#### LESSONS OF EASTER ISLAND

March 17th, 2016

This Chapter presents an analysis of the fundamentals of feedback control for DC/ DC converters and an example of emulator design realized by a buck converter.

The choice of the buck scheme is justified on the basis of the possibility to implement an appropriate control strategy for the emulation purpose.

Both the PV model and the power converter, used for the emulator set up, are first simulated in Matlab-PLECS® environment, then the practical implementation of the control algorithm on a DSP board and the overall PV emulator equipment are described.

Experimental results show that the developed PV emulator is able to reproduce correctly the electrical behavior of a real PV source under any environmental situation, including partial shading and rapidly changing conditions.

The pole placement control technique allows to achieve a dynamics and an output impedance that makes the emulator suitable to be properly used in

association with any converter connected at its output. All these features are obtained by a quite cheap equipment.

The whole equipment can be used to test MPPT algorithm performance and PV inverters both in stand alone and grid-connected operation.

Bolzern P, Scattolini R, Schiavoni N (2008) Fondamenti di controlli automatici, McGraw Hill, 3rd edn

D’Azzo JJ, Houpis C (1995) Linear control system analysis and design. Mc Graw Hill, NY, USA

Di Piazza MC, Vitale G (2010) Photovoltaic field emulation including dynamic and partial shadow conditions. Appl Energy 3(87):814-823

Hercog D, Curkovic M, Edelbaher G, Urlep E (2003) Programming of the DSP2 board with the Matlab/Simulink. In: Proceedings IEEE international conference industrial technology, Vol.2 pp 709-713

Ioannidis G, Kandiais A, Manias SN (1998) Novel control design for the buck converter. IEEE Proc Electron Power Appl 145(1):39-47

Li Q, Zhoun K (2010) Introduction to feedback control. Prentice hall, Upper Saddle River, NJ, USA

Ollila J (1995) A medium power PV-array simulator with a robust control strategy. In: Proceedings IEEE power electron specific conference pp 40-45

[1] The symbol G has been used in Sect. 1.1 to identify the Sun spectral class. It is commonly used

for Newton’s gravitational constant as well, however, it should not confuse the reader because the context in which the two symbols are used is different. In the next chapters, G will denote the solar irradiance and neither the Sun spectral class nor Newton’s gravitational constant will be

[4] The negative value of this energy corresponds to a tied electron

[5] It should be borne in mind that E = p2/2m

[6] The phonon is considered as a particle representation of a lattice vibration in the semiconductor, it is a low energy particle with a relatively high momentum

[7] = Iph – Is(eq(V+IR*)/A? kT – 1)- (V±iR£)

rp

As in the case of Eq. (4.1), five parameters have to be determined to solve Eq. (3.11) and hence to yield the electrical characteristic of the PV source. In this case the five parameters are: the photo-generated current Iph, the dark saturation current due to recombination in the quasineutral region Is, the ideality factor of the diode Aq, the series resistance Rs, and the shunt resistance Rp.

Table 4.1 summarizes the sets of parameters to be identified in the described five-parameter PV model formulations.

The basic modeling process for a PV source is then schematized in Fig. 4.1, for the case of PV five-parameter models, corresponding to Eqs. (4.1) and (3.11). It should be noted that this process has a general validity and can be applied in any case, independently of the model formulation, and of the number of model parameters to be identified.

[8] In this figure, as well as in the next Simulink diagrams, the voltage and current at the output of the PV source are indicated as VPV and IPV respectively.

[9] = I0 – e[(V+iRs)K±K2] – (5.32)

Rp

The effect of Rp consists on lessening the output current and the corresponding model is shown in Fig. 5.17.

In the following example, the above explained Simulink® models have been used to achieve the PV characteristics for different values of Rs and Rp.

The used remarkable points refer to an actual PV module and they have been measured experimentally at G = 773 W/m2. Then, by using the algorithm described in Sect. 4.4.2.3, the four parameters of the model have been determined.

[10] The reader should not confuse the matrix D (in bold case) in Eq. 7.93 with the duty cycle D. In the following, the matrix D will not be considered.

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