Elsevier

Energy

Volume 27, Issue 4, April 2002, Pages 347-361
Energy

An efficient algorithm to simulate the electrical performance of solar photovoltaic arrays

https://doi.org/10.1016/S0360-5442(01)00089-5Get rights and content

Abstract

An efficient algorithm to simulate the performance of solar photovoltaic arrays is developed. The algorithm uses the linear programming technique and minimizes the current across each junction of the array to the order of 10−5. It offers an explicit advantage of execution time for the simulation of large array networks including such interconnected configurations as TCT (Total-Cross-Tied) and BL (Bridge-Linked) configurations. Numerical computations are carried out to investigate the fault-tolerance in field conditions of the simple series-parallel, total-crossed-tied and bridge-linked solar cell interconnection configurations. Results show that the cross-tied arrays (BL and TCT) are comparatively less susceptible to electrical mismatches.

Introduction

Solar photovoltaic (PV) generators are networks of various interconnections between solar cells, diodes, cables and other components. The cells are connected in series and parallel to provide required terminal voltage and current ratings. In practical situations solar cells have neither the identical electrical characteristics nor they are uniformly illuminated. Consequently, in field conditions the cellular array circuits exhibit faults resulting from mismatch losses such as their power output is less than the sum of output power of constituent solar cells. The mismatch loss tends to enhance with time due to degradation resulting from aging of cells. Fault-tolerance for the electrical mismatches has been investigated [1], [2], [3], [4], [5] for both terrestrial as well as satellite born solar PV systems. The array power loss can be reduced if each row of parallel strings is shunted by a bypass diode [6], [7], [8], [9], [10], [11]. Efficiency of an array, which is affected by electrical mismatches, can also be enhanced by such redundant circuit design as series-paralleling [3], [12]. In this scheme, a branch circuit is divided into series blocks. One or more of these series blocks can be bridged by a bypass diode.

In recent years, some solar cell cross interconnection configurations have been proposed and tested to improve the fault-tolerance [13], [14]. These configurations are:

  • 1.

    Total-Cross-Tied (TCT) array which is obtained from the simple SP array (which has almost zero interconnection redundancy) by connecting ties across each row of junctions; it may be characterized as the scheme with the highest possible redundancy, and

  • 2.

    Bridge-Linked (BL) array, in which all cells are interconnected in bridge rectifier fashion.

Several computer simulation models for solar PV generators have been developed during the last two decades [2], [6], [8]. These models involve three types of solar cell interconnection circuits: simple series string, a series-parallel block and series connection of series-parallel blocks. These models also analyze the effects of electrical mismatches and partial shading on these circuits. More recently, computer models of cross-connected cell interconnection circuits have also been developed [13], [15] to evaluate fault-tolerance of the arrays. All the above simulation models consider only small arrays of size up to (36×8) cells. In these models Kirchoff's law is applied to each junction of the array to obtain system of equations specifying the currents and voltages in the network. The core of the mathematical problem resides in the need to determine a set of junction potential values that will cause the junction currents to vanish.

In practice, grid connected solar PV systems of capacity greater than 20 kW use a cellular string of 20 to 24 modules (each having 36 cells) in series. The entire array may consist of 20 to 60 such strings. These types of arrays are often referred to as large arrays and are used to drive 240 Vdc boost or buck inverters in conjunction with the maximum power point tracker. For such large arrays, the computer implementation of algorithms of varying system of nodes and meshes in the network becomes difficult. Therefore, the above algorithms exhibit very slow convergence and take more time in execution. Since time and space used by an algorithm are the two main measures for its efficiency, a faster and more efficient algorithm is needed to achieve the state of equilibrium. The proposed algorithm uses the linear programming technique and minimizes the current across each junction in the array to the order of 10−5. Although the storage required for the input data using this algorithm remains almost the same as earlier algorithms, however, it offers the advantages over the execution time.

Section snippets

Current-voltage relationship

The current voltage relationship for a single diode solar cell (m, n) in an array can be obtained [16] as follows:f(Vm,n,Im,n)=0orIm,n−(Iph)m,n+(Is)m,nexpenkT(Vm,n+Im,n(Rs)m,n)−1+Vm,n+Im,n(Rs)m,n(Rsh)m,n=0

Eq. (1) can further be rewritten asIm,n(Iph)m,n−1+(Is)m,n(Iph)m,nexpe(Voc)m,nnkTm,nVm,n+Im,n(Rs)m,n(Voc)m,n−1+Vm,n+Im,n(Rs)m,n(Voc)m,n(Voc)m,n(Rsh)m,n(Iph)m,n=0Im,n(Iph)m,n−1+(Is)m,n(Iph)m,nexpbm,nVm,n+Im,n(Rs)m,n(Voc)m,n−1+Vm,n+Im,n(Rs)m,n(Voc)m,n(σ)m,n=0wherebm,n=e(Voc)m,nnkTm,n and (σ)m,n=(V

The algorithm

An (M×N) array of solar cells is considered. It consists of N parallel strings with each string having M cells connected in series. If all solar cells are identical, the current generated by each cell of a string must be the same. But, in reality, because of manufacturer's tolerances, the environmental stresses or the shadow effects, the cells of the same string exhibit different current ratings. Hence due to this mismatch in the output of individual cells in an array, the voltage across

Computational results and discussions

To investigate the electrical characteristics of different solar cell interconnection schemes, the characteristic data for all solar cells are required. Based on the analysis of characteristic data for 36 solar cells supplied by the manufacturer, Central Electronics Limited, Sahibabad, India, it was felt that the solar cell parameters Iph and Voc varied randomly between a maximum and a minimum. Besides, mean and standard deviation of the distribution of this data could also be known.

Comparison of algorithms

The algorithm given by [13], [15] follows the regular perturbation method where the value of Jm,n depends on the perturbation series ∑(∂Jm,n/∂Pi,j). The difference between Jm,n and the next iterative value of Jm,n is referred to as a perturbation on the solution of Jm,n.

For a simple series parallel array of size (M×N), the pseudo code for these algorithms can be described as follows:

  • P[m][n] ← m(v/M)

    • V[m][n] ← P[m][n] - P[m-1][n]

  • Evaluate I[m][n]

  • J[m][n] ← I[m][n] - I[m+1][n]

  • if (RMS(J[m][n]) < ϵ)

Conclusions

The electrical network analysis of solar cell interconnection circuits involves the computer implementation of algorithm representing varying system of nodes and meshes in the network. The task becomes more difficult in case of large arrays and the algorithm exhibits very slow convergence. In this paper, an efficient algorithm using linear programming technique is presented. This algorithm has been implemented as a computer program written in C++. The algorithm makes it possible to simulate the

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