1. Security-Constrained OPF and Risk-Based OPF

2. 2 Assume normal condition constraints are satisfied. The word “flow” below refers only to post-contingency flow. How does SCOPF distinguish between the two cases in the following two situations: Situation 1: having one flow at 99% and having one flow at 101%? SCOPF Subject to: OBJECTIVE  Power Flow Eqts  “Normal Condition” constraints  Contingency constraints  Situation 2 having ten flows at 99% and one flow at 101% having all flows below 50% except for one which is at 101%.

3. Basic Concepts 3 Security level: A continuous function of operating conditions reflecting the “strength” of the power system with respect to a defined contingency set. Risk level: A continuous function of operating conditions reflecting the “weakness” of the power system with respect to a defined contingency set. Fact: (1) All “secure” operating conditions not equally secure. (2) All “insecure” operating conditions not equally risky. Why? Because security level (or risk level) depends on (a)All flows (not just ones at the limits) (b)Contingency probabilities

4. Risk Evaluation 4 Contingency Probabilities: Always estimates Reasonable default is proportional to line length Can depend on line length, location, & weather, if outage data available. Consider as weightings on severity reflecting contingency importance. Severity function: Post-contingency loading on each line

5. 5 Risk Visualization Severity circles/squares: represents a post-contingency violation or near-violation with the number corresponding to the violated circuit. Radial distance from the center of the diagram to each small circle is proportional to the extent (severity) of the violation. Security regions : White center corresponds to loadings less than 90% of emergency rating. Yellow “doughnut” corresponds to loadings 90% -100%. Red outside corresponds to loadings in excess of emergency rating. Probability sectors: sector angular spread is proportional to contingency probability

6. Illustration 6

7. 7

8. 8 RB-OPF: Visualization All lines, 40 hrs, no contingency All lines, 1 hr,40 contingencies Vertical axis: angular separation across each line obtained from SCOPF Horizontal axis: angular separation across each line obtained from RBOPF Points above the diagonal indicate lines for which SCOPF solution results in greater stress. Points below the diagonal indicate lines for which RBOPF solution results in greater stress.

9. 9 Preventive RBOPF

10. 10 Preventive-Corrective RBOPF

11. 11 Preventive-Corrective RBOPF (4) SCOPFRBOPF Preventive RB-SCOPFCorrective RB-SCOPF HSM (K c =1) ESM (K c =1.05) EESM (K c =1.25) HSM (K c =1) ESM (K c =1.05) EESM (K c =1.25) Risk15.36.112.27.76.1 Cost ($)1218909 112019 4 1219067 12065061181047120154211465561098027 CEI1021228922210122993912102613755646382875749 ASI39113336 3791 33473020281732133457

12. 12 RB-LMPs Deterministic: Risk-based: Loss cost Energy cost Congest cost Loss component Energy component Congest component for one contingency, (line s, t above 100%, line u at 92%)  Control of risk level is uniform  Price signal for risk-relief is more effective  LMPs are less volatile