Chapter 4 Solar Energy

In this chapter, we will discuss a more accurate equivalent circuit for a PV cell. This circuit helps us to have better prediction and understanding of PV cell current-voltage characteristics as well as at different types of load connected to the PV panel, which is made up of an array of PV cells. Later in this chapter we will discuss the concept of maximum power point tracker (MPPT).
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Chapter 4 Solar EnergyChapter 4Solar Energy II4.1 IntroductionIn this chapter, we will discuss a more accurate equivalent circuit for a PV cell. Thiscircuit helps us to have better prediction and understanding of PV cell current-voltagecharacteristics as well as at different types of load connected to the PV panel, which ismade up of an array of PV cells. Later in this chapter we will discuss the concept ofmaximum power point tracker (MPPT).4.2 More Accurate Equivalent Circuit for a PV CellIf we connect two simple PV cell model as described in Fig. 3.7 in series and simulatethe situation when one of the PV cell is shaded while the other is under strong sunrays, the current source is essentially of zero current. However, in the real PV panelwith PV cells connected in series , such as the BP SX10 with 36 PV cells connected inseries, measurable current is recorded when some of the cells are shaded. This impliesthat the simple PV cell is insufficient to model the PV panel I-V characteristics. Weneed some path to be added to the model to show the current flow within the PV cells. Fig. 4.1 shows a more accurate PV cell equivalent circuit using one parallel resistor,Rp , and one series resistor, Rs , to realize the extra current paths. Let us first derive amathematical expression for this equivalent circuit. By KCL, the current enters node 654. Solar Energy II 66x equal the currents leave this node: ISC = Id + Ip + I (4.1)Substitute (3.23) into (4.1) and re-arrange the terms, we obtain Vd I = ISC − I0 (eqVd /kT − 1)− (4.2) RpAnd Vd and V are related by the following equation Vd = I · Rs + V (4.3)We cannot find a solution of (4.2) with close-loop form. However we may first use anassumed value of Vd to evaluate I and use the value of I to calculate V from (4.3). Anexample as follows shows how to work that out. Example: Given the PV cell has short-circuit current ISC = 4A and at 25◦ Cits reverse saturation current is I0 = 6 × 10−10 A. Show the I-V curves under differentresistance values (a) Rp = ∞, Rs =0; (b) Rp = ∞, Rs = 0.06Ω; (c) Rp = 2.0Ω, Rs = 0Ω;and (d) Rp = 2.0Ω, Rs = 0.06Ω. Solution: With the given temperature and reverse saturation current conditions, q = 38.9 kTUsing the 4 set of values we can now plot the curves as shown in Fig. 4.2. This figureshows that both the series and parallel resistances decrease the maximum power thePV cell can be obtained. Compared to parallel resistance, a small series resistance willcause a dramatic decrease of voltage hence the power delivered by the PV cell.4.3 PV Cells, Modules and ArraysAs the maximum voltage of each PV cell is about 0.6V or below, there is no practicalvalue for application using only 1 PV cell. However, PV cells can be connected in seriesand in parallel to increase the voltage and current respectively. Fig. 4.3 show how thecells are connected both in series then parallel to increase the total deliverable powerof the PV array.4. Solar Energy II 67 x - Rs I ?Id ?Ip + + PV 6 Rp ISC Vd Load V − −Figure 4.1: A more accurate PV cell equivalent circuit with parallel and series resis-tances. Figure 4.2: Plot of I-V curves of a PV cell with equivalent circuit in Fig. 4.1.4. Solar Energy II 68 I - 61 62 I I + Current + PV PV Va cell cell − I + PV PV Va V cell cell − I1 , I2 + PV PV Va cell cell − − ...