Integrating reliability into performance-oriented design of fault-tolerant switch-mode DC-DC converters for photovoltaic energy-conversion applications

This work bridges the disconnect between two consequential design concerns in switch-mode power converters deployed in photovoltaic energy-processing applications: steady-state performance and system reliability. A general framework for fault-tolerant design is presented in the context of a multiphase, interleaved boost converter. A unified, system-level, steady-state description for this topology is proposed. The theoretical derivations are validated against detailed numerical simulations, and their applicability over a wide range of ambient conditions is demonstrated. The steady-state characterization of the converter is then employed to specify the failure rates of circuit components and establish the effects of ambient temperature, insolation, number of phases, and device ratings on system reliability. A Markov reliability model is derived to assess the reliability of a general N-phase converter. The proposed analytical tools provide a methodical framework for design of fault-tolerant, multiphase converters employed in a wide range of photovoltaic systems

Linear Approximations to AC Power Flow in Rectangular Coordinates

This paper explores solutions to linearized powerflow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active and reactive-power injections

Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasi-stationary sinusoidal steady state and operate on phasor quantities. We present two main results in this work. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of non-restrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics

Renewable electric power systems energy yield and performance estimation

This dissertation presents models for reliability assessment, energy yield estimation, and uncertainty analysis of renewable electric power systems. We propose system performability models that describe system attributes while acknowledging failures and repairs in constituent elements. Two broad classes of models are investigated: i) Markov reliability and reward models, and ii) Stochastic hybrid systems (SHS) models. Conventional Markov models capture attributes that are largely static-the only dynamics are due to changes in system configuration due to failures and repairs in constituent elements. On the other hand, SHS can model a wide variety of dynamic phenomena, and provide significant flexibility over Markov models. From an applications perspective, we propose Markov reward models to estimate the performability of photovoltaic energy conversion systems (PVECS) and wind energy conversion systems (WECS). A major impediment in formulating these models is the lack of precise data on model parameters, e.g., component failure and repair rates. Additionally, inputs to these models (e.g., incident insolation in PVECS and wind speed in WECS) are inherently uncertain. Therefore, to ensure validity of the results, we propose set-theoretic and probabilistic methods for uncertainty analysis in these models. With regard to SHS, we first demonstrate how Markov reliability/reward models are a type of SHS. We also present applications to stochastic small-signal modeling of power systems. Case studies demonstrate how to quantify the impact of renewable resources uncertainty on power system dynamics