# ELEN6013 Renewable Energy Principles

At what angle should a PV module at Colombo, Sri Lanka (Latitude +6.9) be tilted up from the horizontal plane for the solar rays to fall perpendicular to the module at solar noon on January 31st (i.e. day number n=31) when facing the direction of the sun? [3 Marks]

(b) At what solar time the sun will rise at Melbourne, Australia (Latitude=-37.8°) on 21st December 2019 (day number n = 355)? Please give the time in hours.minutes format. [4 Marks]

(c) A PV module is mounted on a roof at Perth, Western Australia (Latitude=-32°) facing North-East (NE) and tilted up at an angle of 20° to the horizontal plane. If the altitude angle (β) and azimuth angle of the sun (φs) at a given time are β = 60° and φs = 30° (from North), what percentage of the direct beam of sun would be normal to the PV module at this time? [4 Marks]

(d) The insolation in kWh/m2/day at a selected site is as given in Table 1(d). A PV array is to be designed to capture 130kWh/day of insolation on the average on any day of the year. If the cost of PV modules per unit area is $100/m2, what would be the maximum cost of the tracker of a 1-axis tracked array with tilt angle equal to the latitude angle to be more profitable over fixed mount array with tilt angle equal to the latitude angle? The balance of system cost other than the PV module and the tracker costs can be assumed as equal for the two cases.

South facing PV array mounted on a polar mounted 1-axis tracker at Miri, Malaysia (Latitude = +4.34°) is tracking Sun accurately in the East-West direction. By what percentage the direct beam component of insolation received by this array would be higher compared to a South facing polar-mount fixed array at 10am solar time on the March 21st (day number n=81) at the same site?

[8 Marks]

**Q2 [25 Marks] **

(a) A 72 cell PV module at a cell temperature of 25°C produces a short-circuit current of 7A under 1-sun. The reverse saturation current is 1×10-10A and the fill factor is 72%. Use the simplest equivalent circuit of a PV cell for the predictions

(i) By what percentage the open-circuit voltage drops when the insolation drops by 50%?

[3 Marks]

(ii) What would be the maximum power of the module under half-sun condition?

[3 Marks]

(b) The manufacturer’s specifications of electrical data of a 215W PV module are given in the Table Q2(b) below.

Table Q2(b) Electrical Data Measured at Standard Test Conditions (STC): Irradiance of 1000W/m2, AM1.5 and cell temperature 25°C | ||

Peak Power (±5%) | Pmax | 215W |

Rated Voltage | Vmpp | 39.8V |

Rated Current | Impp | 5.4A |

Open Circuit Voltage | Voc | 48.3V |

Short-Circuit Current | Isc | 5.8A |

Maximum System Voltage | UL | 600V |

Temperature Coefficients | Power | -0.38%/K |

Voltage (Voc) | -136.8mV/K | |

Current (Isc) | 3.5mA/K | |

NOCT | 45°C±2°C | |

Series Fuse Rating | 15A |

What would be the power dissipated by a fully shaded cell carrying 2.9A when there are no bypass diodes connected? [4 Marks]

(ii) What would be the power supplied to a 12V ideal battery when one cell is fully shaded and no by-pass diodes are connected? [4 Marks]

(d) A grid-connected PV array is supplying 5MW of ac power to the grid with inverters having an efficiency of 95% and PV modules with following power losses under operating conditions. 12.5% due to temperature, 1% due to dust, 1.5% due to module mismatch. If the modules are 20% efficient in energy conversion and the operating insolation is 800W/m2, what would be the area occupied by the PV modules in hectares? Note: 1ha = 10,000m2 [3 Marks]

**Q3 [20 Marks] **

A 1.2MW horizontal axis wind turbine with a tower height of 80m and blade diameter of 60m is installed at a site with average temperature of 20°C, an altitude above sea level of 90m at the ground and a friction coefficient (α) of 0.15. An anemometer mounted on a 10m height at the same site records an annual average wind speed of 5m/s. The wind turbine has a cut-in wind speed of 3.5 m/s, a rated wind speed of 12 m/s and a cut-out wind speed of 25 m/s.

(a) What is the ratio of the maximum wind power to the minimum wind power felt by a tip of a turbine blade during its rotation in these winds? [3 Marks]

(b) How much is the wind power in kW experienced by the turbine at average wind speed at the hub height? [6 Marks]

(c) What would be the turbine efficiency at the rated wind speed if it then delivers rated output power? [2 Marks]

(d) If the wind speed at the site follows Rayleigh distribution, calculate the following by considering the wind speed at the hub height.

(i) Hours per year the turbine is producing power [3 Marks]

(ii) Energy generated in MWh per year at rated power [3 Marks]

(iii) Annual Energy supplied to the grid, using the approximate Capacity Factor calculated using the empirical equation. [3 Marks]

**Q4 [15 Marks] **

A 2-jet 0.5m diameter Pelton wheel is operating at its rated speed of 674 rpm with an efficiency of 90%. An induction generator directly coupled to the turbine is feeding the rated power of 32.5kW to the grid. The pressure of water at the end of the pipeline at the powerhouse, just before the nozzles, is measured as 655kN/m2. Of the available head at the end of the pipeline, 5% is lost due to the nozzles. The power losses in the generator can be assumed as 10% of its output power.

Calculate for the rated operation:

(a) Water flow rate to the turbine in m3/s [6 Marks]

(b) Speed of a water jet in m/s and run-away speed of the turbine in rad/s. [4 Marks]

The torque of the turbine with 50% of rated flow to the turbine as calculated in part Q4(a), with the same net head and operating at a turbine speed of 900 rpm. You may assume linear torque-speed characteristic for the turbine. [5 Marks]

**Q5 [15 Marks] **

The enthalpy and entropy of reactants and product for a Proton Exchange Membrane (PEM) Fuel Cell Stack operating at STP conditions of 1 atm pressure and 25°C temperature are given in the Table Q5. If a PEM fuel cell stack operating at STP is supplying 10kW of power to a load with a cell terminal voltage of 0.5V, calculate the following.

(a) Usage of hydrogen and oxygen in the fuel cell stack in g/s. Molecular weight of H2 is 2.02g/mol and that of O2 is 32g/mol. [4 Marks]

(b) How much energy in kWh is lost due to the losses (i.e. non-idealities) of the PEM fuel cells if the system is used for 5 hours? [6 Marks]

If the load voltage required is constant 180V dc, the maximum power per cell is 100W and the load power demand can vary from 0 to 10kW, design the fuel cell power supply as given below.

(c) How many cells should be in series in the stack? [1 Mark]

(d) Draw a schematic diagram with labels to show how the fuel cell stack is connected to the load. If a dc/dc converter is used, state the type of the converter as buck, boost etc. giving reasons for the selection. [4 Marks]

Table Q5 H2 | O2 | H2O (liquid) | |

Enthalpy H (kJ/mol) | 0 | 0 | -285.8 |

Entropy S (kJ/mol/K) | 0.130 | 0.205 | 0.0699 |