PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA ELÉTRICA
INSTITUTO DE ELETRÔNICA DE POTÊNCIA
Thiago Antonio Pereira
COMPENSATION OF THE DOUBLE-LINE FREQUENCY VOLTAGE RIPPLE ON SINGLE-PHASE TWO-STAGE PHOTOVOLTAIC
MICROINVERTER
Florianópolis 2018
COMPENSATION OF THE DOUBLE-LINE FREQUENCY VOLTAGE RIPPLE ON SINGLE-PHASE TWO-STAGE PHOTOVOLTAIC
MICROINVERTER
Dissertação de Mestrado submetida ao Programa de Pós-graduação em Engenharia Elétrica da Universidade Federal de Santa Catarina para obtenção do grau de Mestre em Engenharia Elétrica.
Supervisor: Prof. Roberto Francisco
Coelho, Dr.
Co-supervisor: Prof. Denizar Cruz
Martins, Dr.
Florianópolis 2018
Catalogação na fonte pela Biblioteca Universitária da Universidade Federal de Santa Catarina.
Thiago Antonio Pereira
Compensation of the double-line frequency voltage ripple on single-phase two-stage Photovoltaic Microinverter/ Thiago Antonio Pereira. – Florianópolis, SC – Brasil, 2018.
223 p.
Supervisor: Prof. Roberto Francisco Coelho, Dr.
Dissertação (Mestrado) – Universidade Federal de Santa Catarina – UFSC Programa de Pós–Graduação em Engenharia Elétrica – PGEEL
Instituto de Eletrônica de Potência - INEP, 2018.
1. Double-line frequency. 2. Voltage ripple. 3. Power decoupling. 4. dc Bus voltage. 5. PV Microinverter. I. Roberto Francisco Coelho. II. Universidade Federal de Santa Catarina. III. Programa de Pós-Graduação em Engenharia Elétrica. IV. Compensation of the Double-Line Frequency Voltage Ripple on Single-Phase Two-Stage Photovoltaic Microinverter
COMPENSATION OF THE DOUBLE-LINE FREQUENCY VOLTAGE RIPPLE ON SINGLE-PHASE TWO-STAGE PHOTOVOLTAIC
MICROINVERTER
Esta dissertação foi julgada adequada para a obtenção do Título de Mestre, Área de Concentração em Eletrônica de Potência e Aciona-mentos Elétricos, e aprovada em sua forma final pelo programa de Pós-graduação em Engenharia Elétrica.
Florianópolis, 5 de dezembro 2018.
Prof. Bartolomeu Ferreira Uchoa-Filho, Dr.
Coordenador do Programa de Pós–Graduação em Engenharia Elétrica
Banca Examinadora:
Prof. Roberto Francisco Coelho, Dr.
Supervisor
Prof. Denizar Cruz Martins, Dr.
Co-supervisor
Prof. Carlos Henrique Illa Font, Dr.
Universidade Tecnológica Federal do Paraná
Prof. Telles Brunelli Lazzarin, Dr.
Aos meus pais e irmãos pelo apoio e incentivo. À minha esposa pelo carinho e compreensão nos momentos de ausência durante o mestrado, sobretudo na parte final da escrita da dissertação, e tam-bém pelo seu apoio incansável nos momentos de dificuldades. A todos os meus familiares e amigos que de alguma forma me incentivaram e apoiaram. Muito obrigado, amo vocês. Ao professor Denizar Cruz Martins pela confiança e apoio, que em 2014 me concedeu uma bolsa PIBIT, permitindo eu ingressar no INEP e, assim, dá início a essa incrível trajetória dentro da Eletrônica de Potência. Ao professor Roberto Francisco Coelho pela orientação, motivação, paciência, confiança e sabedoria transmitida. Esteve sempre disposto a colobo-rar no meu aprendizado e nas dificuldades impostas pelo trabalho. Agradeço também, pelas incansáveis correções e sugestões, sem elas nada disso seria possível. A todos os demais professores do INEP pelo convívio e conhecimentos repassados. Aos membros da banca pelas correções e sugestões, as quais contribuíram na melhoria do trabalho. Aos técnicos Antônio Pacheco e Luiz Coelho pelo auxílio e suporte técnico. Ao secretário Diogo Duarte pelo excelente trabalho em manter o laboratório sempre organizado e em funcionamento. Aos amigos de laboratório Andreas Mattos, Diego Morschbacher, Diogo Kenski, Francisco José Viglus, Gustavo Knabben, Lenon Schmitz, Luis Juarez Camurça e Odair José Custódio pela ajuda e parceria. Por fim, agradeço ao povo brasileiro, que permitem a continuação do ensino público e da pesquisa.
they tell us that dragons exist, but because they tell us that dragons can be beaten.” G.K. Chesterson
Introdução
Os inversores (também conhecidos por conversores cc-ca) são os elementos chave para os sistemas de energia conectados à rede. A principal função destes conversores é conectar os módulos fotovol-taico à rede elétrica da concessionária, convertendo a corrente cc gerada pelo módulo fotovoltaico em uma corrente ca sincronizada com a rede. Por esta razão, estes inversores são nomeados como Inversores Fotovoltaicos, cuja estrutura pode ser classificada em cinco grupos distintos: Inversores Centrais; Mini-Inversor Central; Inversor Multistring; Inversor String e Microinversor.
Geralmente, os Microinversores Fotovoltaicos são designados para processar a corrente cc gerada por apenas um módulo fotovoltaico e fornecer à rede elétrica monofásica. Desse modo, os Microinversores estão se tornando uma nova tendência em sistemas de geração de energia fotovoltaica devido a suas inúmeras vantagens, as quais se destacam: maior eficiência do sistema, menores custos de instalação, operação “Plug-and-Play”, maior modularidade e flexibilidade. Além disso, por meio deste tipo de estrutura é possível eliminar as perdas por incompatibilidade entre módulos fotovoltaicos, uma vez que ocorre o ajuste adequado entre o módulo fotovoltaico e o Microin-versor por meio de um MPPT (Maximum Power Point Tracking) individual. Em contrapartida, o Microinversor deve proporcionar um ganho estático entre 10 e 20 para gerar o barramento de tensão cc, dado que a tensão nos terminais do módulo fotovoltaico é
significati-vemente inferior ao valor de pico da rede elétrica. Assim sendo, tal característica pode ser obtida por meio de conversores de alto ganho, o que pode reduzir a eficiência geral e aumentar o custo por watt, devido à complexidade envolvida nestes tipos de conversores cc-cc. Um microinversor fotovoltaico é composto pelos conversores de ener-gia, sistema de refrigeração, controlador, fonte de alimentação auxilar para a parte lógica e de controle, filtro de EMI, componentes auxilia-res como: relé de desconexão, fusíveis e dispositivos de comunicação. Sendo assim, os Microinversores podem ser classificados em duas estruturas, as quais são denominadas por: estágio único (contém apenas o conversor cc-ca para realizar a interface módulo-rede) e de dois estágios (contém um conversor cc-cc, um barramento capacitivo e um conversor cc-ca para realizar a interface módulo-rede) . Atualmente, entre as estruturas supracitadas, o Microinversor de dois estágios ganhou mais atenção e espaço na indústria. Consequen-temente está se tornando uma tendência comercial em virtude do desacoplamento parcial da potência ca executada pelo barramento capacitivo, Cbus. Esse recurso implica em uma maior confiabilidade
quando comparado com a estrutura de estágio único, que possui apenas o capacitor em paralelo com o módulo fotovoltaico, Cpv.
Con-tudo, independentemente da estrutura de processamento de energia, o desacoplamento de energia é tipicamente realizado por meio de um capacitor eletrolítico que é instalado em um dos dois, ou em ambos, os barramentos cc para compensar as flutuações de tensão inerentes da conversão cc-ca. Entretanto, esses capacitores têm a desvantagem de possuir uma vida útil limitada, a qual é inferior ao dos componentes contidos no microinversor, especialmente sob alta temperatura. Desta forma, várias técnicas de desacoplamento de potência foram desenvolvidas na literatura com o intuito de reduzir a capacitância necessária, de modo que os capacitores eletrolíticos possam ser substítuidos por capacitores de filme. Diferentemente dos eletrolíticos, os capacitores de filme apresentam uma vida útil muito superior sem comprometer a função principal que é desacoplar a diferença de potência entre o módulo fotovoltaico e a rede.
O objetivo desta dissertação de mestrado é analisar, desenvolver, implementar e avaliar um sistema de desacoplamento de potência ativo a ser integrado no barramento cc de um Microinversor Foto-voltaico de dois estágios. Este sistema terá a função de deslocar a ondulação de potência do capacitor de barramento principal, Cbus
para um capacitor de desacoplamento de tamanho pequeno loca-lizado na célula de desacoplamento de potência, Cf. Em outras
palavras, a ondulação de tensão é transferida para um segundo capa-citor que não possui restrições quanto a amplitude da ondulação de tensão. Enquanto, que a tensão do barramento principal se mantém praticamente constante.
Os resultados são verificados por meio de simulações e resultados experimentais extraídos diretamente dos protótipos desenvolvidos. As principais contribuições da dissertação são descritas abaixo.
• Análise detalhada do fluxo de potência no Microinversor PV conectado à rede contendo formas de onda não senoidais, de modo que uma expressão analítica que define a ondulação de tensão no barramento cc é determinada em termos da Série de Fourier da tensão e corrente da rede;
• Concepção de uma estratégia de controle aplicada a um con-versor cc-cc bidirecional para realizar o desacoplamento de potência ativa no barramento cc de um Microinversor PV de dois estágios;
• Integração da célula de desacoplamento de potência a um Microinversor conectado à rede, composto por um conversor de alto-ganho e um conversor cc-ca bidirecional baseado na modulação senoidal de 2 níveis (SPWM) e na topologia ponte-completa.
Metodologia
Em aplicações monofásicas conectadas à rede, o fluxo de energia do módulo fotovoltaico para a rede é variável no tempo pgrid(t),
enquanto que a potência extraída do módulo fotovoltaico, Ppv, deve
ser constante, a fim de maximizar a geração de energia por parte do sistema fotovoltaico. Por consequência, surge uma pulsação de potência decorrente desta diferença entre a potência instântanea de entrada, ppv(t), e a potência instântanea entregue à rede elétrica,
pgrid(t). Sendo assim, é necessário inserir um elemento
armazena-dor de energia no barramento cc, entre o módulo fotovoltaico e a rede, capaz de equilibrar este desbalanço de potência por meio do desacoplamento de potência. O desacoplamento de potência consiste em realizar alternadamente o armazenamento da parcela excedente de energia que não é absorvida pela rede, ppv(t) > pgrid(t), e pela
injeção da parcela demandada pela rede ppv(t) < pgrid(t), a qual o
módulo não consegue suprir. Como resultado, surge uma ondulação de tensão no barramento cc como consequência da troca periódica de energia entre o módulo e a rede. Dessa forma, a fim de reduzir essa ondulação e aumentar a efetividade do desacoplamento de potência, utiliza-se grandes elementos armazenadores de energia, dado que estas oscilações de tensão no módulo fotovoltaico degradam a perfor-mance do rastreamento do ponto de máxima potência e a corrente injetada na rede.
Tipicamente, capacitores eletrolíticos são empregados no barramento cc para realizar o desacoplamento de potência passivo. Contudo, conforme mencionado anteriormente, tais capacitores apresentam uma vida útil limitada, na ordem de 1000 a 7000 horas para 105◦C. Assim sendo, o uso de capacitores eletrolíticos não é uma boa opção para processamento de energia fotovoltaica, pois deseja-se que os Microinversores tenham elevada vida útil e confiabilidade.
Com o intuito de substituir os capacitores eletrolíticos por capacitors de filme, diversas estratégias de desacoplamento de potência ativa foram propostas na literatura, de modo a deslocar a ondulação
com tamanho relativamente menor e vida útil superior, tal como é oferecido pelos capacitores de filme ou cerâmicos. Este estágio de desacoplamento de potência pode ser entendido como um capacitor virtual, cuja energia deve ser alternadamente armazenada e liberada dentro de um quarto do período da rede (ou quatro vezes a frequência da rede).
Resultados e Discussão
A partir dos resultados obtidos experimentalmete, pode se concluir que a capacitância do barramento cc foi reduzida em 6,5 vezes em comparação com a quantidade requerida pelo método convencional por meio do desacoplamento de potência passivo, que é baseado em capacitores eletrolíticos. A redução desta capacitância proporcionou um aumento na densidade de potência do conversor, eliminando a necessidade de usar capacitores grandes e volumosos associados em série e/ou em paralelo. Com efeito, a confiabilidade do conversor também é afetada por essa redução no valor da capacitância, visto que os capacitores eletrolíticos tipicamente usados nestas aplicações podem ser substiuídos por capacitores de filme que têm a vida útil muito maior.
Ao mesmo tempo, pode ser provado que o método de desacoplamento de potência ativa é viável, permitindo minimizar grande parte da on-dulação de tensão do barramento cc (reduzindo de ∆VCb= 31 V para
∆VCb = 5 V), e transferindo-o para outros componentes passivos
localizados na célula de desacoplamento de potência, sem restrição quanto ao valor de ondulação.
Considerações Finais
A seguinte dissertação de mestrado é dividida em seis capítulos. O primeiro capítulo começa a introdução do dissertação. O segundo capítulo introduz o princípio de desacoplamento de potência por
meio de uma análise do fluxo de potência em um Microinversor Fotovoltaico contendo formas de onda não-senoidais. O mesmo ca-pítulo apresenta as estratégias e topologias de desacoplamento de potência para reduzir a ondulação da tensão do barramento CC. O terceiro capítulo apresenta a análise, projeto, controle e avaliação de cada etapa que compõe o Microinversor Fotovoltaico: filtro de saída para interface com a rede; conversor cc-ca e por último, o conversor cc-cc. O quarto capítulo apresenta a análise, projeto, modelagem e controle da célula de desacoplamento de potência. O quinto capítulo exibiu a realização do hardware e a verificação experimental. Final-mente, o sexto capítulo conclui a dissertação mestrado com algumas perspectivas e trabalhos futuros.
Por fim, os objetivos propostos para esta dissertação podem ser considerados alcançados, de modo que importantes melhorias nesta linha de pesquisa foram apontadas ao longo do texto e certamente permitirão novos desafios técnicos e científicos a serem estudados e pesquisados.
Em sistemas de conversão de energia conectados à rede elétrica monofásica é comum o uso de capacitores eletrolíticos para lidar com a ondulação de potência de baixa frequência. No entanto, tais capacitores apresentam vida útil limitada. Baseado neste fato, essa dissertação propõe a aplicação de uma célula ativa de desacopla-mento de potência conectada ao barradesacopla-mento cc de um microinversor fotovoltaico de dois estágios, operando como um buffer de energia. O intuito da célula de desacoplamento de potência é deslocar a ondulação de potência do barramento cc para um capacitor de desa-coplamento, cuja restrição de ondulação de tensão é muito menor do que a do barramento principal, tornando possível a utilização de capacitores de baixa capacitância e elevada vida útil. A disser-tação apresenta um procedimento de projeto e dimensionamento da célula de desacoplamento de potência e uma nova estrutura de controle para atender a todos os objetivos supracitados. Resultados experimentais obtidos a partir do protótipo de um microinversor fotovoltaico com célula de desacoplamento de potência validam o desempenho do sistema como um todo.
Palavras-chaves: Dobro da frequência da rede, Ondulação de
ten-são, Desacoplamento de potência, Barramento de tensão cc e Mi-croinversor FV.
In power conversion systems connected to the single-phase power grid it is usual the utilization of electrolytic capacitors to cope with low-frequency power ripple. However, such capacitors have a limited lifetime. Thereby, this master’s thesis proposes the application of an active power decoupling cell connected to the dc bus of a two-stage photovoltaic microinverter, operating as a power buffer. The purpose of the power decoupling cell is to shift the power ripple from the dc bus to a decoupling capacitor, whose voltage ripple may oscillate more than the voltage of the main bus, allowing the use of low capacitance and extended lifetime capacitors. Thus, the master’s thesis presents a procedure to design the power decoupling cell and a new control structure to meet all the aforementioned objectives. Experimental results obtained from the prototype of a photovoltaic microinverter with power decoupling cell validate the performance of the entire system.
Key-words: Double-line frequency, Voltage ripple, Power
Figure 1.1 – PV Microinverter architectures: (a) Single-stage, (b) Two-stage. . . 46 Figure 1.2 – Performance comparisons of the three main types
(MLC, MPPF and AL) of capacitors for power decoupling. . . 48 Figure 1.3 – Power Decoupling Cell (PDC) connected to the
dc bus voltage of a two-stage PV Microinverter. . 49 Figure 2.1 – A bidirectional single-phase dc-ac converter
per-forming the interface between a PV module and the grid. . . 52 Figure 2.2 – Influence of power terms Pav, pac1(t) and pac2(t)
in the energy flow of a system bidirectional. . . . 56 Figure 2.3 – Voltage, current and instantaneous power in a
hypothetical system for three different cases. . . 57 Figure 2.4 – Power flow in a PV Microinverter connected to
the grid, where: (a) is the power generated by the PV module; (b) is the power decoupled in energy storage element and (c) is the power delivered to the grid. . . 59
Figure 2.5 – (a) Power flow at dc bus voltage considering the capacitor as energy storage element Cbusand
wave-forms of a bidirectional single-phase PV Microin-verter: (b) instantaneous grid power pgrid and
constant dc PV power Ppv; (c) and energy storage
capacitor voltage vCb which increases when pgrid
exceeds Ppv and decreases when pgridis less than
Ppv. . . 60
Figure 2.6 – Approximation of the PV module and dc-dc con-verter employing a constant current source of am-plitude equal to Idc. . . 61
Figure 2.7 – Equivalent circuit of the PV Microinverter after replacing the PV module and dc-dc converter by the constant current source Idc. . . 61
Figure 2.8 – Nonsinusoidal waveform composed by the har-monic content listed in Table 2.2 superimposed to a sinusoidal waveform sin(ω0t). . . . 64
Figure 2.9 – Single-phase dc-ac converter connected to the grid (a) and low-frequency waveform. . . 67 Figure 2.10–Comparison between the voltage ripple ˜vCb across
the bus capacitor Cbus obtained from equation
(2.30) (generic equation) and (2.37) (simplified equation) in order to show the similarity of both waveforms after simplification of (2.30). . . 70 Figure 2.11–Behavior of the peak-to-peak value of bus voltage,
∆VCb, in function of the power Ppv and
capaci-tance Cbus. . . 72
Figure 2.12–Effects of the low-frequency ripple in the PV Mi-croinverter. . . 73 Figure 2.13–Overview of common passive power decoupling
cell connected in parallel to the dc bus voltage: (a) capacitor and (b) LC resonant filter tuned to
the peak-to-peak value of bus voltage ∆VCb. . . . 75
Figure 2.15–Behavior of the capacitance,Cbus, in function of
the bus voltage VCb and the peak-to-peak value
of bus voltage ∆VCb. Being that for 420 V the
capacitance is equal to 400 µF and for 520 V the capacitance decreases to 320 µF. . . . 76 Figure 2.16–Overview of common Active Power Decoupling
topologies connected in parallel/series to the dc bus voltage: (a) buck; (b) boost; (c) buck-boot; (d) symmetrical half-bridge (Capacitor-split); (e) and (f) half-bridge; (g) half-bridge with an inductor as energy storage element and (h) half-bridge for connection series with de bus capacitor. . . 78 Figure 2.17–Categorization of power decoupling circuit
topolo-gies in a single-phase systems, which is divided in: passive and active power decoupling method and their subdivisions. . . 79 Figure 2.18–Power Decoupling Cell (PDC) connected to the
dc bus of a two-stage PV Microinverter. . . 79 Figure 2.19–Equivalent circuit of the PV Microinverter
includ-ing the Power Decouplinclud-ing Cell after replacinclud-ing of the PV module and dc-dc converter by the con-stant current source Idc(cf. Figure 2.7). . . 80
Figure 2.20–Behavior of the capacitance Cbus in function of
the peak-to-peak value of bus voltage ∆VCb. . . . 81
Figure 3.1 – Power stages of the PV Microinverter to be devel-oped in this chapter. . . 85 Figure 3.2 – LCL Filter with damping branch - LCL + RC. . 87 Figure 3.3 – LCL Filter with damping branch - LCL + RC. . 88 Figure 3.4 – Resonance frequency fr as a function of the
in-ductor ratio aL for different capacitance values. . 92
Figure 3.5 – Bode diagram of H(s) for different values of the damping resistor Rd. . . 94
Figure 3.6 – Simulation waveform of the current through the converter side inductor L1 and grid side
induc-tance L2. . . 95
Figure 3.7 – Conventional single-phase dc-ac converter with LCL + RC filter that composes the PV Microin-verter. . . 95 Figure 3.8 – Single-phase dc-ac converter integrated to the
con-trol system: dc voltage loop and grid current loop. 98 Figure 3.9 – Illustrative explanation about the effect of the
direct control. . . 98 Figure 3.10–Proposed cascaded control structure of the
single-phase dc-ac converter employed in an grid-connected application. . . 99 Figure 3.11–Block diagram of the closed current loop for
regu-lation of the grid current injected into the grid. . 102 Figure 3.12–Bode plot of the magnitude and phase of the: (a)
T FN Ci(s) and (b) T FCi(s) after insertion of the
Cig(s). . . 104
Figure 3.13–Block diagram of the closed voltage loop for regu-lation of the average voltage VCb of the dc bus. . 106
Figure 3.14–Bode plot of the magnitude and phase with and without the band-stop filter of the: (a) no-compensated-open-loop transfer functions T FN Cv(s) and (b)
compensated-open-loop transfer functions T FCv(s)
after insertion of the compensator Cvcb(s). . . 107
Figure 3.15–Simulation waveform of the grid current reference, i∗grid(t), and actual, igrid(t). . . 109
Figure 3.16–Simulation waveform of current injected into the grid, grid voltage and dc bus voltage . . . 110 Figure 3.17–High Step-up dc-dc Converter employing a gain
cell and coupled-inductor. . . 111 Figure 3.18–MPPT-Temp algorithm flowchart. . . 112 Figure 3.19–Low-bandwidth loop control to ensure the PV
grated. . . 115 Figure 4.1 – Buck-type Power Decoupling Cell (PDC)
con-nected in parallel to the dc bus capacitor Cbus
at the input of the single-phase ac-dc converter. . 118 Figure 4.2 – (a) Operation Mode of the Buck-type Power
De-coupling Cell (PDC): in Storage Mode operates as a buck converter (b)-(c) and in Releasing mode operates a boost converter (d)-(e). . . 119 Figure 4.3 – (a) Electric circuit of the Buck-type PDC;
Ideal-ized current and voltage waveforms in: (b) Stor-age Mode operates as a buck converter for CCM (iLf > 0); (c) the power decoupling cell
quanti-ties over a grid period; and (d) Releasing mode operates a boost converter for CCM (iLf < 0). . 121
Figure 4.4 – Power flow in the PV Microinverter with the power decoupling cell connected to the dc bus. . . 123 Figure 4.5 – Waveform of the decoupling capacitor voltage for
different decoupling capacitance values Cf
includ-ing the peak capacitor voltage ripple ˆVCf for each
capacitance. . . 126 Figure 4.6 – Behavior of the capacitance Cbus in function of
the peak-to-peak value of bus voltage ∆VCb. . . . 127
Figure 4.7 – Power flow in the power decoupling cell. . . 129 Figure 4.8 – Waveform of the decoupling inductor current iLf(t),
or decoupling capacitor current. . . 132 Figure 4.9 – Waveform of the decoupling inductor current iLf(t).133
Figure 4.10–Waveform of the decoupling inductor voltage vLf,hf(t)
and current iLf,hf(t) at the switching frequency
fS,pdc= 1/TS,pdc when the power decoupling
Figure 4.11–(a) Inductor current ripple ∆iLf in function of
voltage VCf for some values of inductance Lf; (b)
inductor current ripple ∆iLf in function of
induc-tance Lf for some values of switching frequency. 135
Figure 4.12–Bode diagram of Zf o(s) for different values of
damping resistor Rf din the interval [0, ∞] for the
LC filter with RC damping shunt of the power decoupling cell filter. The zoom given around of resonance frequency belong to following range: f ∈ [300 Hz; 1 kHz] and |Zf o(jω)| ∈ [10 dB; 40 dB].139
Figure 4.13–Simulation Waveform of the current through de-coupling inductor Lf. . . 139
Figure 4.14–Equivalent electrical circuit of the Buck-type Power Decoupling Cell. . . 140 Figure 4.15–Averaged models of the ideal MOSFET (switch)
in steady-state employing a voltage or current dependent sources. . . 142 Figure 4.16–Low-frequency large-signal model of a buck
con-verter for CCM. . . 142 Figure 4.17–Small-signal ac and dc averaged circuit model of
the buck converter. . . 145 Figure 4.18–Dc circuit model for the buck converter around
the quiescent operation point. . . 145 Figure 4.19–Small-signal ac equivalent circuit model of the
buck converter, assuming that the small ac varia-tions on the ICb is null, i.e. ˜iCb= 0. . . 145
Figure 4.20–Reduction of the output elements to an only out-put equivalent impedance Zo(eq). . . 146
Figure 4.21–Small-signal ac equivalent circuit model of the buck converter after replacing the output elements with the output equivalent impedance Zo(eq) in
the frequency-domain. . . 147 Figure 4.22–Simulation result showing converter transient
buck converter for determining the control-to-output transfer function Gvcf d(s). . . . 150
Figure 4.24–Simulation result showing converter transient per-formance ˜vCb(s) during a small perturbation. . . 152
Figure 4.25–Buck-type power decoupling cell integrated to pro-posed control system. . . 154 Figure 4.26–Proposed control structure of the buck-type power
decoupling cell applied to shift away the power ripple away from the dc bus voltage of a two-stage PV Microinverter. . . 155 Figure 4.27–Illustrative explanation about the obtaining of the
voltage ripple ˜vCb which is calculated by means
of subtracting the average voltage VCb from the
instantaneous bus voltage vCb measured on the
bus voltage. . . 156 Figure 4.28–Block diagram of the closed voltage loop for
reg-ulation of the average voltage VCf across the
de-coupling capacitor Cf of the power decoupling
cell. . . 157 Figure 4.29–Bode plot of the magnitude and phase of the: (a)
T FN Cvcf(s) and (b) T FCvcf(s) after insertion of
the Cvcf(s). . . 159
Figure 4.30–Simulation waveform of decoupling capacitor volt-age vCf(t) and dc bus voltage vCb. . . 160
Figure 4.31–Insertion of the feedforward control loop Cf f,˜vcb(s)
as the first control strategy to regulate the dc bus voltage ripple. . . 162 Figure 4.32–Simulation waveform of decoupling capacitor
volt-age vCf(t) and dc bus voltage vCb(t). . . 163
Figure 4.33–Proposed control strategy to minimize the volt-age ripple of the dc bus voltvolt-age by the use of a Proportional-Resonant Controller. . . 165
Figure 4.34–Simplification of the block diagram displayed in Figure 4.33, in order to determine the PR con-troller parameters. . . 165 Figure 4.35–Bode plot of the magnitude and phase of the: (a)
T FN C ˜vcb(s) and (b) T FC ˜vcb(s) after insertion of
the C˜vcb(s). . . 166
Figure 4.36–Simulation waveform of decoupling capacitor volt-age vCf(t) and dc bus voltage vCb(t). . . 167
Figure 4.37–Representation of the power decoupling cell (PDC) as a virtual capacitor whose capacitance is a func-tion of the power decoupling parameters and duty cycle (D). . . 168 Figure 4.38–Determination of the power decoupling cell input
impedance Zi(s). . . 169
Figure 4.39–A test current source is connected at the power small-signal ac equivalent circuit model to pre-scribe the input impedance. . . 169 Figure 4.40–Bode plot of the magnitude and phase of the:
(a) power decoupling input impedance for the op-erating point designed by Dbuck and (b) power
decoupling input impedance for numerous oper-ating point with duty cycle ranging between 0.1 and 1.0. . . 171 Figure 4.41–Bode plot of the magnitude and phase of the: (a)
closed-loop input impedance employing the feed-forward compensator Cf f,˜vcb(s) and (b)
closed-loop input impedance employing the Proportional plus Resonant controller tunned at ω0 Cvcb˜ (s). . 173
Figure 4.42–PV Microinverter with the control systems inte-grated and the power decoupling cell connected to the dc bus. . . 175 Figure 5.1 – Hardware implementation of the 250 W PV
croinverter. The dimension of the shown PV Mi-croinverter prototype is 180mm x 120mm x 40mm. 180
cell. The dimension of the shown power decoupling cell prototype is 80 mm x 135 mm x 30 mm, which corresponds to a power density of 1.45 W/cm3 without the conditioning and control board. . . . 180 Figure 5.3 – Test Setup at Power Electronics Institute -
IN-EP/UFSC. . . 181 Figure 5.4 – Experimental waveforms 1 . . . 182 Figure 5.5 – Experimental waveforms 2 . . . 182 Figure 5.6 – Experimental waveforms 3 . . . 184 Figure 5.7 – Experimental waveforms 4 . . . 184 Figure 5.8 – Simulation and Experimental waveforms . . . 185 Figure 5.9 – Experimental waveforms 5 . . . 187 Figure 5.10–Experimental waveforms 6 . . . 187 Figure 5.11–Experimental waveforms 5 . . . 188 Figure 5.12–Efficiency of the implemented prototype
concern-ing to PV module power Ppv with (PDC on) and
without (PDC off ) the power decoupling cell. . . 189 Figure C.1 – Single-phase dc-ac converter connected to the grid. 219
Table 1.1 – System parameters & electrical specification of the single-phase two-stage PV Microinverter of the Figure 1.2. . . 49 Table 2.1 – System parameters & electrical specifications of
the dc-ac single-phase converter. . . 64 Table 2.2 – Typical grid voltage spectrum extracted by means
the Power Analyzer YokogawarWT1800. THD
v=
3.295 % and VRM S = 211.64 V. Harmonics 0 to 20
are listed. . . 65 Table 3.1 – Main electrical specification of the LCL+RC filter
design. . . 90 Table 3.2 – Summary of the Filter Parameters. . . 94 Table 3.3 – System parameters & electrical specification of the
electric circuit and control of the dc-ac single-phase converter. . . 105 Table 3.4 – Proportional-Integral Compensator Parameters. . 105 Table 3.5 – Proportional-Integral Compensator Parameters. . 108 Table 3.6 – System parameters & electrical specification of the
High Step-up Converter. . . 113 Table 4.1 – System parameters & electrical specification of the
buck-type power decoupling cell. . . 136 Table 4.2 – Summary of the passive components employed in
the power decoupling cell. . . 139 Table 4.3 – Proportional-Integral controller Parameters. . . . 158
Table 4.4 – System parameters & electrical specification of the electric circuit and control of the buck-type power decoupling cell. . . 159 Table 4.5 – Proportional-Resonant controller parameters. . . . 167 Table 5.1 – The maximum voltage and current stresses on the
active components of the system for steady-state operation. . . 178 Table 5.2 – The maximum voltage and current stresses on the
passive components of the system for steady-state operation. . . 179 Table 5.3 – Main power components employed to build the PV
Microinverter and Power Decoupling Cell experi-mental prototype. . . 179 Table 5.4 – Measurements of the waveforms illustrated in
Fig-ure 5.5. . . 183 Table 5.5 – Measurements of the waveforms illustrated in
Fig-ure 5.9 (a) and (b). . . 186 Table B.1 – Main specifications to ensure the quality for grid
interface of Photovoltaic Systems in accordance with the standards.. . . 217
acronyms
ac Alternate Current
ADC Analog-to-Digital Converter
AL-Cap Electrolytic Capacitors
BSF Band-Stop Filter
CCM Continuous Conduction Mode
dc Direct Current
DOI Digital Object Identifier
DSC Digital Signal Control
DSP Digital Signal Processor ESR Equivalent Series Resistance
FB Full-Bridge
GaN Gallium Nitride
IEC International Electrotechnical Commission IEEE Institute of Electrical and Electronic Engineering INEP Instituto de Eletrônica de Potência
LPF Low-Pass Filter
MLC-Cap Multi-Layer Ceramic Capacitors
MOSFET Metal-Oxide Semiconductor Field Effect Transistor
MPPF-Cap Polypropylene Film Capacitors
MPPT Maximum Power Point Tracking
NBR Brazilian Standard (Normas Brasileiras)
PCB Printed Circuit Board
PDC Power Decoupling Cell
PI Proportional plus Integrator Compensator
PF Power Factor
PFC Power Factor Correction
PLL Phase Locked Loop
PR Proportional plus Resonant Compensator
PSIM Software for Power Electronics Simulation
PV Photovoltaic
PWM Pulse Width Modulation
RMS Root-Mean-Square
STC Standart Test Conditions
Si Silicon
SiC Silicon-Carbide
THD Total Harmonic Distortion
UFSC Universidade Federal de Santa Catarina
VSC Voltage Source Converter
VSI Voltage Source Inverter
αC Capacitor ratio of the LCL-RC filter
αL Inductor ratio of the LCL-RC filter
C1 Capacitance of the LCL-RC filter
Cbus Bus capacitor
Cf f(s) Grid voltage feedforward compensator
Cf Decoupling capacitor of the PDC
Cvcb(s) Bus voltage compensator
Ceq Equivalent Capacitance
Cig(s) Current compensator
Cig(s) Insertion of the compensator
Cvcb(s) Compensator of the
˜
d Duty cycle variations
d Duty cycle
D Duty cycle at operating point
Dbuck Duty cycle at buck-mode
Dboos Duty cycle at boost-mode
∆VCb Peak-to-peak value of bus voltage
∆VCf Peak-to-peak value of bus voltage
∆iLf Current ripple of the low-frequency current
∆iLf,hf Decoupling inductor current
fgrig Fundamental frequency of the grid
fr Resonance frequency
H(s) Transfer function of the LCL-RC filter ˆ
I1 Peak current of the fundamental component
Idc Current source
iLf(t) Instantaneous current on the decoupling inductor Lf
iac(t) Instantaneous input current of the dc-ac converter
iCb(t) instantaneous bus capacitor current
igrid(t) instantaneous grid current
kp Proportional gain of the PI controller
L1 Inductance of the LCL-RC filter (Converter-side)
L2 Inductance of the LCL-RC filter (grid-side)
Leq Equivalent Inductance
Lf Inductance of the power decoupling cell
˜
VCf Peak capacitor voltage ripple
vCf(t) Decoupling capacitor
˜
ILf Low frequency inductor current
vLf,hf(t) Decoupling inductor voltage at high-frequency
fS,pdc Switching frequency of the power decoupling cell
Zf o(s) Output impedance of the power decoupling cell
Gvcf d(s) Control-to-output transfer function
Gvcbd(s) Control-to-intput transfer function
Gvcbvcf(s) Output-to-intput transfer function
pac1(t) ac component of pgrid(t) multiple of nω0
pac2(t) ac component of pgrid(t) multiple of 2nω0
Pav Average power of the Instantaneous grid power
pf(t) Instantaneous power on the power decoupling cell
Ppv Average power generated by the PV Module
Rd Damping resistance of the power decoupling cell
Rf d Damping resistor of the LCL-RC filter
Ro Load resistance
s Frequency domain
sin(ω0t) Sinusoidal waveform
t time
T Grid period
T HD Total Harmonic Distortion
T HDi Total Harmonic Distortion current
TS,pdc Switching period of the Power Decoupling Cell
T FN Cv(s) No-compensated-open-loop transfer function
T FCv(s) Compensated-open-loop transfer function
˜
vCf(s) Converter transient performance
˜
vCf(sw) Voltage ripple on the decoupling capacitor
˜
vCf (T F ) Voltage ripple on the decoupling capacitor from Gvcf d(s)
vCb(t) Instantaneous dc bus voltage
VCf Average voltage on the decoupling capacitor
ˆ
V1 Peak voltage of the fundamental component
Zi(eq) Input impedance transfer function
Zo(eq) Output impedance transfer function
ω0 Angular frequency of the fundamental component
ωc,i Crossover frequency of the grid current control loop
ωz Zero frequency of the PI controller
ωz,v Crossover frequency of the bus voltage control loop
ωz,vcf Crossover frequency of the decoupling voltage control
1 Introduction . . . . 45
1.1 Motivation . . . 45 1.2 Capacitors for Power Decoupling . . . 47 1.3 System Overview . . . 47 1.4 Goals and Contributions of the Master’s Thesis . . . 49 1.5 Outline of the Thesis . . . 50
2 Power Decoupling Principle . . . . 51
2.1 Introduction . . . 51 2.2 Power Flow in Nonsinusoidal PV System . . . 52 2.3 Energy Storage Element on the dc Bus . . . 58 2.3.1 Voltage Ripple in Nonsinusoidal PV System . 60 2.3.2 Voltage Ripple in Sinusoidal PV System . . . 69 2.4 Power Decoupling Cell . . . 72 2.4.1 Passive Power Decoupling . . . 74 2.4.2 Active Power Decoupling . . . 76 2.4.3 Operating Principle of Active Power Decoupling 80 2.5 Comparison of Active Power Decoupling Cells . . . . 82 2.6 Summary and Conclusion . . . 84
3 Design, Modeling and Control of the Microinverter 85
3.1 Introduction . . . 85 3.2 Output Filter for Grid Interface . . . 86 3.2.1 LCL Filter with RC Damping Branch . . . . 86 3.2.2 Design of the LCL Filter with RC Damping
Branch . . . 87 3.2.2.1 Converter-Side Inductor L1 . . . 90
3.2.2.2 Equivalent Inductance Leq . . . 91
3.2.2.3 Equivalent Capacitance Ceq . . . 91
3.2.2.4 Grid side inductance L2 . . . 93
3.2.2.5 Damping Resistor Rd . . . 93
3.3 Single-phase dc-ac Converter . . . 95 3.3.1 Control Strategy . . . 96 3.3.2 Control System Design . . . 100 3.3.2.1 Grid Current Control . . . 100 3.3.2.2 Bus Voltage Control Design . . . 106 3.4 High Step-up Converter . . . 111 3.5 Summary and Conclusion . . . 114
4 Design, Modeling and Control of the PDC . . . 117
4.1 Introduction . . . 117 4.2 Power Decoupling Cell . . . 117 4.2.1 Operation Principle . . . 118 4.2.2 Analysis of Operation and Mathematical Model 122 4.2.3 Decoupling Capacitor Voltage Ripple . . . 125 4.2.4 Decoupling Inductor Current Ripple . . . 131 4.2.5 Design of Passive Components . . . 135 4.2.5.1 Inductor Lf . . . 136
4.2.5.2 Decoupling Capacitor Cf . . . 136
4.2.6 System Modeling for CCM . . . 140 4.2.6.1 Large-Signal Averaged Model . . . . 140 4.2.6.2 Perturbation and Linearization . . . 143 4.2.6.3 Small-Signal Equivalent Circuit Model 145 4.2.6.4 Control-to-Output Transfer Function 147 4.2.6.5 Control-to-Input Transfer Function . 150 4.2.6.6 Output-to-Input Transfer Function . 153 4.2.7 Control Strategy . . . 153 4.2.8 Controller System Design . . . 156 4.2.8.1 Decoupling Capacitor Voltage Control 157 4.2.8.2 Voltage Ripple Control . . . 160 4.2.9 Equivalent Capacitance . . . 168 4.3 Summary and Conclusions . . . 173
5 Hardware and Experimental Verification . . . 177
5.1 Hardware Implementation . . . 177 5.2 Experimental Verification . . . 181 5.3 Summary and Conclusion . . . 190
Bibliography . . . 195
Appendix 209
APPENDIX A Solution for the Differential Equation 211
A.1 Nonhomogeneous Differential Equation . . . 211 A.2 Particular Solution of the Differential Equation . . . 212 A.2.1 Particular Solution - Part 1 . . . 213 A.2.2 Particular Solution - Part 2 . . . 214 A.2.3 Particular Solution Resulting . . . 216 A.3 Conclusion . . . 216
APPENDIX B Quality Standard for Grid Interface 217 APPENDIX C Math Model of the PV Microinverter 219
C.1 Transfer Function Current-to-Voltage . . . 219 C.2 Minimum Bus Capacitance . . . 221 C.3 Conclusion . . . 223
Chapter 1
Introduction
This chapter motivates the study and development of an Active Power Decoupling Converter to be connected to the dc bus of a two-stage Photovoltaic (PV) Microinverter. In addition, it presents the main proposal of the master’s thesis including the goals, contributions and general structure of the master’s thesis.
1.1
Motivation
Inverters (dc-ac converters) are the key elements for grid-connected photovoltaic power systems. Their main function is to connect the PV modules to the grid, converting the dc power generated by the PV module in a grid-synchronized ac power. For this reason, these inverters are appointed as PV Inverters, whose structure may be classified into five groups, such as: Central Inverters; Mini Central Inverter; Multistring Inverter; String Inverter and Microinverter [1–4].
Generally, a PV Microinverter electrical system consists of a power conversion system, a cooling system, controllers, a dc power supply, harmonic and EMI filters and ancillary components, such as: disconnect relay, fuses and communication devices. Figure 1.1 illustrates the structure of a single stage (a) and two-stage PV Microinverter. Regardless of the structure type, they are designated to process the dc power generated only by one PV module and deliver into the single-phase grid. Thereby, the PV Microinverter is becoming a new tendency for PV power generation systems due to their numerous advantages including improved energy harvest, improved system efficiency, lower installation costs, “Plug-and-Play”
46 Chapter 1. Introduction
operation, and enhanced modularity and flexibility. Further, they remove the mismatch losses, since there is only one PV module, provide an optimal adjustment between the PV module and the dc-ac converter by means an individual Maximum Power Point Trdc-acking (MPPT). In addition, PV Microinverters include the possibility of an easy enlarging of the system, due to their modular structure. On the other hand, two-stage PV Microinverters require the use of high step-up dc-dc converters, as an intermediate stage to boost the PV module voltage and build the dc bus voltage. This voltage-gain can reduce the overall efficiency and increase the cost per watt, due to the complexity of these topologies [5].
Currently, among the solutions aforementioned, the two-stage PV Microinverter has been gained more attention in the industry and is becoming a commercial trend due to the partial decoupling of the ac power performing by the capacitor, Cbus. This feature
implies in higher reliability when compared with the single-stage topologies, which presents only the capacitor in parallel with PV module, Cpv [4], [6], [2]. Regardless of the adopted power
process-ing stage-type, the power decouplprocess-ing is typically accomplished by means of large and bulky electrolytic capacitors which are installed at dc bus to compensate the voltage fluctuations. However, these
Figure 1.1 – PV Microinverter architectures: (a) Single-stage, (b) Two-stage.
capacitors have the drawback of a short lifetime, especially under high temperature, and are not compatible with the lifetime of PV module, usually guaranteed for 25 years. Therefore, numerous power decoupling techniques have been developed to reduce the required input capacitance so that film capacitors1 with long lifetime may be applied to decouple the power between the PV module and the grid.
1.2
Capacitors for Power Decoupling
The three types of capacitors typically employed on the dc bus are: the Aluminum Electrolytic Capacitors (Al-Caps), Metallized Polypropylene Film Capacitors (MPPF-Caps) and high capacitance Multi-Layer Ceramic Capacitors (MLC-Caps) [7], [8].
Figure 1.2 illustrates a performance comparison among the capac-itor types aforementioned for different figures of merits. Therefore, among the technologies currently available the MPPF-Cap or just film capacitors are the suitable options to be applied into PV Mi-croinverters. Comparatively to the other capacitor types, the film capacitors present several significant advantages, especially when cost, temperature, reliability and volume are the main specifications required by the project [7], [9].
1.3
System Overview
For single-phase grid-connected PV application, the power flow to the grid is time-varying pgrid(t), while the power extracted from
the PV module, Ppv must be constant to avoid the oscillations on
the PV module voltage, which degrades the MPPT performance. In effect, a power ripple from the mismatch between the input instantaneous power ppv(t) and the output instantaneous grid power
pgrid(t), appears on the dc side. Therefore, a low-frequency energy
storage element should be placed between the PV module and the grid to balance this power ripple. In other words, the low-frequency energy storage element performs the power decoupling by storing energy, when ppv(t) > pgrid(t), and releasing it, when
ppv(t) < pgrid(t).
1Currently, film capacitors with elevated capacitance, around 100 µF are still
extremely expensive and in some cases bulky as well. The solution to this issue is to replace the electrolytic capacitors with a small and reliable film capacitor (or ceramic) and then to connect on the dc bus an power decoupling cell to actively perform the power decoupling.
48 Chapter 1. Introduction
Typically, high capacitances are required to ensure a low-voltage ripple, thus in order to increase the stored energy density (i.e. joules/cm3), electrolytic capacitors are still the most useful
tech-nology in these applications. However, they are bulky and have a limited lifetime, around 1000 - 7000 hours at 105 ◦C operating temperature. Based on this fact, the literature has proposed several decoupling strategies to shift the power ripple to another specific energy storage component with relatively small size and long lifetime by means an extra active switching circuit. Then the aforementioned disadvantages of the electrolytic capacitor are mitigated.
In this Master’s Thesis, a solution of power decoupling cell to be integrated to a two-stage PV Microinverter is proposed, in order to solve the issues regarding the volume, lifetime and reliability of the dc bus. For this reason, it is proposed a power decoupling stage controlled to reduce the voltage ripple. This power decoupling stage can be understood as an energy buffer, so that it must alternately
Figure 1.2 – Performance comparisons of the three main types (MLC, MPPF and AL) of capacitors for power decoupling considering the fol-lowing figure of merits: Capacitance, Voltage, EST and DF, Capacitance Stability, Voltage Derating, Temperature Reliability, Energy Density and cost [7].
store and release energy within a quarter of the grid period. The block diagram illustrated in Figure 1.3 presents the concept of the system that will be developed in this thesis, whereas in Table 1.1 described the system parameters and electrical specification of the developed PV Microinverter [10].
Table 1.1 – System parameters & electrical specification of the single-phase two-stage PV Microinverter of the Figure 1.2.
Rated Average Power (Ppv) 250 W
PV Voltage Range (Vpv) 20-40 V
Maximum Power of the PV Module at STC (Pmp) 250 W
Bus Capacitor (Cbus) 50 µF
Bus Voltage (VCb) 420 V
Peak Grid Voltage ( ˆV1) 311 V
Peak Grid Current ( ˆI1) 1.607 A
Grid Frequency (fgrid) 60 Hz
1.4
Goals and Contributions of the Master’s Thesis
The objective of this thesis is to comprehensively analyze, develop, implement and evaluate an active power decoupling system to be integrated on the dc bus at a two-stage PV Microinverter. This system has the ability to shift the power ripple away from main bus capacitor to a small size decoupling capacitor. The results are verified by means of simulations and measurements of hardware prototypes. The main contributions of the thesis are described below.
Figure 1.3 – Power Decoupling Cell (PDC) connected to the dc bus voltage of a two-stage PV Microinverter.
50 Chapter 1. Introduction
• Derivation of a detailed analysis of the power flow in the PV Microinverter connected to a grid containing nonsinusoidal waveform, so that an analytical expression which defines the voltage ripple on the bus voltage is literally determined in terms of the Fourier Series of the grid voltage and current waveforms.
• Proposal of a control strategy applied to a bidirectional dc-dc converter in order to perform the active power decoupling on the dc bus voltage of a two-stage PV Microinverter is proposed. • Integration of the developed power decoupling cell into a grid-connected Microinverter composed by a high step-up converter and a full-bridge bidirectional 2 levels SPWM based inverter.
1.5
Outline of the Thesis
The following Master’s Thesis is divided in six chapters. The first chapter begins with this briefing introduction presented previously. The second chapter introduces the power decoupling principle by means an analysis of the power flow in a power electronics system containing nonsinusoidal waveforms. The same chapter introduces the power decoupling cell, summarizing the principal strategies and topologies developed in the literature, in order to reduce the voltage ripple in a dc bus.
The third chapter presents the analysis, design, control and evaluation of each stage that compose the PV Microinverter, in the following order: output filter for grid interface; single-phase dc-ac converter and lastly the high step-up dc-dc converter.
The fourth provides a comprehensive survey on the topic of active power decoupling converter for PV Microinverter, presenting the analysis, design, control and evaluation of the power decoupling cell adopted.
The fifth chapter presents the hardware realization and experi-mental verification. Finally, the sixth chapter concludes the Master’s Thesis with some outlook and future works.
Chapter 2
Power Decoupling Principle
2.1
Introduction
In single-phase grid-connected systems, particularly PV Microin-verter, a constant power is drawn from the PV module, while a pulsating instantaneous power is delivered to the grid. As a result, a low-frequency ripple appears on the dc bus during the power conversion. Therefore, since the ideal dc-dc and dc-ac converters that compose the two-stage PV Microinverter do not consume or generate power, neither does it contain significant internal energy storage, it is required to insert to the system a low-frequency energy storage such as a capacitor, which provides inertia to the dc bus and still decouples the PV module from the grid, reducing the voltage pulsation.
In this chapter, it is introduced the main issues regarding the power decoupling principle that is the background to understand and develop the active decoupling strategies. For this purpose, the power flow in single-phase grid-connected converter containing non-sinusoidal and non-sinusoidal waveforms is analyzed. The analysis results in an expression which defines mathematically the voltage ripple on the bus voltage and allows to explain in detail the power decoupling, as well as determine some figures of merit such as: bus capacitance; peak-to-peak voltage ripple, current across the bus capacitor and a electric model of the power decoupling cell when inserted into the PV Microinverter.
Finally, a comprehensive comparison concerning the state-of-the-art is presented.
52 Chapter 2. Power Decoupling Principle
2.2
Power Flow in Nonsinusoidal Photovoltaic
Grid-Connected Systems
In general, the instantaneous power pgrid(t) provided to the grid is
given by the product between the instantaneous grid voltage vgrid(t)
and the instantaneous current igrid(t), as illustrated in Figure 2.1
and expressed by:
pgrid(t) = vgrid(t) · igrid(t) (2.1)
Assuming that vgrid(t), and igrid(t), are periodic, but not purely
sinusoidal, they can be generically defined according to the Fourier series: vgrid(t) = V0+ ∞ X n=1 ˆ Vncos(nω0t − θn) (2.2) igrid(t) = I0+ ∞ X n=1 ˆ Incos(nω0t − φn) (2.3)
where V0and I0are the undesirable dc components, or average values,
present in grid voltage and current; ˆVn and ˆIn are the amplitude
of the nth harmonic; n is the harmonic number; θn and φn are
respectively the phase angle of the nth harmonic voltage and current; and ω0 is the angular frequency of the fundamental grid voltage
component which is defined as ω0 = 2πfgrid. Hence, the grid period
is given by T = 2π/ω0 [11], [12].
Now, an expression for the pgrid(t) may be defined by substituting
of (2.2) and (2.3) into (2.1), which results in:
pgrid(t) = V0I0+ a1V0+ a2I0+ a3 (2.4)
Figure 2.1 – A bidirectional single-phase dc-ac converter performing the interface between a PV module and the grid.
wherein, the coefficients a1, a2 and a3 are defined as following: a1= ∞ X n=1 ˆ Incos(nω0t − φn) a2= ∞ X n=1 ˆ Vncos(nω0t − θn) a3= ∞ X n=1 ˆ VnIˆncos(nω0t − θn)cos(nω0t − φn)
Applying the trigonometric identity:
cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β) (2.5) into a3 and collecting the terms, lead to:
a3 = cos2(nω0t) h cos(θn)cos(φn) i + sin(nω0t)cos(nω0t) h sin(θn+ φn) i + sin2(nω0t) h sin(θn)sin(φn) i (2.6)
In a similar manner, rewritten the terms cos2(nω0t) and sin2(nω0t)
by substituting the trigonometric identity (1 ± cos(2ω0t))/2 into
(2.6), one can derive:
a3= ∞ X n=1 ˆ VnIˆn 2
cos(θn)cos(φn) + cos(θn)cos(φn)
+ cos(2nω0t)
h
cos(θn)cos(φn) − sin(θn)sin(φn) i
+ sin(nω0t)cos(nω0t)sin(θn+ φn)
(2.7)
Thus, using the trigonometric identity to expand the term sin(θn+
φn) in (2.7) and then applying again the trigonometric identity (2.5),
one obtains the simplified expression for a3:
a3 = ∞ X n=1 ˆ VnIˆn 2 cos(θn− φn) + cos(2nω0t − θn− φn) (2.8)
54 Chapter 2. Power Decoupling Principle
Finally, a general expression of instantaneous power provided to the grid in function of the nth harmonics is defined according to:
pgrid(t) = V0I0 + ∞ X n=1 V0Iˆncos(nω0t − φn) + I0Vˆncos(nω0t − θn) + ∞ X n=1 ˆ VnIˆn 2 cos(θn− φn) + cos(2nω0t − θn− φn) (2.9)
Now, carefully analyzing the previous equation, it can be seen that the instantaneous grid power, pgrid(t), is composed of a dc
component, Pav, and an considerable ac component ˜pgrid(t) that
may be split in other two components: the first, pac1(t), is multiple
of the fundamental component (nω0) and the second, pac2(t), is
multiple of the double-frequency grid voltage (2nω0). Thus, (2.9)
may be rewritten as follows:
pgrid(t) = Pav+ ˜pgrid(t) = Pav+ ˜pac1(t) + ˜pac2(t) (2.10)
where, the terms are individually represented by:
Pav = V0I0+ ∞ X n=1 ˆ VnIˆn 2 cos(θn− φn) ˜ pac1(t) = ∞ X n=1 V0Iˆncos(nω0t − φn) + I0Vˆncos(nω0t − θn) ˜ pac2(t) = ∞ X n=1 ˆ VnIˆn 2 cos(2nω0t − θn− φn)
The quality of the power provided from the PV system to the grid is governed by practices and standards on voltage, current, fre-quency, harmonics and power factor. Deviation from these standards represents out-of-bounds conditions and may require disconnection of the PV power system from the grid.
The dc current injection in the utility can saturate the distribu-tion transformers, leading to overheating and trips. In addidistribu-tion, it may also induce metering errors and fault of certain power system protection elements. For the conventional PV systems with galvanic isolation, this problem is reduced, however for the new generation of transformerless PV Microinverter this issue requires more attention.
The limits of injected dc current1 are defined by some quality
stan-dards (cf. Appendix B). The IEEE 929 and NBR 16149 stanstan-dards permit a limit of 0.5 % of the rated output current. On the other hand, the European IEC 61727 suggests a dc injection limit less than 1.0 %. Other standards in the world have fewer restrictions and are easier to cope with [3, 4, 10].
Under these circumstances, the dc component on the grid voltage may be neglected, since the utility ensure this dc component is equal to zero, i.e. V0 = 0, otherwise, the electrical distribution system had
already collapsed. Therefore, the terms of (2.10) can be simplified as follows: Pav = ∞ X n=1 ˆ VnIˆn 2 cos(θn− φn) ˜ pac1(t) = ∞ X n=1 I0Vˆncos(nω0t − θn) ˜ pac2(t) = ∞ X n=1 ˆ VnIˆn 2 cos(2nω0t − θn− φn) (2.11)
Figure 2.2 illustrates the power terms describe in (2.11) for a given voltage and current. In this figure, the fundamental component of the grid voltage and grid current are shifted by a displacement angle φ1, according to Figure 2.2 (a). Furthermore, a fifth harmonic
and a dc component, I0, have been considered in order to highlight
the influence of different harmonics components on the instantaneous power, pgrid(t).
As can be seen, the presence of harmonic content in the current waveforms (including I0) results in the existence of the following
terms Pav, ˜pac1(t) and ˜pac2(t), in according to (2.11). As shown
in Figure 2.2 (b), one observes the presence of a other component multiple of fundamental harmonic (nω0t) summed to the usual
component multiple of second-order harmonic (2nω0t). Therefore,
it is possible to state that the I0 inserts low-frequency harmonics
(multiple of nω0t) in the instantaneous power waveform, which arises
from the term ˜pac1. Otherwise, if I0= 0, then ˜pac1= 0.
In addition, from (2.11) and Figure 2.2 (b), it is straightforward to conclude that the energy flow to the grid is bidirectional and pul-sating. In effect, the instantaneous power grid, pgrid(t), may assume
both positive and negative values at several points over the grid
56 Chapter 2. Power Decoupling Principle
voltage cycle. Thereby, throughout the time interval corresponding to the area under the waveform pgrid(t), denoted by “A”, the source
is delivering energy to the grid, whereas during the time interval corresponding to area “B”, a percentage of this amount of energy is being returned back to the source [13]. For this reason, the energy may flow in both direction through the dc-ac converter between the input source and the grid.
Adopting the current flow illustrated in Figure 2.1 as reference, when pgrid > 0 the energy is injected into grid, while pgrid < 0
indicates the energy is provided by the grid. Thus, under these circumstances, it is possible to determine the net energy Egrid
trans-mitted to the grid within one cycle, according to: Egrid=
Z T
0
pgrid(t)dt (2.12)
Hence, the average power, Pav, is equal to:
Pav= Egrid T = 1 T Z T 0 pgrid(t)dt (2.13)
The analytical solution of (2.13) may be calculated by inspection, since the integral of a sinusoidal function as cos(nω0t) or sin(nω0t),
within of one period, T , is zero, because the area under the positive half cycle of a sinusoidal waveform is successively canceled by the area under negative half cycle. Therefore, by inspection the average
Figure 2.2 – Influence of power terms Pav, pac1(t) and pac2(t) in the energy
power is given by: Pav = ∞ X n=1 ˆ VnIˆn 2 cos(θn− φn) (2.14)
In other words, the average power is different of zero when the Fourier series of vgrid and igrid contains harmonics at the same
frequency, since the product of voltage and current harmonics of the same frequency contribute with the net energy transmitted to the
Figure 2.3 – Voltage, current and instantaneous power in a hypothetical system for three different cases: (a) First; (b) Second and (c) Third.
58 Chapter 2. Power Decoupling Principle
grid, as illustrated in Figure 2.3 (a)-(c).
Figure 2.3 shows three cases of a system containing a different set of harmonics to demonstrate how this harmonic content of the voltage and current affect the generated power.
In the first case, the grid voltage and current contain only the fundamental component, in phase (θ1= φ1), as expressed below and
illustrated in Figure 2.3 (a). It can be seen that the instantaneous power is positive on the entire cycle and has an oscillating component at the double fundamental frequency (2ω0), since both voltage and
current are in phase, as depicted in Figure 2.3 (a).
In the second case, the voltage waveform contains only the funda-mental component while the current contains the third and the fifth harmonic, as illustrated in Figure 2.3 (b). In this case the energy circulates between the source and grid, as ripple power. In effect, the net energy injected to the grid within on period, T , is null, according to instantaneous power depicted in Figure 2.3 (b).
In the third case, the voltage waveform contain the fundamental component and the fifth harmonic while the current contains funda-mental component, third, fifth and seventh harmonic, as illustrated in Figure 2.3 (c).
As can been observed, the shifting between the voltage harmonic and current, θn− φn, decreases the average power, Pav, and
con-sequently the net energy transferred to the grid. In addition, the presence of harmonics in one of the waveforms increase the rms value while keeping the average power unchanged. This is undesirable, because increases the I2
rmsR losses in the system.
2.3
Energy Storage Element on the dc Bus
In a bidirectional single-phase PV Microinverter, as shown in Figure 2.4, the power flow is given from the PV module to the grid. For simplicity, the effects of power losses and output filters are neglected. Thus, the power extracted from the PV module, ppv(t),
is considered constant, as illustrated in Figure 2.4 (a), whereas the instantaneous power provided to the grid is time varying, as illustrated in Figure 2.4 (c).
As can be seen, the instantaneous input power, ppv(t), is not
equal to the instantaneous output power, pgrid(t). This difference
creates a voltage ripple containing nth-order harmonics on the dc bus voltage (cf. Figure 2.4 (b)), which reduces the system efficiency when it is not decoupled from the PV module output. Thereby, this power mismatch must be handled by an energy storage element able
to decouple this unbalance between the input ppv(t) and output
power pgrid(t).
The energy storage might be performed by means an element other than a capacitor, such as an inductor. However, the use of an inductor may be a poor option, because of its high weight and cost. Compar-atively, the energy stored in a capacitor (Cv2/2) of 100 µF /100 V is the same stored in an inductor (Li2/2) of 100 µH/100 A, i.e. both elements may store 1 J each one. In this case, the capacitor is considerably compact, lighter and less expensive. For this reason, the capacitor has been selected as energy storage component at dc bus voltage [11].
As mentioned, the power ripple flows through the bus capacitor, Cbus, as illustrated in Figure 2.5 (a). In effect the voltage across the
bus capacitor vcb(t) varies accordingly to the amount of power it
processed, as is shown in Figure 2.5 (b) and (c). In this way, when pgrid(t) < ppv(t) the energy flows into the capacitor in order to
store the excess energy in the Cbus, consequently the voltage vcb(t)
increases. On the other hand, when pgridt > ppv(t), the capacitor
deliveries the energy to the grid, such that the voltage vcb(t) decreases.
Therefore, the capacitor voltage must be allowed to increase and decrease as necessary to store and release the required energy. It is important to emphasize that the capacitor voltage should be allowed to increase and decrease as necessary to store and release
Figure 2.4 – Power flow in a PV Microinverter connected to the grid, where: (a) is the power generated by the PV module; (b) is the power decoupled
60 Chapter 2. Power Decoupling Principle
the required energy. This swing implies in a pulsating voltage ∆vCb
that oscillates on same frequency of pgrid(t).
In steady-state, if the losses are neglected, there is no net change in the capacitor stored energy over the one grid cycle, that is:
Egrid= Epv (2.15)
Hence, solving the integral, one obtains: Egrid= Epv Z T 0 pgrid(t)dt = Z T 0 ppv(t)dt Pav= Ppv (2.16)
2.3.1 Voltage Ripple in Nonsinusoidal Photovoltaic Grid-Connected Systems
Now, analyzing the low-frequency energy process in detail, it is possible to simplify the system of Figure 2.4 in order to determine the voltage ripple ˜vCb(t) across the capacitor Cbus. For this purpose,
the dc-dc converter and the PV module can be modeled together by means a dc current source whose magnitude corresponds to Idc,
according to Figure 2.6. This approach is valid because the current source preserves the voltage ripple dynamics on the dc bus.
Figure 2.5 – (a) Power flow at dc bus voltage considering the capacitor as energy storage element Cbusand waveforms of a bidirectional single-phase
PV Microinverter: (b) instantaneous grid power pgrid and constant dc PV
power Ppv; (c) and energy storage capacitor voltage vCb which increases
