Fault-tolerant control of energy

Modeling and fault analysis of PV energy conversion systems 

The generation process of energy based on the photovoltaic (PV) effect converts incident sunlight into electric energy. PV cells are the most basic energy conversion element that constitutes the building block of a PV panel. Thus, the modeling and proper characterization of the PV cell are required to better understand the conversion process and the evaluation of the behavior of PV systems in various operating conditions. Simulations of the effect of components faults and environmental influence on operating performance may be then realized. 

Models of photovoltaic cell, panel and array

The combination of photovoltaic cells in series composes PV panels (modules) see figure 2.1. When connected in series and equipped with bypass and blocking diodes, PV panels form a PV string. A PV array is composed with the combination of parallel PV strings. The back-fed current is prevented by the use of blocking diodes. The bypass diodes are activated in the case of faulted PV modules to allow the string to produce power and to prevent hot spots that may permanently damage the PV panels. Electric circuit-based models were proposed in the literature to mimic the 7 Ipv Vpv PV cells Blocking diode PV module Bypass diode PV string FIGURE 2.1: PV array components. experimental current-voltage (I-V) curve of the PV cell [31],[32]. The practical model (also called one diode model) is known to have a good compromise between complexity and accuracy [33]. The one-diode equivalent circuit of Iph Id Rp Rs ipv vpv FIGURE 2.2: Equivalent electric circuit of a PV cell. a PV cell as shown in figure 2.2 consists of a controlled current source Iph, a diode traversed by a current Id with series and shunt internal resistances Rs and Rp respectively. The controlled current source is dependent on the level of solar irradiation and the temperature of the cell surface as follows: Iph = (Iph,n + KI∆T) G Gn (2.1) Where Iph,n is the nominal generated current (given at nominal conditions: (T = 25oC and G = 1000W/m2 ), KI is the short-circuit current/temperature 8 coefficient, ∆T = T − Tn (T and Tn are the current and nominal temperatures), G and Gn are the current and nominal irradiations. The current in the diode Id is given by: Id = I0  exp  V + RsI aVt  − 1  (2.2) I0 the saturation current of the diode is given as follows: I0 = Isc,n + KI∆T exp  Voc,n+KV∆T aVt  − 1 (2.3) Where Isc,n is the nominal short-circuit current, Voc,n is the nominal opencircuit voltage. KV is the open-circuit voltage/temperature coefficient, a is a diode constant, Vt is the thermal voltage of the array: Vt = NskT/q, with Ns cells connected in series. k is the Boltzmann constant and q is the electron charge. Rs is the series resistance which depends on the material used to construct the PV cell, its effect is stronger in the voltage source operating region. Rp is the parallel resistance, its effect is stronger in the current source operating region. For a PV array with Npp parallel panels and Nss series panels, the equivalent circuit is given in figure 2.3 and its output current is as follows: ipv = IphNpp − I0Npp  exp   vpv + Rs  Nss Npp  ipv aVtNss   − 1   − vpv + Rs  Nss Npp  ipv Rp  Nss Npp  (2.4) The dynamic conductance gpv is calculated by taking the derivative of eq. (2.4) with respect to voltage as follows [34],[35]: gpv = ∂ipv ∂vpv = − I0Npp a · Vt · Nss · expvpv + Rs · Nss Npp · ipv a · Vt · Nss  − 1 Rp · Nss Npp (2.5) The dynamic resistance is then obtained from eq. (2.5): 9 rpv = − 1 gpv (2.6) The linearized model around the operating point (Ipv, Vpv) is then given as follows [36]: ipv = Gpv · vpv + Ipv − Gpv · Vpv (2.7) where Gpv = gpv(Vpv, Ipv), is the static conductance. NppIph Nss Npp Rp Nss Npp Rs ipv NppId vpv FIGURE 2.3: PV array equivalent circuit. The parameters given in Table 2.1 are used in the consequent sections for the simulation of the PV array. TABLE 2.1: MSX60 PV Panel characteristics Parameter Value Maximum Power (Pmax) 60 W Voltage at Pmax (Vmp) 16, 8 V Current at Pmax (Imp) 3.56 A Short-circuit current (Isc) 3.87 A Open-circuit voltage (Voc) 21.0 V Temp. coef. of Isc 0.003 A/K Temp. coef. of Voc −0.008 V/K 10 2.3 Effect of environmental conditions on the operation of PV arrays The electrical characteristics of PV arrays are directly affected by the variations in climatic conditions. The effect is noticed in the following particular operating points: • The open-circuit operating point, characterized by zero output current Ipv = 0 and an open-circuit output voltage Vpv = Voc. • The short-circuit operating point, characterized by a zero output voltage Vpv = 0 and a short-circuit current Ipv = Isc. • The Maximum Power Point (MPP), characterized by an output current Ipv = IMPP, an output voltage 

Effect of temperature variation

In addition to the incident solar irradiation, ambient temperature (Ta) affects the characteristic curves of PV arrays with a large variation of the opencircuit voltage Voc compared to a minor change in short-circuit current Isc in addition to the shifting of the MPP. The cell temperature is related to the ambient temperature with the following equation: T = Ta + NOCT − 20 800 · G (2.8) where NOCT is the Nominal Operating Cell Temperature at specific conditions (G = 800W/m2 , Ta = 20oC, wind = 1m/s, open-circuit terminals with open back-side mounting). The effect of temperature’s variation on the I-V characteristic curve is given in figure 2.4. The increase in temperature results in a lower open-circuit voltage Voc and slightly higher short-circuit current Isc. 12 Current (A) 0 2 4 6 8 10 12 14 16 18 20 Power (W) 0 200 400 600 800 1000 1200 1400 1600 20oC 30oC 40oC 50oC FIGURE 2.6: Effect of variable temperature on the P-I characteristic curve. Voltage (V) 0 10 20 30 40 50 60 70 80 90 100 110 Dynamic resistance 0 20 40 60 80 100 120 140 160 20oC 30oC 40oC 50oC FIGURE 2.7: Effect of variable temperature on the dynamic resistance characteristic curve. 13 The P-V and P-I curves in figures 2.5 and 2.6 respectively show the effect of the variation of temperature on the performance of the PV array. The increase in temperature values results in a decreasing MPP (decreased performance) in addition to variations in open-circuit voltage and short-circuit current respectively. It is noticed that the voltage operating point of the MPP (VMPP) changes with the variation of temperature (figure 2.5), whereas the current operating point of the MPP IMPP have negligible change. The dynamic resistance is affected near the MPP region by the increase in temperature as shown in figure 2.7. 2.3.2 Effect of solar irradiation variation The variation of solar irradiation is considered the main perturbing factor of PV energy conversion systems because it has faster dynamics compared with temperature and bigger influence on the PV output power. It affects mainly the short-circuit current Isc of the PV array as shown in figure 2.8 with minor effect on the open-circuit voltage Voc. The voltage operating point of the MPP is practically constant with irradiation change as shown in figure 2.9, whereas the current operating point of the MPP as shown in figure 2.10 changes with irradiation variation. The dynamic resistance remains practically unchanged as demonstrated in figure 2.11. 14 Voltage (V) 0 10 20 30 40 50 60 70 80 90 100 110 Current (A) 0 2 4 6 8 10 12 14 16 18 20 1000W/m2 900W/m2 800W/m2 700W/m2 FIGURE 2.8: Effect of variable irradiation on the I-V characteristic curve. Voltage (V) 0 10 20 30 40 50 60 70 80 90 100 110 Power (W) 0 200 400 600 800 1000 1200 1400 1600 1000W/m2 900W/m2 800W/m2 700W/m2 FIGURE 2.9: Effect of variable irradiation on the P-V characteristic curve. 15 Current (A) 0 2 4 6 8 10 12 14 16 18 20 Power (W) 0 200 400 600 800 1000 1200 1400 1600 1000W/m2 900W/m2 800W/m2 700W/m2 FIGURE 2.10: Effect of variable irradiation on the P-I characteristic curve. Voltage (V) 0 10 20 30 40 50 60 70 80 90 100 110 Dynamic resistance 0 20 40 60 80 100 120 140 160 1000W/m2 900W/m2 800W/m2 700W/m2 FIGURE 2.11: Effect of variable irradiation on the dynamic resistance characteristic curve.  FIGURE 2.12: Configurations of the studied faults on the PV array : (a) Line-Ground, (b) Line-Line fault, (c) Mismatch fault, (d) Partial shading fault

Effect of faults on the operation of PV arrays

Grounding of photovoltaic arrays Photovoltaic installation are composed of different parts constructed using electrically conductive materials (such as PV modules frames, mounting racks,…), which are subject to possible contact with insulated current carrying conductors when insulation is lost due to melting or other causes [37]. The grounding of such conducting parts is required to ensure safe operation in the case of the occurrence of such faults that exposes people or living animals to direct contact with hazardous voltage. Figure 2.13 shows the grounding of PV 17 modules frames. p vpv + – PV module frame Current carrying conductor FIGURE 2.13: Grounding of PV arrays 

The effect of Line-Ground fault

A line-ground fault is a short-circuit between a current carrying conductor (live line) and the ground. When we introduce this fault on the PV array as shown in figure 2.12 (a), the voltage given by the three strings of the PV array drops and causes a mismatch fault (strings with different output voltages) that affects the power-voltage curve of the whole PV array. Back-fed current to the faulted string is prevented by placing blocking diodes at the output of each string. The Power-Voltage (P-V) and the Current-Voltage (IV) characteristic curves of the PV array under line-ground fault are given in figure 2.14 (a). The line-ground fault introduces multiple maximum power points on the P-V curve at different operating points. We note that the shape of the P-V curve changes with the configuration of the fault, the choice made in our case is justified by the presence of the lower MPP at the same operating point (voltage) as the MPP of the healthy array. In such situation, hill climbing based algorithms are trapped in a local extremum and fail to track the global MPP.