IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 4, NO. 1, JANUARY 2013 99 An Optimal Total Cross Tied Interconnection for Reducing Mismatch Losses in Photovoltaic Arrays M. Z. Shams El-Dein, Student Member, IEEE, Mehrdad Kazerani, Senior Member, IEEE, and M. M. A. Salama, Fellow, IEEE Abstract—A mismatch in a photovoltaic array implies differ- ences in the – characteristics of the modules forming the array. This can lead to significant energy losses known as mismatch losses. The mismatch and the resulting losses can be reduced by altering the interconnection of the array. This paper proposes an optimal total cross tied interconnection, based on a thorough mathematical formulation that can significantly reduce mismatch losses. The improvement over existing photovoltaic array in- terconnections has been demonstrated by extensive simulation results. Index Terms—Mismatch losses, partial shading, photovoltaic, se- ries parallel, total cross tied. NOMENCLATURE EA Annual array’s energy during mismatch (Wh). EA Annual array’s maximum energy during mismatch (Wh). Reference irradiance level (W/m ). Time segment index. HA Annual array’s in plane irradiance level during mismatch (Wh/m ). Parallel circuits index. IA Array’s current at time segment (A). IRR Module irradiance level at time segment (W/m ). IRRA Arrays’ irradiance level at time segment (W/m ). Module reverse bias diode saturation current (A). IM Module current at time segment (A). Module short circuit current at reference irradiance level (A). Columns index. Total number of parallel circuits. Manuscript received January 08, 2012; revised May 23, 2012; accepted May 27, 2012. Date of publication July 12, 2012; date of current version December 12, 2012. This work is protected by the international patent number PCT/CA2011/000556. M. Z. Shams El-Dein and M. Kazerani are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada (e-mail: mshamsel@uwaterloo.ca; mkazeran@uwaterloo.ca). M. M. A. Salama is with the Department of Electrical and Computer Engi- neering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada and also with King Saud University, Riyadh, Saudi Arabia (e-mail: msalama@uwaterloo.ca). Digital Object Identifier 10.1109/TSTE.2012.2202325 MPPA Array’s maximum power point at time segment (kW). Total number of columns. Total number of situations. Module total number of series modules. Array’s dc rating (kW). PR Performance Ratio. Module index. Module series resistance ( . Module parallel resistance . Time duration of time segment (h). VA Array’s voltage at time segment (V). VR Row voltage at time segment (V). VM Module voltage at time segment (V). Module thermal voltage (V). Existence variable. I. INTRODUCTION I N late 2006, the government of Canada introduced the clean air act in the Parliament. The act represents a comprehen- sive and integrated approach to regulation of air emissions in Canada. To complement introduction of the act, the govern- ment also released in 2007 Canada’s action plan to reduce green- house gases and air pollution and introduced a series of ecoEN- ERGY initiatives to reduce smog and Green House Gas (GHG) emissions affecting the environment and health of Canadians. In Ontario, there are great incentives to invest in renewable DGs through Ontario Power Authority’s (OPA) Feed-In Tariff (FIT), which is a pricing structure for renewable-based electricity pro- duction. This program pays from 44.3 to 80.2 ¢/kWh for the electricity generated from solar PV, from 13.5 to 19 ¢/kWh for the electricity generated from wind energy, and from 10.4 to 19.5 ¢/kWh for the electricity generated from biogas [1]. By the end of 2010, the FIT program had successfully increased the total connected capacity of PV in Ontario to about 215 MW; moreover, the world’s largest PV farm of 80-MW capacity has been installed in Sarnia, Ontario [2]. The use of large PV farms for power generation has many challenges. For example, passing clouds can cause the PV farm 1949-3029/$31.00 © 2012 IEEE