Sairaj V. Dhople

Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

Low-voltage distribution feeders were designed to sustain unidirectional power flows to residential neighborhoods. The increased penetration of roof-top photovoltaic (PV) systems has highlighted pressing needs to address power quality and reliability concerns, especially when PV generation exceeds the household demand. A systematic method for determining the active- and reactive-power set points for PV inverters in residential systems is proposed in this paper, with the objective of optimizing the operation of the distribution feeder and ensuring voltage regulation. Binary PV-inverter selection variables and nonlinear power-flow relations render the optimal inverter dispatch problem nonconvex and NP-hard. Nevertheless, sparsity-promoting regularization approaches and semidefinite relaxation techniques are leveraged to obtain a computationally feasible convex reformulation. The merits of the proposed approach are demonstrated using real-world PV-generation and load-profile data for an illustrative low-voltage residential distribution system.

A Unified Approach to Reliability Assessment of Multiphase DC–DC Converters in Photovoltaic Energy Conversion Systems

A systematic framework for reliability assessment and fault-tolerant design of multiphase dc-dc converters deployed in photovoltaic applications is presented. System-level steady-state models allow a detailed specification of component failure rates, and in turn establish the effects of ambient conditions and converter design on reliability. Markov reliability models are derived to estimate the mean time to system failure. Case studies applied to two- and three-phase, 250-W converters demonstrate that topological redundancy does not necessarily translate to improved reliability for all choices of switching frequency and capacitance. Capacitor voltage rating is found to be the dominant factor that affects system reliability.

High efficiency wide load range buck/boost/bridge photovoltaic microconverter

Series strings of photovoltaic modules with integrated dc-dc microconverters can harvest more energy compared to conventional string-inverter architectures if the arrays are partially shaded or the modules mismatched. This work presents a multi-mode dc-dc converter as a candidate microconverter topology for photovoltaic modules. The topology constitutes a single inductor and four switching devices and can function in either buck, boost or an intermediate bridge mode based on the load. The proposed maximum power point tracking scheme is capable of tracking the true maximum even in partially-shaded PV modules. An experimental prototype demonstrates efficiency above 95 % at 215 W over a load range of 3 A to 7 A.

Estimation of Photovoltaic System Reliability and Performance Metrics

A framework to integrate reliability and performance analysis of grid-tied photovoltaic (PV) systems is formulated using Markov reward models (MRM). The framework allows the computation of performance metrics such as capacity and energy yield, and reliability metrics such as availability. The paper also provides an analytical method to compute the sensitivity of performance metrics to MRM-parameter variations. The approach to sensitivity analysis is demonstrated to be particularly useful to formulate optimal operational policies, e.g., repair strategies, as the impact of variations in model parameters on system performance can be rapidly evaluated. Case studies demonstrate several applications of the proposed framework, including analysis of residential and large utility-level installations, and emerging distributed inverter architectures.

Synchronization of Parallel Single-Phase Inverters With Virtual Oscillator Control

A method to synchronize and control a system of parallel single-phase inverters without communication is presented. Inspired by the phenomenon of synchronization in networks of coupled oscillators, we propose that each inverter be controlled to emulate the dynamics of a nonlinear dead-zone oscillator. As a consequence of the electrical coupling between inverters, they synchronize and share the load in proportion to their ratings. We outline a sufficient condition for global asymptotic synchronization and formulate a methodology for controller design such that the inverter terminal voltages oscillate at the desired frequency, and the load voltage is maintained within prescribed bounds. We also introduce a technique to facilitate the seamless addition of inverters controlled with the proposed approach into an energized system. Experimental results for a system of three inverters demonstrate power sharing in proportion to power ratings for both linear and nonlinear loads.

Multiple-input boost converter to minimize power losses due to partial shading in photovoltaic modules

A multiple-input boost (MIB) converter is proposed to implement maximum power point tracking (MPPT) for series strings of solar cells, typically connected across bypass diodes in photovoltaic (PV) modules. The proposed configuration is intended to increase energy harvest from the PV module during instances of partial shading. Results from an experimental prototype demonstrate that the MIB converter extracts up to 9.6 % more power compared to a single-input boost converter in a 120W PV module. The proposed topology can be adopted in emerging distributed MPPT system architectures that utilize microconverters and microinverters.

Synchronization of Nonlinear Oscillators in an LTI Electrical Power Network

Sufficient conditions are derived for the global asymptotic synchronization of a class of identical nonlinear oscillators coupled through a linear time-invariant network. In particular, we focus on systems where oscillators are connected to a common node through identical branch impedances. For such networks, it is shown that the synchronization condition is independent of the number of oscillators and the value of the load impedance connected to the common node. Theoretical findings are then leveraged to control a system of parallel single-phase voltage source inverters serving an impedance load in an islanded microgrid application. The ensuing paradigm: i) does not necessitate communication between inverters, ii) is independent of system load, and iii) facilitates a modular design approach because the synchronization condition is independent of the number of oscillators. We present both simulation and experimental case studies to validate the analytical results and demonstrate the proposed application.

Analysis of Power System Dynamics Subject to Stochastic Power Injections

We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechanical phenomena. In this framework, the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard differential algebraic equation (DAE) model. The DAE model is linearized around a nominal set of active/reactive power injections, and the combination of the linearized DAE model and the CTMC forms a stochastic process known as a stochastic hybrid system (SHS). The extended generator of the SHS yields a system of ordinary differential equations that governs the evolution of the power system dynamic and algebraic state moments. We illustrate the application of the framework to the computation of long-term power system state statistics, and to short-term probabilistic dynamic performance/reliability assessment.

Spatiotemporal model reduction of inverter-based islanded microgrids

Computationally efficient and scalable models that describe droop-controlled inverter dynamics are key to modeling, analysis, and control in islanded microgrids. Typical models developed from first principles in this domain describe detailed dynamics of the power electronics inverters, as well as the network interactions. Consequently, these models are very involved; they offer limited analytical insights and are computationally expensive when applied to investigate the dynamics of large microgrids with many inverters. This calls for the development of reduced-order models that capture the relevant dynamics of higher order models with a lower dimensional state space while not compromising modeling fidelity. To this end, this paper proposes model-reduction methods based on singular perturbation and Kron reduction to reduce large-signal dynamic models of inverter-based islanded microgrids in temporal and spatial aspects, respectively. The reduced-order models are tested in a modified IEEE 37-bus system and verified to accurately describe the original dynamics with lower computational burden. In addition, we demonstrate that Kron reduction isolates the mutual inverter interactions and the equivalent loads that the inverters have to support in the microgrid - this aspect is leveraged in the systematic selection of droop coefficients to minimize power losses and voltage deviations.

Synchronization of Nonlinear Circuits in Dynamic Electrical Networks With General Topologies

Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction-a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chuas circuits.