Eq3.1.1 Modules in Pv Systems

EQ3.1.1 MODULES IN PV SYSTEMS

Consider a crystalline PV module with the following output parameters mentioned at STC (Standard Test Conditions) conditions by the manufacturer.

PMAX = 250 W

VOC= 50 V

ISC = 6 A

NOCT = 40°C

Temperature coefficient of power = –1 W/°C

If the ambient temperature falls to 0°C while the irradiance is 1000 W/m², what is the cell level temperature in °C, as per the NOCT model?

EQ3.1.2 MODULES IN PV SYSTEMS

What is the new power output of the PV module in watts, under the ambient temperature of 0°C and 1000 W/m² irradiance?

EQ3.2.1 MPPT CONCEPTS

Consider a PV module with the following parameters as measured at STC (Standard Test Conditions):

VOC = 55 V

ISC = 5 A

IMPP = 4.7 A

Fill factor (FF) = 75%

Efficiency = 19.75%

Suppose that under normal operation at STC conditions, the module is not connected to an MPPT device, and is instead directly connected to a purely resistive, variable loadR. The load R can be tuned to give a resistance between 0 to 1 k.What value of resistance will you keep the load at, if you wish to derive maximum power from the PV module under STC conditions?

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a)R = 9.34

b)R = 11

c)R = 11.71

d)R = 5

e)Irrespective of the value R takes, the module can never be made to deliver maximum power under STC.

To maximize power, we want to match the load to the “characteristic “ resistance,.

Since , the characteristic resistance can be written as:

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EQ3.3.1 BATTERIES IN PV SYSTEMS

Consider a lead-acid battery with 100 Ah capacity and a rated voltage of 24 V.

What is the total capacity of energy in watt-hours that can be stored in the battery?

EQ3.3.2 BATTERIES IN PV SYSTEMS

Assume that the battery is completely empty. The battery is now charging at a C-rate of 0.50C. What is the charging current in amps that is going into the battery?

A C-rate of 0.5 C means a rate of 50% of the charge per hour. 50% of the total charge is 250 A hr, so the charging current is:

EQ3.3.3 BATTERIES IN PV SYSTEMS

How much time in minutes will it take for the battery to go from 50% SOC to 100% SOC, assuming a constant C-rate of 0.5C? You may assume a linear rate of charging.

The charge rate is 50% per hour. So it will take one hour to provide the second half of the charge. Algebraically,

EQ3.3.4 BATTERIES IN PV SYSTEMS

If the battery is charged at an average constant voltage of 26 V, and discharged at an average constant voltage of 23.4 V, what is the voltaic efficiency of the battery in %?

EQ3.3.5 BATTERIES IN PV SYSTEMS

If the battery takes in a total charge of 100 Ah, and discharges a total of 90 Ah over one charge cycle, what is the coulombic efficiency of the battery in %?

EQ3.3.6 BATTERIES IN PV SYSTEMS

What is the roundtrip efficiency of storage in % for the battery? Assume the same voltaic efficiency and coulombic efficiency as you calculated above.

EQ3.4.1 STAND-ALONE PV SYSTEM

Family Cartman has a small house in the countryside which is not connected to the grid. The place enjoys 4 equivalent sun hours. Therefore, Mr. Cartman has decided to install an off-grid PV system in the house to supply the required electricity in the house.The house electricity needs are summarized in the table below.

When all loads are connected, what is the total DC power load in W?

EQ3.4.2 STAND-ALONE PV SYSTEM

When all loads are connected, what is the total AC power load in W?

EQ3.4.3 STAND-ALONE PV SYSTEM

Assuming that the overall efficiency for the cables, batteries and charge controller is 85% and the efficiency of the inverter is 95%, how much energy in watt-hours will the PV panels have to produce to cover the electricity demand?

EQ3.4.4 STAND-ALONE PV SYSTEM

The available panels that Mr. Cartman is looking at have the following specifications:

Power output = 120 Wp

VMPP = 20 V

IMPP = 6 A

VOC = 22 V

ISC = 7 A

Assume the panels work under MPP conditions. How many panels will be needed to produce that energy?

(120 W / panel)(4 hr) = 480 W hr / panel per day

(1263 W hr) / (480 W hr / panel) = 2.63 panels.

So MrCartman will need to install 3 panels .

EQ3.4.5 STAND-ALONE PV SYSTEM

Since the system is disconnected from the grid, the family Cartman will also need some energy storage. Mr. Cartman has specified that 3 days of autonomy will be sufficient. In this case, batteries with the following specifications will be used:

Battery capacity = 105 Ah

Battery voltage = 12 V

Maximum allowed depth of discharge = 60%

The system is designed to use 24 V as operating voltage. What will be the minimum battery capacity needed in Ah?

He needs to provide 1263 W hr per day for 3 days, so he needs to store 3789 W hr.

Delivered at 24 V,the system needs (3789 W hr) / (24 V) = 157.875Ahr of charge.

At an efficiency of 0.6, the full battery capacity must be (157.875 A hr) / (0.6) = 263.125 A hr.

EQ3.4.6 STAND-ALONE PV SYSTEM

How many of the batteries specified will be needed?

He will need 6 batteries.

EQ3.5.1 ECONOMICS OF PV SYSTEMS

Which of the following variables doesNOTaffect the economic payback period of a PV system?

a)Insolationreceived by the PV system

b)Subsidies and feed-in tariffs

c)Cost of electricity

d)Overall lifetime of the PV system

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EQ3.6.1 ENVIRONMENTAL CONSIDERATIONS OF PV SYSTEMS

Consider a 250 Wp rated crystalline silicon PV module. It results from a manufacturing process that consumes 8 kWh/Wp of PV module.What is the total energy consumed (in kWh) during the production of the module?

2000 kW hr

EQ3.6.2 ENVIRONMENTAL CONSIDERATIONS OF PV SYSTEMS

Assume that the PV module is used in a location where it gives an average annual PV yield of 500 kWh over its lifetime of 30 years. Also assume that the balance of system (BOS) requires a total of 1000 kWh for its production.

What is the energy yield ratio of the entire PV system over its lifetime of 30 years?

Yield ratio = 5

EQ3.6.3 ENVIRONMENTAL CONSIDERATIONS OF PV SYSTEMS

What is the energy payback period for the entire PV system in years?

Payback period = 6 years