Hopkinson Demand Rate Tariff Explained

Understanding different electricity tariff structures is crucial for analysing billing methods. Tariffs are pricing schemes used by utility companies to charge customers for electricity consumption.

Understanding the Tariff Formula

The question asks to identify the tariff type represented by the expression:

$$z = a + by$$

Let's break down the components of this formula:

• z: Represents the total tariff or the final amount billed to the consumer.
• a: Represents a fixed charge component. This part of the tariff is usually based on the customer's maximum demand (the highest rate at which electricity is used over a specified period) and does not change with the amount of energy consumed.
• b: Represents the variable rate charged per unit of energy consumed (e.g., per kilowatt-hour, kWh).
• y: Represents the total energy consumption measured in the corresponding units (e.g., kWh).

Therefore, the formula describes a pricing structure with a fixed component based on demand and a variable component based on energy usage.

Hopkinson Demand Rate Analysis

The Hopkinson demand rate is a type of two-part tariff that accurately reflects the given formula. This tariff structure consists of:

1. A fixed charge (a) based on the customer's maximum demand. This covers the costs related to the infrastructure needed to supply that peak power.
2. A charge (by) based on the actual energy consumed during the billing period.

The structure of the Hopkinson rate directly matches the mathematical expression $$z = a + by$$, making it the correct answer.

Comparison with Other Tariff Rates

It's helpful to understand why the other options are not the best fit for the formula $$z = a + by$:

• Flat Demand Rate: This tariff typically charges a flat rate per unit of maximum demand, regardless of how much energy is actually used. It doesn't usually include a separate, variable energy consumption charge like the '$by$' term in the formula.
• Straight Meter Rate: This is the simplest tariff, where the total charge z is directly proportional to the energy consumed y. It can be represented as $$z = by$$, lacking the fixed demand charge component (a) present in the given formula.
• Doherty Rate: This is also a two-part tariff, often structured as $$z = k \times P + x \times kWh$$. While similar in principle (demand charge + energy charge), the energy charge component in the Doherty rate sometimes has specific conditions, like declining rates after a certain usage threshold. The Hopkinson rate is a more direct and standard representation of the simple linear relationship $$z = a + by$$.

Based on the structure aligning perfectly with a fixed demand charge plus a variable energy charge, the Hopkinson demand rate is the tariff described by the expression $$z = a + by$$.