Photovoltaic Power System: Modeling, Design, and Control by Weidong Xiao

Author:Weidong Xiao [Xiao, Weidong]
Language: eng
Format: azw3, pdf
ISBN: 9781119280323
Publisher: Wiley
Published: 2017-05-05T04:00:00+00:00

Figure 6.5 Dynamics comparison of simulation model and small-signal model.

6.3.4 Boost Converter as the PV-link Power Interface

The design, analysis, and simulation of the boost topology were discussed in Section 5.1.4. Based on the schematic in Figure 5.16, the system dynamics can be derived.

Q on-state dynamics:

6.30a

6.30b

Q off-state dynamics:

6.31a

6.31b

Averaging:

6.32a

6.32b

where is the switching duty cycle and the control variable.

The small-signal model can be derived using the standard linearization process, as expressed in (6.10). The small-signal model to represent the system dynamics is shown in state-space form in (6.33) and the transfer function is shown in (6.34):

6.33

6.34

where and represent the PV terminal voltage and the inductor current, respectively. These are considered to be constant in the steady state. The signals and are the state variables, and represents the control variable in the small-signal model. This is a second-order system with two poles and no zero. It can be standardized in a general form, which is expressed in the transfer function:

6.35

where the undamped natural frequency and damping factor are expressed as and , respectively. To represent (6.34), the following coefficients can be derived:

6.36a

6.36b

6.36c

To continue the case study in Section 5.1.4, the small-signal model is developed with the same system parameters and expressed in state-space form as

6.37

It can be transferred to a SISO transfer function, which represents the small-signal dynamics between and the duty cycle, :

6.38

The undamped natural frequency is 21 720 rad/s and the damping ratio is 0.39. For the step response, the settling time can be estimated as 0.5 ms. The above information is useful in determining the MPPT bandwidth and designing a linear controller to regulate .

The case study in Section 5.1.4 has a nominal duty cycle of 22.9%, representing the steady-state condition when the output voltage is nominal and the PV module is at STC. When the system enters the steady state, a small perturbation of 0.5% is applied periodically to the duty cycle in order to evaluate the step response of . For comparison, the small-signal model works in parallel with the simulation model described in Figure 5.18.

Figure 6.6 compares the output of the small-signal model and the simulation model. Unlike the simulation model, the output of the small-signal model does exhibit switching ripples, but captures the critical dynamics during each transient state. Since the small-signal model is developed according to the MPP condition, the model matches very well at the nominal operating condition, which is around a voltage of 37 V.

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