SecurityConstrained OPF and RiskBased OPF OPF SCOPF OBJECTIVE
Security-Constrained OPF and Risk-Based OPF
OPF SCOPF OBJECTIVE Subject to: Power Flow Eqts “Normal Condition” constraints Contingency constraints SCOPF solution will always cost > OPF solution. SCOPF constraint moves from OPF solution only when a contingency constraint becomes binding. Occurs when post-contingency flow moves from just < 100% to >100% of rating. Indicates a qualitative difference between having 1 flow at 99% and 1 flow at 101%. Indicates no difference between having 10 flows at 99%, 1 flow at 101% and having 1 flow at 101%. 2
Basic Concepts 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 3
Risk Evaluation Severity function: 1 Severity 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. 4 90 100 Flow as % of rating POSTCONTINGENCY LOADING FOR EACH LINE
Risk Visualization Security regions : Probability sectors: sector White center angular spread is corresponds to proportional to loadings less than contingency probability 90% of emergency rating. Yellow “doughnut” corresponds to loadings 90% -100%. Red outside corresponds to loadings in excess of emergency rating. Severity circles/squares: represents a post-contingency violation or near-violation with the number corresponding to the violated circuit. 5 Radial distance from the center of the diagram to each small circle is proportional to the extent (severity) of the violation.
Illustration 6
Illustration 7
RB-OPF: Visualization All lines, 40 hrs, no contingency All lines, 1 hr, 40 contingencies 8 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.
RB-LMPs Deterministic: Energy component cost Loss component cost Congest component for one contingency, (line s, t above Congest 100%, line cost u at 92%) Risk-based: èControl of risk level is uniform èPrice signal for risk-relief is more effective èLMPs are less volatile 9
- Slides: 9