Merit-Order Dispatch for a 1000 MW Evening Peak with a Must-Run Unit and a Costly Exchange Offer
A Telangana discom control room must meet a 1000 MW evening demand from its own units. The dispatch desk holds the following data, all at the sending end of the station:
| Unit | Capacity | Auxiliary | Heat rate at 100% | Heat rate at 75% | Coal GCV | Landed coal |
|---|---|---|---|---|---|---|
| A | 600 MW supercritical | 6.5% | 2280 kcal/kWh | 2340 kcal/kWh | 3600 kcal/kg | Rs 4200/t |
| B | 500 MW supercritical | 7.0% | 2320 kcal/kWh | 2380 kcal/kWh | 3500 kcal/kg | Rs 3800/t |
| C | 210 MW subcritical | 9.5% | 2500 kcal/kWh | 2620 kcal/kWh | 3900 kcal/kg | Rs 4600/t |
Unit C is running at 120 MW because its 220 kV corridor is required for voltage support, and its technical minimum is 55%. Unit A's technical minimum is also 55%. The exchange offers 100 MW at Rs 4.20/kWh. A is supplied by rail, and a freight revision of Rs 250/t is under consideration.
1. Compute the variable cost per net kWh at full load for each unit and establish the merit order. State clearly how auxiliary consumption is treated.
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Method. Variable cost per net kWh = (heat rate / coal GCV) x coal price / (1 - auxiliary fraction). This is the correct basis for dispatch because auxiliary power is not sold; using gross cost would bias the merit order towards high-auxiliary units.
Unit A. Coal rate = 2280/3600 = 0.6333 kg/kWh; gross cost = 0.6333 x 4.20 = Rs 2.660/kWh; net = 2.660/0.935 = Rs 2.85/kWh.
Unit B. 2320/3500 = 0.6629 kg/kWh; gross = 0.6629 x 3.80 = Rs 2.519/kWh; net = 2.519/0.93 = Rs 2.71/kWh.
Unit C. 2500/3900 = 0.6410 kg/kWh; gross = 0.6410 x 4.60 = Rs 2.949/kWh; net = 2.949/0.905 = Rs 3.26/kWh.
Merit order: B (2.71), A (2.85), C (3.26). Note that C has the best heat rate of the three yet the highest cost, because its coal is the most expensive and its auxiliary consumption is the highest; a heat-rate-only merit order would dispatch C first and be wrong. Also note how close B and A are - a small freight change can invert them.
2. Schedule the 1000 MW with and without C's must-run constraint, and quantify the daily cost of the constraint.
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Case 1 - unconstrained. B at 500 MW (Rs 2.71), A at 500 MW, i.e. 83.3% load. Interpolating A's heat rate between 2280 at 100% and 2340 at 75%: 2280 + 60 x (16.7/25) = 2320 kcal/kWh. Coal cost = 2320/3600 x 4.20 = Rs 2.707 gross; net = 2.707/0.935 = Rs 2.895. Hourly cost = 500,000 x 2.709 + 500,000 x 2.895 = Rs 28.02 lakh; unit cost Rs 2.80/kWh.
Case 2 - C must run at 120 MW. Remaining 880 MW: B at 500 and A at 380 MW, i.e. 63.3% load, which is above A's 55% minimum but below the 75% point, so its heat rate is worse than 2380 - take about 2385. A's net cost = 2385/3600 x 4.20/0.935 = Rs 2.98. C at 120 MW is 57% load, heat rate about 2680, net cost = 2680/3900 x 4.60/0.905 = Rs 3.49. Hourly cost = 500,000 x 2.709 + 380,000 x 2.976 + 120,000 x 3.493 = Rs 29.05 lakh; unit cost Rs 2.90/kWh.
Cost of the constraint = about Rs 1.03 lakh per hour, or roughly Rs 24.6 lakh per day. That is the figure to put in front of the system operator: is 120 MW of must-run worth Rs 24.6 lakh a day for voltage support, or can the reactive requirement be met more cheaply by capacitors or a STATCOM at the 220 kV substation?
3. Should the desk buy the 100 MW exchange offer at Rs 4.20/kWh, and how does the proposed Rs 250/t freight rise change the decision?
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Marginal cost test. Buying power is justified only if it displaces generation that costs more than Rs 4.20/kWh at the margin. The most expensive unit running is C at about Rs 3.49/kWh, and A at about Rs 2.98/kWh; both are well below the offer. So on pure economics the answer is no - the discom should generate, not buy.
Feasibility check. Even if the desk wanted to take 100 MW, the only unit it could reduce is A, from 380 MW to 280 MW, which is below A's 55% technical minimum of 330 MW. So the purchase is not merely uneconomic, it is infeasible without shutting A down entirely - and a shut-down and restart of A costs more than the saving and loses the unit for hours.
Freight sensitivity. With Rs 250/t added, A's coal cost becomes Rs 4450/t. A's net cost at 2320 kcal/kWh = 2320/3600 x 4.45/0.935 = Rs 3.07/kWh - still cheaper than C at Rs 3.49 and still far below Rs 4.20. The breakeven coal price at which A becomes dearer than C is 3.258 x 0.935 x 3600/2320 = about Rs 4720/t, so a Rs 250/t rise does not change the merit order.
Caveats to state. The offer price excludes transmission charges and losses; the merit order assumes coal quality as billed rather than as received; and the real question is whether C's reactive support can be replaced, which is a separate engineering decision from the energy cost.