Lyapunov-Based Control Scheme for Single-Phase Grid ... - ITM

528 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 20, NO. 2, MARCH 2012characteristics, one corresponding to an irradiance of1000 Wm and another corresponding to an irradianceof 500 Wm . The experimental test consisted in thesudden change of the 1000 Wm electrical characteristicsset to the 500 Wm and then restoring the 1000Wm electrical characteristics set after a given time.This operation is shown in Fig. 11. This test is equivalentto an improvable worst case scenario and therefore itis a good way to validate the robustness of the designedcontroller.The values of the tunable parameters of the controller, i.e.,gains and , have been defined mainly to avoid numericalproblems (e.g., saturation of the signals, quantization problems).Therefore the gain has been chosen as large as possible butavoiding saturation of signal . The adaptive gain has beenchosen such that a smooth non-oscillating dynamics is obtained.The final values of gains used were and.Figs. 12 and 13 show the results of the aforementioned experimentaltests. In the case of Experimental Test 1 (see Fig. 12) itcan be seen that the output current is always in phase with thegrid voltage and that the capacitor voltage eventually reachesits desired steady-state value. The controller parameters havebeen intentionally set such that a smooth closed-loop voltagedynamics is obtained in order to avoid the introduction of unwantedharmonics in the output current, i.e., in single-phase PVpower inverters the effects of the voltage dynamics directly affectsthe output current.Fig. 13 shows the electrical behavior of the full-bridge inverterprototype with the designed control scheme for ExperimentalTest 2. Notice that when the abrupt step-down irradiancechange occurs ( 2.8 s), after a settling time approximatelyequal to 0.3 s, the system is able to reach the desired steady state.A similar settling time is obtained when the step-up irradiancechange occurs ( 7.05 s). Note that during the complete experimentaltest the current injected to the utility grid is always inphase with the grid voltage. It should be remarked that the differencein the response of during the step-down and step-upirradiance change is due to the nonlinear behavior of the system.The nonlinear behavior becomes more apparent in the presenceof large set-point changes, disturbances, or errors that cause thesystem to deviate from its nominal point of operation.VI. CONCLUSIONA novel approach to the controller design for single-phasesingle-stage grid-connected power inverters is presented. Insteadof linearizing the system, the control design approachaims to derive a global asymptotically stable closed-loopsystem that takes into account the nonlinear time-varying characteristicsof the system. The robustness of the controller hasbeen improved by adding an adaptive control law. A further theoreticalanalysis of the closed-loop system supported by meansof numerical simulations allows to simplify the implementationof the controller. A laboratory prototype was built in order totest the closed-loop performance of the controlled system. Theexperimental test performed consisted of an abrupt change ofthe PV array irradiance. Even though such sudden and largechange is not likely to occur in reality, it serves to underscorethe robustness and effectiveness of the proposed controller. Theexperimental results showed that the implemented controllerwas able to meet the desired control requirements, i.e., toextract a given amount of power from the PV array (solar arraysimulator, in the case of the experimental prototype) and toinject to the utility grid a current in phase with the grid voltageeven under extreme changes in the system parameters.The results of this paper should be considered as a proofof principle. It is expected that the proposed controller providesa similar performance as those obtained using standardlinear controller design techniques. Moreover, the inclusion ofthe nonlinear characteristics guarantees the closed-loop systemto operate robustly and reliable, even in the presence of largeset-point changes, disturbances, or errors that cause the systemto deviate from its nominal point of operation. 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