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My attention was drawn earlier today to a statement made by President Mahama to the effect that:

“Ghana’s population is 25 million, but statistics indicates that mobile phone lines in Ghana is over 27 million and these phones are charged every night, and this is one of the causes of the load-shedding”.

  1. The President in linking the growth in mobile phone usage to the ongoing power crisis, known locally as ‘dumsor’, seems to suggest a causal factor even above things like industrial demand. My good friend Bright Simons earlier provided some calculations which refuted the President’s assertion that the demand in power consumption can be attributed to mobile phone usage. Following in a similar fashion, I present to you some calculations with additional factors. So, here we go:
  2. According to the NCA, Ghana’s Mobile Voice subscriber base grew by 0.47% and ended the year from 30,219,162 in November 2014 to 30,360,771 lines.
  3. Let’s consider the upper limit by assuming the each of these 30.36 million lines is connected to an active smartphone (used for calls, web browsing and other multimedia activities) and is only charged once in a day for full-cycle usage.
  4. Even though it is highly unlikely that all phones in the system are smartphones and that all the 30m plus lines are being concurrently used at the same time, we use these nonetheless as our proxy. For example, smartphones such as an iPhone 5 consume the most amount of power, which necessitates charging every night as compared to say a Nokia 3310.
  5. For starters, let us also assume each of these smartphones is a typical iPhone 5 or Samsung Galaxy 4 and most of these new phones utilize lithium-ion batteries with typical capacities circa 3,000 mAh (milliamp-hours) and rated at 3.8V
  6. We shall utilize the following key equations:  Watt Hours = Volts X Ampere Hour (Ah); and Power (Watts) = Energy (Watt Hours)/Time (Hour)
  7. Hence for 30.36 million lines all using a typical Samsung galaxy battery this would consume: 3.8V x 3Ah X 30.36 million units = 346,112,789 Watt-hours per day
  8. Again let’s allow for an efficiency loss for heat and resistance – tropics factor! This is conservatively reasonable for a modern Li-Ion battery. So, say the typical smartphone takes about 3 hours to go from red battery 0% to 100% full charge in the tropics compared to a standard 2hrs in more temperate conutries and will be only used once in 24hr cycle before recharging.
  9. Hence, power consumption for all phone units becomes: 346,112,789 Watt-hours/3hrs = 115,370,930 Watts or 115MW.
  10. Total installed peak time demand for electricity in Ghana is circa 2,000MW. Ghana has2,600MW of effective installed capacity and in a well-managed system with a capacity factor of 70-80%; we should have about 2,200 MW of rated capacity available to be delivered to the system.
  11. Therefore, using the base case peak load demand of 2,000MW, mobile phones will only consume about 5.75% (115MW/2,000MW) of daily electricity demand.
  12. The reality is that is figure is likely to be substantially lower than 5.75% of electricity demand when we consider that the utilization rate for all the 30m plus lines will be lower and not all of them will be connected to a smartphone anyway. Even if they were, there is a greater probability that some could be off for days.
  13. Perhaps, the President meant to talk about the increasing demand patterns due to urbanisation but his contextual analogy could have been better placed or maybe it was lost in translation from Twi to English.
  14. Regardless of this, Nana Kwadwo’s call that maybe every person seeking political office in Ghana should be tested for aptitude in mathematics, [including grammar and logical reasoning] is an interesting one.
—– Amperage (amps for short) is a measure of the AMOUNT of electricity used. Voltage (volts) measures the pressure, or FORCE, of electricity. The amps multiplied by the volts gives you thewattage (watts), a measure of the WORK that electricity does per second.
—– News story with the President’s Statement: