5. Maximum power point tracking techniques
5.2. Techniques to find local maximum power point
5.2.1. Perturb and Observe algorithm
Perturb and observe (PO) algorithm is based on perturbation of the operating voltage of the photovoltaic generator. By increasing or decreasing voltage of the photovoltaic generator and observing changes in power, whether it increases or decreases, it is possible to find a local maximum power point. This is done periodically and thus the operating point oscillates around the maximum power point once it has been reached. If perturbation step size is short, tracking is slower but more accurate. If perturbation step size is long then tracking is fast but the oscillation around the maximum power point is greater. It is also possible to make a two stage algorithm that is fast when farther away from the maximum power point and slower near the maximum power point.[Yaf07, p.
2]
Figure 5.1. Flowchart of Perturb and Observe maximum power point tracking algorithm.[Yaf07, p. 2]
The flowchart of the Perturb and Observe MPP tracking algorithm illustrated in Figure 5.1 shows the simplicity of this algorithm. In Figure 5.1, i is a discrete step.
Power of the photovoltaic generator, P(i), is calculated from the product of measured voltage and current. This is then compared to its previous value, P(i-1), which was calculated and saved during the previous time the algorithm was performed. Uref is the reference voltage that is given to the converter in order to move to a new operating point. In an ideal case, the measured voltage U(i) should be the same as the last calculated Uref(i), but in practice the control of the converter might not be completely accurate. If power increases, the sign of the voltage perturbation, U, is kept the same.
Otherwise, it is reversed. A tracker can be made to stop once the maximum power point (MPP) is reached within a certain error term or can be left to oscillate around the MPP.[Esr07, p. 440]
Measure U(i), I(i)
Calculate power P(i) = U(i)I(i)
P(i)>P(i-1)
U(i)>U(i-1) U(i)>U(i-1)
Uref(i)=
Uref(i-1)+ U
Uref(i)=
Uref(i-1)- U
Uref(i)=
Uref(i-1)- U
Uref(i)=
Uref(i-1)+ U
U(i-1)=U(i), I(i-1)=I(i)
Return No
Yes No
No Yes
Yes
Figure 5.2. Operation of perturb and observe algorithm in rapidly changing atmospheric conditions.[Was83, p. 3035]
Perturb and observe algorithm can, however, fail under rapidly changing illumination as illustrated in Figure 5.2. At first the system is in operating point A. If there is no change in atmospheric conditions, perturbation U moves the operating point to point B and perturbation will be reversed because power decreased. If irradiance changes rapidly so that the P-U characteristics change from P1 to P2, perturbation U will change the operating point from point A to point C. In this case the algorithm calculates new power in point C to be more than it was in point A. Next perturbation would then be in the direction of increasing voltage although the maximum power point would be at much lower voltage. If irradiance steadily increases the operating point will move further and further towards the open-circuit voltage instead of maximum power point. To avoid this it is possible to use three-point weighted comparison perturb and observe method that compares the actual power point to two preceding ones [Jia05, p. 149]. In perturb and observe technique a sensor is required to measure voltage and another to measure current of the photovoltaic generator. Using measured voltage and current, the power of the generator is computed.[Esr07, p. 440]
5.2.2. Incremental conductance algorithm
The incremental conductance (IC) algorithm uses the slope of the photovoltaic generator power curve to find the MPP. The slope of the power curve is zero at the MPP, positive when U<UMPP and negative when U>UMPP as is shown in Equation (16).[Esr07, p. 441]
MPP can be tracked by calculating the incremental conductance I/ U. If it equals to –I/U, the MPP has been found. If incremental conductance is larger than –I/U, then
the operating point is at U <UMPP and if it is smaller than –I/U, then the operating point is at U>UMPP. Once MPP is found there is no need to calculate new incremental conductance until a change in conditions occur.[Esr07, p. 441]
An effective way to perform incremental conductance algorithm is to create an error signal e as in Equation (17)
dU dI U
e I . (17)
With PI-controller, it is easy to drive the error signal to zero and thereby the operation point to the maximum power point. The flowchart of the incremental conductance algorithm is shown in Figure 5.3.[Esr07, p. 441]
Figure 5.3. Flowchart of the Incremental conductance maximum power point tracking algorithm.[Liu07, p. 637]
Measure U(i), I(i)
U = U(i)-U(i-1) I = I(i)-I(i-1)
U=0
I/ U = -I/U I = 0
Uref(i)=
Uref(i-1)+ U
Uref(i)=
Uref(i-1)- U
Uref(i)=
Uref(i-1)- U
Uref(i)=
Uref(i-1)+ U
U(i-1)=U(i), I(i-1)=I(i) Return
No
Yes No
No Yes
Yes
I/ U > -I/U I > 0
No No Yes
Yes
In Figure 5.3, i is a discrete step. Once voltage and current are measured, the incremental conductance can be calculated from measured values, U(i) and I(i), and from saved values, U(i-1) and I(i-1), from previous time the algorithm was performed.
If the change in voltage is zero, then it is checked if the change in current is also zero. If the change in current is zero, no action is taken. Otherwise, if the change in current is larger than zero, voltage is increased. If the change in current is less than zero, voltage is decreased. If the change in voltage is not zero, then incremental conductance is compared to -I/U. If they are equal, system is in maximum power point. Otherwise, a step U, to increase or decrease voltage is taken depending on the sign of error signal e.
Uref is the reference voltage that is given to the maximum power point tracker in order to move the operating point towards the maximum power point. One sensor is needed to measure the voltage and another to measure the current of the photovoltaic generator.
[Esr07, p. 441]