Module 13

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Module 13A: Cost of Electrical Energy

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Three Types of Cost

1. Fixed Cost (a)

Does NOT depend on Maximum Demand AND Energy Output.

Examples: High grade officer salary, Interest on capital cost of land, Equipment install cost.

2. Semi-Fixed Cost (b·kW)

Depends on Maximum Demand but NOT Energy Output.

Examples: Interest on machine investment, Management salary, Building depreciation.

3. Running / Operating Cost (c·kWh)

Depends on Maximum Demand AND Energy Output.

Examples: Fuel cost, Maintenance cost, Operating staff salary.

Total Cost Formula

$$ \boxed{E = a + b(kW) + c(kWh)} $$
  • $a$ = Fixed cost constant (₹)
  • $b$ = Semi-fixed cost per kW of demand
  • $c$ = Running cost per kWh of energy

$$ \text{Standing Cost} = a + b(kW) $$

Fixed + Semi-fixed do NOT depend on energy output.

Total Cost Bill Calulator

Fixed (a): ₹10,000 Max Demand: 500 kW
Running (c): ₹4/kWh Energy: 10000 kWh
Total E: ₹150,000

Module 13B: Depreciation Methods

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Depreciation & Salvage

Depreciation: Decrease in value of an asset due to use.
Salvage Value (S): Value of asset at end of useful life ($n$).

1. Straight Line Method

$$ \boxed{d = \frac{P - S}{n}} $$

Depreciation is CONSTANT each year.

2. Declining Balance Method

$$ \boxed{x = 1 - \left(\frac{S}{P}\right)^{1/n}} $$
$$ BV_t = P(1-x)^t $$

Depreciation is HIGHER in early years and decreases.

3. Sinking Fund Method

$$ \boxed{q = (P - S)\left[\frac{r}{(1+r)^n - 1}\right]} $$

Fund grows with compound interest $(r)$. Reaches $P-S$ at year $n$.

MethodAnnual Dep.Book Value
Straight LineConstantLinear decay
Declining Bal.DecreasingExponential
Sinking FundIncreasingCompound Drop

Book Value Over Time (n years)

■ Straight Line ■ Declining ■ Sinking Fund
Asset Life (n): 20 Yrs Salvage (S): ₹500k

Module 13C: Tariff Types & Formulas

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General Tariff Formula (Three Part)

$$ \boxed{z = ax + by + c} $$
  • $z$ = Total Bill (₹)
  • $x$ = Maximum demand (kW)
  • $y$ = Energy consumed (kWh)

Key Tariff Types

1. Simple/Uniform: $z = by$ (High cost, drops other fees).
2. Flat Rate: $z = ax$ (Depends on load type: Light vs Power).
3. Block Rate: $z = b_1y_1 + b_2y_2 + b_3y_3$ (Tariff reduces on succeeding blocks).
4. Two Part (Hopkinson): $z = ax + by$ (For large consumers).
5. Maximum Demand: Two part + Max demand meter.
6. Power Factor: Based on kVA instead of kW.
7. Three Part (Doherty Rate): $z = ax + by + c$ (Most accurate).
8. Seasonal Rate: Varies by season.
9. TOD / TOU / STOD: Time of Day - peak/off-peak rates.

Doherty Rate Builder ($z = ax + by + c$)

ax
by
c
Demand (x): 100 kW
Energy (y): 5000 kWh
Bill (z): ₹70,500

Module 13D: Power Factor & Tariff Comparison

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Power Factor Penalty

Industries pay for kVA maximum demand instead of kW.

$$ kVA = \frac{kW}{\cos\phi} $$
$$ kVA^2 = kW^2 + kVAR^2 $$

Power Factor Correction

To improve $\cos\phi$, consumer adds Capacitor Banks.

$$ \boxed{Q_c = P(\tan\phi_1 - \tan\phi_2) \text{ kVAR}} $$

Load Factor (LF) Benefits

$$ LF = \frac{\text{Average Demand}}{\text{Maximum Demand}} $$

High LF means less Maximum Demand for the same Energy = lower cost per unit under a Two Part Tariff (Hopkinson).

Original PF ($\cos\phi_1$): 0.60
Target PF ($\cos\phi_2$): 0.95
Capacitor $Q_c$: 133.3 kVAR

Module 13E: Complete Reference Flashcards

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Master Formulation Table

ParameterFormula / Rule
Standing Cost$a + bkW$
Running Cost$ckWh$
Energy Conversion$1\text{ kWh} = 3.6\times10^6\text{ J}$
Straight Line $d$$(P-S)/n$
Declining Balance $x$$1 - (S/P)^{1/n}$
Sinking Fund $q$$(P-S)[r/((1+r)^n-1)]$
Three Part Tariff$z = ax + by + c$
Two Part / Hopkinson$z = ax + by$
Capacitor $Q_c$$P(\tan\phi_1 - \tan\phi_2)$

Module 13 Flashcards

What does Fixed Cost (a) depend on?

Neither maximum demand nor energy output

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