vilket är den enda tillgängliga förnybara energikällan. Den första uppgiften är utvecklingen av en optimal utbyggnadsplan för produktionskapaciteten för de kommande tre åren med optimeringsverktyget HOMER Energy. Från början fanns det bara dieselgeneratorer på öarna. För varje studerat år optimeras den installerade kapaciteten av PV och BESS samt aktivering av möjliggörande teknologier som begränsning av PV-produktion och grid-forming växelriktare. Den andra uppgiften fokuserar på utvecklingen av en ny driftsstrategi, förbättring av den basala driftsalgoritm som är inbyggd i HOMER.

Driftsstrategin minimerar kostnaden av elproduktionen och är baserad på en 48 timmars prognos av laster och PV. Den är implementerad i MATLAB och kopplad till HOMER via det inbyggda MATLAB- gränssnittet. Eftersom HOMER fokuserar på produktionsutbyggnad och drift och i praktiken försummar elnätet, krävs en studie av elnätet för att utvärdera stabiliteten av elnätet. Studien av denna sista uppgift i examensarbetet är begränsad till att bestämma spänningen vid jämnviktsläge och den utvärderade lasten på en av de studerade öarna genom belastningsfördelningsberäkning i DIgSILENT PowerFactory. Det visade sig att det inte fanns några stora problem även med stora andelar PV, men elnätets prestanda kan förbättras om PV-omriktarna är utrustade med reaktiv effektstyrning som kontrollerar spänningen. En studie avinverkan från Q(U)-styrning och PQ-kapacitet av PV- och BESS-växelriktare har utförts.

Nyckelord: Utbyggnadsplanering, optimering, driftsstrategi, belastningsfördelning, grid-forming, grid- following, HOMER Energy, PowerFactor

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Acknowledgements

First of all, I would like to thank my supervisors Egill Tòmasson and Eckehard Tröster for their support and confidence during all my master thesis. I thank also my examiner Mikael Amelin for his interest in my master thesis. I would also thank Lennart Söder for his involvement in my master thesis.

I would also like to thank Pablo Gambin and Peter-Philipp Schierhorn for their support and the share of their knowledges during my entire thesis.

I thank all my colleagues at Energynautics from their welcome and the cooperation throughout my master thesis.

Finally, I would like to thank all the people who participated in the smooth running of my master thesis as well as to those who helped me during the writing of this report.

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Table of figure

Figure 1: Evolution of the LCOE of the PV projects from the IRENA report [10] ... 15

Figure 2: Flow chart of the master thesis ... 17

Figure 3: HOMER Energy capability ... 20

Figure 4: HOMER Energy model of Island A in 2019 ... 21

Figure 5: Optimal generation capacity expansion ... 27

Figure 6: Solar PV characteristics for different irradiation level [20] ... 28

Figure 7: Control model for a grid following inverter [23]... 29

Figure 8: Frequency-watt function for a grid-following inverter when the frequency reference is 60 Hz [23] ... 29

Figure 9: Control model for a grid forming inverter [23] ... 29

Figure 10: Droop function for grid forming controller ... 30

Figure 11: Flow chart of the methodology used to assume the load curve ... 31

Figure 12: Daily load curve in January and June (top) and seasonal profile in per-unit of Island A (bottom) ... 32

Figure 13: Efficiency curves of the generators (left: generators A1 and A3, right: generator A2) ... 33

Figure 14: Solar profile of Island A ... 34

Figure 15: Wind direction and speed on the island [8] ... 35

Figure 16: Daily load profile in per-unit (top) and seasonal load profile in 2020 of Island B (bottom) 36 Figure 17: Efficiency curves (top left: generator B1, top right: generators B2 and B3 and bottom: generator B4) ... 38

Figure 18: Solar profile of Island B ... 38

Figure 19: Wind direction and speed on the island B [8]... 39

Figure 20: Dispatch in 2018... 40

Figure 21: Levelized cost of electricity according its different components ... 40

Figure 22: Installed capacity per technology in 2019 ... 41

Figure 24: Levelized cost of electricity according its different components (left) and electricity mix (right) ... 42

Figure 25: Installed capacity per technology in 2020 ... 43

Figure 28: Installed capacity in 2021 for the system with 3 generators ... 46

Figure 31: Installed capacity in 2021 for the system with 2 diesel generators ... 48

Figure 33: Optimal generation capacity expansion plan for Island A ... 49

Figure 34: Above: Dispatch in 2021 for the cycle charging dispatch and without minimum runtime. Below: State of charge of the battery ... 50

Figure 35: Above: Dispatch in 2021 for the cycle charging dispatch and minimal runtime of 4 hours. Below: State of charge of the battery ... 51

Figure 36: Levelized cost of electricity according its different components (left) and electricity mix (right) for a minimum runtime of 4 hours ... 51

Figure 37: Battery state of charge for 100% of renewable without capacity shortage ... 53

Figure 38: Battery state of charge for 100% renewable and 5% capacity shortage ... 53

Figure 39: Levelized cost of electricity according its different components ... 54

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Figure 40: Installed capacity on Island B in 2019 ... 55

Figure 41: Dispatch for one week in February for Island B in 2019 ... 55

Figure 43: Dispatch for one week in July for Island B in 2020 without batteries ... 57

Figure 44: Levelized cost of electricity according its different components (left) and electricity mix (right) for the system without the BESS... 57

Figure 45: Installed capacity on Island B in 2020 ... 58

Figure 46: Dispatch for one week in July for Island B in 2020 with batteries ... 58

Figure 47: Levelized cost of electricity according its different components (left) and electricity mix (right) for the system with the BESS ... 58

Figure 48: Installed capacity in 2021 ... 60

Figure 49: Dispatch for Island B in 2021 ... 60

Figure 51: State of charge of the battery for the Island B when the share of renewable energy is 100%... 62

Figure 52: Critical day for Island B in 2021 with 100% renewable energy ... 62

Figure 53: Optimal generation capacity expansion plan ... 63

Figure 54: Efficiency curve of the generation B4 of Island B and its linearization ... 67

Figure 55: Dispatch for the HOMER Predictive strategy ... 69

Figure 56: Dispatch for the new strategy with an optimisation time window of 48 hours ... 69

Figure 57: Proposed predictive dispatch with 24h forecast ... 70

Figure 58: Proposed dispatch with 48h forecast and rolling window ... 71

Figure 59: Proposed dispatch with 48h forecast and rolling window and battery reserve participation to 10 minutes ... 72

Figure 60: Load following dispatch of Island B in 2020 without considering the maintenance schedule ... 73

Figure 61: Proposed predictive dispatch with a rolling window of Island B in 2020 ... 73

Figure 62: Proposed predictive dispatch with a rolling window of Island B in 2020 for short-term battery reserve participation ... 73

Figure 63: Load following dispatch of Island B in 2021 without considering the maintenance schedule ... 76

Figure 64: Proposed predictive dispatch with a rolling window of Island B in 2021 ... 76

Figure 65: Proposed predictive dispatch with a rolling window of Island B in 2021 for short-term battery reserve participation ... 76

Figure 66: Model of the grid on Island B in 2018 ... 81

Figure 67: Load flow calculation in PowerFactory ... 82

Figure 68: Q(U)-control defined by the German grid code with P and Q respectively the output active and reactive power ... 83

Figure 69: PQ capability curve according to the German grid-code [34] (left) and the the “Q at night” PV inverter [35] (right) ... 84

Figure 70: Voltage profile of the north feeder (left) and south feeder (right) for the night peak operation scenario with a voltage at the substation equal to 1 pu ... 87

Figure 71: Lines' loading when the load is equal to the night peak load in summer and with the voltage setpoint equal to 1pu ... 87

Figure 72: Voltage profile of the north feeder (left) and south feeder (right) for the night peak operation scenario with a voltage at the substation equal to 1.025 pu ... 88

Figure 73: Voltage profile of the north feeder (left) and south feeder (right) for the minimum load operation scenario with a voltage at the substation equal to 1.025 pu ... 88

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Figure 74: Voltage profile of the north feeder (left) and south feeder (right) for solar peak operation scenario with a voltage at the substation equal to 1.025 pu ... 89 Figure 75: Voltage profile of the north feeder (left) and south feeder (right) for extreme peak

operation scenario with a voltage at the substation equal to 1.025 pu ... 89 Figure 76: Lines' loading when the correlation factor of the load is high ... 90 Figure 77: Heatmap of the network when the correlation factor is high ... 91 Figure 78: Voltage profile of the north feeder (left) and south feeder (right) for the night peak

operation scenario in 2020 with a voltage at the substation equal to 1.025 pu ... 93 Figure 79: Voltage profile of the north feeder (left) and south feeder (right) for the night peak

operation scenario in 2020 with a voltage at the substation equal to 1.037 pu ... 94 Figure 80: Voltage profile of the north feeder (left) and south feeder (right) for the minimum load operation scenario in 2020 with a voltage at the substation equal to 1.037 pu ... 94 Figure 81: Voltage profile of the north feeder (left) and south feeder (right) for the solar peak

operation scenario in 2020 with a voltage at the substation equal to 1.037 pu ... 95 Figure 82: Voltage profile of the north feeder (left) and south feeder (right) for the extreme peak operation scenario in 2020 with a voltage at the substation equal to 1.037 pu ... 95 Figure 83: Lines’ loading during the maximal correlation factor of the loads with the voltage control equal to 1.037pu and the QV-control and PQ-capability of Germany... 96 Figure 84: Total losses of the system with the voltage setpoint of the substation to 1.037pu ... 97 Figure 85: Lines' losses of the system with the voltage setpoint of the substation to 1.037pu ... 97 Figure 86: Transformer losses of the system with the voltage setpoint of the substation to 1.037pu 98 Figure 87: Total losses of the system with a voltage setpoint at the substation equal to 1 pu ... 99 Figure 88: Lines' losses of the system with the voltage setpoint of the substation to 1 pu ... 99 Figure 89: Transformer losses of the system with the voltage setpoint of the substation to 1 pu.... 100 Figure 90: Voltage profile of the north feeder (left) and south feeder (right) for the night peak

operation scenario in 2021 with a voltage at the substation equal to 1.037 pu ... 103 Figure 91: Voltage profile of the north feeder (left) and south feeder (right) for the minimum load operation scenario in 2021 with a voltage at the substation equal to 1.037 pu ... 103 Figure 92: Voltage profile of the north feeder (left) and south feeder (right) for the solar peak

operation scenario in 2021 with a voltage at the substation equal to 1.037 pu ... 104 Figure 93: Heatmap of the grid during the extreme peak load and with the voltage control equal to 1,037pu and with the SMA PQ capability for the PV and BESS inverter ... 105 Figure 94: Voltage profile of the north feeder (left) and south feeder (right) for the extreme peak load operation scenario in 2021 with a voltage at the substation equal to 1.037 pu ... 105 Figure 95: Lines' loading when the correlation factor of the load is high ... 106

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Table of tables

TABLE 1: ISLANDS DESCRIPTION ... 18

TABLE 2: ISLAND A CHARACTRISTICS ... 30

TABLE 3: EXPECTED GENERATION ON ISLAND A ... 32

TABLE 4: GENERATOR CHARACTERISTICS ... 33

TABLE 5: MAINTENANCE SCHEDULE ... 34

TABLE 6: INPUT DATA FOR THE SOLAR PV ... 34

TABLE 7: ISLAND B CHARACTERISTICS ... 35

TABLE 8: LOAD PROFILE COMPOSITION FOR ISLAND B ... 36

TABLE 9: EXPECTED GENERATION ON ISLAND B ... 37

TABLE 10: GENERATOR CHARACTERISTICS ... 37

TABLE 11: STUDY OF THE IMPACT OF THE BATTERY ... 45

TABLE 12: RESULTS OF THE SIMULATION WITH THE GRID FORMING INVERTER AND THE LOAD FOLLOWING DISPATCH ... 46

TABLE 13: OPTIMAL GENERATION CAPACITY EXPANSION PLAN FOR ISLAND A ... 49

TABLE 14: RESULTS OF THE SIMULATIONS WITH THE GRID-FORMING INVERTER AND THE CYCLE CHARGING DISPATCH ... 50

TABLE 15: SUMMARY OF THE DIFFERENT SCENARIOS FOR 2021 ... 52

TABLE 16: OPTIMAL CAPACITY AND LCOE FOR DIFFERENT RE FRACTIONS ... 52

TABLE 17: COMPARISON BETWEEN A SYSTEM WITH BATTERIES AND A SYSTEM WITHOUT BATTERIES FOR THE ISLAND B ... 56

TABLE 18: RESULTS OF THE SIMULATION WITH THE GRID-FORMING INVERTER AND THE LOAD FOLLOWING DISPATCH FOR ISLAND B ... 59

TABLE 19: OPTIMAL CAPACITY AND LCOE FOR DIFFERENT RE FRACTIONS ... 61

TABLE 20: OPTIMAL GENERATION CAPACITY EXPANSION PLAN FOR ISLAND B ... 63

TABLE 21: LCOE FOR THE TWO ISLANDS ... 64

TABLE 22: COMPARISON BETWEEN THE HOMER PREDICITVE AND THE NEW DISPATCH STRATEGY WITH 48 HOURS-TIME WINDOW ... 68

TABLE 23: COMPARISON BETWEEN THE NEW DISPATCH STRATEGY WITH 48 HOURS-TIME WINDOW AND 24 HOURS-TIME WINDOW ... 70

TABLE 24: COMPARISON BETWEEN THE NEW DISPATCH STRATEGY WITH 48 HOURS-TIME WINDOW WITH AND WITHOUT ROLLING WINDOW ... 71

TABLE 25: COMPARISON BETWEEN THE NEW DISPATCH STRATEGY WITH 48 HOURS-ROLLING TIME WINDOW WITH LONG-TERM RESERVES AND SHORT-TERM RESERVES ... 72

TABLE 26: COMPARISON BETWEEN THE LF DISPATCH OF HOMER ENERGY AND THE NEW DISPATCH STRATEGY WITH ROLLING WINDOW FOR ISLAND B IN 2020 ... 74

TABLE 27: COMPARISON BETWEEN THE LF DISPATCH OF HOMER ENERGY AND THE NEW DISPATCH WITH ROLLING WINDOW IN 2021 ... 75

TABLE 28: LOAD CHARACTERISTICS ... 80

TABLE 29: OVERHEADLINES DATA ... 80

TABLE 30: VOLTAGE REQUIREMENT FOR THE FOUR OPERATION SCENARIOS ... 85

TABLE 31: LOAD LEVEL AND DIESEL GENERATION PROVIDED BY HOMER ENERGY FOR THE OPERATION SCENARIOS ... 86

TABLE 32: PV PLANT AND BESS DATA IN 2020 ... 92

TABLE 33: LOAD LEVEL AND DIESEL GENERATION PROVIDED BY HOMER ENERGY FOR THE OPERATION SCENARIOS ... 93

TABLE 34: MINIMUM VOLTAGE OF THE TWO FEEDERS AND GRID LOSSES FOR TWO PQ-CAPABILITIES ... 101

TABLE 35: PV PLANTS AND BESS DATA ... 102

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TABLE 36: LOAD LEVEL AND DIESEL GENERATION PROVIDED BY HOMER ENERGY FOR THE

OPERATION SCENARIOS ... 102

TABLE 37: GENERAL ECONOMIC DATA FOR THE PRJECT ... 113

TABLE 38: FUEL COST EVOLUTION ... 113

TABLE 39: CAPITAL COST FOR THE DIFFERENT TECHNOLOGY USED ... 113

TABLE 40: O&M COST FOR THE DIFFERENT TECHNOLOGY USED ... 114

TABLE 41: MAINTENANCE SCHEDULE OF THE DIESEL GENERATORS... 114

TABLE 42: OPTIMISATION PARAMETERS ... 115

TABLE 43: OPTIMISATION VARIABLES ... 117

TABLE 44: LINE DATA FOR ISLAND B GRID MODEL ... 121

TABLE 45: DIESEL GENERATORS MODEL IN POWERFACTORY ... 121

TABLE 46: SIZING OF THE TRANSFORMERS CONNECTED TO THE LOADS ... 122

TABLE 47:DATA ON THE TRANSFORMER CONNECTED TO THE LOADS ... 122

TABLE 48: DATA FOR THE TRANSFORMER CONNECTED TO THE PV PLANTS ... 123

TABLE 49: DATA ON THE TRANSFORMER CONNECTED TO THE DIESEL GENERATORS... 124

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Abbreviations

AC: Alternative current

BESS: Battery energy storage system CC: Cycle charging dispatch strategy CO2: carbon dioxide

DC: Direct current GHG: greenhouse gas

HOMER: Hybrid Optimization for Multiple Energy Resources h: hours

LCOE: Levelized cost of energy LF: Load following dispatch strategy MILP: Mix integer linear programming NPC: Net present cost

O&M: Operation and maintenance PV: Solar photovoltaic

RE: Renewable energy

RES: Renewable energy sources VRE: Variable renewable energy y: year

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1. Introduction

1.1 Decarbonisation of the electricity sector

Climate change is an important issue nowadays. In fact, the problems due to this change can already be observed and solutions must be found to contain it. Therefore, world leaders meet every year for a global climate conference. In 2015, this conference took place in Paris and it came to major agreements. One of the objectives fixed by the Paris agreement is to limit climate warming to 2°C by limiting greenhouse gas emissions [1]. The reduction of the emission involves the decarbonisation of the industry and electricity sectors.

In 2013, the worldwide electricity and heat sector represented 31% of the greenhouse gas emission in the world [2]. In this world, the electricity mainly comes from fossils fuel like coal and natural gas. The combustion of these energy sources induces, among other, carbon dioxide (CO2) emission, which is a greenhouse gas (GHG). The electricity sector can play an important role in respecting the decarbonisation wishes of the Paris agreement. To reduce this emission of greenhouse gases, the incentive is to use renewable energy sources instead of fossil fuel. The replacement of conventional generator by variable renewable energy (VRE) is one of the solutions for the decarbonisation of the electricity sector.

1.2 Integrating VRE in power system

The integration of the VRE into power system causes some challenges. One of these challenges is the variability of the renewable energy sources. The variations of the RE happen in different time frames and have to be dealt with in different ways. For example, solar PV is sensitive to cloud coverage. If a cloud passes over the PV panels, their generation decreases quickly. In order to keep the balance between the generation and the demand, the conventional generator must be able to increase their production to cover the RE loss. Moreover, there is no PV production during night so the conventional generators must be sized without RES. Due to the variability of the production, one kilowatt of conventional generation cannot be replaced only by one kilowatt of VRE. Measures have to be taken to have enough backup capacity available, either from conventional generators or energy storage.

Another challenge due to VRE is the frequency stability of the system due to the low inertia in the system. Replacing conventional generators by VRE reduces the share of rotating generators directly connected to the electric network. The inertia of the system is important for frequency control. VRE sources are connected to the network through converters and these converters do not contain mechanical inertia. Therefore, the frequency stability is a challenge in integrating VRE and new frequency control method must be developed [3].

Generators (RE or not) placed in the distribution grid without sufficient voltage control cause voltage problems. In traditional power system, the distribution systems are unidirectional because only loads are connected to this grid. However, the integration of RES changes this. The generation is not only on the transmission grid but also to the distribution one. This changes the voltage control of the grid.

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1.3 Variable renewable energy in the Caribbean

The study which is carried out in this report takes place in the Caribbean area. According to Rebekah Shirley et al. [4], 90% of the produced energy comes from petroleum which has to be imported. That induces a high generation cost of around 0.30 $/kWh in 2015 [5]. In large interconnected systems of Europe, the generation cost is between 0.04 and 0.06 $/kWh [6].

In 2015, the overall energy generated in the Caribbean area was equal to 56,390 GWh and the renewable generation was only 2,929 GWh [7]. Renewable energy covered in 2015 in average only 5

% of the load. However, there are available wind and solar energy resources of the Caribbean area capable to increase such share [8], [9]. Moreover, the cost of electricity generated by these VRE sources is decreasing worldwide with weighted average costs around 0.09 $/kWh for solar PV and 0.06

$/kWh for wind as reported by IRENA “Renewable power generation costs in 2018” [10]. As shown in Figure 1, the typical range of the PV generation cost is between 0.06 $/kWh to 0.22 $/kWh. Even the top end price of 0.22 $/kWh is cheaper than diesel generation. That is why renewable energy sources are not negligible for Caribbean states to reduce the cost of electricity. In addition to reducing the cost of electricity, it allows also to respect Paris agreements as mentioned previously.

Figure 1: Evolution of the LCOE of the PV projects from the IRENA report [10]

One of the Caribbean states¹ wants to increase the renewable penetration in its electricity mix. Their objective is the reach at least 30% of renewable fraction in average for the whole country.

Energynautics GmbH has been asked to study this feasibility of this objective. The work presented in this report is part of the project.

1 The exact location cannot be provided in this thesis due to NDA agreements.

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2. Objective

This master thesis is part of larger project in which its main objective is to build a RE roadmap that allows a Caribbean state to accomplish the 30% RE’s penetration committed by its government for 2030. The Caribbean state under study counts with more the 20 different power systems ranging from 0.16 MW to 61.8 MW. The study will be performed for two different islands of such state. The two islands selected for this project are representative for the small and middle size islands. These two islands are a starting point for the development that is expected to later spread to the rest of the country.

The study comprises in the first part on a techno-economic analysis that aims to determine the optimal generation expansion plan. The technologies considered are the solar PV and the battery energy storage system (BESS). This study consists in building a plan for the integration of variable renewable energy (VRE) sources for islands for the next three years. At the beginning only diesel generation is present on the islands. To perform this study, the software HOMER Energy is used. It allows to perform capacity optimisation of microgrid with conventional generators and RES. The capacity optimisation of HOMER Energy is based on dispatch strategies which provide generation schedule. For every step of the integration of RE, the installed capacity is optimised, and the technical capability of the available components is improved.

The optimization of the generation capacity expansion made by HOMER Energy is based on a dispatch strategy. To have a better understanding of the dispatch strategy, a new one is developed in MATLAB and is used by HOMER Energy. The dispatch developed in MATLAB will provide to HOMER Energy the generation schedule. The second software uses this schedule to calculate the economic data related to the generation. This new dispatch is used after the optimisation of the generation capacity to schedule the generation.

In a second part of this master thesis, the scenarios obtained in the previous step are investigated for one the islands via load flow simulation. Special focus is put on the status of the voltage and the loadings in the systems.

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3. Methodology

In order to reach the objective defined in the previous chapter, the master thesis is divided into three main parts. Each part corresponds to one colour in Figure 2. This chapter aims to provide an overview of the methodology and content of this master thesis. The next three chapters present the theoretical background, the detailed method and the results for each of the three main parts.

3.1 The optimal capacity expansion

In the first step of this master thesis, a techno-economical study is carried out, which consists in determining the economic optimal capacity expansion plan for the period of 2019-2021. The optimal capacity expansion plan is developed for two islands using the investment optimization toolbox based on dispatch simulation available in the software HOMER Energy. The specifics of this toolbox are explained in section 4.1.1. The technologies which are made available in the investment tool to be expanded are solar PV and BESS. Wind power is not considered in the generation capacity expansion because the wind resource of the studied area is too low. No constraints are added to the dispatch problem regarding the renewable fraction to be achieved. It means that the solar PV

Techno-economic study

Collection of the data of the islands

Creation of an optimal generation capacity expansion plan based on the

dispatch algorithms built in HOMER Energy

Development of a new dispatch algorithm implemented in MATLAB

Comparison between the results of the HOMER’s

dispatch and the new dispatch algorithm

Grid study: Load flow investigation on the impact on PV in loading and voltage

with PowerFactory

Figure 2: Flow chart of the master thesis

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penetration reached on each yearly step is purely driven by its economics. HOMER Energy counts on several dispatch strategies which are described in in the part 4.1.1 of chapter 4.

In order to build the model in HOMER Energy, data such as the ones depicted in the following list have to be collected for this model.

- the load curves

- the existing electricity generation on the island with all the related costs - the efficiency curves

- the maintenance schedules

A more detailed description about the data can be found in appendix 1 and the detailed description of the data specific for the two studied islands can be found in chapter 4, section 4.2.

The two islands which are studied are respectively named Island A and Island B. Currently, all the electricity is generated via diesel generators and their system operator wants to add renewable energy in the generation mix. The information on the islands is summarized in TABLE 1. Island A respects the (N-2) criterion in terms of generation whereas Island B respects the (N-1) criterion. In the interconnected power systems, (N-1) usually refers to actual operational security. So, a (N-1) secure dispatch would have to have enough generation so that there is no interruption if one of the assets suddenly fails. However, it is not what is happening in these islands. They merely have enough generation capacity on site to supply in case of unavailability, but they do not have a contingency secure dispatch. The study of these two islands of different size and level consumption allows to compare the RE integration plan for each island. The consumption level and the number of generators needed to cover the load can have an impact of the renewable share installed on the island.

TABLE 1: ISLANDS DESCRIPTION

Island A Island B

Surface area 10 km² 389 km²

Number of inhabitants 66 1,522

Number of diesel generators

present on the island 3 4

Consumption level in 2017 366.084 MWh 5,771 MWh Number of diesel generators

mainly needed to cover the maximum load

1 2

The optimal generation capacity expansion plan developed is realized in three steps. Each step stands for one year. Each year, the evolution of the cost and the load are considered, and a technical improvement is added in order to reach a higher renewable fraction. The three steps are:

1. Initial phase: PV is uncontrolled. The energy provided by the PV power plants must be fully absorbed by the system.

2. Advanced phase: PV controllability allows curtailment of PV to accommodate higher capacity.

3. Final phase: The grid-forming capability of the PV inverter allows the disconnection of the conventional generators.

In the continental system, the curtailment of RES must be avoided, but on islands’ system this curtailment is inevitable. It is also a quite powerful tool to increase the share of RE in the electricity mix.

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The stepwise approach enables the system operator to add renewable sources gradually. The amount to pay for each yearly investment will be lower than if the optimal renewable share would be added in one year. In this case, a large amount of investments has to be done in one step. Moreover, based on the stepwise approach, the system operator can have feedback before moving to the next step.

3.2 Development of a new dispatch algorithm

The dispatch simulations which are part of the generation expansion plan depicted in the previous section, are performed using the dispatch algorithms available in HOMER Energy. To have a better understanding of the dispatch strategies used in the software HOMER Energy, a new dispatch strategy has been developed. This dispatch strategy developed in HOMER Energy is capable to interface with scripts developed in MATLAB. The equations of the dispatch are coded in MATLAB and HOMER Energy is used as an interface to input the data, tomodel the systems and to visualise the results.

The dispatch strategy is not used to develop the optimal capacity expansion but only as a dispatch strategy when the capacity of all generators and storage are known. A comparison of the performances between the new dispatch strategy and the ones available in HOMER Energy is performed.

The objective function of the new dispatch strategy is to minimise the cost of electricity of the system as it optimizes the generation scheduled for a time window of 48 hours using forecasts for the load and PV. The constraints of the system such as, for example, the minimum level of generation of the diesel generators, the operating reserve are implemented. The algorithm is then tested and validated on a simple system before being used on the master thesis’ study cases.

3.3 Grid study of Island B

The optimization of the generation capacity expansion carried out in the first step is not sufficient to deduce if the generation capacity expansion is feasible. A grid study has to be part of a generation expansion plan in order to investigate whether the existing grid is capable to accommodate the new expanded capacity, thus guaranteeing a reliable and safe supply of the demand. In this master thesis, the impact of the grid expansion in terms of voltage level and line loading of Island B is investigated via steady-state simulations. This study is done by performing load flow calculation based on the software DIgSILENT PowerFactory. Although a complete grid study will require running steady state and dynamic simulations, it has been decided to study the grid only in steady state and to study only four operation scenarios instead of running an annual simulation.

- Peak load in summer - Solar peak in summer - Minimum load in winter

- Extreme peak load which happens when the coincidence factor between all the load is high

If the voltages and the loading do not respect the limits fixed by the system operator, measures like voltage control has to be taken.

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4. Optimisation of the generation capacity

The generation capacity expansion of the two studied islands required an investigation of the capacity of solar PV and BESS. As mentioned in chapter one, the sizing of the integration of the VRE is a challenge. The VRE and the BESS should be sized in order to minimise the cost of electricity. However, the system is under technical constraints which limit the integration of the VRE. This chapter describes, first, the software used to perform the optimal generation expansion, HOMER Energy, and the basics of the integration of high share VRE on islands. The theoretical background presented in this section is necessary to understand the reasons why this choice has been made and also to understand its results. In a second section, the method used to collect the data about the two studied islands is explained. Finally, based on HOMER Energy and on the data collection, the optimal capacity expansion plan is built. The last section of this chapter presents the different steps of the expansion plan and the results.

4.1 Theoretical background and software used for the study

4.1.1 Capacity optimization and dispatch formulation in HOMER Energy

To perform the economic study of the islands and to develop an investment plan for the integration of VRE, HOMER Energy² software is used. This software allows to perform investment and dispatch strategies of small power systems (Figure 3). Diesel generators, wind turbine, PV panels as well as different types of storage can be modelled. Figure 4 shows an example of a HOMER Energy model.

The simulation capability of HOMER Energy consists in calculating the generation schedule of the generators. Based on this schedule, the cost of the system over its lifetime is calculated. The economics basis used in HOMER Energy are explained in section 4.1.1.2. The second capability of HOMER Energy is the optimisation tool. It runs many simulations with different capacities. The optimal investment strategy is the one which has the lowest net present cost and thus the lowest LCOE.

2 https://www.homerenergy.com/, originally developed by the National Renewable Energy Lab NREL, available as a commercial tool since 2009.

Simulation Optimisation Sensitivity Analysis

Figure 3: HOMER Energy capability

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HOMER Energy allows also to perform sensitivity analysis to study the impact of the variables on the system optimisation.

The study performed in this master thesis focuses on the integration of solar PV and BESS on the islands on which the generation fleet is initially constituted only by diesel generators. Therefore, the input data of HOMER Energy needed are:

- The hourly based load profile and the hourly solar irradiance for one year, - The generator characteristics and maintenance schedule,

- The proportion of the load and the VRE which can go through short term variation, - The capital and operation and maintenance (O&M) costs of all technology.

The investment strategy implemented in HOMER Energy uses a dispatch strategy which can be selected from those already available in the software. The dispatch strategies play a very important role in the capacity expansion. In the economic dispatch, the output of the generation facilities is determined depending on the time scale used by the dispatch algorithm. For example, when the objective of the dispatch is to minimise the cost of electricity algorithm for one hour like the two dispatch used in this chapter, the outputs of the generators must cover the load and satisfy the system constraints at the lowest cost [11]. The term “dispatch strategy” refers to the set of rules which is used to control the generators and the storage bank. These are the rules used to determine the economic dispatch. According to the dispatch, the optimal generation capacity may vary. In this report, two dispatch strategies are used: load following and cycle charging. These dispatch strategies are provided by HOMER Energy. To perform the investment strategy, HOMER Energy runs many simulations with different PV and BESS capacity. The simulation with the lowest cost of electricity is set as the optimal one.

In all of the dispatch algorithm, some assumptions have been made while the system is modelled. During a timestep, the load, the PV output, the charged and discharged power of the storage are constant. The very short-term (lower than the time step duration) variations are neglected. The grid topology of the islands is neglected in the dispatch models in HOMER Energy.

Figure 4: HOMER Energy model of Island A in 2019

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Two dispatch strategies implemented in the software have been used in this part of the master thesis. The following subsections describe these strategies.

4.1.1.1.1 Load following dispatch

Objective function: The objective of the load following dispatch is to minimise the cost of electricity generation for a time step of one hour. So, the optimisation is run every hour of the year. This cost includes the generator and battery cost.

According the Homer user manual [12], the generator cost is calculated according the following equation.

𝐶_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟} = 𝐶_{𝑓𝑖𝑥𝑒𝑑},_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟}+ 𝐶_{𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙},_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟}∗ 𝑃_𝑔 With

𝐶_{𝑓𝑖𝑥𝑒𝑑},_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟}= 𝐶_𝑂&𝑀+𝐶𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑇_{𝑙𝑖𝑓𝑒} + 𝐶_{𝑁𝑜−𝑙𝑜𝑎𝑑} 𝐶_{𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙},_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟}=𝛼_{𝑓𝑢𝑒𝑙}∗ 𝑝_{𝑓𝑢𝑒𝑙}

𝜂_{𝑔𝑒𝑛𝑒}(𝑃_𝑔) With:

𝐶_𝑂&𝑀 the hourly operation and maintenance cost ($/h), 𝐶𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 the replacement cost ($),

𝑇_{𝑙𝑖𝑓𝑒} the generator´s lifetime in hour (h),

𝐶𝑁𝑜−𝑙𝑜𝑎𝑑 the no load fuel consumption cost ($/h), 𝛼_{𝑓𝑢𝑒𝑙} the fuel curve slope (L/kWh),

𝑝_{𝑓𝑢𝑒𝑙} the fuel price ($/L),

𝜂_{𝑔𝑒𝑛𝑒}(𝑃_𝑔) the efficiency of the generator depending of the output power (%), 𝑃_𝑔 the output power of the generator (kW).

The cost of the BESS is also considered for the cost minimisation. In HOMER Energy, this cost is defined as the following:

𝐶_{𝑏𝑎𝑡𝑡𝑒𝑟𝑦}= 𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑐ℎ𝑎𝑟𝑔𝑒∗ 𝐸_{𝑏,𝑐ℎ𝑎𝑟𝑔𝑒}− 𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒∗ 𝐸𝑏,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

With

𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑐ℎ𝑎𝑟𝑔𝑒 = 𝐶𝑟𝑒𝑝,𝑏𝑎𝑡𝑡𝑒𝑟𝑦

𝑁_{𝑏𝑎𝑡𝑡}∗ 𝑄_{𝑙𝑖𝑓𝑒𝑡𝑖𝑚𝑒}∗ √𝜂𝑟𝑡

𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 = 𝐶𝑟𝑒𝑝,𝑏𝑎𝑡𝑡𝑒𝑟𝑦

𝑁_{𝑏𝑎𝑡𝑡}∗ 𝑄_{𝑙𝑖𝑓𝑒𝑡𝑖𝑚𝑒}∗ √𝜂𝑟𝑡

+ 𝐶_{𝑠𝑡𝑜𝑟𝑎𝑔𝑒,𝑛} With:

𝐶𝑟𝑒𝑝,𝑏𝑎𝑡𝑡𝑒𝑟𝑦 the replacement cost of the storage bank ($), 𝑁_{𝑏𝑎𝑡𝑡} the number of batteries in the storage bank,

𝑄_{𝑙𝑖𝑓𝑒𝑡𝑖𝑚𝑒} the lifetime throughput of a single storage (kWh), 𝜂𝑟𝑡 the roundtrip efficiency of the storage,

𝐶_{𝑠𝑡𝑜𝑟𝑎𝑔𝑒,𝑛} the battery energy cost at the time step n (cost of the energy used to charge the battery, for the load following dispatch this cost is null),

𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑐ℎ𝑎𝑟𝑔𝑒 the cost to charge of the battery,

𝐶𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 the marginal cost to discharge the battery,

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𝐸_{𝑏,𝑐ℎ𝑎𝑟𝑔𝑒} the energy which charges the storage bank (kWh), 𝐸𝑏,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 the energy which discharges the storage bank (kWh)

Constraints: A set of constraints are applied to the equation, reflecting operational constraints of the power system. The following constraints are considered in HOMER Energy. The documentation provided by the software [12] does not provide all the equations which will be used.

- The balance between the demand and the generation must be satisfied. This constraint is modelled by Equation 7.

∑ 𝑄_𝑔,𝑡

𝑁_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟𝑠}

𝑔=1

+ 𝑃𝑃𝑉,𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒,𝑡+ ∑ (𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒,𝑏,𝑡∗ 𝜂_𝐼𝑁𝑉−

𝑁_{𝑏𝑎𝑡𝑡𝑒𝑟𝑖𝑒𝑠}

𝑏=1

𝑃_{𝑐ℎ𝑎𝑟𝑔𝑒,𝑏,𝑡}

𝜂_𝑅𝐸𝐶 ) ≥ 𝐷_𝑡 ∀𝑡 With

𝑁_{𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟𝑠} the number of generators in the system, 𝑄_𝑔,𝑡 the power output of the generator g at time t (kW),

𝑃𝑃𝑉,𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒,𝑡 the available power output of the PV at time t (kW), 𝑁_{𝑏𝑎𝑡𝑡𝑒𝑟𝑖𝑒𝑠} the number of BESS in the system,

𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒,𝑏,𝑡 the power discharge of the BESS b at time t (kW), 𝑃_{𝑐ℎ𝑎𝑟𝑔𝑒,𝑏,𝑡} the charging power of the BESS b at time t (kW), 𝜂_𝐼𝑁𝑉 the inverter efficiency (%),

𝜂_𝑅𝐸𝐶 the rectifier efficiency (%), 𝐷_𝑡 the demand at time t (kW).

- The operating reserve must be satisfied. In the context of VRE, the electricity generation can vary unexpectedly and quickly. To adapt to the VRE generation variation and to keep the balance between generation and consumption, some reserves in the generation capacity must be kept during the dispatch. In fact, the conventional generators and BESS must be able to cover the fast variations of the VRE as backup generator while the load is served. Moreover, as the load forecast is not perfect, reserves are also needed for the load. If the load increases, the generation must be able to vary to reach the load level. The amount of reserve constraint can be set by the user.

- The minimum renewable fraction can be fixed for the simulation. It is the minimum share of the generation that needs to be covered by VRE sources like solar PV and wind power [12].

- The maximum capacity shortage can also be set by the users. It is the maximum share of operating reserves that is not satisfied.

- The minimum runtime of the diesel generator

- The minimum technical level of the conventional generators: The diesel generators cannot operate below a certain limit due to the wet stacking issue. Fuel particles remain in the engine instead of being evacuated. This can lead to faster engine ageing.

- The state of charge of the BESS must stay between certain limits. In HOMER Energy, the upper limit is set the 100% and the lower limit is set by the user.

- The control of the BESS charge and discharge: With the LF algorithm, the BESS are charged only with the excess of renewable energy [12]. When RES are not sufficient to cover the load, conventional generators produce only enough power to cover it. For each time step, the dispatch decision is made according the following cases.

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▪ If the output power of the PV panels is equal or larger to the load, the load is fed by the PV. The excessive power is used to charge the battery. If the battery is not fully charged, the excessive power will charge the battery. If the battery is fully charged, the excess of power cannot be used. So, it is curtailed.

▪ In case of a non-grid forming system, another constraint applies, which is the must run on at least one diesel. In that case the battery can be charged if the sum of minimum diesel generation and PV exceeds the load

▪ If the output PV power is lower than the load, the battery can be discharged, and the generator can be used. The choice between the generators and the use of the stored energy is made in order to minimise the cost so that the load and the operating capacity requirements are respected. To calculate the lowest cost dispatch, the solver has to calculate the fixed cost and the marginal cost of every generator and battery.

4.1.1.1.2 Cycle charging dispatch

The cycle charging dispatch strategy has the same objective function as the load following.

Only one constraint differs from the dispatch strategy described above: the control of the BESS charge and discharge. Under the cycle charging strategy, when the generators are needed, they produce at the highest setpoint possible. By doing that, the generators can operate at their maximum efficiency.

The excessive power due to the diesel generation is stored in the storage bank. When the discharge rate is sufficient to cover the load, the energy stored is used. By doing this, there is not always the possibility to store the renewable energy [13].

4.1.1.2 Economic evaluation of the investment scenarios

The economic costs of a project are important to decide if the project is feasible. The economic study is based on indicators, used to compare two possible technical solutions. Two investment strategies are compared from an economic point of view. The scenario with the lowest cost is the economic optimum. In order to compare them, some economic indicators must be calculated. This section will define the terms and the formula used to calculate the indicators.

• Inflation rate

Inflation is a term which defines as the decrease in the purchasing power of a currency over time. This is translated by an increase of the price of goods and services according to [14]. The inflation rate is the coefficient of increase in prices.

• Discount rate

The discount consists of calculating the present value of an item in comparison to its future value. In fact, the item can have a price of 1 in 2030. Due to the inflation, its value increases. So, the value of the same good in 2020 is lower than 1. In order to know the cost in 2020, the cost of 2030 has to be multiplied by the discount factor fd. The discount factor is quantifying how much 1 in the future worth today [15].

𝑓_𝑑= 1 (1 + 𝑖)^𝑁 Where i is the inflation rate (%) and N the number of years.

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The discount rate “is the rate of interest used to adjust future value to present value” [15]. In Homer Energy, this annual discount rate is calculated according the formula below.

𝑟 =𝑟´ − 𝑖 1 + 𝑖

Where r´ is the nominal discount rate (it is the rate at which the money is borrowed) and i the expected inflation rate.

• Net present cost

The net present cost (NPC) of a system is “the present value of all the costs over its lifetime, minus the present value of all the revenues it earns over its lifetime” [12]. In Homer, the calculation is done by summing all the discounted cash flows for each year of the project. A cash flow of a component or a system is the difference between the money received and the money paid. For one component, the net present cost is:

𝐶_{𝑁𝑃𝐶,𝑐} = ∑ 𝑋_𝑡 (1 + 𝑟)^𝑡

𝑇

𝑡=0

With T the lifetime of the project, Xt the cash flow at year t and r the annual discount rate.

The NPC of the system is the sum of all the NPC of its components.

𝐶_{𝑁𝑃𝐶,𝑡𝑜𝑡} = ∑ 𝐶_{𝑁𝑃𝐶,𝑐}

𝑚

𝑐=1

With m the number of components in the system.

• Levelized cost of energy

The levelized cost of energy (LCOE) is one key value for the economic comparison of different power systems. It can also be useful to compare different technologies like wind power, solar PV and diesel generator. This cost is defined as the sum of all annualized investment’s costs, annualized fuel costs and annualized operation and maintenance (O&M) cost divided by the total energy produced [16]. Its formula is the following:

𝐿𝐶𝑂𝐸 =𝐶_{𝑡𝑜𝑡𝑎𝑙,𝑎𝑛𝑛} 𝐸_{𝑡𝑜𝑡𝑎𝑙} With 𝐿𝐶𝑂𝐸: the levelized cost of energy ($/kWh)

𝐶_{𝑡𝑜𝑡𝑎𝑙,𝑎𝑛𝑛}: the total annualized cost of the system ($/year) 𝐸𝑡𝑜𝑡𝑎𝑙: the total electrical load served (kWh/year)

The total annualized cost is calculated as the formula below:

𝐶_{𝑡𝑜𝑡𝑎𝑙,𝑎𝑛𝑛}= 𝐶𝐹𝑅(𝑟, 𝑅_{𝑝𝑟𝑜𝑗}) ∗ 𝐶_{𝑁𝑃𝐶,𝑡𝑜𝑡} Where r: the annual discount rate (%)

𝑅_{𝑝𝑟𝑜𝑗}: the project lifetime (year) 𝐶_{𝑁𝑃𝐶,𝑡𝑜𝑡}: the total net present cost ($)

𝐶𝐹𝑅: a function returning the capital recovery cost factor

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The capital recovery cost factor is a function of the project lifetime and the annual discount rate which can be expressed as the following:

𝐶𝐹𝑅(𝑟, 𝑅𝑝𝑟𝑜𝑗) = 𝑟(1 + 𝑟)^𝑅^{𝑝𝑟𝑜𝑗} (1 + 𝑟)^𝑅^{𝑝𝑟𝑜𝑗}− 1

4.1.2 Integration of high share of renewable energy

The integration of high share of VRE in an island’s grid has some benefits. In fact, most of the islands’ power generation are based on diesel generator, so integrating new generation coming from sources other than fuel allows the island to be less dependent to fuel imports [17]. However, high share of VRE induces challenges for the grid operation. Due to the variability of the RES, system stability and power quality issues can arise. These issues are detailed in [18]. These challenges have to be taken into account during the building of the optimal generation capacity expansion.

4.1.2.1 Stepwise capacity expansion

As explained before, the techno-economic study consists of developing an integration plan for renewable energy sources. This plan is developed for each island and is realized within three years.

Each year, RE capacity and an improvement of the technical capability are added in order to reach a higher renewable fraction. Electricity consumption also increases every year by 5.8 % for Island A and 3.8 % for Island B. The stepwise approach enables the system operator to add renewable sources gradually. The amount to pay for each yearly investment will be lower than if the optimal renewable share would be added in one year. In this case, a large amount of investments has to be done in one step. Moreover, based on the stepwise approach, the system operator can have feedback before moving to the next step.

- 2018: This step corresponds to the situation of the island in 2018. There are no PV installed on the island. The consumption is covered by the diesel generators presents on the island.

This step is an initialcase. It allows to calculate a reference of the levelized cost of energy.

- Step 1 (2019): The objective of this step is to decrease the cost of energy without increasing the complexity of the control system. Therefore, solar PV are included in the dispatch without addition of other elements like BESS and curtailment. The solar PV will represent a small amount of the generation mix.

- Step 2 (2020): The objective is to determine an optimal solution without allowing diesel- off mode. The curtailment possibility is added. The curtailment allows to increase the share of renewable energy because if the difference between the load and the variable renewable power is lower than the minimum generation level, it is possible to use less renewable power. It is also possible to add storage with a grid-following inverter and some solar PV capacity. The grid-following inverters do not enable operation without synchronous generators. The diesel generators and the solar PV from 2019 are on the island. Due to the grid following inverter, the generation without diesel generator is not possible. The objective is to find an economic optimum considering storage, PV and curtailment.

- Step 3 (2021): The objective is to find an economic optimal by using all technologies available. Grid-forming capability of the BESS inverter is added. The renewable share can increase as all conventional generators can be disconnected if enough other resources are available. The addition of the PV, converter and battery capacities is made to obtain an economic optimum. Before the addition of all these elements, the island is equipped with

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all the diesel generators, the solar PV from 2019 and 2020 and if it was needed the batteries and converters from 2020. It is also the optimal case compare to the other steps.

In each step, the amount of PV capacity, batteries and converters capacities are determined to minimise the cost of energy under the assumptions made during the step. Based on these simulations, an integration plan of RE will be compiled.

Outside the framework of the optimal generation capacity expansion plan, other cases have been studied to understand the impact of the renewable share on the battery size. In these simulations, the minimal renewable share is imposed. Three different values of renewable share have been studied: 90%, 95% and 100%. The chosen data for the load and the costs are the ones from 2021.

The converter has the grid-forming capability and as the chosen year is 2021, there are still, on the island, the diesel generators and the solar PV from 2019 and 2020 which cannot be removed.

4.1.2.2 The technical stepwise approach followed in the generation expansion plan According to the plan depicted in the previous section, several technical improvements are used. This section provides a description of the technical elements used and provides information about the implementation of the induced constraints in HOMER Energy.

• Curtailment

In small islands systems such as the ones studied, the increasing VRE penetration levels can result in situations when the potential net load which is “the total electric demand in the system minus wind and solar generation “ [19] is smaller than the minimum technical level of the conventional generators. These ones cannot operate in a stable manner below this level. In such circumstances VRE should be curtailed in order to prevent the diesel generator from operating below their minimum technical level. The term “curtailment” means to use less energy for RE than available. As the curtailment of the solar PV plants is a function of the generator operation point, communication infrastructures and a more sophisticated operation of the system are required. The study of these technical requirement is out of the scope of this master thesis, therefore no details about it are given.

Because of the non-linearity characteristic of the PV cell and their low efficiency, it is needed to “extract maximum power from solar PV cells” [20]. This is called maximum power point (MPP). The solar irradiation varies in time, therefore the MPP is changing during time (Figure 6). The output cell

Initial case (2018)

Step 1 (2019):

No PV curtailment allowed

Step 2 (2020):

Curtailment and battery with grid following inverter allowed

Step 3 (2021):

Grid forming capability

Figure 5: Optimal generation capacity expansion

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voltage must change in order to reach the MPP. The methods used to control the voltage are called maximum power point tracking (MPPT). Haque [20] describes a popular method of MPPT. When the PV has to be curtailed, the output power of the PV cell is limited. It is no longer possible to reach the MPP.

Figure 6: Solar PV characteristics for different irradiation level [20]

In this master thesis, VRE sources are curtailed if the net load is negative or below the minimum level of generation of the conventional generators. The amount of energy which is curtailed is called energy surplus.

During the first step of the optimal generation expansion plan, PV curtailment is not allowed.

So, a constraint must be added in HOMER Energy to prohibit the PV curtailment. However, there is no capability to automatically avoid it. So, to prevent it, the solar capacity deployed must be limited. To determine the PV capacity which can be installed, a number of consecutive simulations have been done in HOMER Energy. For each simulation, the PV capacity is set to a fixed value. If there is some excess of electricity, the PV capacity is reduced gradually until the excess of electricity becomes equal to zero. The selected value of the PV capacity should be the highest one without excess of electricity.

• BESS

In the second step of the optimal generation expansion plan, BESS are available. The technology of the battery has to be chosen according to its use. The BESS is integrated in an off-grid system to reduce the electricity cost. The suitable technologies for this application are the lead-acid and Lithium-ion (Li-ion) batteries according to [21] because these technologies are typically sized for small scale systems. The BESS is expected to be charged and discharged once per day. Since, it will be placed on an island, so the battery must need maintenance. Even if the cost of the Li-ion batteries is higher than the one for the lead-acid batteries [21], the longer life-time and the lower maintenance effort of the Li-ion are more suitable for Caribbean island’s project. Moreover, the specific power of the Li-ion batteries is higher than for lead-acid batteries. It can handle better the frequency variations.

• The control of the inverter

The replacement of the conventional generation by the renewable energy sources decreases the inertia of the network. This inertia is necessary to maintain the grid frequency. Therefore, while the renewable energy generation reaches 100%, the converters used between the AC and DC grid must be able to generate a synchronous voltage in order to work without synchronous generation.

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29 o Grid-following inverter

The grid-following inverters are controlled in such way that they can adapt their output current according to the voltage and the frequency of the grid. These inverters are, thus, acting as a current source from the grid. Due to this operation, the grid-following inverter cannot be connected to a grid without synchronous generation as the voltage and frequency of the grid must be controlled by other devices in the grid.

The grid-following inverter can participate in the frequency control by using advance grid support functions (Figure 8). One of these functions is called the frequency-watt (FW) function. It adjusts the active power output of the inverter according the curve in Figure 8. This controller is how the control the output current of the inverter and the active and reactive power flowing through it.

o Grid-forming inverter

The output voltage of the grid-forming inverter is controlled. This voltage is alternative, so its frequency and its level are fixed by the inverter level. The grid-forming inverter act as a voltage source.

So, it can operate in a grid without synchronous generation.

The voltage is controlled based on active and reactive power measurements. The droop functions on Figure 10 define the frequency and the voltage according to the active and reactive power. Another control of the grid-forming inverter consists in creating a virtual synchronous machine (VSM). Jia et al. describe the VSM control [22].

The grid-forming inverters can operate without synchronous generation. These inverters, by measuring the active and reactive power, can control the inverter’s voltage output and its frequency [23]. The inverter’s controller is based on droop control. It is defined by two functions which set the frequency evolution and voltage reference according to the active and reactive powers as presented in Figure 10. This control comes from the traditional control method of synchronous machine [24]. In contingency case, the grid-forming inverter controls the output current in order to balance the load and to keep the grid voltage and frequency constant [25]. It can be seen from the grid point of view as a voltage source. Grid-forming controller can also be controlled via a virtual synchronous machine (VSM) [23]. Liu and al. [22] describe the VSM control.

Figure 8: Frequency-watt function for a grid- following inverter when the frequency

reference is 60 Hz [23]

Figure 9: Control model for a grid forming inverter [23]

Figure 7: Control model for a grid following inverter [23]

Study of a generation capacity expansion on an island

Study of a generation

capacity expansion on an island

JUSTINE VALÉRIE MAGALI GUILMINEAU

Study of a generation capacity expansion on an island

Abstract

Sammanfattning

Acknowledgements

Table of Contents

Table of figure

Table of tables

Abbreviations

1. Introduction

1.1 Decarbonisation of the electricity sector

1.2 Integrating VRE in power system

1.3 Variable renewable energy in the Caribbean

2. Objective

3. Methodology

3.1 The optimal capacity expansion

3.2 Development of a new dispatch algorithm

3.3 Grid study of Island B

4. Optimisation of the generation capacity

4.1 Theoretical background and software used for the study

4.1.1 Capacity optimization and dispatch formulation in HOMER Energy

Simulation Optimisation Sensitivity Analysis

4.1.2 Integration of high share of renewable energy