Diseño y control de una microred en dc de baja tensión con recursos distribuidos de energía Juan Sebastián Vélez Ramírez Universidad Tecnológica de Pereira Facultad de ingenierías Maestría en Ingeniería Eléctrica

2021

Design and control of a low voltage dc-microgrid, with distributed energy resources Juan Sebastián Vélez Ramírez Final draft submitted as a partial requirement to obtain the title of: M.Sc. in Electrical Engineering Director:

Eduardo Giraldo Suárez, PhD. Investigation group:

Control Automático Universidad Tecnológica de Pereira School of Engineering Master in Electric Engineering

2021

Acceptance note Jury Jury Jury Pereira, 2021.

Acknowledgments To my parents who have given me everything. To my family and friends that gives light to my life. With the purpose of envisioning other futures for humanity... iv

Motivation The current global needs, demand drastic changes in the way we interact with our environment. Being the production of energy, the pillar that sustains the modern society, and also, the one that more contribute to the environmental damages that we now face. The need to reduce the use of fossil fuels, moves us towards a future with a growing electrical market, full of a diversity of loads such as electric vehicles, small industries, and homes [1, 2]. The challenges that climate change presents to humanity have motivated the investigation and development in renewable energies, a field with so many open issues. One of them is the problem of clustering and control distributed energy resources (DERs), like photo-voltaics (PV), wind-power (WP), and small hydro-power (SHP).

A micro-grid group loads and DERs in a single controllable entity, with clearly defined electrical boundaries. As a small scale power system, a microgrid can ensure self-supply and a considerable autonomy with respect to the grid, satisfying the needs of its network, bringing stability and reliability in the service, and isolating the loads from the grid failures. [3, 1, 4].

In the national context, Colombia’s geographical location makes it one of the most vulnerable countries in terms of climate change, since its electricity generation network is composed mostly of hydroelectric power plants, a weak technology against droughts and phenomena such as El niño. However, the DERs deployment capacity available in the country, particularly in the Andes region, is virtually unlimited. In this aspect, the PV and SHP generation methods excel [5, 6]. In addition, with the growth of the country’s energy demand, is estimated that by 2025 the total capacity must be increased by 60% [5]. In social terms, is well known that the high energy costs and the number of failures in remote sites, difficult the implementation of industrial developments in a little or middle scale. The lack of technology access for the rural population, makes the investigation and investment in the distributed generation, a need to achieve economic equity and overcome extreme poverty in the countryside.

v

Abstract In this document a brief review of the DC microgrids generalities with emphasis in the control architecture is done. A novel hybrid-control architecture to take care of the inner, primary and secondary levels of DC microgrids monitoring, is simulated under different conditions. In the inner control architecture an Modified Exact Feedback Linearization with integral action approach, is proposed for control current or voltage in a Buck converter, designed to be part of the DC microgrid. The controllers are tested in simulation using Matlab-Simulink®. Results are compared with classic PID controllers and evaluated under two different mathematical tools (Mean Square Error, Integral Time Absolute Error) in order to prove their effectiveness. The evaluated data show that the proposed approach outperform the classical methods.

Different models of the said converters are clustered to build the microgrid scenario. Primary and secondary control architectures were designed in a centralized way with PI regulators of voltage and current. The microgrid was tested in Matlab- Simulink® with two disturbances, including a forced isolation of the microgrid, showing and acceptable performance.

0.1

Document structure Chapter 1 enumerates the project objectives. In chapter 2 an introduction over the microgrids topic is done, considering state of the art in the distributed generators field, the differences between AC and DC distributions systems, and an introduction to the control architectures. Chapter 3 present the case study used to design the microgrid considering the generators topologies and the needs of the Colombian countryside. In chapter 4, the overall control architecture theory is described. Finally, chapters 5 and 6 present the results of the proposed controllers and the project’s conclusions, respectively.

vi

Contents

0.1

Document structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

1

Objectives

2

1.1

General objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Specific objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2

Introduction

3

2.1

Generalities of the microgrids

. . . . . . . . . . . . . . . . . . . . . .

3

2.1.1

Distributed energy resources (DERs) and distributed generators (DGs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.1.2

Energy storage systems (ESS) . . . . . . . . . . . . . . . . . .

5

2.1.3

Power electronics converters . . . . . . . . . . . . . . . . . . .

5

2.1.4

Microgrid definition . . . . . . . . . . . . . . . . . . . . . . . .

6

2.2

DC vs AC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.3

Introduction to DC microgrids control strategies . . . . . . . . . . . .

9

2.3.1

Internal control . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.3.2

Primary control strategies . . . . . . . . . . . . . . . . . . . .

11

2.3.3

Secondary control strategies . . . . . . . . . . . . . . . . . . .

11

3

Design of a low voltage DC microgrid

13

3.1

Distributed generators classification . . . . . . . . . . . . . . . . . . .

13

3.1.1

Grid forming/supporting node . . . . . . . . . . . . . . . . . .

13

3.1.2

Grid feeding node . . . . . . . . . . . . . . . . . . . . . . . . .

13

3.2

Case study: Intensive fish farming project

. . . . . . . . . . . . . . .

14

3.2.1

Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

3.2.2

APISBAL project . . . . . . . . . . . . . . . . . . . . . . . . .

14

3.3

Proposed design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

4

Hierarchical control in a DC microgrid

17

4.1

Inner control

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

4.1.1

The Buck Converter

. . . . . . . . . . . . . . . . . . . . . . .

18

vii

Contents viii

4.1.2

Modified Feedback linearization with integral action to control current and voltage . . . . . . . . . . . . . . . . . . . . . . . .

23

4.2

Primary control:Droop control . . . . . . . . . . . . . . . . . . . . . .

26

4.3

Secondary control . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

4.3.1

DC link Voltage Regulation

. . . . . . . . . . . . . . . . . . .

28

4.3.2

Current Regulation . . . . . . . . . . . . . . . . . . . . . . . .

28

4.3.3

General scheme . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5

Simulation Results

30

5.1

Feed back linearization control . . . . . . . . . . . . . . . . . . . . . .

30

5.1.1

Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . .

30

5.1.2

Results and discussion . . . . . . . . . . . . . . . . . . . . . .

32

5.2

Simulation of the microgrid

. . . . . . . . . . . . . . . . . . . . . . .

40

5.2.1

Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . .

40

5.2.2

Results and discussions . . . . . . . . . . . . . . . . . . . . . .

43

6

Conclusions

List of Figures

2.1

Example of a microgrid with distributed energy resources.

. . . . . .

6

2.3

Classic current PI controller in power electronic devices.

. . . . . . .

10

2.2

Hierarchical control structure in a microgrid [7]. . . . . . . . . . . . .

10

2.4

Classic voltage cascade PI controller in power electronic devices. . . .

11

3.1

Simplified microgrid nodes. (a) Grid forming/supporting node. (b) Grid feeding node.

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

3.2

Project location map. . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3.3

Simplified microgrid design to the fish farm project. . . . . . . . . . .

16

4.1

General structure of a Buck converter.

. . . . . . . . . . . . . . . . .

18

4.2

Waveform of the diode voltage in period T of the PWM. . . . . . . .

18

4.3

Buck converter when µ = 1, neglecting power losses. . . . . . . . . . .

20

4.4

Buck converter when µ = 0, neglecting power losses. . . . . . . . . . .

20

4.5

Poles and zeros locations of the current transfer function. . . . . . . .

22

4.6

Poles and zeros locations of the voltage transfer function. . . . . . . .

22

4.7

EFL current control schematic.

. . . . . . . . . . . . . . . . . . . . .

25

4.8

EFL voltage control schematic.

. . . . . . . . . . . . . . . . . . . . .

26

4.9

Voltage vs current graphic based on (4.32). . . . . . . . . . . . . . . .

27

4.10 Simplified droop law circuit approach. . . . . . . . . . . . . . . . . . .

27

4.11 (a) Voltage regulator. (b) Current regulato.

. . . . . . . . . . . . . .

28

4.12 Diagram of a centralized control architecture with voltage and current

regulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.1

Current control performance: (a) PID. (b) EFL.

. . . . . . . . . . .

32

5.2

Current control transient state behaviour: (a) PID. (b) EFL. . . . . .

33

5.3

Current control disturbance response behaviour: (a) PID. (b) EFL . .

33

5.4

Current control duty cycle comparison: (a) PID. (b) EFL.

. . . . . .

34

5.5

Current control voltage response comparison: (a) PID. (b) EFL. . . .

34

5.6

Voltage control performance: (a) PID, (b) EFL. . . . . . . . . . . . .

36

5.7

Voltage control transient response behaviour: (a) PID. (b) EFL. . . .

37

ix

5.8

Voltage control disturbance response comparison: (a) PID. (b) EFL. .

37

5.9

Voltage control, duty cycle comparison: (a) PID. (b) EFL. . . . . . .

38

5.10 Voltage control, inductor current response: (a) PID. (b) EFL.

. . . .

38

5.11 Experimental setup of the microgrid. . . . . . . . . . . . . . . . . . .

40

5.12 (a) DGs current injection response. (b) Transient state response. (c)

Load connection response. (d) Grid islanded operation mode.

. . . .

44

5.13 (a) DGs voltage output. (b) Transient state response. (c) Load con-

nection response. (d) Grid islanded operation mode. . . . . . . . . . .

45

5.14 DC-Link voltage behaviour.

. . . . . . . . . . . . . . . . . . . . . . .

45

5.15 Distributed generators inductor currents response. . . . . . . . . . . .

46

5.16 Duty cycle of the distributed generators response. (a) PV node. (b)

ESS node. (c) SHP power node. . . . . . . . . . . . . . . . . . . . . .

46

5.17 Loads input current.

. . . . . . . . . . . . . . . . . . . . . . . . . . .

47

5.18 (a) Current consumption of isolated loads.

(b) DC/DC interfaces output voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

5.19 Duty Cycle of the load DC/DC interfaces. (a) Load 1. (b) Load 2. . .

List of Tables

2.1

Main non renewable DGs technologies [7].

. . . . . . . . . . . . . . .

4

2.2

Main renewable DGs technologies [7]. . . . . . . . . . . . . . . . . . .

4

2.3

Main ESS technologies [7]. . . . . . . . . . . . . . . . . . . . . . . . .

5

2.4

Comparison between AC and DC distribution lines [8]. . . . . . . . .

7

2.5

Comparison between AC and DC control tasks [8]. . . . . . . . . . . .

8

3.1

Main loads of the fish farm project. . . . . . . . . . . . . . . . . . . .

15

3.2

Suggested nominal power of the DGs nodes. . . . . . . . . . . . . . .

16

5.1

Simulation development. . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.2

Constants of the PID controllers.

. . . . . . . . . . . . . . . . . . . .

31

5.3

EFL control Constants. . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.4

Comparison of current controllers performance.

. . . . . . . . . . . .

35

5.5

Comparison of voltage controllers performance.

. . . . . . . . . . . .

39

5.6

Grid forming/supporting Nodes nominal parameters.

. . . . . . . . .

41

5.7

Grid feeding node’s nominal parameters. . . . . . . . . . . . . . . . .

41

5.8

DC/DC load interfaces nominal parameters. . . . . . . . . . . . . . .

41

5.9

EFL control constants. . . . . . . . . . . . . . . . . . . . . . . . . . .

42

5.10 PI control regulators constants. . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1

Objectives

1.1

General objective Design and control a low voltage DC microgrid powered by distributed energy resources.

1.2

Specific objectives

1. Research over the most suitable renewable DGs, their physical characteristics,

dynamic models and control strategies.

2. Design a low voltage DC microgrid with the selected DGs and loads.

3. Design primary control strategies with a non-linear control technique and val-

idate it through simulation.

4. Prove and validate primary and secondary control architecture in order to

achieve acceptable voltage and current regulation.

CHAPTER 2

Introduction

2.1

Generalities of the microgrids This section explores the main concepts involved in the microgrids investigation framework as well as general information relevant to the investigation process.

2.1.1

Distributed energy resources (DERs) and distributed generators (DGs) Formally, a DER is any renewable or non-renewable energy source that, by means of small or medium-scale equipment, called DG, could produce electrical energy.Unlike the large power plants, the DGs are characterised by being located and distributed to guarantee the maximum exploitation of a region’s energy resources; with low monetary and environmental costs, among other strengths.

The global electric market’s projection foresees that by 2030, the 80% of the new installed capacity will come from fossil fuels, with all the environmental problems that this implies. Despite these forecasts, the concept of large power plants has been discussed through the DGs’ high penetration in global networks. Also, the advent of DERs based on renewable technologies could help mitigate of the damages produced by the use of fossil fuels. [9].

In the technical field, the main impacts resulting from large-scale DGs integration are the voltage rise effect, power quality issues, branch overload problems, protection issues, and stability issues [10].

Tables 2.1 and 2.2 compares the principal DGs technologies and shows their differences in some remarkable aspects.

Chapter 2. Introduction

4

Technology Primary energy Output type Module power (kW) Electrical efficiency

(%)

Overall efficiency

(%)

Advantages Disadvantages Reciprocating engines Diesel or gas.

AC mar-00

30-43

∼80 −85

• Low cost.

• High efficiency.

• Ability to use various.

• Environmentally unfriendly emissions.

Gas turbine Diesel or gas.

AC

0.5-

30000

21-40

∼80 −90 Environmentally friendly.

• Cost effective

• Too big for Small

costumers.

Microturbine Bio-gas propane or natural gas.

AC

30-1000

14-30

∼80 −85

• Small size and light

weight.

• Easy start-up and shut

down.

• Low maintenance costs

• Expensive technol-

ogy • Cost-effectiveness sensitive to the price of fuel.

• Environmentally unfriendly emissions.

Fuel Cell Ethanol, H2, N2, natural gas, phosphoric acid or propane.

DC

1-20000

05-55

∼80 −90

• One of the most envi-

ronmentally friendly generator.

• Extremely quiet.

• Useful for combined

heat and electricity applications.

• Expensive infras-

tructure for hydrogen.

Table 2.1: Main non renewable DGs technologies [7]. Technology Primary energy Output type Module power (kW) Electrical efficiency

(%)

Overall efficiency

(%)

Advantages Disadvantages Windpower Wind AC

0.2-3000

-

$\sim50-

80$

• Day and night power generation.

• One of the most developed re-

newable energy.

• Still expensive.

• Need energy storage.

Photovoltaic Sun DC

0.02-1000

-

$\sim40-

45$

• Emission free.

• usable in many applications

• Need energy storage.

• High up-front cost.

Biomass gasification Biomass AC

100-20000

15-25

$\sim60-

75$

• Minimal environmental impact.

• Available throughout the world.

• Alcohols and other fuels pro-

duced by biomass are efficient, viable, and relatively clean burning.

• Still expensive.

Small Hydro power Water AC

5-100000

-

$\sim90-

98$

• Economic and environmentally

friendly.

• Relatively low up-front invest-

ment costs and maintenance.

• Useful for providing peak power

and spinning reserves.

• Suitable site charac-

teristics required.

• Difficult energy ex-

pansion.

• Local environmental

impact.

Geothermal Hot water AC

5000-

100000

10-32

$\sim35-

50$

• Environmentally friendly.

• Low running costs

• No-availability of geothermal spots in the land of interest.

Ocean energy Ocean waves AC

10-10000

-

-

• High power density.

• More predictable than solar or

wind.

• Lack of commercial

projects.

• Unknown operations

and maintenance costs.

Solar thermal Sun and water AC

1000-

80000

30-40

$\sim50-

75$

• Simple, low maintenance.

•Operation costs nearly zero.

• Developed technology.

• Unknown operations

and maintenance costs.

• Low energy density.

• Limited scalability.

Table 2.2: Main renewable DGs technologies [7].

2.1. Generalities of the microgrids

2.1.2

Energy storage systems (ESS) The ESS are devices that can store energy in any of its forms, and deliver it as electrical power (current or voltage sources). The use of storage systems in microgrids is fundamental to ensuring power-sharing during fails and operational changes. Table 2.3 shows the most important technologies in this area. Technology Efficiency

(%)

Capacity (MW) Energy Density (Wh/kg) Capital e/kW Lifetime (years) Maturity Environmental Impact Examples

TES

30-60

0-300

80-250

140-220

5-40

Developed Small Solar tow Central Receiver Solar Power Plant California (USA).

PHS

75-85

100-5000

0.5-1.5

400-1500

40-60

Mature Negative Rocky River PHS plant, Hartford(USA).

CAES

50-89

3-400

30-60

250–1500 20–60 Developed Negative Huntorf (Germany) and MacIntosh, Alabama(USA).

Flywheel

93-95

0-25

10-30

250

$\sim15 Demonstration Almost Commercially supplied by AFS-Trinity (USA), Beacon Power (USA), Piller (USA), etc.

Pb acid battery

70-90

0-40

30-50

200

5-15

Mature Negative BEWAG Plant, Berlin (Germany). NiCd battery

60-65

0-40

50-75

350-1100

10-20

Commercial Negative Golden Valley, Alaska USA.

Li-ion battery

85-90

0-1

75-200

3000

5-15

Demostration Negative Kyushu Electric Power and Mitsubishi Heavy Industries (Japan).

Fuel Cells

20-50

0-50

800-10000

350-1100

5-15

Developing Small Topsoe FuelCell, Lyngby, (Denmark). Flow battery capacitors

75-85

0.3-15

10-50

400-1100

5-15

Developing Negative Innogys Little Barford Power Station, (UK). Capacitors

60-65

0-0.05

0.05-5

250

$\sim5 Developing Small Commercially supplied by SAFT (France), NESS (Korea), ESMA(Russia) etc. Supercapacitors

90-95

0-0.3

2.5-15

200

> 20 Developed Small PowerCache (Maxwell,USA), ELIT(Russia), PowerSystemCo.

(Japan), Chubu Electric Power (Japan), etc.

SMES

95-98

0.1-10

0.5-5

200

>20 Demonstration Positive Wisconsin Public Service Corporation (USA). Conventions:

TES: Thermal energy storage.

PHS: Pumped hydro storage.

CAES: Compressed sir energy storage. Pb-acid battery: Lead-acid battery. Ni-Cd battery: Nickel-cadmium battery. Li-ion battery: Lithium-ion battery. SMES: Superconduction magnetic energy storage. Table 2.3: Main ESS technologies [7].

2.1.3

Power electronics converters The central operation systems of a microgrid, are the power electronics converters. With appropriated control algorithms, these devices enable the transformation of different forms of electric energy (DC and AC of high and low voltage). The most used power converters topologies are different variants of the classical converters, as the Buck, Buck-Boost and Boost, that can be mono-directional or bi-directional depending of the controlled DG; and the implementation of cascade voltage source converters (VSC) in DC-AC or AC-DC applications.

Chapter 2. Introduction

6

Small Hydropower Distribution Line Photo voltaic energy Wind power Diesel Generator Load Energy storage systems

PCC

Energy storage systems Load Load Load Figure 2.1: Example of a microgrid with distributed energy resources.

2.1.4

Microgrid definition In the discussion about the new distribution systems topologies, the integration of the non-conventional energy resources, and the standardization of the so-called smart grid, the microgrid concept has won special attention due to the flexibility, reliability, and benefits that these network topologies will add to the distribution lines in the near future [9].

Several definitions have been established for a microgrid, and each country has legislation about the grid features, and its operational capabilities. In general, all definitions agree that a microgrid is a cluster of distributed generators and loads, with clearly defined electrical boundaries and the capacity of operating in connection with the grid or autonomously (island mode) [2, 3, 1]. According with these definition, Fig. 2.1 shows an arbitrary microgrid architecture with distributed generators and loads.

A relevant characteristics of every microgrid is the Point of common coupling abbreviated PCC, in which the system interacts with the utility grid, and the inte-

2.2. DC vs AC

gration of several distributed generators.

2.2

DC vs AC The first known microgrid was made by Thomas Edison in 1882, when he installed

50 small scale power plants in a course of four years [1]. But, as a concept, the word

microgrid was introduced by professor R.H Lasseter of university of Wisconsin- Madison in 2001. This year is the beginning in the investigation on the microgrid field. [1], [2]. Multiple laboratories and test facilities were deployed around the world during this period, some of the most important were located in Greece, United States, Italy, England, Japan and China. The development of microgrids around the world revive the old battle between the two modes of electric energy distribution (AC and DC). This, due to the advances in the power electronics converters field and the developments in the microgrids deployment, leading the integration of new generation technologies. Microgrids topologies are now divided between AC and DC operation modes. Has been proved that the implementation of DC-based microgrids, will transform the way of the energy management; specially, in the fields of transport, telecommunications, informatics and industry. This, due to the design and control simplicity, and efficiency compared to AC microgrids [4], [8]. Differences between these two technologies can be seen in table 2.4.

Influence parameter AC distribution line DC distribution line Power transmitted Less efficiency due to high line loss, hence less power transmission.

Require more conductors More efficiency and more power transmission.

Require few conductors System stability Less stable due to easily affected by external disturbances More stable and can also increase the stability of the AC microgrid systems.

Reluctance Have reactance in line No reactance in the line and hence more power transmitted Frequency (50 Hz or 60 Hz Frequency monitoring is mandatory Frequency is zero, so no need of frequency monitoring Resistance High line resistance and hence high losses Have low line resistance and hence low line losses.

Susceptance Charging current and over-voltage problem lead to high cost and low power transmission. Do no exist, and hence effect of overvoltage and over-charging leading and high power transmission.

Analysis Involve complex numbers and hence difficult to analyze.

Involve only real number i.e more simple. Table 2.4: Comparison between AC and DC distribution lines [8]. Table 2.5 compare research results in the control aspect of AC and DC microgrids.

Chapter 2. Introduction

8

Operating mode AC microgrids DC microgrids Grid-connected Mode

MGCC

• Monitoring system diagnosis by collection information from the

LVAC network, DGs units and loads (AC and DC).

• Performing state estimation and security assessments, evaluate

economic generation scheduling active and reactive power control of the DGs units and demand side management function using the available information.

• Ensuring synchronized operation with the main grid, maintaining

the power exchange at prior contract points.

• The main function of the MGCC is to independently con-

trol the power flow and load-end voltage profile of the DC units in response to any disturbance and load changes.

• Participation in economic generation scheduling, load

tracking or management and demand side management (DSM) by controlling the storage devices.

DGCS

• Ensuring that each DG unit rapidly picks up its generation to

supply its share of the load in stand-alone mode and comes back to the grid connected mode automatically with the help of the MGCC

• Ensuring that each DG unit quickly picks up its generation

to supply its share of the load in stand-alone mode and comes back to the grid connected mode automatically with the help of MGCC.

Island mode

MGCC

• Performing active reactive power control of the DGs in order to

maintain stable voltage and frequency at the load ends.

• Managing load interruption/shedding strategies using demand

side management (DSM) with ESS support for maintaining power balance and voltage.

• Initializing local black start to ensure reliability and continuity

of the service.

• Switching the microgrid to grid-connected mode after the main

grid supply is restored without hampering the stability.

• Independently control the power flow and load-end voltage

profile of the DG units in response to any disturbance and lad changes.

• Ensuring the DG units rapidly pick ups its generation to

supply its local load islanding mode and automatically reconnect to grid with the help of the MGCC.

DGCs

• Commanding each DG unit to rapidly pick up this generation to

supply its corresponding local in the stand-alone mode and automatically re-synchronize to grid with the help of the MGCC.

• Ensuring that each DG unit rapidly picks up this genera-

tion to supply this share of the load in stand-alone mode and comes back to the grid-connected mode automatically with the help of the MGCC.

Conventions:

MGCC: Microgrid central controller.

LVAC: Low voltage AC network.

DGCS: Distributed generator control system Table 2.5: Comparison between AC and DC control tasks [8]. Accurate, actualised and detailed information about the state of art in microgrids control is provided in [11], [12] and [13]. With a exhaustive revision of the literature, is possible to conclude that DC microgrids have a considerable advantage against AC microgrids.

2.3. Introduction to DC microgrids control strategies

2.3

Introduction to DC microgrids control strategies The growing of the distribution generation, makes the control structure a fundamental axes of the microgrids operation.

The main control objectives are given below.

• Efficient voltage and current control in every operating mode.

• Proportional load sharing.

• Stable operation with constant and non-linear loads.

• Coordination among different DERs and ESS.

• Synchronisation with the utility grid.

• Power flow control within DC microgrid and the utility grid.

• Smooth transition between grid-connected to island mode.

Different control task are required by an MG in order to satisfy the objectives above. The main control challenges in this field arise from the unknown behaviours of the renewable sources such as photo-voltaic and wind-power. Usually, the control of microgrids is designed according to the structure depicted in Fig. 2.2, in which each layer seeks to meet specific control objectives, determined by the system’s operational needs.

The primary layer (field level) takes care of the internal control of each distributed generator and loads, regulating the power production and loads consumption. The secondary layer (management level) seeks to maintain the grid’s stable operation, exchanging information with the tertiary layer to set the appropriate references to the first layer. In the end, the tertiary layer (grid level) regulates the economic dispatch, determining the times to sell or buy energy from the utility grid and the charge or discharge of energy storage nodes [7, 14, 15].

Chapter 2. Introduction

10

Inner Control DC/DC Converter + Input Voltage

-

DC-based Distributed Generator PI (Current) Controller Inductor Current Duty Cycle

PWM

Generator Current Reference Figure 2.3: Classic current PI controller in power electronic devices. Field Level Manegement Level Grid Level Tertiary Control Secondary Control Primary Control Market prices bargaining and dispatch Microgrid operation (control and monitoring of the global variables Internal control of the ditributed generators, loads, and energy storage systems.

Figure 2.2: Hierarchical control structure in a microgrid [7].

2.3.1

Internal control Most of the literature refers the internal control as a part of the primary control strategies, since it must be located internally in the DG or load interfaces, with the objective of control the primary variables of the power electronic converter. For explanatory purposes, a separation of the internal and primary controllers is made in this research.

A PI controller is applied with current feedback in classical architecture to track a reference current as is depicted in Fig. 2.3.

To control the output voltage, over the current loop in Fig. 2.3, is implemented a PI outer loop with an output voltage feedback, as is shown in Fig. 2.4, this is known as voltage-current cascade control.

PI controllers are simple and with relative easy tuning. This research proposes a non-linear control technique that has better response and better sturdiness against perturbations. The detailed explanation is developed in chapter 4.

2.3. Introduction to DC microgrids control strategies

Inner Control DC/DC Converter + Input Voltage

-

DC-based Distributed Generator PI (Current) Controller PI (Voltage) Controller Output Voltage Inductor Current Voltage Reference Duty Cycle

PWM

Generator Figure 2.4: Classic voltage cascade PI controller in power electronic devices.

2.3.2

Primary control strategies In the field level, the conventional controller implemented is the droop control. In DC microgrids the power is proportional to the current, and hence both, voltage and current, can be used to implement the droop controller [16, 17, 18]. Detailed explanation about this control architecture is available on chapter 4.

2.3.3

Secondary control strategies The microgrid’s main control objectives are performed in the second layer. These control objectives include the turn-on, the turn-down, isolation, and re-connection protocols, besides the regulation of the internal power production and consumption [10]. The control architecture in this layer does not have a consensus due to the different topologies proposed in the literature. These are the centralized, distributed, and decentralized methods, [17, 14, 19].

Centralized control The centralised control uses an overall communication system ruled by a Microgrid central controller (MGCC) usually located at the PCC. Generally, it gives better performance throughout optimising the system by collecting all required information in one single algorithm driven by the central processor.

Due to the better performance and efficiency, the centralized control has lead to significant developments in optimization and robustness, as is shown in [20, 21], and the coordination of different renewable sources power dispatch shown in [22]. Notwithstanding, as demonstrated in [23, 17], a significant issue that centralized architecture has, is the single point failure, since the central controller carries out all the microgrid operations, a fail in this point will lead to a generalized system collapse; also this kind of controller lacks of scalability, which hinders the growth of the microgrid, associated with the integration of new DGs and loads.

Chapter 2. Introduction

12

Decentralized control The decentralised control methods operates based on local information, observed by each node of the microgrid, this guarantee the free connection of new nodes. Examples of decentralized controllers whit significant improvements could be seen in [24, 25], with a robust drop control strategies in [24], and a sliding mode control in [25]. A well-known drawback of the decentralized control, also developed by [23] is the poorer energy and frequency quality (compared with centralized structures) to the time delays among the controller’s response; this strategy also have to overcome problems of communication derived of the noise injected in the digital buses by the power lines, and issues in the regulation of voltage and load sharing. [26],[27].

Distributed control The distributed strategies seek to obtain the best features of both architectures: the improved variable management of the centralized, and the flexibility and plug and play service of the decentralized. The literature in distributed topologies includes complex methodologies like H∞norm, model predictive control (MPC), and intelligent control, among others, all have in common model-based math techniques and complex implementation to the algorithms computational cost. In [28] an MPC technique is applied to a renewable-based microgrid with satisfactory results. In [29] a novel broadcast gossip technique with applicability in real-world scenarios is presented. In [30], a resilient distributed control with the capability of avoiding certain sensor faults is shown.

CHAPTER 3

Design of a low voltage DC microgrid This chapter present the design criteria of a small scale microgrid, taking as a reference, the project that served as inspiration to carry out this research.

3.1

Distributed generators classification According to its utility, every DG could be divided in dispatchable and non-dispatchable units. Dispatchable units can be controlled to provide the necessary power to maintain the grid stability, non-dispatchable units only deliver a specific amount of power according to the actual capacity of the associated DER. Three variations of these divisions can be considered [19]:

3.1.1

Grid forming/supporting node With a classical control scheme depicted in Fig. 2.4, a dispatchable unit could work as grid forming or grid supporting node. The grid forming node assume the role of master of the microgrid, setting the voltage reference of the DC-link; in grid connected mode, usually this role is carried out by the utility grid. A grid supporting node, set the voltage to its neighborhood, supporting the grid forming node; in island operation, all the supporting nodes must work together to maintain stability in the microgrid, this is called Cooperative control. A simplified model of grid forming/supporting node is depicted in Fig. 3.1-(a).

3.1.2

Grid feeding node The control scheme shown in Fig. 2.3 is normally implemented in non-dispatchable units called grid feeding nodes. With a maximum power point tracking (MPPT),

Chapter 3. Design of a low voltage DC microgrid

14

like the developed by Ospina [31], these sources only inject power o current to the DC-link. A simplified model of grid feeding nodes is presented in Fig. 3.1-(b). +

-

Current Reference Voltage Reference (a) (b) Figure 3.1: Simplified microgrid nodes. (a) Grid forming/supporting node. (b) Grid feeding node.

3.2

Case study: Intensive fish farming project

3.2.1

Generalities An intensive fish farming project is an automated food production project, in which the final product is fresh fish. Differs of the traditional fish farms in crucial aspects: the production volumes, the level of automation, and the energy consumption. The main aspect of this kind of developments is the production area. In a small area, a well deployed intensive fish farm, could produce, near six or seven times the same amount of fish that a traditional farm with same extension. This is only possible with the implementation of an aeration system that allows bigger fish concentrations in a smaller space. The aeration system must operate 24 hours, 7 days a week, because if it stops will lead to the loss of all production. However, the constant use of electro-mechanical aireators is a considerable load to handle with. Other loads that must to be taken into account are: illumination and general porpoise sockets, an electric pump, and an industrial freezer. More information about the issues related to this projects are available in references [32, 33, 34]

3.2.2

APISBAL project Fig. 3.2 refers the location and geography of the project developed by the APISBAL association.

With an estimated production of 1 ton per month, the project is considered small. However, about 10 rural families depend on the success of the project.

3.3. Proposed design

LAKE

LAKE

LAKE

LAKE

B W.R.

6.00

6.00

LAKE

LAKE

CONVENTIONS

B W.R.

LINEA DE CONDUCCIÓN

Water Reservoi.

HOUSE

1620

Water intake.

Water condution line.

Water Fall.

80Lit/minute

COORDINATES

4.946355185745703, -75.98776835981742

Figure 3.2: Project location map.

The total load calculated is shown in table 3.1. This information is a basis of the microgrid design.

Element Nominal power (Watts) Variable-frequency drive 7500W Electric pump 1500W Other loads 1900W Total 10900W Table 3.1: Main loads of the fish farm project.

3.3

Proposed design Fig. 3.2 shows a near water fall that can sustain an SHP plant. This kind of DG is optimal to be implemented as a grid supporting node.

Additional information can be obtained of the Global solar atlas provided by The world bank [35]. With the location coordinates is possible to determine that the full sun hours (FSH) annually are approximately of 1680h/y, which is an optimal value to deploy PV arrays. PV generation, as a renewable source is suitable to be a grid feeding node in a microgrid.

Every microgrid needs an energy supply system, the battery energy storage (BES) is the best solution in this kind of projects. Due to the size of the battery bank, BES has better operation as a grid feeding node.

Suggested nominal power of each node is available on table 3.2. These values were estimated having in account the variability of SHP and PV sources, and the possibility of a net metering exchange with the utility grid.

Chapter 3. Design of a low voltage DC microgrid

16

Node Nominal Power

SHP

9500W PV 7600W

ESS

5700W Table 3.2: Suggested nominal power of the DGs nodes. AC DC AC DC DC DC DC DC DC DC DC DC DC AC DC Bus Small Hydropower Led Lighting Variable DC Loads Variable AC Loads Distribution Line Photo voltaic energy Energy storage systems Figure 3.3: Simplified microgrid design to the fish farm project. With this information is easy to propose a simple DC microgrid design that can handle the local loads in connection with the utility grid. Fig. 3.3 shows the one-line diagram of the proposed microgrid.

In terms of reliability this kind of microgrid might have energy losses due to the variability of the renewable sources. This model could be improved with the inclusion of a diesel generator.

CHAPTER 4

Hierarchical control in a DC microgrid This chapter explores the theoretical and mathematical background related to the microgrid control levels from the internal converter control to the secondary level.

4.1

Inner control This chapter references are supported in [36].

The constant search for more robust primary level controllers has become a relevant field of investigation in the state of the art of DC distribution systems. The Buck converter has been widely studied in recent years due to its simplicity, reliability, and relatively low construction cost, which make it suitable to be part of every DC microgrid. Being a reducer-type converter, in exchange for the difference between input and output voltages, the Buck converter can handle higher output currents than the input equivalent [37]. These facts make it suitable to be located in the load-side, controlling voltage, current or power of led-based illumination systems, internet servers, industrial automation arranges, and other DC loads. As said above, a Buck converter integrated into a microgrid must have a robust controller with the capability to operate over contingencies and disturbances like changes in the input voltage or the load size. This capability is required to improve the whole system performance. The Exact Feedback Linearization (EFL) is a non-linear control technique that searches for a linear transformation of nonlinear systems. The objective is to construct a control signal that can eliminate nonlinearities’ effects on the dynamic system’s behavior [38, 39].

Chapter 4. Hierarchical control in a DC microgrid

18

4.1.1

The Buck Converter In Fig. 4.1, the classic electrical structure of a buck converter is shown, where E is the input voltage, µ is the boolean control signal that activates the electronic switch (usually a MOSFET or IGBT transistor), i is the inductor current, and v is the output voltage.

Figure 4.1: General structure of a Buck converter.

The constants of the model that define its operation characteristics are the inductance L in Henrys, the capacitance C in Farads, and the load resistance R in Ohms.

Design The design of a converter depends on its application. In this case, it must be part of a DC microgrid with a structure, as shown in Fig. 3.3. The Buck converter could be connected to the DC bus, feeding the led lighting system or the variable DC-load node.

In terms of the design criteria, the most used switching strategy is the known pulse width modulation (PWM), in which the energy of the input voltage is managed by the time of the "On" state of the switch. In Fig. 4.2 is shown the behavior of the diode voltage during the PWM signal period (T).

Vd E t T T =1 =0 D(t) Figure 4.2: Waveform of the diode voltage in period T of the PWM.

4.1. Inner control

This lets the introduction of the duty cycle variable (D(t)), as a percentage of T, that can be expressed along with µ as presented in (4.1). µ =      1;

0 ≤t ≤D(t)T

0; D(t)T < t ≤T

(4.1)

Equation (4.1) can be simplified in terms of D giving (4.2). µ =     

1

D(t)

0

(1 −D(t))

(4.2)

With this, it is possible to calculate the critical inductor and capacitor in terms of a continuous conduction mode of operation.

Lc = (1−D∗)R 2f ; Cc = 1−D∗ 16Lcf2

(4.3)

where f is the switching frequency related to the switching period by expression (4.4), and D∗is the nominal value of the duty cycle in the equilibrium point. Being f defined as:

f = 1 T

(4.4)

being T the time between two consecutive rising flanks.

With the above set of equations is possible to design a standard Buck converter in continuous conduction mode. It is important to note that E and R are taken theoretically as constants, but they are subject to disturbances that test the control’s robustness in practice.

Dynamic model To obtain a proper dynamic model is a need to understand the input signal yield’s behaviors in the system.

Let be the input µ = 1. Then, Fig. 4.1 neglecting power losses, can be simplified as shown in Fig. 4.3.

Defining the states of the new system (i,v), the differential equation that model its behavior in function of the time are (4.5).

Ldi dt = E −v(t) (4.5a) C dv dt = i(t) −1 Rv(t) (4.5b)

Chapter 4. Hierarchical control in a DC microgrid

20

Figure 4.3: Buck converter when µ = 1, neglecting power losses. Figure 4.4: Buck converter when µ = 0, neglecting power losses. Now, let be µ = 0. The new schematic of the converter could be simplified as shown in Fig. 4.4 And the resulting differential equations are shown in (4.6), as follows: Ldi dt = −v(t) (4.6a) C dv dt = i(t) −1 Rv(t) (4.6b) The sets (4.5) and (4.6) depend exclusively on the state of the input signal µ. Multiplying (4.2) by both expressions respectively, the set (4.5) becomes (4.7). Ldi dt =  E −v(t)  D(t) (4.7a) C dv dt =  i −1 Rv(t)  D(t) (4.7b) The same procedure is performed with the set (4.6), resulting in (4.8).

4.1. Inner control

Ldi dt = −v(t) 

1 −D(t)

 (4.8a) cdv dt =  i −1 Rv  (1 −D(t)) (4.8b) Finally, equations (4.7) and (4.8) are added in order to create an averaged model of converter, as presented in (4.9).

Ldi dt = ED(t) −v(t) (4.9a) C dv dt = i(t) −1 Rv(t) (4.9b) The pack of equations (4.9) could be expressed in state space, as shown in (4.10). " ˙x1 ˙x2 # = "

0

−E L

1

C −1 RC # " x1 x2 # + " E L

0

# ∆u

(4.10)

With (4.9) and (4.10) it is possible to introduce the different control strategies implemented below.

Behavior analysis Calculation of the transfer function throw essential facts about the dynamic response of the converter’s state variables. By applying the Laplace transform to (4.9) and building the equivalent transfer functions of current (4.11) and voltage (4.12), it is possible to analyze some facts that guarantee the performance of the non-linear controllers.

I(s) =  E Ls + E

LCR

 D(s) s2 +

1

RCs +

1

LC

(4.11)

V (s) = E LRD(s) s2 +

1

RCs +

1

LC

(4.12)

One remarkable thing about the Buck converter is the zero location of both of the transfer functions. Unlike other kinds of converters like the Boost or the Buck-Boost, the Buck does not present zeros located on the positive side of the complex plane for both transfer functions. This means that it is a minimum-phase system, so the voltage and current have stable inner dynamics [31, 38]. Replacing

Chapter 4. Hierarchical control in a DC microgrid

22

the parameters of table 5.1 in (4.11) and (4.12), is possible to get the poles and zeros values of both transfer functions.

Current transfer function is depicted in Fig. 4.5, and have a zero located in the negative side of the complex plane.

Figure 4.5: Poles and zeros locations of the current transfer function. Voltage transfer function has two poles and does not have zeros, as presented in Fig. 4.6.

Figure 4.6: Poles and zeros locations of the voltage transfer function. This is a key to develop the EFL controllers since the order stability of the internal dynamic determines the designed control law’s applicability. It can be concluded that both state variables: current, and voltage, have stable inner dynamics, so that an EFL technique could be proposed for each one [39].

4.1. Inner control

4.1.2

Modified Feedback linearization with integral action to control current and voltage The generalized model of a nonlinear dynamic system is given by (4.13) ˙x = f(x) + g(x)u(t)

(4.13)

A nonlinear state space model, where x(t) is a vector that contains the state variables, and f(x) and g(x) are independent functions of x. The set of equations of (4.9) can be transformed into state space model giving (4.14).

˙x1 = E L D(t) −1 Lx2(t) (4.14a) ˙x2 = 1 Lx1(t) −

1

RC x2(t) (4.14b) where x1 is the inductor current (i) and x2 is the output voltage (v). Current control By defining the output of the system as x1(t), as is shown in (4.15). y(t) = x1(t)

(4.15)

The derivative of this equation is given by (4.16). ˙y(t) = ˙x1 = E L D(t) −1 Lx2(t)

(4.16)

In this case, for current control, the output of a second-order system appears in the first derivative, throwing a reduced-order control. This is not a problem since it was demonstrated that the current inner dynamics are stable. Thus, equation (4.16) can be compared to a corrective function Ψ as shown in (4.17). ˙x1 = Ψ (4.17a) E L D(t) −1 Lx2(t) = Ψ (4.17b) Defining e(t) as the error (4.18), the following equation is obtained: e(t) = x1(t) −x1d(t)

(4.18)

Chapter 4. Hierarchical control in a DC microgrid

24

where x1d(t) is the reference. The function Ψ can be defined to guarantee a reference tracking, with a proportional gain K and an integral action that ensures the error correction, adjusting the value of the integral gain Ki. Resulting Ψ is (4.19). Ψ = −Ke(t) + Kiei(t)

(4.19)

where ei(t), known as the integrative error, is defined as: ei(t) = Z t

0 e(τ)dτ

(4.20)

By applying derivatives at both sides of expression (4.20), the expression (4.21) is obtained.

˙ei = e(t) = x1(t) −x1d(t)

(4.21)

A new closed-loop state space model can be built from the first order differential equations (4.17) and (4.21), as shown in (4.22).

" ˙x1 ˙ei # = "

0

0

1

0

# " x1 ei # + "

1

0

# Ψ − "

0

1

# x1d

(4.22)

And the control law that guarantee the reference tracking is given by (4.23), as follows:

D(t) =  −Ke(t) + Kiei(t) + 1 Lx2(t)  L E

(4.23)

Since the input voltage E is a non-controlled input instead of a constant, and for microgrids applications, must be a global variable available for all the primary level controllers, then the feedback of E ensures a fast response against changes in the main DC bus. This guarantees the operation of the node. Fig. 4.7, shows a simplified schematic, in which the control law of (4.31) is embedded in the the inner control block.

Voltage control Unlike other standard converters, the Buck does not present unstable behaviors in the voltage loop side, this means that an EFL procedure can be developed. Lets define the voltage as the output of the system.

In order to guarantee a linear transformation of the model, a new space must be defined, lets call this as the vector z(t).

y(t) = x2(t) = z1(t)

(4.24)

The first derivative of (4.24) is given by (4.25).

4.1. Inner control

Inner Control Buck Converter + Input Voltage

-

DC-based Distributed Generator EFL Current controller Output Voltage Inductor Current Current Reference Duty Cycle

PWM

Generator Figure 4.7: EFL current control schematic.

˙z1 = −1 RC x2(t) + 1 C x1(t) = z2(t)

(4.25)

Since the control signal D doesn’t exist in the first derivative, the second derivative must be calculated. The resulting expression contains the control signal so it can be equalized to the corrective function Ψ as shown in (4.26). ˙z2 = −1 RC x1(t) +

1

(RC)2 −1 LC !

x2(t) +  E LC  D(t) = Ψ

(4.26)

The corrective function Ψ is designed for a complete order model. By adding the integral action, the expression (4.27) is obtained. Ψ = −K1z1(t) −K2z2(t) + Kiei(t)

(4.27)

where the error is given by (4.28), e(t) = x2 −x2d

(4.28)

And the integrative error ei given by (4.29) ei(t) = Z t

0 e(τ)dτ

(4.29)

The augmented state space model is presented in (4.30), as follows:   ˙z1(t) ˙z2(t) ˙ei(t)  =  

0

1

0

0

0

0

1

0

0

    z1(t) z2(t) ei(t)  +  

0

1

0

 Ψ −  

0

0

1

 x2d

(4.30)

Clearing D(t) from expression (4.26) the model’s control law is given (4.31).

Chapter 4. Hierarchical control in a DC microgrid

26

Inner Control Buck Converter + Input Voltage

-

DC-based Distributed Generator EFL Voltage controller Output Voltage Inductor Current Voltage Reference Duty Cycle

PWM

Generator Figure 4.8: EFL voltage control schematic.

D(t) = " −K1z1(t) −K2z2(t) + Kiei(t) + ...

...

1

RC2x1(t) +

1

LC −

1

(RC)2 !

x2(t) #LC E

(4.31)

where z1 = e(t), is defined in function of the error, and z2 is defined by the expression (4.25).

As explained in section 4.1.2, feedback of the input voltage E might ensure a fast response against changes in the DC bus. In voltage control (4.31) is dependant of the load resistance R. In a variable load node, R could change abruptly, leading to instabilities. In the buck converter case, this problem can be solved by doing a digital calculation of the resistances value, from the known values of i and v. With this feedback, the control law is strong enough to overcome several disturbances at the load side.

Fig. 4.7, shows a simplified schematic, in which the control law of (4.31) is embedded in the the inner control block.

4.2

Primary control:Droop control The droop control is implemented as a primary control strategy in grid forming and grid supporting converters (see 3.1) in order to neglect the effects of the lines resistance among the DC-link circuit. Equation (4.32) shows the general form of the droop law, where V ref is the reference voltage of the converter, V is the dc-link nominal voltage, Rd is the droop coefficient, and io is the source current. V ref = V + Rdio

(4.32)

4.2. Primary control:Droop control

Current Figure 4.9: Voltage vs current graphic based on (4.32).

+

-

+

-

DC-DC Converter Figure 4.10: Simplified droop law circuit approach.

As can be seen, the droop law depicted in (4.32) has the general form of the line equation; this could be graphically represented in Fig 4.9, in which is easy to see that the droop gain is the slope of the line.

For that reason, Rd must be calculated such that it guarantees the stability of the system. Therefore the maximum allowable voltage variations, and the rated capacity of the converter are the factors that must be taken into account in the droop gain design procedure. This lead expression (4.33), where, In is the rated current of the converter, Vmin is the minimum voltage deviation allowed, and V is the microgrid nominal voltage.

Rd = V −Vmin In

(4.33)

Otherwise Rd could be adjusted experimentally with a voltage regulation approach. The droop law (4.32) can be seen, electrically, as a voltage source (V ∗) provided by the power electronic device, with (Rd) as a virtual series resistance as shown in Fig. 4.10. This simplified approach eases the simulation process.

Chapter 4. Hierarchical control in a DC microgrid

28

PI PI Figure 4.11: (a) Voltage regulator. (b) Current regulato.

Higher droop gains reduce the effect of line resistances on the current sharing accuracy, however, may cause large voltage drops in the output terminal of the converters [16].

Though The droop control acts as a primary proportional regulation that establish the output voltage reference of each converter in a microgrid, as every proportional control, has not reference tracking, so present a steady state error, known as voltage deviation. By itself, the droop law cannot guarantee the appropriate operation of the microgrid. To correct this issue a secondary control architecture must be implemented.

4.3

Secondary control [16] In chapter 2.3.3 a brief introduction to the main secondary control strategies was presented. In terms of reliability, efficiency and sturdiness, was said that the centralized architecture is the most accurate option in small microgrid applications.

4.3.1

DC link Voltage Regulation Is expected that a centralized voltage regulator track a reference of the DC-link voltage, in a small microgrid, with a single DC-bus and relatively small line resistance, this task could be accomplished with a simple PI voltage controller as depicted in Fig. 4.11 (a). Where V ∗ dc is the reference voltage of the DC-link, Vdc is the DC-link actual voltage, and V ∗is the voltage reference of the distributed generators.

4.3.2

Current Regulation Proportional power load sharing is a common term that refers a percentage sharing of the load, based on the nominal output values of each dispatchable DG unit. This is, that every DG contributes with the current injection according with its nominal capacity. A PI current control could achieve this goal as depicted in Fig. 4.11 (b).

4.3. Secondary control

Secondary Control Communica
on Network On-site Secondary Control (Current Regulator) Primary Control DG 1 DC/DC Converter Inner Control
… ]
PI 

∗

 ∗ On-site Secondary Control (Current Regulator) Primary Control DG n DC/DC Converter Inner Control
 … ]
 PI    ∗

  ∗ Averaging ∗  ∗  PI 

 Figure 4.12: Diagram of a centralized control architecture with voltage and current regulation.

Where Ipu n is the per-unit value of the current shared by the n DG, being n the number of dispatchable units, and Iavg is a value computed by the expression (4.34). Iavg = mean  [Ipu

1 , ..., Ipu

n ]T 

(4.34)

This means that the current regulator has an on-site controller 4.11 (b), and a centralized estimator that computes the current reference Iavg

4.3.3

General scheme

.

The current regulator output I∗is added to the voltage regulator output V ∗ to compute the reference voltage of the droop law V ref, and the per-unit value of the injected current Ipu n is computed with (4.35), where I is the actual value of the injected current, and Inom is the nominal current of the DG unit. Ipu n = I Inom

(4.35)

The hierarchical control scheme until the second layer could be summarized in Fig. 4.12, where [R1, ...Rn] are the line resistances, and [RL1, ...RLi] are the load resistances being i the number of loads.

To refer the control schematic that rules over the grid feeding converters see Fig. 4.7, the load side converters use the same structure than depicted by Fig. 4.8.

CHAPTER 5

Simulation Results This chapter summarizes the results of the inner, primary and secondary control architectures developed in chapter 4 and tested with a simulation tool.

5.1

Feed back linearization control

5.1.1

Experimental Setup Model constants Table 5.1 shows the model parameters, taking into account the critical inductor and capacitor given by (4.3).

Gains of the PID are adjusted with the PID tune environment of Simulink® and are presented in the table 5.2.

The constants of the non-linear controllers K and Ki, for current control, and Name Symbol Value Input voltage E 220V Nominal output voltage vn 24V Nominal inductor current in 16.66A Switching frequency f 80kHz Capacitance C 220µF Inductance L 6.7mH Resistance R 1.44Ω Equilibrium Duty Cycle D∗

11%

Table 5.1: Simulation development.

5.1. Feed back linearization control

PID CONTROLLER

Constant Value Current controller Ki

106.830662

Kp

0.106327

Kd 7.852402e −6 Voltage controller Ki

9.45698

Kp

0.023592

Kd 1.15975e −5 Table 5.2: Constants of the PID controllers.

EFL controller Constant Value Current controller K 1.009e + 04 Ki −9e5 Voltage controller K1 12.711e6 K2

15.845

Ki −54e7 Table 5.3: EFL control Constants.

K1, K2 and Ki, for voltage control, are adjusted experimentally and are shown in table 5.3.

Simulation Settings Simulations are made in Matlab-Simulink® with a duration of 230ms. All controllers begin with the reference value in 0 and have a reference change at t = 5ms. For current control, the new reference is set to in, and for voltage control, the reference is set to vn. In order to test the controllers’ robustness, two different disturbances are programmed, the first one at t = 110ms, an input voltage loss of 30%. The second one, at t = 150ms, is a parallel connection of a resistive load equal to R’s nominal value, simulating a sudden load increase.

To compare the performance of the EFL and PID controllers, mean square error (MSE) and Integral time absolute error (ITAE) are applied to each simulation and compared in tables 5.4 and 5.5.

Chapter 5. Simulation Results

32

0

0.05

0.1

0.15

0.2

0

5

10

15

20

Current (Amps) (a) Reference PID Inductor Current (i)

0

0.05

0.1

0.15

0.2

Time (s)

0

5

10

15

20

Current (Amps) (b) Reference EFL Inductor Current (i) PID Inductor Current (i) Reference Reference EFL Inductor Current (i)

(

r r EFL I d C (i) R f r L r Figure 5.1: Current control performance: (a) PID. (b) EFL.

5.1.2

Results and discussion Current control In Fig. 5.1 is depicted the response of PID (a) current controller, and EFL (b) current controller whose control law is defined by the expression (4.23). Note that both methods fulfill the objective, reaching the reference and overcoming the disturbances. Due to the speed of both responses, a detailed analysis is presented. In Fig. 5.2 is shown the transitory response to the reference change at t = 5ms. There is a clear difference between both graphs. Fig. 5.2 (a), depicts a maximum overshoot of 2.3649A and a settling time less than 5ms, instead Fig. 5.2 (b), depicts a maximum overshoot of 0.3963A and a settling time of 20ms. It can be concluded that the EFL, although it is slower than the PID, has a better transient response. Fig. 5.3 depicts a zoom over the disturbances between t = 100ms and t = 200ms. Note that PID (a), has a current loss of 0.3347A at t = 110ms due to the first disturbance. The same graph depicts a current increment of 0.4371A at t = 150ms due to the load connection. EFL (b) does not present representative changes against any of the disturbances, showing more sturdiness than the PID control.

5.1. Feed back linearization control

PID Inductor Current (i) Reference Reference EFL Inductor Current (i) Figure 5.2: Current control transient state behaviour: (a) PID. (b) EFL. PID Inductor Current (i) PID Inductor Current (i) Reference Reference Figure 5.3: Current control disturbance response behaviour: (a) PID. (b) EFL .

Chapter 5. Simulation Results

34

PID Duty Cycle (D) EFL Duty Cycle (D) Figure 5.4: Current control duty cycle comparison: (a) PID. (b) EFL. EFL Output Voltage (v) PID Output Voltage (v) Figure 5.5: Current control voltage response comparison: (a) PID. (b) EFL.

5.1. Feed back linearization control

Control method

MSE

ITAE

PID

2.6482e + 05 2.1765e + 03

EFL

2.3316e + 05 1.5045e + 03 Table 5.4: Comparison of current controllers performance. Fig. 5.4 shows the performance of the control signal, the duty cycle (D), through all the simulation. It can be seen that PID response (a), and EFL response (b), have a similar behaviour, with a slightly difference at the disturbances response, at t = 5ms, 110ms, 150ms. It is worth noting that the PID is slower but has less oscillations, meanwhile the EFL is faster, and virtually avoids the overshoots caused by the disturbances. The output voltage response (v) presented in Fig. 5.5 shows the voltage behaviour through all the simulation, showing a sudden voltage loss at t = 150ms due to the second load connection, equivalent to a half o the nominal output voltage v = 12V . To clarify the results, table 5.4 compare the MSE and ITAE measures of both controllers, where the higher performance of the current EFL controller is validated.

Chapter 5. Simulation Results

36

Reference Reference PID Output Voltage (v) EFL Output Voltage (v) Figure 5.6: Voltage control performance: (a) PID, (b) EFL. Voltage control Fig. 5.6 is depicts the response of PID (a), and EFL (b) whose control law is defined by expression (4.31).

Transient response is clearer presented in Fig. 5.7, where PID (a), have a maximum overshoot of 1.7545V , and a settling time less than 15ms. In contrast, EFL (b), have a maximum overshoot of 2.0498V , and a settling time less than 26ms. In this case, PID control shows a better transient response. Disturbances response is depicted in Fig. 5.8. The input voltage loss at t = 110ms, in PID graph (a), induce a sudden oscillation with a negative peak of 1.2738V . Note that this disturbance is virtually ignored by the EFL (b). It can be seen that the extra load connection at t = 150ms trigger a highly oscillatory response in both methods. On the other hand, the PID reaches a maximum deviation of 9.3431V . However, the EFL reaches a maximum deviation of 7.9628V . Therefore, the EFL with input voltage (E), and load ( R) feedback, demonstrate better sturdiness than the PID control.

5.1. Feed back linearization control

Reference Reference PID Output Voltage (v) EFL Output Voltage (v) Figure 5.7: Voltage control transient response behaviour: (a) PID. (b) EFL. Reference Reference PID Output Voltage (v) EFL Output Voltage (v) Figure 5.8: Voltage control disturbance response comparison: (a) PID. (b) EFL.

Chapter 5. Simulation Results

38

PID Duty Cycle (D) EFL Duty Cycle (D) Figure 5.9: Voltage control, duty cycle comparison: (a) PID. (b) EFL. PID Inductor Current (A) EFL Inductor Current (A) Figure 5.10: Voltage control, inductor current response: (a) PID. (b) EFL.

5.1. Feed back linearization control

The control signal comparison is presented in Fig.

5.9. In this case EFL (b), have a more aggressive response compared with the PID (a). In order of overcome the disturbances at t = 150ms, the EFL duty cycle shows a higher oscillatory peak. Behaviour of the current with the voltage controllers is presented in Fig.

5.10.

It can be seen that both models ensure acceptable stability even in front of major disturbances. At t = 150ms the second load is connected in parallel, demanding an increase on the output current, equivalent to the nominal value of the inductor current i = 16.66A. To clarify the results, table 5.5 compare the MSE and ITAE measures resulting from the experimental setup for both controllers. In this case, the higher performance of the voltage EFL controller against the voltage PID controller, is proved by a narrow margin.

Control method

MSE

ITAE

PID

2.0264e + 06 2.8987e + 04

EFL

1.3401e + 06 8.8262e + 03 Table 5.5: Comparison of voltage controllers performance. These experimental results are summarized in Ref. [36].

Chapter 5. Simulation Results

40

5.2

Simulation of the microgrid

5.2.1

Experimental Setup Fig. 5.11 show the general structure of the microgrid tested in the simulation tool. Three different DGs with different line resistances are connected to a common DCbus. The DGs configuration obeys all the theory documented in chapters 3,4. Note the switches S1, S2 are included to simulate two different disturbances. All the variables involved in the microgrid control are average values, this due to the converters commutation, that cause interruptions in the current flux.
 +

-



GRID

FEEDING

BUCK CONVERTER

GRID

FEEDING

BUCK CONVERTER

GRID

SUPPORTING

BUCK CONVERTER

VOLTAGE

CONTROL

BUCK CONVERTER

VOLTAGE

CONTROL

BUCK CONVERTER

UTILITY

GRID

+

-



SMALL

HYDROPOWER

(SHP)

ENERGY STORAGE

SYSTEM (ESS)

+

-

PHOTOVOLTAIC

(PV)  

 

 

 

 


ℎ     ℎ ∗


   Load 1 Load 2 Load 3     

ℎ 

 

 
      Figure 5.11: Experimental setup of the microgrid.

Model constants Internal constant parameters of the converters, inductance and capacitance, are the same of the table 5.1. In order to test the EFL method in different conditions, some variations were considered in each of the converters and the whole microgrid operation.

Table 5.6 refers the properties of the grid forming/supporting nodes which inner control strategy is the voltage controller described in the section 4.1.2.

5.2. Simulation of the microgrid

Forming/Supporting node Name Value Utility grid (Forming) Input voltage (Controlled variable)

-

Nominal output voltage 380V Nominal inductor current (controlled variable) 30A Line resistance 0.01Ω Drop coefficient Rd

0.09

SHP (Supporting) Input voltage (controlled variable) 1200V (Nominal) Nominal output voltage 380V Nominal inductor current (controlled variable) 25A Line resistance 0.204Ω Drop coefficient Rd

0.1

Table 5.6: Grid forming/supporting Nodes nominal parameters. DG node Name Value PV Input voltage 760V Output voltage 380V Nominal inductor current (controlled variable) 20A Line resistance 0.4Ω

ESS

Input voltage 645V Output voltage 380V Nominal inductor current (controlled variable) 15A Line resistance 0.2Ω Table 5.7: Grid feeding node’s nominal parameters. Load converters nominal parameters Name Value Load 1 Input voltage 380V Output voltage (controlled variable) 48V Nominal inductor current 41.66A Nominal resistance (RL1) 1.1520Ω Load 2 Input voltage 380V Output voltage (controlled variable) 36V Nominal inductor current 31.25A Nominal resistance (RL2) 1.1520Ω Load 3 (Directly connected to the DC-link) Input voltage 380V Nominal resistance (RL3) 7Ω Table 5.8: DC/DC load interfaces nominal parameters. Table 5.7 refers the parameters of the grid supporting nodes that have integrated the current controllers developed in the section 4.1.2 and which results are presented in section 5.1.2. The nominal inductor current parameter is used as current references in order to simulate the MPPT operation. The parameters of the load-side converters are depicted in table 5.8. L1 converter isolates a 48V DC-link, and L2 isolates a 36V DC-link.These devises imitate a microgrid with different voltage levels. In order of simplify the simulation, the

Chapter 5. Simulation Results

42

considered AC loads were changed for L3, note that this node is directly connected to the DC Voltage line, and has a relative low resistance value. The constants of the EFL have to be adjusted in each new application of the buck converters. The new gains are depicted in table 5.9. Each case required an experimental adjustment.

Converter Node Constant Value

PV, ESS

K

6060

Ki −3.6e5

SHP

K1 1.36e5 K2

820

Ki −2.4e6 Loads 1, 2 K1 12.474e6 K2 15.83e3 Ki −36e7 Table 5.9: EFL control constants.

The PI constants of the voltage and current regulator are shown in table 5.10. The tuning of this gains was made through experimental analysis. PI controller Constant Value Current regulator Ki

1600

Kp

800

Voltage regulator Ki

200

Kp

0.5

Table 5.10: PI control regulators constants.

Simulation Settings The simulation was made in Matlab-Simulink® with a duration of 800ms. All control references begin with their nominal values. Grid forming/supporting node’s output voltage, is controlled by the voltage and current regulator as depicted in Fig. 4.12 and Fig. 5.11, whose references are the DC-link nominal voltage (380V ) and the estimated average current (Iavg).

In order to test the controllers’ robustness, two different disturbances were programmed in the switch’s S1 and S2. The first one at t = 250ms, S2 normally open, is closed, inducing a parallel connection of a resistive load equal to 5RL1, simulating a sudden load increase in L1 node. The second one, the disconnection of the utility grid at 310ms, when normally closed S1 is opened, simulating a forced isolating of the microgrid, testing the capacity of the SHP node of maintaining the DC-link voltage, and all interfaces sturdiness.

5.2. Simulation of the microgrid

5.2.2

Results and discussions Below are presented the results of the microgrid simulation. Fig. 5.12, show the current behaviour of all the DG units. (a) Is the response through all the simulation.

(b) Is a zoom of the transient response in which is evident a high overshoot of the grid current of 16.223A around 100% of the steady state value, is evident that all the DG units have a better behaviour. The overall settling time is approximately 20ms.

(c) Is a zoom of the response against the first perturbation, a medium overshot of 6.761A is visible among all the DGs. The settling time is around 15ms, is visible too, how the dispatchable units work together in order to supply the extra load current requirement. (d) Is the zoom of the isolation behaviour, at t = 310ms the utility grid is disconnected through the opening of S1, the new grid forming node is now the SHP generator, is easy to see how the current injection of this node grows in proportion to the supply loss of the utility grid. The overshoot for SHP is 2.8633A, around 9.87% of the steady state value and, the grid feeding sources experiment a perturbation of 6A for PV node and 7A for ESS node. The whole isolation process has a settling time of 328ms.

Fig. 5.13 show the behaviour of the DGs output voltage. (a) Is the whole simulation graphic. (b) Is the transient state response zoom, showing a smooth transition whit a negligible overshoot of 6.19V around 1.63% of the steady state value and a estimated settling time of 50ms. (b) Shows the response against the first disturbance, with an average voltage loss of 13.07V around the 3.5% of the steady state value, and a settling time of 26.9ms. Finally, a considerable oscillation is triggered by the utility grid disconnection, the voltage loss reach 85.06V a 23% of the steady state value, but the disturbances is controlled in approximately 190ms. Fig. 5.14 compares the performance of the DC-link voltage against its reference. Note that the signal follows the behaviour of the voltages in Fig. 5.13, but tracking the nominal voltage reference.

Plot. 5.15 shows the performance of the internal current of the DG’s converters. The grid feeding nodes response are compared whit the respective reference value, is clear that this nodes exceeds in the current control performance. The case of the SHP source is not less important, a fast response against perturbations ensures the stability of the microgrid, even without the utility grid support. Other information about the controllers response is available on Fig. 5.16. The performance of the internal control signal (duty cycle) shows smooth changes against the disturbances and no saturation even in the isolation process. The analysis of the responses at the loads-side of the microgrid must be done. A interesting behaviour is depicted in Fig. 5.17, that shows the current consumption at the load converters input.

When this graph is compared with Fig. 5.12 (a), is possible to check that the addition of all the DG’s current injection is equal to the addition of all the load input current consumption. Is important to note

Chapter 5. Simulation Results

44

(a) (b) (c) (d) Time Iess Ipv Iess Ipv Iess Ipv Iess Ipv Figure 5.12: (a) DGs current injection response. (b) Transient state response. (c) Load connection response. (d) Grid islanded operation mode.

5.2. Simulation of the microgrid

(a) (b) (c) (d) Time Vshp Vshp Vshp Vshp Vess Vpv Vess Vpv Vess Vpv Vess Vpv Time (a) (b) Figure 5.13: (a) DGs voltage output. (b) Transient state response. (c) Load connection response. (d) Grid islanded operation mode.

Figure 5.14: DC-Link voltage behaviour.

the disturbances effects among the graphs. The addition of extra load in L1 at t = 250ms causes a sudden current increase in IL1, but this doesn’t affect drastically the behaviour of the rest of load nodes. Instead, the disconnection of the microgrid at t = 310ms visibly affects L3, since this load is directly connected to the DC-link, the current is dependent of its variations. Remarkable conclusions can be drawn from this result.

Finally, in order to check the controllers sturdiness, Fig. 5.18 (a) shows the response of the currents at the output of the DC/DC interfaces, is clear that the firs disturbance increases the current consumption in a 20% of the original value for L1 node; out of that, any disturbance is visible through all the simulation time. Plot (b) shows the output voltage of the load DC/DC interfaces compared with the references values, the first disturbance triggers a small voltage loss that is quickly corrected.

Fig. 5.19 present the behaviour of the duty cycle of the load interfaces. The ability of read the input voltage changes, clearly improve the performance of the EFL inner controllers.

Chapter 5. Simulation Results

46

Time Figure 5.15: Distributed generators inductor currents response. (a) (b) (c) Time Figure 5.16: Duty cycle of the distributed generators response. (a) PV node. (b) ESS node. (c) SHP power node.

5.2. Simulation of the microgrid

Time Figure 5.17: Loads input current. (a) (b) Time Figure 5.18: (a) Current consumption of isolated loads. (b) DC/DC interfaces output voltages.

Chapter 5. Simulation Results

48

(a) (b) Time Figure 5.19: Duty Cycle of the load DC/DC interfaces. (a) Load 1. (b) Load 2.

CHAPTER 6

Conclusions The first chapters of this project highlight the importance of the investigation in the field of renewable energy’s and the open issues that have to deal with. Summarized research about the microgrids history, characteristics, and architectures was done. The relevance of appropriating these topics as a society, motivates the design of a low scale microgrid, thought for the countryside, with the purpose of take advantage of the almost, inexhaustible distributed energy resources that Colombia has. In the theoretical frame, to validate the feedback linearization control theory, two different internal EFL controllers for current and voltage regulation of a Buck converter were designed, tested, and compared to a well-known PID control method. Despite being based in a reduced order model, the current controller shows better performance and sturdiness than the usual PID. Another feature of this controller is its simplicity and relative easy adjustment. The non-linear voltage controller has shown a slight advantage compared to the PID, but, just like the PID, the difficulty to tune the controller parameters adequately adds complexity to the tuning. However, these controllers have proved sturdiness and reliability under complex simulation arrangements. The microgrid operation shows a stable behaviour and smooth transitions against the tested disturbances, especially in the forced isolation event, that is considered a basis of the microgrid operation. More research is needed to reach a better understanding of microgrids control architecture and design. The comparison between different schemes (centralized, decentralized, distributed) to reach the ideal one, the implementation of disconnection and connection protocols, the addition of the third control layer that search for regulating the economic dispatch, the research about better management of the energy storage systems, and the junction of AC and DC technologies in hybrid microgrids, are relevant investigation axes in this topic.

Bibliography [1] S. Parhizi, H. Lotfi, A. Khodaei, and S. Bahramirad, “State of the art in research on microgrids: A review,” IEEE Access, vol. 3, pp. 890–925, 2015. [2] R. H. Lassater, “MicroGrids,” in 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309). New York,

NY, USA, USA: IEEE, 2002,

pp. 305–308. [Online]. Available:

https:

//ieeexplore.ieee.org/abstract/document/985003 [3] L. Fusheng, L. Ruisheng, and Z. Fengquan, Microgrid Technology and Engineering Application.

Joe Hayton,

2016. [Online]. Available:

http:

//www.sciencedirect.com/science/article/pii/B9780128035986000115 [4] P. Brian, “DC, Come Home: DC Microgrids and the Birth of the "Enernet",” IEEE Power and Energy Magazine, vol. 10, no. 6, pp. 60–69, 2012. [5] H. García, A. Corredor, L. Calderón, and M. Gómez, “Análisis Costo Beneficio De Energías Renovables No Convencionales En Colombia,” Fedesarrollo - Documento preparado para WWF, p. 90, 2013. [Online]. Available:

http://www.fedesarrollo.org.co/wp-content/uploads/2011/08/WWF_ Analisis-costo-beneficio-energias-renovables-no-convencionales-en-Colombia. pdf [6] D. C. Mora Navarro and J. M. Hurtado Liévano, “Guía para el estudio de prefactibilidad de pequeñas centrales hidroeléctricas como parte de sistemas híbirdos.” Ph.D. dissertation, Pontificil Universidad Javeriana, 2004. [7] E. Planas, J. Andreu, J. I. Gárate, I. Martínez De Alegría, and E. Ibarra, “AC and DC technology in microgrids: A review,” 2015.

[8] J. J. Justo, F. Mwasilu, J. Lee, and J. W. Jung, “AC-microgrids versus DC-microgrids with distributed energy resources: A review,” Renewable and Sustainable Energy Reviews, vol. 24, pp. 387–405, 2013. [Online]. Available: http://dx.doi.org/10.1016/j.rser.2013.03.067

Bibliography [9] M. F. Akorede, H. Hizam, and E. Pouresmaeil, “Distributed energy resources and benefits to the environment,” Renewable and Sustainable Energy Reviews, vol. 14, no. 2, pp. 724–734, 2010.

[10] B. Hernandez, E. Giraldo, S. Ospina, and A. Garces, “Master-slave operation of DC microgrids: An adaptive control approach with estimation,” in 4th IEEE Colombian Conference on Automatic Control: Automatic Control as Key Support of Industrial Productivity, CCAC 2019 - Proceedings, 2019. [11] M. S. Mahmoud and N. M. Alyazidi, “Pilot-Scale Implementation of Coordinated Control for Autonomous Microgrids,” pp. 341–367, 2016. [12] Y. Han, W. Chen, and Q. Li, “Modeling, control, and energy management for DC microgrid,” Smart Power Distribution Systems, pp. 69– 90, 2019. [Online]. Available:

https://linkinghub.elsevier.com/retrieve/pii/ B9780128121542000043 [13] J. Kumar, A. Agarwal, and V. Agarwal, “A review on overall control of DC microgrids,” Journal of Energy Storage, vol. 21, no. November 2018, pp. 113–138, 2019. [Online]. Available: https://doi.org/10.1016/j.est.2018.11.013 [14] A. Mehrizi-Sani, “Distributed Control Techniques in Microgrids,” Microgrid: Advanced Control Methods and Renewable Energy System Integration, pp. 43–

62, 2016.

[15] H. Yang, Q. Li, and W. Chen, “Microgrid communication system and its application in hierarchical control,” Smart Power Distribution Systems: Control, Communication, and Optimization, pp. 179–204, 2018.

[16] S. Peyghami, H. Mokhtari, and F. Blaabjerg, Hierarchical Power Sharing Control in DC Microgrids.

Elsevier Inc., 2016. [Online]. Available:

http:

//dx.doi.org/10.1016/B978-0-08-101753-1.00003-6 [17] Y. Khayat, J. M. Guerrero, H. Bevrani, Q. Shafiee, R. Heydari, M. Naderi, T. Dragicevic, J. W. Simpson-Porco, F. Dorfler, M. Fathi, and F. Blaabjerg, “On the Secondary Control Architectures of AC Microgrids: An Overview,” IEEE Transactions on Power Electronics, vol. 35, no. 6, pp. 6482–6500, 2020. [18] B. Wunder, L. Ott, J. Kaiser, Y. Han, F. Fersterra, and M. Marz, “Overview of different topologies and control strategies for DC micro grids,” 2015 IEEE 1st International Conference on Direct Current Microgrids, ICDCM 2015, pp. 349–354, 2015.

Bibliography

52

[19] M. Shahbazi and A. Khorsandi, Power Electronic Converters in Microgrid Applications.

Elsevier Inc., 2016. [Online]. Available: http://dx.doi.org/10. 1016/B978-0-08-101753-1.00010-3 [20] A. G. Tsikalakis and N. D. Hatziargyriou, “Centralized control for optimizing microgrids operation,” IEEE Power and Energy Society General Meeting, pp. 1–8, 2011.

[21] G. Agundis-Tinajero, N. L. D. Aldana, A. C. Luna, J. Segundo-Ramirez, N. Visairo-Cruz, J. M. Guerrero, and J. C. Vazquez, “Extended-Optimal-Power- Flow-Based Hierarchical Control for Islanded AC Microgrids,” IEEE Transactions on Power Electronics, vol. 34, no. 1, pp. 840–848, 2019. [22] N. L. Díaz, A. C. Luna, J. C. Vasquez, and J. M. Guerrero, “Centralized Control Architecture for Coordination of Distributed Renewable Generation and Energy Storage in Islanded AC Microgrids,” IEEE Transactions on Power Electronics, vol. 32, no. 7, pp. 5202–5213, 2017.

[23] A. Bani-Ahmed, M. Rashidi, A. Nasiri, and H. Hosseini, “Reliability Analysis of a Decentralized Microgrid Control Architecture,” IEEE Transactions on Smart Grid, vol. 10, no. 4, pp. 3910–3918, 2019.

[24] Q. Shafiee, V. Nasirian, J. M. Guerrero, F. L. Lewis, and A. Davoudi, “Teamoriented adaptive droop control for autonomous AC microgrids,” IECON Proceedings (Industrial Electronics Conference), pp. 1861–1867, 2014. [25] M. Cucuzzella, G. P. Incremona, and A. Ferrara, “Decentralized Sliding Mode Control of Islanded AC Microgrids With Arbitrary Topology,” IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6706–6713, 2017. [26] Y. Hakuto, T. Tsuji, and J. Qi, “Autonomous decentralized stabilizing control of DC microgrid,” 2017 IEEE 2nd International Conference on Direct Current Microgrids, ICDCM 2017, pp. 292–296, 2017.

[27] S. Anand, B. G. Fernandes, and J. M. Guerrero, “Distributed control to ensure proportional load sharing and improve voltage regulation in low-voltage DC microgrids,” IEEE Transactions on Power Electronics, vol. 28, no. 4, pp. 1900–

1913, 2013.

[28] Y. Shan, J. Hu, Z. Li, and J. M. Guerrero, “A Model Predictive Control for Renewable Energy Based AC Microgrids Without Any PID Regulators,” IEEE Transactions on Power Electronics, vol. 33, no. 11, pp. 9122–9126, 2018.

Bibliography [29] J. Lai, X. Lu, F. Wang, P. Dehghanian, and R. Tang, “Broadcast gossip algorithms for distributed peer-to-peer control in AC microgrids,” IEEE Transactions on Industry Applications, vol. 55, no. 3, pp. 2241–2251, 2019. [30] X. Li, Q. Xu, and F. Blaabjerg, “Adaptive Resilient Secondary Control for Islanded AC Microgrids With Sensor Faults,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 6777, no. c, pp. 1–1, 2020. [31] S. O. Hurtado, ANÁLISIS DE CONTROLADORES NO LINEALES PARA

CONVERTIDOR DC-DC TIPO BUCK-BOOST APLICADO A UN GENER-

ADOR EÓLICO.

Universidad Tecnológica de pereira, 2019.

[32] “AUNAP | Inicio.” [Online]. Available: https://www.aunap.gov.co/ [33] “María Claudia Merino Bióloga Marina Dirección Técnica de Administración y Fomento AUTORIDAD NACIONAL DE ACUICULTURA Y PESCA-AUNAP 2018 ACUICULTURA EN COLOMBIA,” Tech. Rep.

[34] “Guía Práctica de Piscicultura en Colombia.”

[Online].

Available:

https://www.aunap.gov.co/wp-content/uploads/2016/04/ Guia-Practica-de-Piscicultura-en-Colombia.pdf [35] “Solar Photovoltaic Power Potential by Country.”

[Online].

Available:

https://www.worldbank.org/en/topic/energy/publication/ solar-photovoltaic-power-potential-by-country [36] J. S. Vélez-Ramírez, L. A. Riós-Noreña, and E. Giraldo, “Buck converter current and voltage control byexact feedback linearization with integral action,” Engineering Letters, vol. 29, no. 1, pp. 168–176, 2021. [37] M. H. Rashid, “Electronica de Potencia Muhammad Rashid 3º.pdf,” p. 904,

2004.

[38] H. Sira-Ramírez, R. Márquez, F. Rivas-Echeverría, and O. Llanes-Santiago, Control de Sistemas No Lineales.

Prentice Hall, 2004.

[39] Q. Lu, Y. Sun, and S. Mei, Nonlinear Control Systems and Power System Dynamics.

Kluwer Academic Publishers, 2001.