Open Access
Mishra, Partha Pratim
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
May 08, 2018
Committee Members:
  • Hosam Kadry Fathy, Dissertation Advisor
  • Hosam Kadry Fathy, Committee Chair
  • Christopher Rahn, Committee Member
  • Stephanie Stockar, Committee Member
  • Nilanjan Ray Chaudhuri, Outside Member
  • Self-Balancing Systems
  • Maximum Power Point Tracking
  • Extremum-Seeking
  • Lyapunov Methods
  • Controls
  • Model-based Estimation
  • Renewable Energy Systems
  • Lithium-ion Batteries
  • State Estimation
  • Input Estimation
  • Model Reduction
  • Stability
  • Hardware-in-the-loop Simulation
This dissertation examines the problem of integrating lithium-ion (Li-ion) batteries and photovoltaic (PV) cells in modern solar farms. Rapid growth in the global solar power generation has made battery energy storage integration increasingly important for PV farms in order to accommodate generation intermittency. One critical challenge is that extensive power electronics are needed in these integrated power systems to achieve functionalities such as battery pack balancing and PV maximum power point tracking (MPPT). This dissertation examines the degree to which such functionalities in integrated PV-battery systems can be achieved automatically through novel system designs. In particular, the dissertation develops integration topologies that allow solar farm battery packs to achieve cell-to-cell charge equalization purely by design, eliminating the need for active balancing via power electronics. This synergistic behavior is termed self-balancing. Moreover, one can adjust the relative sizing of the battery cells and photovoltaics in this integration topology in order to achieve rapid MPPT by design, again without requiring active power electronics. Specifically, this dissertation proposes two “hybrid” topologies for integrating PV and battery cells, both of which connect PV generation to each battery cell directly, with or without intermediate power conversion. Furthermore, using Lyapunov stability methods, this dissertation proves that both topologies are globally, asymptotically self-balancing. This means that initial differences among battery cells in either state of charge (SOC) or other internal state variables are guaranteed to diminish asymptotically with time. This reduces the amount and hence the cost of power electronics, otherwise needed for cell balancing in solar farm battery packs. The Lyapunov candidate function used for the stability analysis represents a measure of the “rise in energy” when the system becomes imbalanced compared to a balanced state. Linearization of the system dynamics around an equilibrium value furnishes an analytic expression for self-balancing time constant. Using this time constant and equilibrium conditions for the system dynamics, this dissertation identifies two sets of system properties, one set that only affects the self-balancing speed and the other that can affect both the speed and the equilibrium location. Such analysis further elucidates the impact of various system heterogeneities on the self-balancing behavior. Additionally, through a small-signal analysis, this dissertation shows that the self-balancing topology without power conversion can also achieve rapid MPPT passively under varying solar irradiation levels, that is, without using active MPPT control. Model-based analysis of the passive MPPT behavior leads to the derivation of analytic design rules for passive MPPT-capable systems, development of dynamic models for possible departure of the system from MPP over time, and identification of system parameters influencing the passive MPPT behavior. This dissertation further identifies a fundamental tradeoff between passive MPPT and self-balancing in these hybrid systems. While rapid MPPT can be achieved purely by design, at slower time scales active control is still needed for MPPT in the proposed topology. To that end, this dissertation develops a novel method to achieve such active MPPT inexpensively. The method involves using disturbance estimation methods, together with extremum-seeking (ES), in order to achieve MPPT with minimal current sensing requirements. This estimation-based ES method becomes necessary because sensing requirement for most MPPT control algorithms is quite intensive and for the hybrid topologies in this dissertation, distributed sensing at the hybrid unit sites can render the system cost prohibitive and offset the benefits of self-balancing. Therefore, through a cost analysis, whose details are provided in the Appendix, this dissertation estimates that the cost of the self-balancing topology exhibiting passive MPPT behavior can be 15% less than that of a traditional integration topology of commensurate power and capacity. On the other hand, for the self-balancing topology employing the estimation-based active MPPT controller, a 12% cost reduction is achieved. The overall outcome of this work is a cohesive set of integration topologies and methods that allows solar farms to integrate battery systems and PV modules with minimal cost, without compromising the ability to perform MPPT. From a higher-level, fundamental perspective, the dissertation shows how classical tools from estimation and control theory such as Lyapunov stability analysis, disturbance estimation, and extremum-seeking, can together create a new design concept for energy systems, namely: self-balancing systems.