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In this paper, a four power semiconductor switch based three-phase inverter is proposed for renewable energy integration to a generalized micro-grid system. The proposed topology b-4 of three-phase inverter is investigated to make the commercial micro-grid system to be cost effective and hardware optimized. A simple Sine PWM (SPWM) based control strategy is proposed for the b-4 inverter topology instead of the traditional complex four-switch based Space Vector techniques. The overall control structure is implemented using the Lyapunov function based non-linear controller to track the inverter current directly in the a-b-c frame so that a specific amount of active and reactive grid power flow can be controlled in a de-coupled manner along with low THD of grid currents in the presence of non-linear load at the point of common coupling. A novel technique of using the Spatial Repetitive Controller (SRC) is also proposed to eliminate the effect of mid-point voltage fluctuation of the DC link even in the case of asymmetrically split DC link capacitors without any extra voltage or current sensors unlike conventional methods. Detailed experimental results are provided to show the efficacy of the proposed hardware system for grid connected applications in the micro-grid.Index Terms-four-switch based three-phase inverter (b4-topology), Generalized three-phase micro-grid bus, Sine PWM based control, Non-linear load

A phenomenological model of the bulk force exerted by a lithium ion cell during various charge, discharge, and temperature operating conditions is developed. The measured and modeled force resembles the carbon expansion behavior associated with the phase changes during intercalation, as there are ranges of state of charge (SOC) with a gradual force increase and ranges of SOC with very small change in force. The model includes the influence of temperature on the observed force capturing the underlying thermal expansion phenomena. Moreover the model is capable of describing the changes in force during thermal transients, when internal battery heating due to high C-rates or rapid changes in the ambient temperature, which create a mismatch in the temperature of the cell and the holding fixture. It is finally shown that the bulk force model can be very useful for a more accurate and robust SOC estimation based on fusing information from voltage and force (or pressure) measurements. Lithium intercalation and de-intercalation result in volumetric changes in both electrodes of a li-ion battery cell. At the anode, carbon particles can swell by as much as 12% during lithium intercalation, and the resulting stress can be large.6 Commercial battery packs involve numerous cells assembled to occupy a fixed space as shown in Fig. 1 and held in mild compression to resist changes in volume associated with lithium intercalation and deintercalation. A small compression prevents de-lamination and associated deterioration of electronic conductivity of the electrodes. A large compression, however, can decrease the separator thickness and lead to degradation and power reduction due to the separator pore closing. 18The effect of expansion and the system's mechanical response on the cell performance and life 18,5,2,24 are under intense investigation with studies ranging from the micro-scale, 4,6,24 the particle level, 4 and multiple electrode layers. 22,8 While progress toward predicting the multi-scale phenomena is accelerating, 9,28 the full prediction of a cell expansion and its implications to cell performance depends heavily on the boundary conditions associated with the cell construction and electrode tabbing and crimping. Moreover, the wide range of conditions with respect to C-rates and temperatures that automotive battery cells must operate make the physics-based modeling approach very challenging. 17 Finally, measuring and quantifying the internal stress or strain to tune or validate the multi-scale models requires complex instrumentation. 23,30 In contrast to the micro-scale, the macro-scale stress and strain responses are directly observable and measured with high accuracy, 16,19,26 thus could be used to develop phenomenological models inspired by the underlying physics.To this end, a phenomenological model is developed in this paper in an attempt to mimic the evolution of bulk force/stress and to quantify the contributions of state of charge dependent intercalation and thermal expansion. A rudimentary version of this model ...

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This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of physical systems undergoing contact, the construction of a numerical method for their optimal control has proven challenging due to the combinatorial nature of the state-dependent switching and the potential discontinuities that arise during switches. This paper constructs a convex relaxation-based approach to solve this optimal control problem. Our approach begins by formulating the problem in the space of relaxed controls, which gives rise to a linear program whose solution is proven to compute the globally optimal controller. This conceptual program is solved by constructing a sequence of semidefinite programs whose solutions are proven to converge from below to the true solution of the original optimal control problem. Finally, a method to synthesize the optimal controller is developed.Using an array of examples, the performance of the proposed method is validated on problems with known solutions and also compared to a commercial solver.