1. Direct Non-Iterative Power System State Solution and Estimation B. Fardanesh NYPA Advanced Energy Conference New York, 2013

2. Basics of the Re-Linearization Method X1X1 X2X2 f(x 1,x 2 ) (X 1 *, X 2 *) X 1 X 2 X12X12 X22X22 X1X1 X2X2 Ys and Zs

3. A Simple Example Redundant Polynomial Equations Dual Transformation and Direct One-Shot Solution

4. Basics of the Re-Linearization Method If only one Z If Z 1 and Z 2, we will have three ts t Y 1 (t) Y 2 (t) Y 3 (t) t*t* Y 3 (t 1,t 2, t 3 )=0 t1t1 t2t2 (t 1 *, t 2 *, t 3 *) t3t3 Y 2 (t 1,t 2, t 3 )=0 Y 1 (t 1,t 2, t 3 )=0

5. Basics of the Re-Linearization Method Form the hyperplanes: In term of Zs and change variables to t s :

6. Vi2ViVi2Vi Vj2VjVj2Vj V i V j Vk2VkVk2Vk Vj2VjVj2Vj Vi2ViVi2Vi V j V k V i V k V k V l V i V k V i V j Vj2VjVj2Vj Vi2ViVi2Vi Vk2VkVk2Vk V j V l Vl2VlVl2Vl Relation to Network Topology

7. Historically we have used iterative techniques to solve the state estimation problem A direct one-shot solution for the state of a power system is now possible Full AC solution-No Simplifications No more iterations No reliance on the “goodness” of the initial guess An envisioned faster more robust solution New Paradigm

8. What is Required? Accurate measurements from the system at the control center Bus voltage phasor and line current phasor measurements Locally (at the substation) validated data– “Super-calibrator “ a plus Reliable and redundant communications network

9. A Power System State Estimator/Solver Power Flow equations in Rectangular from Naturally in the desired form: Measurement equations have similar form =a i + jb i

10. Envisioned Benefits Direct State Estimation More robust– No more iterations No reliance on the initial guess Fast– Perhaps limited only by the communication links’ latency A much more “dynamic” assessment of the system conditions and behavior Potential for ultimate use in closed-loop and automatic control of power systems

11. NYPA ECC Implementation Snapshot from the Siemens EMS Reduced NYS data—230kV and above Solve for bus voltage phasors one bus away from each PMU Purely phasor based direct SE Output can be utilized as “anchor points: for the traditional SE Will report on the performance soon