Linear controller design for a large dc gain converter

Article history: Received 10 January 2017 Received in revised form 29 April 2017 Accepted 11 May 2017 Environmental friendly energy sources like solar, fuel or wind cells provide low voltage levels. Grids work with higher voltage levels so step up is required before connecting these new energy sources to grid. Conventional boost converter is not able to provide a large DC gain. There are some topologies available in literature which provides required high DC gain. Without a suitable control system, converter’s output may change due to disturbances like: Input voltage’s changes and output load’s changes. This paper designs a controller for one of the recently proposed high DC gain topologies. Converters dynamical equations are extracted using State Space Averaging (SSA). Controller is designed based on the obtained dynamics. Close loop system has been tested in Simulink® environment. Simulation results showed the performance of designed controller.


Introduction
*Energy has an important role in modern world. Increasing use of fossil energies raises serious environmental concerns. Burning of fossil fuels produces CO2, one of the greenhouse gases which contribute to global warming. Recently, renewable energy sources have attracted much attention. Sun is one the most important sources of renewable energy (Leyva-Ramos et al., 2013;Danandeh et al., 2012). Conversion of sun radiation to electric power is done by solar panels. According to I-V characteristic of solar panels, a DC-DC converter is required for maximum power point tracking. Also, DC-DC converter increases the low voltage of solar panels to the level required by the load. Used converter must have low input current ripple (Evran and Aydemir, 2013), so converters with an inductor in series with input source like boost converter are preferred. However, boost converter can't be used to provide a high conversion ratio (Hsieh et al., 2013).
Cascading two or more boost converters can be used to obtain a higher conversion ratio but this method needs a more complex controller (Rahimi and Emadi, 2009). Plenty of high voltage gain topologies has been introduced (Luo and Ye, 2003;Wu et al., 2005;Jang and Jovanovic, 2007;Axelrod et al., 2008;Ismail et al., 2008a;Wu et al., 2008;Fardoun and Ismail, 2010;Choi et al., 2011;Jiao et al., 2011;Luo, 2011;Qian et al., 2012;Rosas-Caro et al., 2013;Li et al., 2015;Yang et al., 2009). Although control engineering has considerable progress over recent decades, most applications use PID controllers, because of their low price and simplicity. Generally speaking, using derivative term is not so common in power electronics converters control. Usually a P or PI controller is all that is required. This paper designs a controller for one of the recently published topologies (Li et al., 2015). Fig. 1 shows the high dc gain step up converter suggested by Li et al. (2015).

Working principles of large DC gain step-up DC-DC converter
When switch is closed (Fig. 2), L is charged by voltage source, D2 is forward bias while D1 and D3 are reverse bias. C1 and C2 are charged very quickly since there is no resistance in their path except of parasitic resistances. When switch is opened (Fig. 3), inductor releases the stored energy to the load.
Voltage stress on the switches is an important issue in high gain converters. High voltage stress limits performance and efficiency of converter. Voltage stress of aforementioned converter is equal to 2 . A comparison between some of the topologies available in literature has been done in Table 1 (Li et al., 2015). Applying volt-second balance (Mohan et al., 2003) to this circuit leads to Eqs. 1 and 2: and

Small signal model extraction
Equivalent circuit for closed switch is shown in Fig. 4. Using Kirchhohff's Voltage and Current Law (KVL and KCL), Eq. 3 is obtained.
Axelrod et al.
Ismail et al.
Prudente et al.
Averaging and small signal linearization is key steps of SSA. Applying the aforementioned steps to Eqs. 4 and 6 is quite tedious, time consuming and error prone for hand analysis.

Controller design
Tracking step reference signals with zero steady state error is possible if and only if (open) loop transfer function contains at least one integrator. Plant's transfer function contains no integrator so a simple I type controller with the following transfer function is selected (Eq. 15): Using Routh-Hurwitz table, 0 < < 0.73 make the close loop unity feedback system stable. Using MATLAB's control system toolbox = 0.41 is selected to have no overshoot in step response. Following scenario is used to test the close loop system: Input voltage's value changes from 10 V to 10 V at t=1 ms. Output load changes from 514 Ω to 168 Ω at t=200 ms. Test scenario is summarized in Table 2. = 116.4 is selected. As shown, output voltage of system without controller changes (It decrease to 91 Volts.) while system with controller bypass the disturbances and keeps output voltage constant and has no overshoot.

Conclusion
Development of renewable energy sources has a great influence on daily life. Connecting these sources to grid needs a high DC gain converter. Disturbances like: Input voltage source's changes and output load's changes, may change converter's output voltage, so a controller is required to keep output voltage constant. This paper designs a linear controller for one of the recently proposed high DC gain topologies. Next step is applying nonlinear techniques.