The many different techniques for maximum power point tracking of photovoltaic (PV) arrays are discussed. The techniques are taken from the literature dating back to the earliest methods. It is shown that at least 19 distinct methods have been introduced in the literature, with many variations on implementation. This paper should serve as a convenient reference for future work in PV power generation.

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Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques

This paper proposes a method of modeling and simulation of photovoltaic arrays. The main objective is to find the parameters of the nonlinear I-V equation by adjusting the curve at three points: open circuit, maximum power, and short circuit. Given these three points, which are provided by all commercial array data sheets, the method finds the best I-V equation for the single-diode photovoltaic (PV) model including the effect of the series and parallel resistances, and warranties that the maximum power of the model matches with the maximum power of the real array. With the parameters of the adjusted I-V equation, one can build a PV circuit model with any circuit simulator by using basic math blocks. The modeling method and the proposed circuit model are useful for power electronics designers who need a simple, fast, accurate, and easy-to-use modeling method for using in simulations of PV systems. In the first pages, the reader will find a tutorial on PV devices and will understand the parameters that compose the single-diode PV model. The modeling method is then introduced and presented in details. The model is validated with experimental data of commercial PV arrays.

Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays

Maximum power point tracking (MPPT) techniques are used in photovoltaic (PV) systems to maximize the PV array output power by tracking continuously the maximum power point (MPP) which depends on panels temperature and on irradiance conditions. The issue of MPPT has been addressed in different ways in the literature but, especially for low-cost implementations, the perturb and observe (PO moreover, it is well known that the P&O algorithm can be confused during those time intervals characterized by rapidly changing atmospheric conditions. In this paper it is shown that, in order to limit the negative effects associated to the above drawbacks, the P&O MPPT parameters must be customized to the dynamic behavior of the specific converter adopted. A theoretical analysis allowing the optimal choice of such parameters is also carried out. Results of experimental measurements are in agreement with the predictions of theoretical analysis.

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Optimization of perturb and observe maximum power point tracking method

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Low power dissipation and maximum battery runtime are crucial in portable electronics. With accurate and efficient circuit and battery models in hand, circuit designers can predict and optimize battery runtime and circuit performance. In this paper, an accurate, intuitive, and comprehensive electrical battery model is proposed and implemented in a Cadence environment. This model accounts for all dynamic characteristics of the battery, from nonlinear open-circuit voltage, current-, temperature-, cycle number-, and storage time-dependent capacity to transient response. A simplified model neglecting the effects of self-discharge, cycle number, and temperature, which are nonconsequential in low-power Li-ion-supplied applications, is validated with experimental data on NiMH and polymer Li-ion batteries. Less than 0.4% runtime error and 30-mV maximum error voltage show that the proposed model predicts both the battery runtime and I-V performance accurately. The model can also be easily extended to other battery and power sourcing technologies.

Accurate electrical battery model capable of predicting runtime and I-V performance

Presents here a complete dynamic model of a lithium ion battery that is suitable for virtual-prototyping of portable battery-powered systems. The model accounts for nonlinear equilibrium potentials, rate- and temperature-dependencies, thermal effects and response to transient power demand. The model is based on publicly available data such as the manufacturers' data sheets. The Sony US18650 is used as an example. The model output agrees both with manufacturer's data and with experimental results. The model can be easily modified to fit data from different batteries and can be extended for wide dynamic ranges of different temperatures and current rates.

Dynamic lithium-ion battery model for system simulation

The performance of a battery-ultracapacitor hybrid power source under pulsed load conditions is analytically described using simplified models. We show that peak power can be greatly enhanced, internal losses can be considerably reduced, and that discharge life of the battery is extended. Greatest benefits are seen when the load pulse rate is higher than the system eigenfrequency and when the pulse duty is small. Actual benefits are substantial; adding a 23 F ultracapacitor bank (3 /spl times/ 7 PC10 ultracapacitors) in parallel with a typical Li-ion battery of 7.2 V and 1.35 A hr capacity can boost the peak power capacity by 5 times and reduce the power loss by 74%, while minimally impacting system volume and weight, for pulsed loads of 5 A, 1 Hz repetition rate, and 10% duty.

Power and life extension of battery-ultracapacitor hybrids

An actively controlled battery/ultracapacitor hybrid has broad applications in pulse-operated power systems. A converter is used to actively control the power flow from a battery, to couple the battery to an ultracapacitor for power enhancement, and to deliver the power to a load efficiently. The experimental and simulation results show that the hybrid can achieve much greater specific power while reducing battery current and its internal loss. A specific example of the hybrid built from two size 18650 lithium-ion cells and two 100-F ultracapacitors achieved a peak power of 132 W which is a three-times improvement in peak power compared to the passive hybrid power source (hybrid without a converter), and a seven times improvement as compared to the lithium-ion cells alone. The design presented here can be scaled to larger or smaller power capacities for a variety of applications.

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Power enhancement of an actively controlled battery/ultracapacitor hybrid

An approach to model the solar cell system with coupled multiphysics equations (photovoltaic, electro-thermal, direct heating and cooling processes) within the context of the resistive-companion method in the Virtual Test Bed computational environment is presented.. Appropriate across and through variables are defined for the thermal terminal of the system so that temperature is properly represented as a state variable, rather than as a parameter of the system. This allows enforcement of the system power conservation through all terminals, and allows simultaneous solutions for both the electrical potentials and the system temperature. The thermal port built accordingly can be used for natural thermal coupling. The static and dynamic behaviors of the solar array model based on the approach are obtained and validated through comparison of simulation results to theoretical predictions and other reported data. The electro-thermal modeling method developed here can be generally used in the modeling of other devices, and the method to define the across and through variables can also be generalized to any other interdisciplinary processes where natural coupling is required.

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Dynamic Multi-Physics Model for Solar Array

A state space approach to the design of a maximum power point (MPP) tracking system for photovoltaic energy conversion is presented. The problem of optimal-power control of a nonlinear time-varying system is reduced to an ordinary problem of dynamic system stability in state space by applying MPP conditions in controller design. The resulting tracking system searches for the reference point and tunes the converter for maximum power delivery to a load that may represent an end-user, or an energy-storage element, or a power grid-interface. The proposed design procedure for the MPP tracking system ensures a global asymptotic stability under certain conditions, and a minimum degree of the dynamic feedback. The design is verified using the virtual test bed, demonstrating accurate MPP tracking capability under unpredictable weather change, parameter variation, and load disturbance. The tracking system can be applied either to a stand-alone or grid-connected photovoltaic installations, and can be implemented in either analog circuitry or a digital microcontroller.

Shengyi Liu

Papers

Dynamic lithium-ion battery model for system simulation

Power and life extension of battery-ultracapacitor hybrids

Power enhancement of an actively controlled battery/ultracapacitor hybrid

Dynamic Multi-Physics Model for Solar Array

Power controller design for maximum power tracking in solar installations