UNIVERSIDADE FEDERAL DE SANTA CATARINA CAMPUS TRINDADE
PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA DE AUTOMAÇÃO E SISTEMAS
José Diogo Forte de Oliveira Luna
Contributions to MPC-Based Microgrid Central Controllers
Florianópolis 2019
José Diogo Forte de Oliveira Luna
Contributions to MPC-Based Microgrid Central Controllers
Dissertação submetida ao Programa de Pós-Graduação em Engenharia de Automação e Sistemas da Univer-sidade Federal de Santa Catarina para a obtenção do tí-tulo de mestre em Engenharia de Automação e Sis-temas.
Supervisor: Prof. Julio Elias Normey-Rico, Dr. Co-supervisor: Paulo Renato da Costa Mendes, Dr.
Florianópolis 2019
Ficha de identificação da obra elaborada pelo autor,
através do Programa de Geração Automática da Biblioteca Universitária da UFSC.
Luna, José Diogo Forte de Oliveira
Contributions to MPC-based microgrid central controllers / José Diogo Forte de Oliveira Luna ;
orientador, Julio Elias Normey-Rico, coorientador, Paulo Renato da Costa Mendes, 2019.
181 p.
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2019. Inclui referências.
1. Engenharia de Automação e Sistemas. 2. Microrrede. 3. Controle preditivo baseado em modelo. I. Normey-Rico, Julio Elias. II. Mendes, Paulo Renato da Costa. III. Universidade Federal de Santa Catarina. Programa de Pós Graduação em Engenharia de Automação e Sistemas. IV. Título.
José Diogo Forte de Oliveira Luna
Contributions to MPC-Based Microgrid Central Controllers
O presente trabalho em nível de mestrado foi avaliado e aprovado por banca examinadora composta pelos seguintes membros:
Prof. Eduardo Camponogara, Dr. Universidade Federal de Santa Catarina
Prof. Marcelo De Lellis Costa de Oliveira, Dr. Universidade Federal de Santa Catarina
Prof. Marcelo Lobo Heldwein, Dr. Universidade Federal de Santa Catarina
Certificamos que esta é a versão original e final do trabalho de conclusão que foi julgado adequado para obtenção do título de mestre em Engenharia de Automação e Sistemas.
Prof. Werner Kraus Junior, Dr. Coordenador do Programa
Prof. Julio Elias Normey-Rico, Dr. Supervisor
Florianópolis, 09 de dezembro de 2019.
Documento assinado digitalmente Werner Kraus Junior
Data: 23/01/2020 12:37:02-0300 CPF: 531.085.239-53
Documento assinado digitalmente Julio Elias Normey Rico Data: 23/01/2020 21:44:38-0300 CPF: 762.840.859-15
ACKNOWLEDGEMENTS
I give thanks to the Lord, for He is a compassionate and gracious God, slow to anger, abounding in love and faithfulness, for He gave me strength to see this work complete.
I would like to deeply thank my advisor Julio and my co-advisor Paulo, for their guidance, counseling and motivation. This has been an incredibly fruitful time and I could not have learned as much without their effort. In particular, I thank professor Julio for showing me "Julio’s way of teaching control". And I thank Paulo for providing me opportunities to shape up as a researcher.
I would also like to thank the Federal Institute of Rondônia for allowing me to take the leave to pursue the master degree. I have to thank my colleagues of the Electrotechnical Technical Course Coordination and the Automation and Control Engi-neering Course Coordination for their immense support, without which I could not have finished this endeavour. Namely, I would like to greatly thank professors Akira, Artur, Douglas, Franks, Gromiko, Jefferson, Joab, Josieudo, Juliano, Kariston, Lígia, Magela, Marcos, Paulo, Rayan, Ricardo, Tatiana, Tayana and Vítor.
Furthermore, I have to thank my coleagues in the master, my companions from the LTIC and the Mestrandos Anônimos group: Gabriel, Georgios, Guilherme, Hage, João, Juan, Matheus, Nilton, Pedro, Pedro, Ramon and Silvan. You guys are awesome, thank you for your friendship!
I would also like to thank my family, my mother Maria, my grandmother Rocicler, my uncle Forte and my aunt Telma, for their unyielding support.
Finally, I thank my dearest Lígia for her love and affection, for keeping me strong to endure this long journey, so far from home.
“To know in order to predict. To predict in order to power.” (Auguste Comte)
RESUMO
O presente trabalho apresenta um conjunto de contribuições para controladores cen-trais de micorrede (MGCCs) baseados em controle preditivo por modelo (MPC), fo-cando primariamente em dotá-los de capacidades de compensação de desbalanço de tensão e gestão de demanda. Em uma microrrede híbrida, a presença de conversores interfacenado os barramentos CA e CC pode ser utilizada para mitigar desbalanços de tensão, desde que sejam capazes de controlar a tensão de sequência negativa dos bar-ramentos aos quais estejam conectados. Todavia, a menos que cada barramento conte com um conversor, é necessário estabelecer uma forma de compartilhar o esforço de compensação entre os múltiplos conversores presentes na microrrede. De modo a tratar deste desafio, duas abordagens são apresentadas neste trabalho, a primeira sendo uma nova formulação convexa baseada no circuito equivalente de sequência negativa da rede, enquanto a segunda integra a compensação de desbalanço dentro de uma aproximação convexa para o problema do fluxo de potência ótimo. No tocante à resposta à demanda, técnicas baseadas no uso de qualidade de experiênca (QoE) têm recebido atenção crescente nos últimos anos, por sua capacidade de considerar o desconforto causado ao usuário pelas ações de gestão de demada. Enquanto a maior parte das propostas encontradas na literatura até o momento tem utilizado soluções baseadas em regras ou em técnicas de controle nebuloso, o presente trabalho integra métricas de QoE dentro do problema de otimização resolvido por um sistema gestor de energia (EMS), baseado em MPC, para uma casa inteligente. Primeiramente, uma pesquisa foi conduzida utilizando um questionário digital para avaliar a disposição da população local em permitr que o EMS interfira em seus hábitos de consumo de ener-gia. A pesquisa foi conduzida em Florianópolis e conseguiu um intervalo de confiança de 95% e uma margem de erro de 4,63%. As respostas foram utilizadas para levantar curvas de QoE descrevendo o nível de incômodo causado pela interferência do EMS em vários dispositivos domésticos. Essas curvas foram utilizadas, então, para propor um esquema de resposta à demanda QoE-aware em um EMS baseado em MPC. Todas as técnicas propostas neste trabalho foram testadas através de simulações computacionais confiáveis e obtiveram resultados promissores.
Palavras-chave: Microrrede. Desbalanço de Tensão. Gestão de Demanda. Controle
RESUMO EXPANDIDO
Introdução
Com o advento da geração distribuída e o avanço da tecnologia da informação, as re-des inteligentes, Smart Grids, têm sido um tema relevante nos anos recentes. Por sua vez, as microrredes são as unidades elementares deste novo paradigma. Microrredes congregam fontes renováveis e tradicionais de geração, sistemas de armazenamento de energia e cargas a serem supridas. Estes elementos são gerenciados por um con-trolador central de microrrede (MGCC) que ainda negocia o fluxo de potência com a concessionária. O MGCC tem de lidar com a intermitência da geração renovável e a variabilidade do perfil de carga, em um ambiente naturalmente multivariável, resul-tando em requerimentos complexos para o controle. Uma técnica que a literatura tem mostrado como adequada para abordar estes desafios é o controle preditivo baseado em modelo (MPC). O MPC é um controle que utiliza predição baseada em modelo, onde a predição é realizada em um horizonte deslizante. A predição é utilizada para encontrar uma sequência de ações de controle ótimas dentro do horizonte, porém apenas a primeira é implementada no processo, visto que o procedimento é repetido a cada instante de amostragem, onde um problema de otimização restrita é resolvido. Considerando que o MPC é uma técnica que permite uma formulação flexível, pode-se utilizar dessa característica para dotar o MGCC com capacidades para atacar proble-mas presentes na operação da microrrede, em particular, é possível mitigar questões concernentes à qualidade de energia e gestão de demanda. Um dos problemas pre-sentes em microrredes CA e híbridas (CA/CC) é a ocorrência de desbalanço de tensão. Este fenômeno é causado pela presença de cargas monofásicas desequilibradas entre as fases e causa degradação de cargas sensíveis. Por outro lado, uma questão rele-vante para a operação de microrredes é o uso de políticas de gestão de demanda, que buscam deslocar os horários de pico de consumo, achatando a curva de demanda, de forma aproveitar melhor a geração renovável, reduzir o carregamento da rede em horários críticos e minorar o custo por energia comprada da concessionária. Todavia, a gestão de demanda acaba por causar desconforto nos usuários, uma vez que im-plica em interferir nos hábitos de consumo de energia. Uma técnica que tem ganhado espaço na literatura por ser capaz de considerar o impacto no conforto do usuário é o uso de métricas de qualidade de experiência (QoE) dentro do contexto de gestão de demanda.
Objetivos
O presente trabalho objetiva dotar MGCCs baseados em MPC de capacidades de com-pensação ótima de desbalanço de tensão e realizar gestão de demanda considerando
um compromisso entre a redução do consumo de energia e o conforto do usuário.
Metodologia
Na vertente da correção de desbalanço de tensão, investigou-se formulações conve-xas para o problema do compartilhamento do esforço de compensação de desbalanço de tensão entre os conversores presentes na microrrede. Validou-se sua formulação através de simulação computacional. Paralelamente, quanto à gestão de demanda, realizou-se um questionário por meio eletrônico de modo a caracterizar a aceitabili-dade da intervenção de um sistema de gestão de energia nos hábitos de consumo de energia dos usuários. A partir das respostas foram utilizadas técnicas de clus-terização para encontrar perfis médios que representam classes de consumidores quanto à disposição de permitir intervenção no uso de diversas aplicações domésticas. Utilizando-se os resultados da pesquisa, examinou-se a formulação de um sistema de gestão de energia, o qual foi avaliado através de simulação computacional.
Resultados e Discussão
Para o desbalanço de tensão foram apresentadas duas abordagens, dentro do con-texto de um MGCC baseado em MPC hierárquico com duas camadas, uma econômica superior e uma camada inferior de compartilhamento de carga. A primeira proposta faz o uso do modelo equivalente de sequência negativa da rede e modela as cargas des-balanceadas como fontes de corrente constante, resolvendo o problema de otimização para um horizonte unitário. Em contrapartida, a segunda abordagem se baseia em uma aproximação convexa do fluxo de potência ótimo, integrando no mesmo problema de otimização o compartilhamento de carga e a compensação de desbalanço, permitindo cargas ZIP e resolvendo o problema para um horizonte maior, de modo a considerar a correção de desbalanço no uso dos armazenadores de energia. Ambas as formu-lações tiveram desempenho adequado nos testes por simulação, sendo capazes de compensar desbalanços de tensão. Quanto à gestão de demanda, o questionário foi aplicado em Florianópolis e obteve respostas com uma margem de erro de 4.63 % e um intervalo de confiança de 95 %. Os resultados mostraram-se favoráveis à possibili-dade de implantação de gestores de energia com estratégias de gestão de demanda baseada em QoE. Neste sentido, foi realizado um estudo por simulação, onde se ado-tou a inclusão das métricas de QoE dentro do problema de otimização de um gestor de energia baseado em MPC e obteve-se resultados promissores, com o mesmo sendo capaz de realizar a gestão de demanda fazendo um equilíbrio entre custo e conforto.
O presente trabalho mostrou o potencial para inclusão de capacidades de compen-sação de desbalanço de tensão e do uso de métricas de qualidade de experiência para gestão de demanda no contexto de controladores centrais de microrrede, obtendo resultados de simulação promissores.
Palavras-chave: Microrrede. Desbalanço de Tensão. Gestão de Demanda. Controle
ABSTRACT
This work presents a set of contributions to microgrid central controllers (MGCCs) based on model predictive control (MPC), mainly focusing on providing them with voltage unbalance compensation and demand management (DM) capabilities. In a hybrid microgrid context, the presence of converters interfacing AC and DC buses can be used to tackle voltage unbalances, as long as the converters can control the negative sequence voltage of the bus they are connected to. However, unless each bus has a converter connected to it, it is necessary to establish a way to share the voltage unbalance compensation effort between the multiple converters in the microgrid. To address the challenge, two approaches are presented in this work, the first one being a novel convex formulation based on the negative sequence equivalent circuit of the grid, while the second one integrates the voltage unbalance compensation within a convex approximation of the optimal power flow problem. Concerning the demand response, in recent years, the usage of quality of experience (QoE) techniques has been getting attention, due to its ability to take into account the annoyance caused by DM actions to the user. While most of the proposals found in the literature, so far, only employ rule-based or fuzzy solutions, the present work integrates QoE metrics within the optimization problem solved by an MPC-based energy management system (EMS) for a smart home. Firstly, a survey was conducted using a digital questionnaire to assess the willingness of the local population to allow the EMS to interfere in their energy consumption pattern. The survey was conducted in Florianópolis and achieved a confidence interval of 95% and an error margin of 4.63%. The responses were used to leverage QoE curves describing the level of annoyance caused by the EMS interfering in several domestic appliances. These curves were used, then, to propose a QoE-aware demand response scheme on an MPC-based EMS. All of the techniques proposed in this work were tested by trustworthy simulations and provided promising results.
Keywords: Microgrid. Voltage Unbalance. Demand Management. Model Predictive
LIST OF FIGURES
Figure 1 – MPC control loop. . . 26
Figure 2 – Balanced voltage on a symmetric load condition (above) and unbal-anced voltages due to asymmetric load (below). . . 37
Figure 3 – Hierarchical MPC. . . 45
Figure 4 – Study-case microgrid. . . 53
Figure 5 – dc Buses. From top to bottom: dc power balance and SOC for DG 1 (a and b), DG 2 (c and d) and DG 3 (e and f). . . 55
Figure 6 – ac buses. From top to bottom: active power balance, reactive power balance, power factor at the point of connection and state of the capacitor bank. . . 56
Figure 7 – Diesel generator. From top to bottom: state of the unit, electric power generation, mechanical power generation. . . 57
Figure 8 – Converters. From top to bottom: bus 8, bus 11, bus 12. . . 58
Figure 9 – Study case Microgrid. . . 59
Figure 10 – ac bus performance for single day scenario. . . 66
Figure 11 – dc bus performance for single day scenario. . . 67
Figure 12 – Buses on a radial network. . . 71
Figure 13 – 12 buses three phase microgrid. . . 72
Figure 14 – The feasible region, colored in light green, is not convex. . . 76
Figure 15 – The new feasible region, colored in light red-ish color, is now convex. 77 Figure 16 – An asymmetrical three-phase system is represented as the summa-tion of three symmetrical systems. From left to right: a positive, a negative and a zero sequence system. . . 81
Figure 17 – Nodal analysis for a bus on the MG. . . 83
Figure 18 – A 7 buses microgrid. . . 86
Figure 19 – Voltage unbalance profile without the VUC. . . 87
Figure 20 – Voltage unbalance profile with the VUC. . . 88
Figure 21 – Phase voltage of each converter under VUC. . . 89
Figure 22 – Proposed MGCC Structure. . . 90
Figure 23 – Voltage unbalance compensation scheme. . . 93
Figure 24 – Study case low-voltage ac 3-phase 4-wires Microgrid. . . 95
Figure 25 – VUF values at each bus. On the instant a the VUC is turned on. On instant b an unbalanced load is added to bus 3. On instant c an unbalanced load is added to bus 2. . . 96
Figure 26 – Apparent power of each phase of each load bus. Phase A: solid line, phase B: dashed line, phase C: dotted line. . . 98
Figure 27 – Apparent power of each phase of each converter. Phase A: solid line,
phase B: dashed line, phase C: dotted line. . . 99
Figure 28 – Study-case microgrid. . . 108
Figure 29 – Total MG load profile. . . 111
Figure 30 – DC bus power balance and SOC of the ESS. From top to bottom, DC bus of: DG 1 (a and b), DG 2 (c and d), DG 3 (e and f). Left, dashed blue: RES power on MPPT, light blue: RES power delivered, green: battery power, red dashed: converter power. Right, black dashed: SOC target, green: SOC. . . 112
Figure 31 – Bus 01. From top to bottom: active power, reactive power, power factor, state of the capacitor bank. . . 113
Figure 32 – Diesel generator. From top to bottom: state, mechanical power, active power, reactive power. . . 114
Figure 33 – Converters active and reactive power. From top to bottom, Bus 8 (a and b), Bus 11 (c and d), Bus 12 (e and f). . . 114
Figure 34 – Phase voltage on each bus. . . 115
Figure 35 – VUF at each bus. . . 115
Figure 36 – Division of Group B consumers. . . 117
Figure 37 – Relative prices for the conventional tariff and the white tariff. Red: peak hours, yellow: intermediate hours, green: off-peak hours, black: conventional tariff. . . 118
Figure 38 – Example of question asking the interviewee to rate the degree of annoyance resulting from the intervention of a EMS. . . 123
Figure 39 – Elbow method results for the washer machine anticipation. . . 129
Figure 40 – CQoE curve for the surveyed appliances. From left to right and from top to bottom: washing machine anticipation, washing machine post-poning, clothes dryer anticipation, clothes dryer postpost-poning, dish-washer anticipation, dishdish-washer postponing, heating curtailing, air conditioning curtailing, electric shower curtailing and electric vehicle charger curtailing. . . 134
Figure 41 – Curves for the average shiftable load. . . 135
Figure 42 – Curves for the average curtailable load. . . 135
Figure 43 – Equivalent circuit model. . . 142
Figure 44 – Black: piecewise affine representation. Colored: affine functions. . . . 143
Figure 45 – Black: piecewise affine representation. Colored: affine functions. . . . 145
Figure 46 – Load profile for the simulation scenario. . . 146
Figure 47 – External temperature profile for the simulation scenario. . . 147
Figure 48 – Composition of the study-case smart house. . . 148
Figure 50 – dc bus. From top to bottom: dashed blue: available RES power, light blue: power provided by the RES converter, green: power stored in the battery, red: power processed by the converter, black: SOC of the battery. . . 152 Figure 51 – ac bus. From top to bottom and left to right: power bought from the
main grid, the power consumed by the smart washer, power delivered by the converter from the dc bus, the power consumed by the air conditioning, the total power consumed, power consumed by the BEV charger. . . 153 Figure 52 – Shiftable washing machine. On the top, light blue: user’s setpoint
for the washer latch variable, dashed blue: actual latch variable, red: desired starting time. Bottom: state of the washer. . . 154 Figure 53 – Air conditioning. Top, dashed black: temperature set-point, red:
exter-nal temperature, green: indoor temperature. Bottom: percentage of cooling power used. . . 155 Figure 54 – BEV charger. Top: state of charge of the BEV battery. Middle, light
blue: time during which the BEV is parked at home, dashed blue: latch variable that indicates the completion of the charge. Bottom: power consumed by the charger. . . 156 Figure 55 – Temperature response to different curves of CQoE for air conditioning
curtailment. From top to bottom these are the responses for groups 1, 2, 3, 4, and 5. Red: outdoor temperature, green: indoor temperature, black dashed: desired temperature. . . 157
LIST OF TABLES
Table 2 – Optimization problem variables. . . 52
Table 3 – White tariff prices for each given times. . . 54
Table 4 – Weights of the objective function. . . 54
Table 5 – Optimization problem variables. . . 64
Table 6 – Comparison on a 30 days scenario. . . 68
Table 7 – Scheduled Power for each bus in kVA. . . 73
Table 8 – Voltage magnitudes and angles on each bus, measured in Volts and degrees. . . 74
Table 9 – Dispatch for buses 8, 11 and 12, in kVA. . . 77
Table 10 – Voltages on each bus with the dispatches found by solving the OPF problem. . . 78
Table 11 – Load buses. Admittances in siemens. . . 85
Table 12 – Line admittances, in siemens. . . 86
Table 13 – Installed load values for each bus in kVA. . . 95
Table 14 – Installed load values for each bus in kVA. . . 107
Table 15 – Optimization problem variables. . . 108
Table 16 – Weights for the load sharing layer. . . 110
Table 17 – Answer of the objective questions. S.E.: secondary education, T.E.: technical education, G.: graduate, P.G.: post-graduate. . . 127
Table 18 – Answer of the objective questions, by age group. . . 127
Table 19 – Answer of the objective questions, by sex. . . 128
Table 20 – Answer of the objective questions, by income bracket. . . 128
Table 21 – Resulting clusters for the anticipation of the starting time of washing machine, clothes dryer and dishwasher. . . 130
Table 22 – Resulting clusters for the postponing of the starting time of washing machine, clothes dryer and dishwasher. . . 131
Table 23 – Resulting clusters for the intervention on the temperature of heating, air conditioning and shower, and extension on the electric vehicle loading time. . . 132
Table 24 – Number of members belonging to each cluster. . . 133
Table 25 – Resulting clusters for general shiftable loads. . . 133
Table 26 – Number of members on each cluster for the electric car battery charging.135 Table 27 – Resulting clusters for general curtailable thermal load, considering a change in the temperature of a given value. . . 136
Table 28 – Number of members on each cluster for the general curtailable thermal load. . . 136
LIST OF ABBREVIATIONS AND ACRONYMS
BEV battery electric vehicle
BSF backward-forward sweep
CCMPC chance-constrained model predictive control DER distributed energy resource
DG distributed generation
DM demand management
EMS energy management system
ESS energy storage system
EV electric vehicles
GA genetic algorithm
HVAC heating, ventilation and air conditioning HVDC high voltage direct current
MG microgrid
MGCC microgrid central controller
MILP mixed integer linear programming MLD mixed logical dynamical
MPC Model Predictive Control MPPT maximum power point tracking
OPF optimal power flow
pu per-unit
PV photovoltaic
QCP quadratic constrained programming
QCQP quadratically constrained quadratic program QoE Quality of Experience
RES renewable energy resource
SGCC synchronous generator capability curve
SOC state of charge
SOCP second-order cone programming VUC voltage unbalance compensator VUF Voltage Unbalance Factor
CONTENTS 1 INTRODUCTION . . . . 21 1.1 OBJECTIVES . . . 23 1.1.1 General Objective . . . . 23 1.1.2 Specific Objectives . . . . 23 1.2 CONTRIBUTIONS . . . 23 1.3 PUBLICATIONS . . . 24 2 LITERATURE REVIEW . . . . 25
2.1 MODEL PREDICTIVE CONTROL . . . 25
2.1.1 Mixed Logical Dynamical Systems . . . . 30
2.2 MICROGRID CENTRAL CONTROLLERS . . . 31
2.3 OPTIMAL POWER FLOW . . . 35
2.4 VOLTAGE UNBALANCE . . . 37
2.4.1 Review on Voltage Unbalance Compensation . . . . 38
2.5 DEMAND MANAGEMENT . . . 39
2.5.1 Quality of Experience . . . . 40
2.6 FINAL REMARKS . . . 43
3 MODEL PREDICTIVE CONTROL APPROACHES ON MICROGRID CENTRAL CONTROLLER . . . . 44
3.1 TWO LAYER MPC-BASED MGCC . . . 45
3.1.1 Formulation . . . . 46
3.1.2 Simulation Results . . . . 53
3.2 CHANCE CONSTRAINED MPC-BASED MICROGRID CENTRAL CON-TROLLER FOR BUILDING-SIZED HYBRID MICROGRIDS . . . 57
3.2.1 Building Sized Microgrid . . . . 58
3.2.2 MGCC Formulation . . . . 59
3.2.3 Simulation Results . . . . 64
3.3 OPTIMAL POWER FLOW . . . 68
3.3.1 Power Flow Formulation . . . . 69
3.3.2 Backward-Forward Sweep . . . . 70
3.3.3 Linearized Power Flow Equations . . . . 73
3.4 FINAL REMARKS . . . 78
4 A CONVEX OPTIMAL VOLTAGE COMPENSATOR . . . . 80
4.1 VOLTAGE UNBALANCE . . . 80
4.2 VOLTAGE UNBALANCE COMPENSATION . . . 81
4.2.1 Formulation . . . . 82
4.2.2 Study Case MG and VUC . . . . 85
4.3 FURTHER DEVELOPMENT . . . 89
4.3.1 MPC Based MGCC . . . . 90
4.3.2 Voltage Unbalance Correction . . . . 91
4.4 SIMULATION RESULTS . . . 94
4.5 A HIERACHICAL MPC-BASED MGCC WITH VOLTAGE UNBALANCE COMPENSATION CAPABILITY . . . 97
4.5.1 Economic Level Formulation . . . . 98
4.5.2 Load Sharing Level Formulation . . . 102
4.5.3 Simulation Results . . . 107
4.6 FINAL REMARKS . . . 113
5 QOE-AWARE DEMAND MANAGEMENT . . . 116
5.1 BRAZILIAN ENERGY SECTOR OVERVIEW . . . 116
5.1.1 Distributed Generation . . . 119 5.1.2 Energy Management . . . 120 5.2 QOE SURVEY . . . 120 5.2.1 Methodology . . . 120 5.2.2 Survey . . . 121 5.2.3 Data Availability . . . 123 5.2.4 Clustering . . . 123
5.2.5 Objective Questions Results . . . 124
5.2.6 Quantitative Questions Results . . . 129
5.2.7 A CQoE Curve for a General Shiftable Load . . . 132
5.2.8 A CQoE Curve for a General Curtailable Load . . . 135
5.3 QOE-AWARE MPC-BASED EMS . . . 136
5.3.1 Formulation . . . 137
5.3.1.1 DC Bus . . . 137
5.3.1.2 Photovoltaic Generation . . . 137
5.3.1.3 Battery Energy Storage System . . . 137
5.3.1.4 Interfacing Converter . . . 138
5.3.1.5 AC Bus . . . 139
5.3.1.6 Power Factor . . . 139
5.3.1.7 Battery Electric Vehicle Charger . . . 139
5.3.1.8 Air Conditioning . . . 141
5.3.1.9 Shiftable Load . . . 142
5.3.1.10 Curtailable Load . . . 144
5.3.1.11 Cost Function . . . 146
5.3.2 Study Case Smart House . . . 146
5.4 FINAL REMARKS . . . 157
BIBLIOGRAPHY . . . 162 APPENDIX A – QOE-AWARE DEMAND MANAGEMENT
21
1 INTRODUCTION
Non-renewable resources, such as diesel, coal, and gas, have been playing a major role in the traditional power generation. However, with a 2.5 % annual load growth, an unmatched gap is arising in between demand and conventional power generation (SEN; KUMAR, 2018). Along with the depletion of reserves of non-renewable resources, the environmental pollution resulting of the large usage of non-renewable resources have caused the power generation scenario to start shifting to more environmentally friendly energy resources (FAN et al., 2013). The development of cost-effective sources tailored to provide generation in smaller quantities, such as photovoltaic panels and microturbines, allowed the dissemination of distributed generation (DG), creating a new paradigm where the generation units are located near the consumers, offering support to the main sources (OLIVARES et al., 2014). Parallel to this, the advances in information and communications technologies have paved the road to smart grids: more reliable and flexible networks, integrating distributed generation and smart houses (FAN et al., 2013).
Regarded as the elementary units of a smart grid, microgrid (MG) has undergone vigorous research for more than one and a half-decade and is a technology brewed to face those ever-growing challenges. The MG paradigm is not only economical, resilient and reliable but also provides environmental benefits as compared to the existing utility networks because of the use of renewable energy resource (RES) in a distributed generation fashion. Microgrids can be classified as dc, ac or hybrid (ac/dc), regarding the nature of the transmission between each bus of the microgrid (SEN; KUMAR, 2018).
Provided that the MG operates under a centralized control scheme, a microgrid central controller (MGCC) takes care of the power flow between the main grid and the MG, optimizing the MG operational cost, deciding the operation mode, controlling the generation dispatch and energy storage management (LI; NEJABATKHAH, 2014). Loads, energy storages, renewable and non-renewable DGs are commanded by an MGCC which also manages the connection to the main grid. In particular, on hybrid MGs, there are at least a dc and an ac bus. Energy storages and renewable generation are usually connected to the dc buses, while loads and non-renewable generators are usually connected to ac buses. dc/ac converters are employed to interface dc and ac buses.
The MGCC sends commands to the local controllers (LCs) in each DG or dis-patchable load (LI; NEJABATKHAH, 2014). Concerning the implementation of the MGCC, the inherent complexity and multivariable characteristic of the system requires an advanced control approach. Model Predictive Controllers (MPCs) present them-selves as a well-accepted option in the literature (ADAMEK; ARNOLD; ANDERS-SON, 2014; FORTENBACHER et al., 2014; JABR; KARAKI; KORBANE, 2015; BRUNI;
Chapter 1. Introduction 22 CORDINER; MULONE; ROCCO, et al., 2015; BRUNI; CORDINER; MULONE; SIN-ISI, et al., 2015; DU et al., 2017; DALL’ANESE; BAKER; SUMMERS, 2017; DONGOL; FELDMANN; BOLLIN, 2018; MORSTYN et al., 2018; GARIFI et al., 2018; JIANG et al., 2019; GUO et al., 2019). MPCs are largely adopted in the industry due to their ability to treat constraints and multivariable systems naturally. In an MGCC it is also impor-tant that MPC strategies are flexible and accept different objective functions that may include cost and performance metrics of the MG.
Despite the well-known benefits provided by the arrival of MGs, they also provide a set of challenges, as they require complex control strategies to operate and present power quality and user comfort issues that must be addressed. In this work two of the operating aspects of an MG will be given special attention: voltage unbalance correction as a power quality aspect and a QoE-aware (Quality of Experience) approach on demand management.
Voltage unbalance is a power quality condition that arises due to the presence of unbalanced single-phase loads. The presence of voltage unbalance affects negatively a series of sensible equipment and, therefore, is undesirable. In a hybrid microgrid environment, the presence of distributed generators connected by converters to the ac side can be used to tackle the voltage unbalance, by unbalancing their output. That said, if there is a converter on each bus of the grid, each converter can solve the unbalance of its bus. However, if there are fewer converters than buses, then it is necessary to find a strategy to share the compensation effort between the converters to decrease the overall unbalance of the grid.
On the other hand, demand management comprehends a series of actions that aim to flatten the demand curve by the means of shifting and curtailing controllable loads. While this reduces the financial cost, it also produces a negative impact on the comfort of the users. To address demand management considering the effects on the users’ comfort, the usage of Quality of Experience (QoE) metrics presents itself as an approach that has been gaining increased attention in the literature.
Considering these issues, the present work aims to present some contributions to MPC-Based MGCC strategies, addressing both voltage unbalance compensation and QoE-aware demand management. To do so, this document is organized as follows. In the second chapter a brief literature review is presented, showing the state of art on MGCCs, voltage unbalance compensation on MGs and QoE-aware demand man-agement and also introducing fundamental concepts to the subsequent developments. In the third chapter some basic ideas on MPC-based MGCC are examined, as well as power flow concepts and a novel MGCC formulation based on active and apparent power. The fourth chapter delivers three techniques for voltage unbalance compen-sation within the scope of the MGCC, two of them based on the negative sequence equivalent circuit of the grid and the third one based on optimal power flow (OPF).
Chapter 1. Introduction 23 After that, the fifth chapter presents the results of a survey conducted in Florianópolis regarding QoE-aware demand management and further applies the QoE metrics lever-aged in this experiment to propose a QoE-aware demand management scheme within an MPC-based EMS. Lastly, the sixth chapter provides some final remarks and future works perspectives.
1.1 OBJECTIVES
The general and specific objectives are detailed below.
1.1.1 General Objective
This work aims to deploy contributions on MPC strategies for MGCCs, providing them with optimal voltage unbalance compensation and QoE-aware demand manage-ment capabilities.
1.1.2 Specific Objectives
• Formulate a two-layer MPC-based MGCC in terms of active and reactive power. • Formulate the voltage unbalance compensation effort sharing between
convert-ers as a convex optimization problem, guaranteeing the global optimality of the solution.
• Incorporate the voltage unbalance compensator to the MGCC.
• Obtain a QoE profile for home appliances that portray the local (Florianópolis) reality.
• Allow an MPC-based energy management system (EMS) to consider QoE when performing demand management actions.
The third and fifth specific objectives are the ultimate goals of this work and are the capstones of chapters four and five, respectively.
1.2 CONTRIBUTIONS
The present work encompasses some relevant results that are summarized below.
• A novel formulation for the MGCC formulation in terms of apparent and active power.
Chapter 1. Introduction 24 • A convex formulation for the voltage unbalance compensation effort sharing be-tween multiple converters on an MG environment, ensuring the global optimal solution of this problem.
• The integration of such voltage unbalance compensation in a two-layered MPC-based MGCC using an approximation of the optimal power flow.
• A survey on the acceptability of the intervention of an energy management system on the user energy consumption pattern.
• A set of experimental QoE curves leveraged from the survey data, fit for the usage of QoE-aware demand response policies aiming at the local reality.
• The inclusion of QoE-aware demand on an MPC-based EMS.
These contributions are fully detailed and discussed in the following chapters.
1.3 PUBLICATIONS
To disclose the contributions achieved during this work, some of the results have been already published in conferences proceedings and journals, and some others are currently in evaluation process, as follows:
• A Convex Formulation for Voltage Unbalance Compensation Problem on Hybrid Microgrids, (LUNA; MENDES; NORMEY-RICO, 2019a), has been published in Revista Principia, a national journal.
• A Convex Optimal Voltage Unbalance Compensator for Hybrid ac/dc Microgrids, (LUNA; MENDES; NORMEY-RICO, 2019b), has been presented as full paper at the Innovative Smart Grid Technologies Latin America 2019, an international IEEE Power & Energy Society conference.
• A Chance Constrained MPC-Based Microgrid Central Controller for Building-Sized Hybrid Microgrids, (LUNA; MENDES; NORMEY-RICO, 2019c), has been pre-sented as full paper at the Simpósio Brasileiro de Automação Inteligente 2019, a national conference promoted by the Sociedade Brasileira de Automática.
• Characterizing Quality of Experience for Demand Management in South Brazil, has been submitted in Energy, an international Elsevier journal.
25
2 LITERATURE REVIEW
In the last years, the penetration of DGs has been increasing at a steady pace. This brings a series of benefits but also several challenges that ultimately increase the complexity of the power system. Renewable sources suffer from intermittency, require energy storage to magnify their usefulness and make usage of interfacing converters. Along with DGs, controllable, shiftable and critical loads as well as a specified control architecture, compose the complete MG framework. The coordination of the MG is performed by the MGCC. It takes care of the power flow between the utility grid and the MG, cost optimization of the MG, deciding the mode of operation and islanding detection, controllable generation dispatch and demand management (SEN; KUMAR, 2018). In the following sections a brief review of the literature related to the main topics considered in this work is presented: MPC, as it is the adopted control technique, mixed linear dynamics (MLD) in order to address hybrid systems, MGCCs, as to lay out the state of art, voltage unbalance compensation and QoE-aware demand management, as those are relevant foci of the contributions delivered later on.
2.1 MODEL PREDICTIVE CONTROL
Concerning the implementation of the MGCC, Model Predictive Control (MPC) has been adopted in various works, due to its capabilities of dealing with constraints in multivariable systems and flexibility concerning the choice of different cost functions.
MPC control has been used for decades, now, as a powerful and straightforward technique, being one of the few advanced control techniques that has actually been largely used in the industry. Its widespread adoption can be credited to a myriad of factors: multivariable applications, feedback action, feedforward compensation, ability to integrate constraints on both manipulated and controlled variables, optimal control, and inherent dead-time compensation (NORMEY-RICO; CAMACHO, 2007).
MPC does not describe a specific strategy, rather a philosophy of control that encompasses a large family of control methods that share common ideas founded upon the concept of model-based prediction. The general MPC controller is composed of a process model and an optimizer. The controller solves an optimization problem within each sampling instant to compute an optimal control sequence, but only the first value is actually applied to the process, as the MPC will compute a new optimal sequence on the next sampling instant. The concept of a receding horizon is also quite central to MPC. The optimization is performed considering the predictions of future outputs in a defined time window, the prediction horizon. On each sampling instant, the optimizer finds the optimal control sequence over that horizon. Usually, the horizon size is kept constant, and, on each sampling instant, the prediction horizon will move one step on the time axis. Thus, only the first element of the computed control action in the horizon
Chapter 2. Literature Review 27 As the optimizes tries to minimize the cost function, this term will smooth the control actions calculated by the controller, as this term encompasses the desire to avoid jittery or too aggressive control actions. Furthermore, using the increment instead of the actual control allows the second term to be zero when the system reaches steady-state, also providing integral-like action to the control loop. The future control increments are computed from n, as at sample instant n the present output of the plant have already been measured, but the control action at that instant remains to be calculated, up to n + Nu,i– 1. Therefore the control horizon, i.e. the time window for which future control actions are planned, is Nu,i samples long. If Nu,i is adopted to be 1, the controller will have to set the manipulated variable to the steady-state value that drives the controlled variable to the desired set-point, thus causing the system to respond as fast as in open-loop. If larger Nu,i is chosen, then the controller have more freedom to deploy faster or slower responses, based on the weighing of the cost function.
The weights δi and λi are employed to tune a trade-off between fast set-point
tracking and smooth control. If λi was set to zero, the controller would use try to spend
as much energy on the i-th input as needed to drive the output to the reference in a single step. On the other hand, ifδi was set to zero, the controller would not move the
manipulate variables to reduce the tracking error of the i-th output. Therefore, choosing weights in between these two extremes, it is possible to find adequate compromise and settle to a desired controller behavior.
While (2) is a usual choice of cost function, the flexibility of a MPC strategy allows the designer to adopt other functions. For instance, it is also possible to provide targets for the states and for manipulated variables of the system:
J = Ny X i=1 N2,i X k =N1,i δi yi,ref(n + k) –yˆ i(n + k) 2 + Nx X i=1 N2,i X k =N1,i γi xi,ref(n + k) –xˆ i(n + k) 2 + Nc X i=1 NXu,i–1 k =0 αi ui,ref(n + k) – ui(n + k)2+ Nc X i=1 NXu,i–1 k =0 λi∆ui(n + k)2, (2)
where xi,ref is the state target and ui,ref is the manipulated variable target. γi and αi
are the respective weights.
Alternatively, a more economical approach can be used, were the weights rep-resent the financial cost of different control actions. In an MG context, for example, the cost function can consider the cost of buying energy from the utility grid, the price of fuel required to run a generator, the cost of starting up an equipment and penalties for disconnecting load.
The model of the process is used to produce a prediction of the future outputs of the process, but such prediction must comprehend some prediction correction strategy, that accounts for modeling errors, considering the measured output of the process to compute the errors. This provides feedback capacity to the MPC, allowing it to perform
Chapter 2. Literature Review 28 acceptably even if the model is not perfect. The model itself may be one of many possible representations, such as impulse response, step response, transfer function, state-space, fuzzy logic, artificial neural network or any other that may describe the behavior of a dynamical system. This prediction can be included implicitly, in such way that the control actions are the only decision variables of the problem, or they can be included explicitly in the constraints of the optimization problem.
If, for instance, a state space approach is chosen, then the model can be con-veyed to the problem by formulating it into the equality constraints of the problem, imposing the state equation:
ˆ
x(n + k ) = Ax(n + k – 1) + Bˆ 1u(n + k – 1) + B2w (n + k – 1),ˆ ∀k∈[1,N2], (3)
and the output equation:
ˆ
y (n + k ) = Cx(n + k ) + Dˆ 1u(n + k ) + D2w (n + k ),ˆ ∀k∈[1,N2], (4)
where A, B, C and D are the state space model. In such case, the predicted statesxˆ
and the predicted outputy are also decision variables of the problem. On a MG context,ˆ
the state equation can be used to portray the state of charge of energy storage systems and the output equation can convey power balances, with controllable generators being computed into the control vector u and the uncontrollable generators and the loading being accounted into the disturbance vector w.
Equality constraints can also be employed to enforce other strict behaviors, such as the usage of final state constraints, which aim to force the states of the system to reach a certain condition at the end of the prediction horizon:
ˆ
x(n + N2) = xf. (5)
Other operational limits of the system can be addressed by the MPC by having them being included as inequality constraints. For instance, value of the control action can be limited to avoid, for example saturation, by:
umin≤u(n + k )≤umax,∀k∈[1,N2], (6) the maximum increment can also be limited, to comply with slew rate limitations:
∆umin≤∆u(n + k )≤∆umax,∀k∈[1,N2], (7) the value of states and output can also be constrained to address engineering limits:
xmin≤ ˆx(n + k )≤xmax,∀k∈[1,N2], (8)
Chapter 2. Literature Review 29 Additionally, it is also possible to include more general constraints, for example, linear combinations of outputs and/or control inputs.
Then, the set of constraints and the cost function can be gathered to formulate the optimization problem solved by the controller on each sample time:
min
z J(z) (10)
s.t. g(z)≤0
h(z) = 0 (11)
where z∈ Rm is the decision variable vector, J(z), the objective or cost function which
is a scalar real-valued function J :Rm→ R, that is aimed to be minimized. g(z)≤0 are
the inequality constraints, which represent the operational limits of the system, such as saturation on manipulated variables, the slew rate of actuators and bounds for controlled variables, as previously discussed. While the most common constraints are linear ones, other non-linear constraints, such as quadratic ones, may also be used. h(z) = 0 are the equality constraints, which can be used to represent strict operational limits or, as mentioned before, to include static and dynamic relations of the model. The decision variable vector z is composed of the future control sequence and, for the discussed case, the future states of the system and even other variables, e.g., slack variables used to ensure feasibility of the optimization problem.
On each sample instant the controller will perform several tasks. The cycle starts by reading the outputs of the system. Then, given the current outputs, the controller solves the optimization problem, i.e., minimizes the cost function subject to the con-straints. This solution can be obtained by using one of several commercial solvers available today, depending on the class of the optimization problem the controller has to solve. The solution of the optimization problem provides the controller with the knowl-edge of the decision variables values that gives the optimal value of the cost function. Among this decision variables is the control action to be deployed on the current sam-ple instant, either given by its absolute value u(n), or its increment ∆u(n). Then, the controller updates the the manipulated variables, finishing the cycle and waits until the next samples instant.
A remarkable feature of MPC is that if the prediction is exact, i.e. the model describes perfectly the process, the output will follow the prediction and the planned control sequence will be followed in each subsequent sample instant. Otherwise, if the model is inexact or if there is a disturbance acting on the system, the predicted output will deviate from the actual output of the process. In that case, the planned control sequence will be altered on each sample instant. In either case, the MPC runs the prediction for the horizon and finds the optimal control sequence, in such way that the first control, the one that will be effectively fed to the processes will not cause undesired responses on the next time steps of the horizon.
Chapter 2. Literature Review 30 Another feature of the MPC is that, provided that prediction of the future dis-turbances w are available, the MPC can perform feed-forward action based on thatˆ
prediction, thus improving the performance of the control loop. On a MG context, the predictions of loading and renewable generation are used to support the optimal deci-sions of the MPC controller.
All things considered, MPC presents itself as an adequate approach to design MGCCs. With that in mind, specifics and a brief review are presented in the next sections.
2.1.1 Mixed Logical Dynamical Systems
The MG control presents a specific challenge concerning the coexistence of both continuous and binary variables. On that matter a remarkable development was achieved in (BEMPORAD; MORARI, 1999) where a framework for modeling and con-trolling mixed logical dynamical (MLD) systems, which are described by interdependent physical laws, logic rules, and operating constraints, was proposed. That work pre-sented a way to treat bilinearities between binary and continuous variables by adding a set of constraints and an auxiliary variable, as well as techniques for treating piece-wise linear dynamic systems, piece-wise linear output functions, discrete inputs, qualitative outputs, bilinear systems and finite state machines.
It takes from the work of (WILLIAMS, 1993) which had already presented the usage of auxiliary variables to treat bilinearities between two binary variables and between a binary and a continuous variables, and incorporated these to MLD systems.
A product of binary decision variables,δ1δ2 can be replaced by an auxiliaryδa,
and the usage of the following constraints will ensure thatδa=δ1δ2:
–δ1+δa≤0, (12)
–δ2+δa≤0, (13)
δ1+δ2–δa≤1. (14)
(15) The product δf (x), with δ being binary and f :Rn 7→ R can be replaced by an
auxiliary continuous variable z =δf (x) with the usage of the following constraints to implicitly force the equivalence:
z≤Mδ, (16)
z≥mδ, (17)
z≤f (x) – m(1 –δ), (18)
z≥f (x) – M(1 –δ), (19)
Chapter 2. Literature Review 31 with m and M being the minimum and maximum values of f (x), or, at least, a reasonable estimation of them.
As for MLD systems, they are described in (BEMPORAD; MORARI, 1999) as the class of systems that can be written as:
x(k + 1) = Ax(k ) + B1u(k ) + B2δ(k) + B3z(k ) (21) y (k ) = Cx(k ) + D1u(k ) + D2δ(k) + D3z(k ) (22) E2δ(k) + E3z(k )≤E1u(k ) + E4x(k ) + E5, (23) where x =hxc xl
i
is the state of the system, with continuous xc and binary xl compo-nents. y =
" yc yl
#
is the output vector, with continuous yc and binary yl components, and
u = "
uc ul #
is the command input, with continuous uc and binary ul commands. δ is an
auxiliary logical variable and z is a continuous variable. A, Bi, C, Di and Ei are constant real matrices.
In some cases, the control problem can be hybrid nonlinear, and this framework can be added to the MPC for transforming the problem into a mixed integer quadratic programming (MIQP) problem, which can be solved by commercial packages.
2.2 MICROGRID CENTRAL CONTROLLERS
Considering the complexity of the control problem posed by an MG, it is neces-sary to conduct a review of the state of art techniques, in which the developments in the next chapters are founded. This section presents some relevant works on the theme from the last few years.
In 2014, (MALYSZ; SIROUSPOUR; EMADI, 2014) proposed an online optimal energy management strategy for the operation of energy storage in grid-connected microgrids. The proposal is based on a mixed-integer-linear-program optimization for-mulated over a rolling horizon window, considering predictions of both renewable gen-eration and load profile. Performance objectives included electricity usage cost, battery operation costs, and utility-oriented objectives related to the peak demand and load smoothing. It also presented a robust counterpart formulation of the optimization prob-lem to handle uncertainty in the predictions. The study neglected reactive power in the problem formulation as well as power factor, the ratio between active and apparent power, and did not account for voltage unbalance issues. No demand response policy was adopted.
In the same year, the influence of storage capacity and prediction horizon on the cost-optimal multi-energy supply of a single-family house and a network of three interconnected houses, discussing similarities and differences between the two cases
Chapter 2. Literature Review 32 is examined in (ADAMEK; ARNOLD; ANDERSSON, 2014). The energy hub concept was used to model the conversion and storage of electricity, gas, and heat and an MPC controller was applied to determine the optimal cost strategy of the available conversion and storage. This work neglected reactive power in the problem formulation as well as power factor and did not account for voltage unbalance issues nor any load demand response policy was adopted.
Focusing more specifically in photovoltaic (PV) generation, (DALL’ANESE; DHO-PLE; GIANNAKIS, 2014) developed, a systematic method for determining the active and reactive power setpoints for PV inverters in residential systems with the objective of optimizing the operation of the distribution feeder and ensuring voltage regulation, addressing the increased penetration of roof-top PV systems effects on power quality and reliability of the system.
An MPC approach for power dispatch of a large number of power system units dispersed both in distribution grids and transmission networks is presented in (FORTEN-BACHER et al., 2014). The studied network including Renewable Energy sources (RES), conventional generation sources, flexible loads, and storage devices, which are modeled using the Power Nodes on a centralized optimal power dispatch strategy with a combined ac Optimal Power Flow (ac-OPF) explicitly accounting for grid constraints. The problem is divided into stages where, on the first stage a dc power-flow model is adopted, neglecting voltage magnitude constraints and reactive power injection. On the second stage a subsequent ac-OPF is computed to obtain full grid state information. To obtain a degree of freedom, controllable generators may vary their power output by 10% up/down from their planned set-points of the first-stage dispatch. The study neglected power factor issues and did not account for voltage unbalance compensation nor treated demand management.
A sparse formulation and solution for the affinely adjustable robust counterpart (AARC) of the multi-period OPF problem was presented by (JABR; KARAKI; KORBANE, 2015) in 2015. The AARC aims at operating a storage portfolio via receding horizon con-trol. It computes the optimal base-point conventional generation and storage schedule for the forecast load and renewable generation, together with the constrained partici-pation factors that dictate how conventional generation and storage adjust to maintain feasible operation whenever the renewables deviate from their forecast. The work used a dc approximation for the power flow, neglecting reactive power and power factor as well as voltage unbalance compensation. No demand management policy was used.
The authors of (BRUNI; CORDINER; MULONE; ROCCO, et al., 2015) proposed an MPC algorithm, based on weather forecasts, to perform power management in a domestic off-grid system. The proposed solution aimed to minimize energy costs while maintaining the optimal environmental comfort in the case study house, thus optimizing the use of renewable sources and energy storage. It was considered a hybrid MG, but
Chapter 2. Literature Review 33 the model only accounted for the dc bus behavior. Thermal comfort was considered. In the same year, those authors published (BRUNI; CORDINER; MULONE; SINISI, et al., 2015) where they examined MPC control for domestic microgrid applications, assuming real weather forecast as input data. Deterministic and Stochastic Model Predictive Control concepts were applied to the system and the results have been compared showing the advantages of a stochastic approach given forecast uncertainties. The work considered a hybrid MG, but the model only accounted for the dc bus behavior. Thermal comfort was included in the problem.
An MPC strategy was employed by (DU et al., 2017) to optimize real-time micro-grid power dispatch to counteract the unfavorable influences of uncertain factors in an energy price varying scenario and the possibility of using a flexible cost function in the optimization problem they solve at each sample time.
Still, in 2017, (DALL’ANESE; BAKER; SUMMERS, 2017) presented an MPC strategy, based on ac optimal power flow, aiming to optimize system-level performance objectives while dealing with uncertainty in both renewable generation and load profile. The system is modeled in terms of active and reactive power. The authors of this text didn’t consider limitations on the power factor for the power consumed from or sold to the main grid nor took into account the voltage unbalance compensation. Furthermore, the study does not use any demand response technique.
A stochastic optimization framework for day-ahead (DA) energy management of a renewable-based isolated rural microgrid was proposed in (GHASEMI; ENAYATZARE, 2018). Non-dispatchable distributed generations (DGs) including wind and photovoltaic (PV) power plants have been operated by the microgrid to meet consumers’ demand. The main challenge in this condition is to keep the balance between generation and de-mand at all times. To cope with this challenge, a pumped-storage unit and an incentive-based demand response program has been used in this work. Moreover, the accurate model of pumped-storage unit, responsive demand and distribution network and also the inherent uncertainty of wind and PV power generation have been considered in this paper. Finally, the effectiveness of the proposed optimization framework has been eval-uated through extensive numerical studies. The results show that the pumped-storage unit optimal scheduling and demand response implementation, significantly improve economic and technical performance indexes.
Also in 2018, (DONGOL; FELDMANN; BOLLIN, 2018) an MPC scheme was de-veloped for a domestic microgrid to manage energy storage and perform peak shaving. This work only considered active power in their formulation. The adopted prediction correction strategy was performing a linear interpolation between the last measured value and the hour ahead prediction.
A convex MPC strategy for dynamic optimal power flow between energy storage systems distributed in an ac microgrid was presented by (MORSTYN et al., 2018).
Chapter 2. Literature Review 34 The proposed control strategy formulates the problem based on a linear d–q reference frame voltage-current model using linearized power flow approximations, allowing the optimal power flows to be solved as a convex optimization problem. The work did not consider power factor limitation nor tackled voltage unbalance compensation and no demand management technique was employed.
Still in 2018 (GARIFI et al., 2018) presented a chance-constrained MPC algo-rithm for demand response in a home energy management system (HEMS). The HEMS optimally schedules controllable appliances given user preferences such as thermal comfort and energy cost sensitivity, availability of renewable generation and state of battery systems. The proposed control architecture ensures both the demand response (DR) event and indoor thermal comfort are satisfied under uncertainty in available PV generation and outdoor temperature forecast. This work neglected reactive power, and only accounted for HVac appliances as controllable loads.
Early in 2019 (JIANG et al., 2019) proposed a stochastic receding horizon con-trol method based on modified stochastic MPC framework to integrate high penetration of distributed generation with uncertainties due to the renewable sources. Multiple con-trollable resources are jointly optimized while ensuring relevant security restrictions. A simplified Z-bus sensitivity for active distribution networks is developed for estimation of system nonlinearity and is combined with the sequential linear programming to iter-atively derive the linear state-space model for compensation of cumulative modeling errors. Furthermore, the voltage limitations are reformulated as chance constraints to in-dicate the probabilistic reliability index of voltage qualification rate and achieve tradeoffs between cost reduction and voltage regulation. The affine-disturbance feedback control policy is leveraged here to enforce closed-loop control performance and analytically transforms intractable chance constraints into second-order cone constraints. This work does not consider dispatchable renewable generations nor demand management.
Later in 2019, (GUO et al., 2019) presented an MPC-based coordinated voltage control scheme for distribution networks with high penetration of distributed genera-tion and energy storage. In this scheme, the DG units, energy storage devices and on-load tap changer (OLTC) were optimally coordinated to maintain all bus voltages in the network within a permissible range. To better coordinate the economical operation and voltage regulation, two control modes were designed according to the operating conditions. The first one, called preventive mode, allowed the DG units to operate in the maximum power point tracking (MPPT) mode, while the state of charge of energy storage system units and power outputs of DG and energy storage systems (ESS) units were optimized while maintaining the voltages within the feasible range. If a voltage violation occurred the control started to act in corrective mode, where active power curtailment of DG units was also used to correct the severe voltage deviations. The grid was modeled using voltage sensitivity coefficients for the power injections and tap
Chapter 2. Literature Review 35 changes, which were updated in real-time using an analytical sensitivity calculation method to improve the computation efficiency. Although the strategy was proposed for distribution networks it could be easily adapted to ac and hybrid microgrids. Nonethe-less, this work does not take into account voltage unbalance or power factor issues.
2.3 OPTIMAL POWER FLOW
Optimal power flow (OPF) is a tool for economic planning and operation of power grids, which poses the dispatch of generation units and, possibly, other equipment, as decision variables in an optimization problem, aiming to minimize some objective func-tion, usually energy loss or generation cost (JABR, 2008). The power flow formulation is non-convex and has been conducted using iterative methods such as Newton-Raphson or Backward-Foward Sweep. In spite of that, the solution of the OPF requires the usage of some convex relaxation or the adoption of some metaheuristic approach.
Concerning convex formulations for the OPF problem, in 2008 an extended conic quadratic (ECQ) formulation was proposed in (JABR, 2008). The paper delivered a study of the implementation of the load flow equations format in an optimal power flow which accounts for control devices such as tap-changing transformers, phase-shifting transformers, and unified power flow controllers. The ECQ-OPF formulation was employed to solve the economic dispatch and active power loss minimization problems. Numerical testing was used to validate the proposed approach by comparing solution methods and results of standard test systems.
In 2015, (DHOPLE; GUGGILAM; CHEN, 2015) explored solutions to linearized power flow equations with bus voltage phasors represented in rectangular coordinates. The idea was to solve for complex-valued perturbations around a nominal voltage pro-file from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. Additionally, the work proves that, for lossless networks, the voltage profile where the real part of the perturbation is suppressed, satis-fies active-power balance in the original nonlinear system of equations. This result, then, motivates the development of approximate solutions that improve over conventional dc power-flow approximations, since the model includes ZIP loads, i.e. loads composed by terms of constant impedance, constant current and constant power. For distribution networks that only contain ZIP loads in addition to a slack bus, a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active and reactive-power injections is found.
Further developing the conic convex relaxation, (FERNANDES; PAUCAR; SAAVE-DRA, 2017) proposed a solution method for the optimal power flow (OPF) problem, including the synchronous generator capability curve (SGCC) constraints. If the syn-chronous generator operational limits are neglected, the OPF solution may be po-tentially not applicable in real scenarios, taking the machine to operate with winding
Chapter 2. Literature Review 36 currents above acceptable values. The SGCC used in this research included current and power limits allowed in the generator, preventing the machine operation against overheating and excessive mechanical efforts. The OPF was formulated over a second-order cone programming (SOCP) approach from convex relaxation techniques, aiming the active power generators cost minimization, subject to the electrical transmission network constraints. SGCC used has a convex form, which allows the convex program-ming method application, with no convexification need for the optimization model. The proposed method was applied to IEEE 30-bus test system. Simulation results demon-strated the applicability and good performance of the proposed method so that solutions do not violate the constraints imposed by the actual operational limits of the generators.
The work of (DALL’ANESE; BAKER; SUMMERS, 2017) used a chance-constrained ac OPF formulation, where probabilistic constraints were used to enforce voltage regula-tion with a prescribed probability. Linear approximaregula-tions of the ac power-flow equaregula-tions, as well as convex approximations of the chance constraints, are employed to grant global optimality. A distributed solver was developed to strategically distribute the solu-tion of the optimizasolu-tion problems across utility and customers.
The study present in (FRANCO; OCHOA; ROMERO, 2017) proposed a novel quadratic programming formulation and compared it against the non-linear, quadrati-cally constrained, and linearized approaches. Two cases were carried out to assess their performance: management of distributed generation units to maximize renewable energy harvesting (continuous control variables) and control of capacitors to minimize energy losses (discrete control variables).
Also in 2018, a study by (CHEN; XIANG; LI, 2018) proposed an OPF model con-sidering current margins in radial networks. The objective function of this OPF model has a term of current margins of the line beside the traditional transmission losses and generations costs, which contributes to the thermal stability margins of power systems. The model was a reformulated bus injection model that aims to have clear physical meaning. Second-order cone program (SOCP) relaxations for the proposed OPF were also adopted here, followed by the over-satisfaction condition guaranteeing the exact-ness of the SOCP relaxations. A simple 6-node case and several IEEE benchmark systems were studied to illustrate the efficiency of the developed results.
Early in 2019 (SERNA-SUÁREZ et al., 2019) provided a solution to optimally exploit distributed energy resource (DER) without compromising the network reliability, a novel algorithm to solve the 3-phase OPF as a sequence of convex quadratically constrained quadratic program (QCQP). Results show that the solution had a lower voltage unbalance and computation time than its non-linear counterpart.
In the same year (ERGUN et al., 2019), on a work that focuses on the pres-ence of high voltage direct current (HVDC) system, developed an optimal power flow model for ac and dc grids. A variety of formulations, from non-linear to convexified to
lin-Chapter 2. Literature Review 38 Power electronics converters and adjustable speed drives also suffer from the presence of voltage unbalance (ACHARYA et al., 2019).
2.4.1 Review on Voltage Unbalance Compensation
In order to tackle the voltage unbalance several strategies have been proposed in the literature.
The ideal approach would be simply redistributing the loads among the phases in an online fashion. An early proposal suggested a realization of this by rearranging and balancing phases in the primary side of the distribution transformer, obtaining a reduction in voltage unbalance and loss reduction, using a genetic algorithm to find the optimal phase arrangement (TSAI-HSIANG CHEN; JENG-TYAN CHERNG, 1999). This constitutes a design technique, to avoid future unbalance, but has no dynamic impact on the operation of the grid. Another option found in the literature is switching loads among phases using static transfer switches on the residential environment instead (SHAHNIA; WOLFS; GHOSH, 2014), which would require the installation of additional switching devices to perform the unbalance correction.
A set of less explicit approximations of the ideal solution relies on demand-side response techniques, using, for example, electric vehicles (MARTINENAS; KNEZOVI ´C; MARINELLI, 2017) or thermostatically controlled loads (ACHARYA et al., 2019), even though demand-side based strategies may impact on user comfort.
Departing from the ideal solution and delving into active filters, both series and parallel active filters have been used operating in series with the network, injecting negative sequence voltage, or operating in parallel with the network, injecting negative sequence current (MENG; TANG, et al., 2014).
In a microgrid environment, the presence of DG can be exploited to address voltage unbalance issues. In that case, each DG unbalances its output to mitigate the unbalance on the loads. The multiple DGs present on the system can share the compensation effort aiming to achieve the reduction of voltage unbalance under various strategies, several of them including a centralized control on a secondary level (MENG; GUERRERO, 2017).
An early proposal, from 2012, developed a secondary control approach for volt-age unbalance compensation where the MGCC receives measurements of positive and negative sequence voltages and uses a PI controller to calculate the correction negative sequence voltage set-point for each converter (SAVAGHEBI et al., 2011). A more elaborate scheme was presented in (MENG; TANG, et al., 2014), proposing a tertiary control strategy for unbalance compensation. Based on the studied case of (SAVAGHEBI et al., 2011), the authors proposed a new topology adding a third level which employs a genetic algorithm (GA) to calculate optimal weights for the set-points found by the secondary level, to improve the division of correction effort between the
