1. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS © 2002 Fernando L. Alvarado May 28, 2002

2. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Objetives Voltage constrains interpretation for dispatching purposes. –Uplift payments. –Voltage limits replaced with equivalent flow limits. –The voltage constraint is treated directly. How interpretation affects the market overall efficiency and optimal solution.

3. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Study system: FIRST CASE 3272.3 $/h

4. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Study system: SECOND CASE 4063.78 $/h

5. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Study system: THIRD CASE 3846.86 $/h

6. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Determination of nodal prices: Lagrange multiplier associated with optimal power flow at the solution point –Construction of Jacobian system for equality constrains. Equations Variables

7. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Jacobian augmented Equations Variables

8. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Computations: Case 1: Case 2: Case 3: with

9. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Analizing Case 3: Flow limit: Volt & flow limit: Voltage limit: “Same operating point but different prices”

10. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Summary of Nodal Price calculations (*) Value could be larger, depending on Bus 2 energy price

11. VOLTAGE CONSTRAINTS AND POWER NOMOGRAMS Nodal prices depend on what constraints and limits are assumed for the operating point. The common practice of using nomograms where a flow limits is used in lieu of a voltage limit can result in prices that greatly depart from the correct nodal prices. Starting generators in order to meet reactive and voltage constraints results in an “uplift” cost. It also lowers the marginal energy cost. Conclusions