Tie-Line Congestion and Inframarginal Rents in a Two-Zone Dispatch
Northbridge system has two load zones, A and B, connected by one 500 MW tie-line. Demand is 650 MW in A and 1,200 MW in B; B also has 100 MW of price-taking wind. Generation in A: G1 600 MW at €18/MWh and G2 700 MW at €30/MWh. Generation in B: G3 500 MW at €52/MWh and G4 400 MW at €95/MWh. All units are available, and each bid equals its short-run marginal cost. The system operator first clears the market ignoring network constraints, then checks the tie-line. A 100 MW tie-line upgrade is proposed at an annualised cost of €2.5 million, equivalent to about €6,850/day. The constraint is expected to bind for 4,000 hours per year. The operator uses locational marginal pricing and does not apply a separate uplift for this hour.
1. Determine the constrained dispatch, the zonal prices, total production cost, and inframarginal rents. Show why the unconstrained merit order cannot be used.
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Unconstrained, total conventional demand is 1,850 - 100 = 1,750 MW. Merit order would be G1 600 at €18, G2 700 at €30, G3 450 at €52, so the price would be €52. But B net load is 1,200 - 100 = 1,100 MW. If B generated only 450 MW, it would need 650 MW of imports, above the 500 MW tie-line. The constraint therefore binds.
With a 500 MW line, B must generate 1,100 - 500 = 600 MW: G3 at 500 MW and G4 at 100 MW. A must generate 1,750 - 600 = 1,150 MW: G1 at 600 MW and G2 at 550 MW. A price is €30/MWh, set by G2. B price is €95/MWh, set by G4. Flow is 500 MW from A to B.
Total cost = 600×18 + 550×30 + 500×52 + 100×95 = 10,800 + 16,500 + 26,000 + 9,500 = €62,800/h. Inframarginal rents: G1 earns (30-18)×600 = €7,200/h; G3 earns (95-52)×500 = €21,500/h. G2 and G4 are marginal and earn zero rent. The unconstrained merit order fails because it ignores the transfer limit and would require 650 MW of imports into B.
2. Evaluate the 100 MW tie-line upgrade. Calculate the production-cost saving if the constraint binds 4,000 hours per year, compare it with the annualised cost, and explain who may capture the benefit.
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With a 600 MW line, B generation is 1,100 - 600 = 500 MW, all from G3. A generation is 1,750 - 500 = 1,250 MW: G1 600 and G2 650. Total cost = 10,800 + 19,500 + 26,000 = €56,300/h. The saving is €6,500/h. At 4,000 binding hours per year, the annual production-cost saving is 6,500×4,000 = €26.0 million. Against an annualised cost of €2.5 million, the upgrade has a large net benefit on cost grounds.
However, the B price remains €95/MWh because G3 is at its maximum and G4 remains the marginal source for an increment in B. The upgrade mainly displaces 100 MW of G4 with 100 MW of G2. Congestion rent rises from (95-30)×500 = €32,500/h to (95-30)×600 = €39,000/h, an increase of €6,500/h. Unless congestion rents are rebated to load, B consumers may see no price reduction. The welfare gain is real, but its distribution depends on congestion-rent allocation and on whether the line owner is regulated.