SMALL SIGNAL MODEL OF SINGLE-PHASE QUASI-Z-SOURCE INVERTER WITH COUPLED INDUCTORS

ТЕХНІЧНІ НАУКИ ТА ТЕХНОЛОГІЇ № 2 (2), 2015 TECHNICAL SCIENCES AND TECHNOLOGIES РОЗДІЛ V. ЕНЕРГЕТИКА УДК 621.314.1 Oleksandr Husev, PhD in Technical Sciences Chernihiv National University of Technology, Chernihiv, Ukraine SMALL SIGNAL MODEL OF SINGLE-PHASE QUASI-Z-SOURCE INVERTER WITH COUPLED INDUCTORS О.О. Гусев, канд. техн. наук Чернігівський національний технологічний університет, м. Чернігів, Україна МАЛОСИГНАЛЬНА МОДЕЛЬ ОДНОФАЗНОГО КВАЗІ-ІМПЕДАНСНОГО ІНВЕРТОРА З МАГНІТО-ЗВ’ЯЗАНИМИ ІНДУКТИВНОСТЯМИ А.А. Гусев, канд. техн. наук Черниговский национальный технологический университет, г. Чернигов, Украина МАЛОСИГНАЛЬНАЯ МОДЕЛЬ ОДНОФАЗНОГО КВАЗИ-ИМПЕДАНСНОГО ИНВЕРТОРА С МАГНИТО-СВЯЗАННЫМИ ИНДУКТИВНОСТЯМИ Focus is on the single-phase quasi-Z-source inverter with coupled inductor. State space averaging method is used for small-signal analysis. Small signal behavior of the converter expressed analytically in form of set of transfer functions. It can be used for controller design in closed loop system and analysis of inductor coupling. Key words: single-phase inverter, qZS network, small signal model. Розглянуто однофазний квазі-імпедансний інвертор з магніто-зв’язаними індуктивностями. Проведено лінеаризацію за методом усереднення в просторі станів. Складено матричний вираз, що описує в p-області поведінку перетворювача для малого сигналу. Аналітично отримано передавальні функції, які можна використовувати для синтезу замкнутої системи керування та проводити аналіз впливу магнітного зв’язку між індуктивностями. Ключові слова: однофазний інвертор, квазі-імпедансна ланка, малосигнальна модель. Рассмотрен однофазный квази-импедансный инвертор с магнито-связанными индуктивностями. Проведена линеаризация по методу усреднения в пространстве состояний. Составлено матричное выражение, описывающее в p-области поведение преобразователя для малого сигнала. Аналитически получены передаточные функции, которые можно использовать для синтеза замкнутой системы и анализа влияния магнитных связей между индуктивностями. Ключевые слова: однофазный инвертор, квази-импедансное звено, мало-сигнальная модель. Introduction. Renewable energy capacity is growing rapidly. These energy sources supplied 21,7 % of the world electricity consumption in 2014 [1]. In particular, solar Photovoltaic (PV) and wind power grew by almost 45,2 % and 22,2 % during the last years respectively [1]. Dc-ac converters are used to inject renewable energy into the grid. Traditionally, Voltage Source Inverters (VSIs) or Current Source Inverters (CSIs) are used. However, typically they cannot provide more than double input voltage regulation ratio because of the losses. To overcome that drawback, intermediate voltage boost dc-dc converters are used. At the same time, this solution as well as the control system are topologically complex due to the twostage power conversion. Z-source inverters overcome the limitation of the conventional inverters: they have buck, boost operation capability and do not suffer from short circuit. The Quasi-Z-Sourсe Inverter e (qZSI) has appeared as a derivation from the Z-source inverter. This circuit has continuous input current and used in different application [2–5]. Many review and comparison papers have been published [6; 7]. At the same time, the qZSI with coupled inductors is not studied enough. In particular influence of coupling on the input current ripple and dynamic behaviour. Objective of the paper. The main goal of the paper is a composition of the small signal model of the qZSI with coupled inductor. The small signal model will allow further analysis of the current and voltage ripple in the passive components. Also dynamic behavior analysis can be done by means of small signal model. Fig. 1 illustrates investigated topology of the single-phase qZSI. 199 № 2 (2), 2015 ТЕХНІЧНІ НАУКИ ТА ТЕХНОЛОГІЇ TECHNICAL SCIENCES AND TECHNOLOGIES C2 L1 L2 S1 D1 VIN S3 Output Filter Li C1 Lg Ig VDС S2 Cf S4 RL qZS network Fig. 1. Investigated topology of the single-phase qZSI Main part of the paper. The averaging method in a state space is used to analyze the stability of PWM converters [8] and current and voltage fluctuating [9]. In general, switching period of the any switching converter is broken into intervals on which it is replaced by a linear circuit. On the i-th interval of his work describes the system of equations:  dx(t ) = Ai x(t ) + Bi u (t ), K (1) dt   y (t ) = Ci x(t ) + Ei u (t ), where K, Ai, Bi, Ci, Ei – the matrix of coefficients on the i-th interval; x(t) – the state vector; u(t) – vector of input variables; y(t) – vector of output variables. Hereinafter, bold matrices and vectors. As states decided to choose a minimum set of voltages and currents in containers inductances, which completely describe the system. Further averaging system of equations over the period of the converter. Averaged model of the system of equations in matrix form:  d x(t ) T = A av x(t ) T + B av u(t ) T ,   dt  y (t ) = C x(t ) + E u(t ) . av av  T T T (2) where Aav, Bav, Cav and Eav – averaged coefficient matrix describing the behavior of the adjustable in the averaged values. Here and below, angle brackets <> T denote averaging of magnitude over the period of switching T. We write more, which are averaged matrix. Further, all state averages, input voltage and the control signal represented as a constant component and a variable component of small amplitude with a frequency below the switching frequency drive:  x(t ) T = X + xɶ (t ); u (t ) T = U + uɶ (t ) y (t ) T = Y + yɶ (t ), (3)  ɶ  d i (t ) T = Di + d (t ). In order to estimate values of the passive components and dynamic properties the steady state analysis is detailed below. The operating period of the qZSI in the CCM can be divided into only two time intervals and can be represented by means of two equivalent circuits. It means that all switching states can be separated into two modes: active states (Fig. 2, a) and ST state (Fig. 2, b) correspondently. The magnetically coupled inductors are represented by means of an equivalent circuit that contains an ideal transformer with a turns ratio N1:N2, magnetizing inductance LM and leakage inductance LL [10; 11]. 200 ТЕХНІЧНІ НАУКИ ТА ТЕХНОЛОГІЇ № 2 (2), 2015 TECHNICAL SCIENCES AND TECHNOLOGIES vC2 vC2 iIN LL iM VIN N1 C2 C2 N2 iIN LL iDС LM vC1 C1 N2 iM LM VIN VDС N1 C1 vC1 VDС IDС а b Fig. 2. Equivalent circuits of the proposed topology: a – active states; b – shoot-through states Output side of the inverter is represented by means of the dc and ac current sources. It models power flow from the input to the grid or load through the dc-link. It has constant and variable components, which is the characteristic of the single-phase system: ~ ~ sin(mωt ) , i DC =I MAX iDC=I DC+ i DC , (4) ~ where IDC is a constant component of the load current, i DC is a variable component, IMAX. is the peak value of the variable component. Both (...truncated)