Firm power and plant load factors

Firm and secondary power

• Firm (primary) power is the power that is available continuously (100% of the time), even in the driest period. It is fixed by the minimum flow.
• Secondary (surplus) power is the power above firm power that is available only part of the time, when flow is higher than the minimum. It is sold at a lower rate or used for non-essential loads.

Data

Minimum load = 12,000 kW; maximum load = 35,000 kW; two units of 22,000 kW each. The load is assumed to vary linearly (uniformly) between minimum and maximum, so the average load is the mean of the two.

$$P_{avg} = \frac{12{,}000 + 35{,}000}{2} = 23{,}500\ \text{kW}$$

(i) Total installed capacity

$$P_{inst} = 2 \times 22{,}000 = 44{,}000\ \text{kW}$$

(ii) Plant factor (capacity factor)

$$PF = \frac{\text{average load}}{\text{installed capacity}} = \frac{23{,}500}{44{,}000} = 0.534 = 53.4\%$$

(iii) Maximum demand

Maximum demand = peak load = 35,000 kW.

(iv) Load factor

$$LF = \frac{\text{average load}}{\text{maximum demand}} = \frac{23{,}500}{35{,}000} = 0.671 = 67.1\%$$

(v) Utilization factor

$$UF = \frac{\text{maximum demand}}{\text{installed capacity}} = \frac{35{,}000}{44{,}000} = 0.795 = 79.5\%$$

Check: $PF = LF \times UF = 0.671 \times 0.795 = 0.534$.

Answer: 44,000 kW; 53.4%; 35,000 kW; 67.1%; 79.5%.