Engineering: solar energy

This online test contains 4 questions, each worth 25 marks.

Attempt ALL FOUR questions.






Q1. a.      Calculate the sun altitude and azimuth angles at 2 pm on 20th May in Aberdeen         (latitude 57.1o north). Then determine the solar collector angles (both tilt and azimuth), assuming the collector uses an ideal tracking system.

b.      Calculate the daytime hours for that day. Hint: the altitude angle is zero at sunrise and sunset times, and the daytime is the difference between these two times.

c.       Calculate the global solar radiation (sum of direct and diffuse solar radiations) at that time (2 pm).

d.      Now assume that the solar irradiance variation is approximately given by I = 900 × cos(15o×(local solar hour-12)) W/m2 for a specific day, and the sunrise and sunset times are respectively 6 am and 6 pm. Calculate the absorbed solar irradiation (energy) for that day and the peak sun hour.


[8 marks]



[6 marks]


[6 marks]


[5 marks]







Total Question 1 [25 marks]
Q2. a.       In an ideal buck DC/DC converter, the input and output voltages are respectively 30 V and 15 V, the output current is 5 A, the switching frequency is 50 kHz, the output inductance is 0.5 mH and the capacitance is 100 μF. Determine the converter operating mode and calculate the peak-to-peak output voltage ripple.  

b.      Assume that a PV module with below IV characteristics is directly connected to a load with resistance R=3 ohm. Determine the approximated power delivered to the load, and its voltage and current.

[6 marks]




[6 marks]



[6 marks]

  1. Now assume a buck DC/DC converter (operating in CCM) is placed between the PV module and load R, and P&O MPPT algorithm is  implemented to keep the output of the PV module at MPP.

Calculate the power delivered to the load, and its voltage and current.     


  1. The PV module is composed of 72 cells in series, and each cell has a [3 marks] parallel resistance of 4.8 ohm. Ignore the series resistance. If only            [4 marks] the top PV cell is shaded and the module current is the same Impp, calculate the module MPP voltage and power for two cases;
    1. Without bypass diode,
    2. With a bypass diode across each cell with on-state voltage of

0.6 V.


             Total Question 2                                                                                                                                         [25 marks]




Q3.      It is required to design a stand-alone PV system for a house in a remote    location, where the annual insolation is 1800 kWh/m2 and the energy    

consumption is given in Table Q3a. The PV module data (under STC) and

 battery specifications are given in Table Q3b. The PV system nominal DC voltage is 48 V. Assume the irradiance at earth in a sunny day is 1000  


Table Q3a.                                                                    

DC devices Power (W) Hours   AC devices Power (W) Hours
Air conditioner 1500 8   Fridge/  Freezer 100 24
Lamps 200 5   TV 100 3
        Washing machine 1000 1
        Microwave 800 0.5


Table Q3b.                                                                    

PV module   Battery module
Voc 59 V   Nominal voltage 48 V
Isc 5.8 A   Capacity 8.8


Vmp 51.5 V   Type Li-ion
Imp 4.86 A   efficiency 92%
Temperature coefficient of Pmax -0.4 %/oK   depth of discharge (DoD) 88%
Temperature coefficient of Voc -0.3 %/oK      

coefficient of Isc






  1. Calculate the total electricity required (in Wh per day) and the [8 marks] module arrangement for the solar array. Assume the inverter efficiency is 97% and other losses (excluding inverter loss) is 9%.
  2. According to the battery specification given in Table Q3b, [5 marks] calculate the required battery capacity and number of battery modules if reserve time of 3 days is required.
  3. Assume that the PV system overall cost is £10,000, the retail energy [6 marks] price is £0.18/kWh and it is constant over time (no inflation). Also, assume the Feed in Tariff (FiT) payment is £0.03/kwh with an extra export tariff of £0.04/kwh for 50% of the generation. Calculate the  pay-back time for this PV system with and without FiT.
  4. The PV cells temperature may increase to much higher degrees in [6 marks] summer. Calculate the power generated by the PV array assuming the PV cell average temperature is 45 o Comment if the number of PV modules should be changed at this temperature.


             Total Question 3                                                                                                                                         [25 marks]





Q4.      You need to design a 250 kW PV plant with the inverter and PV modules  data given below (under STC) for a location with average sunny hours of       

4.5 hours/day. Assume the irradiance at earth in a sunny day is 1000

W/m2, and the system other losses (excluding inverter) is 8%.                                     


Table Q4.a – Inverter data                               Table Q4.b – PV module data



AC power output 300 kVA
Maximum DC voltage 1000 V
MPP tracking 250 V – 750 V
Maximum DC current 600 A
Efficiency 98 %

PV module  
Output Power 415 W
VOC 54.1 V
ISC 9.9 A
Vmpp 45 V
Impp 9.22 A
Efficiency 20%


  1. Calculate the area of each module (in m2).
  2. Determine the PV array arrangement and calculate the annual  

energy generation.    [2 marks] c. The PV modules degrade 2% for year 1 and then 0.6% for years        [8 marks] 2-25. Calculate the Annual generated energy for year 20. Assume          the degradation happens at the end of each year.   [4 marks]


  1. i) Repeat the design and determine the PV array arrangement if  the inverter maximum DC current is 500 A.
  2. ii) Determine the lowest limit of the “maximum DC current” of [6 marks] the inverter that makes it inappropriate for this design. Consider  a safety margin of 10% for maximum DC voltage/current.         [5 marks]


             Total Question 4                                                                                                                                         [25 marks]




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