Calculation for Locational Marginal Price

In today’s world all the power utilities are unbundled and de-regulated to a certain extent. The price of electricity is the most important factor to nearly all the market participants. The most basic electricity pricing mechanism is the Market Clearing Price (MCP).

In a power market, after receiving the bids, the System Operator (SO) aggregates the supply bids into a supply curve ‘S’ and aggregates the demand bids into a demand curve ‘D’. The intersection of S and D is the  Market Clearing Price (MCP)

Generally when there is no transmission congestion, MCP is the same for the entire power system, but when there is congestion, the concept of Zonal Market Clearing Price (ZMCP) or Locational Marginal Price (LMP) is used. In other words when there is no congestion, the LMP is the same as the MCP but in the congested state, the marginal cost of each bus is the LMP.

Let’s have a look into the LMP concept using a small example. A small 4 bus system is shown in the figure below.

Fig.  A four bus system.

The system has 4 buses with 2 generators each of capacity 125 MW at bus 1 and 3. A load of 100 MW is connected at bus 4. Suppose that there is no congestion and no losses, then for supplying 100 MW of load at bus 4, the power flows in line –

1-2 is 25 MW,

2-3 is 25 MW,

3-4 is 25 MW, and

1-4 is 75 MW if the lines are identical.

As per the definition, LMP at any node or bus is the cost of supplying add 1 MW at that node. Suppose we have to calculate the LMP at node 4. When there is no congestion and no losses, the power flow in the lines are –

25.25 MW at line 1-2,

25.25 MW at line 2-3,

25.25 MW at line 3-4, and

75.75 MW at line 1-4.

Thus, the additional load of 1 MW at node 4 is supplied by generator 1 at it’s offer price of 300 INR. This generator is the marginal generator and the LMP at node 4 is 300 INR.

LMP when there is Congestion in Lines:

Now suppose that the maximum flow through line 1-4 is limited to 75.2 MW. In this case, to meet the additional 1 MW load at node 4, the generators have to re-scheduled as the old scheduling will overload line 1-4. As per the new scheduling, which can be obtained by running Optimum Power Flow (OPF), the output of generator 1 is to be reduced by 0.1 MW and generator 3 has to supply 1.1 MW. The new line flows are-

24.7 MW in line 1-2,

24.7 MW in line 2-3,

25.8 MW in line 3-4, and

75.2 MW in line 1-4.

Thus, the LMP at node 4 can be calculated as

(1.1 x 350) – (0.1 x 300) = 355 INR

Similarly, the LMP at other buses can be calculated. Now I think that the calculation of LMP is clear to you.