Mathematics of Electricity Billing in Nigeria

When I was in Primary school, I loved Arithmetic and the ‘Quantitative Reasoning’. In the early 90s in Nigeria, The Education Ministry’s approved textbook for Quantitative Reasoning for all Primary schools in Lagos (maybe all over Nigeria) was the Olunloyo Quantitative Reasoning workbook. I was always fascinated with the often complex reasoning behind some of the intricate questions in the workbook. Some of our uncles and aunties find it difficult in helping us out with solving some of the assignments in the workbook.

When I got to Junior Secondary School, my love for mathematics and quantitative reasoning ascended to another level through some of the mathematically word problems that needed to be broken down into x and y. For example, 5 years ago, Bayo was 10 years old, how old will Bayo be in 20 years’ time. Mathematically, Bayo will be represented with x and an equation will be formed to solve the problem.

This love for mathematics was largely responsible for my choice of studying Engineering in the university. Engineering is actually a mathematical field in which complex engineering theories are explained with mathematical formulas and theories. I was thrown into the world of Complex mathematics in my five year engineering study which further enlightened me to the endless possibilities of mathematics in solving every day problem.

From my interactions with friends and colleagues on electricity billing system, I confirm without any gainsaying that most people using post-paid meters in Nigeria do not really understand the billing system used by PHCN (IKEDC, IBEDC or whatever ‘discos’ operating in their area). The DISCOs use a monthly billing system in which the unit that is consumed in a previous month is paid in the succeeding month. In a typical electricity bill, there are 8 columns which contain: Description, Tariff code, Read date, Present reading, Previous reading, Multiplier, Consumption, and Current charges. Under the Description column, there are always two rows which are Energy charges and fixed charges. There will be a number in the consumption column which is calculated by subtracting Previous reading from the Present reading.

However, sometimes you can see a number with ‘E’ by the side under the consumption column like 150E. This means that the consumption figure is not gotten from the meter reading but an estimate figure. The Current charges is obtained by multiplying the consumption figure with the energy multiplier charge which is dependent on the classification of your premises (R1, R2SP, R2TP, C1SP, etc…). For R2SP premises, the energy multiplier charge is ₦13.20/kwh. A further fixed charge of ₦750 or ₦500 is then added to the resultant current charges

Using mathematics to explain the electricity billing, Current Charge= (Consumption x Energy multiplier charge) + fixed charge. For example, for a R2SP premise with a fixed charge of ₦750 and a monthly consumption of 140 units. The current charge is calculated thus: (140 X₦13.20/kwh) + ₦750, which is equal to ₦2598.

Late last year, The Nigerian Electricity Regulatory Commission (NERC) announced a planned increase in electricity tariff with effect from February 1st 2016. With the planned increase in electricity tariff, which some people have described as 40% increase in tariff. I decided to do a mathematical model to investigate the effect of the planned tariff increase. It is noteworthy that R2SP customer energy multiplier charge will now be ₦21.30/kwh with the elimination of the ₦750 monthly fixed charge. Mathematically, the equation of the current billing system is +750, while the proposed billing system is.

Using set of equations and graphs, the effect is explained in the graph below:

As seen from the graph above, the low energy consumer will be the greatest beneficiary of the planned increment while the higher consumer will bear the brunt of the increment. Consumers with average monthly consumption between 10 and 95 units will pay lesser under the proposed price regime with price savings of 3% to 58% depending on actual consumption. Similarly, Consumers with average monthly consumption of 100 and above will pay more with price increment of 6% to 55 % depending on actual consumption.

Of-course, all these apply to you even if you are using a Pre-paid meter. The only exception is the aspect of IKEDC Energy sales representatives not coming to your house to read your meter, hence no issue with estimate billing.