# Proposed MPPT algorithms

The maximum power point (MPPT) tracking algorithms use the I(V) characteristic and the P(V) characteristic. All over the world there are many studies concerning the maximum power point (MPP) tracking. The performance of various types of MPPT algorithms (Chenni et al., 2007), (Faranda et al., 2007), (Santos et al., 2006), (Hui, 2008) is always measured by precision tracking of MPP and responsiveness to changes in the power curve.

In several studies we have addressed MPP tracking algorithms (Zafiu et al., 2009) and have designed new solutions, original circuits and applications for this purpose (Milea, 2010).

To determine the MPP we used previous mathematical relationships to create the algorithms presented in this section.

The proposed MPP tracking algorithms stands upon the relation dP/dV=0 and involves the continuous adjustment of impedance adaption circuit (increasing or decreasing). Initially we choose two points so that dP/dV<0, respectively dP/dV>0, and the MPP is estimated to the medium value of these two points. Then, while dP/dV>err, the distance between points will be decreases and the MPP will take again the medium value of these points. The principle of MPP determination follows two phases. Firstly there is the measurement of three successive points (according to V) in the coordinates of I and V. Secondly, starting from these three points, the control circuit will decide the next adjustment to achive the MPP.

1.1 General presentation of the algorithms principle This algorithm considers the values of three points (the last measured values) and A the distance between points. The measured value is in the middle and the other points are equidistant positioned on the left and on the right side of middle point (Fig. 9.).

It is considered that the three points are equidistant. Variable d corresponds to the value of the middle range (maximum power point value). Boundary values of the range are given by d-A (first point) and d+A (last point).

At each step of the algorithm, values of d and A are adjusted so that the middle point is located on top of the curve describing the power given by the photovoltaic module. If the points come to be on the same slope of the curve, distance A is increased so that move the middle point at the peak of the curve. If MPP was not peaked and the three points are in the pattern P1 < P0 and P2 < P0 then A will be reduced.

The domain of values used to represent voltage points is building using an n-bit representation. The number of bits determines the adjustment quantum and the algorithm error. The intermediate values couldn’t be represented.

Xmin егг=йх/2лп, n=bits xm„

—1 t………………………………………………………………………………………… …………………………………. 11 —*

ЛХ=Хтах-Хтіп

Fig. 12. The principle of building range of values using the n-bit representation

The values and errors are computed by starting from minimum and maximum values. The interval is spitted into 2n intervals. The subinterval lentgh is err = (xmax – xmin) /2n . This length is also used as error value.

Following studies and tests, we designed two original algorithms to determine the maximum operating point.