THANK YOU FOR COMING TO THIS TALK. I AM FENG. I RECENTLY GRADUATED FROM GEORGIA TECH IN THE SPRING. I JOINED ARGONNE NATIONAL LABS. TODAY I'M GOING TO REPORT MY RESULTS ON THE STUDIES USING TRANSMISSION SWITCHING. THIS IS A JOINT WORK. FIRST I'M GOING TO TALK ABOUT OUR MOTIVATIONS AND THE PROBLEM SCOPE. THEN WE ARE GOING TO SEE HOW WE CAN MODEL IT. AFTER THAT WE LOOK AT VALID INEQUALITIES. WHEN TALKING ABOUT WIND ENERGY INTEGRATION, ENERGY IS THE BIGGEST ISSUE. YOU DON'T KNOW HOW MUCH WIND YOU'RE ACTUALLY GETTING. YOU KNOW THE PROBABILITY. THERE IS A CHANCE OF HIGH WIND AND THE CHANCE OF LOW WIND. IF YOU GET MORE WIND THAN YOU PLANNED FOR -- THIS CURTAILMENT HAPPENS A LOT. MONTHLY CURTAILMENT, YOU CAN SAY THE BLUE BAR IS THE AMOUNT OF ENERGY. THE AMOUNT OF POWER IS HUGE. THE PICTURE ON THE RIGHT SHOWS THE CURTAILMENT BY THE ENERGY COMPANY. THE MONTHLY PAYMENT GOES ABOVE A MILLION DOLLARS. THE REASON IS [INAUDIBLE] THE CURRENT TRANSMISSION NETWORK IS NOT PREPARED FOR WIND POWER. IF WE CAN ADJUST, CAN WE MAKE BETTER WIND ENERGY? THIS IS OUR MOTIVATION. LET'S QUICKLY GO THROUGH THE HISTORY OF TRANSMISSION SWITCHING. TRANSMISSION LINES HAVE BEEN TRADITIONALLY TREATED AS A STATIC ASSET. RECENT STUDIES, PEOPLE START USING TRANSMISSION AS A DYNAMIC STRUCTURE. THIS WAS RESEARCHED. THANKS TO THIS RESEARCH, WE KNOW MORE AND MORE ABOUT WHAT TRANSMISSION SWITCHING CAN DO FOR US. FOR THOSE OF YOU NOT FAMILIAR, I OFFER SOME EXAMPLES IN THIS PRESENTATION. THE FIRST QUESTION YOU WILL ASK IS, HOW CAN THIS ACTUALLY HELP YOU? [INAUDIBLE] YOU GET MORE OPTIONS AND YOU HAVE A BETTER CHANCE TO GET BETTER SOLUTIONS. THE PROBLEM SCOPE IS THAT ONCE YOU USE THAT MUCH WIND ENERGY, WE WANT TO MINIMIZE THE CURTAILMENT ON THERMAL UNITS. AT THE END OF THE FIRST TIME PERIOD, WE DON'T KNOW HOW MUCH WIND WE ARE GOING TO GET. WE OPTIMIZE SUCH THAT THE PRODUCTION -- THE COST OF THE PRODUCTION WILL BE MINIMIZED. WE HAVE A FEW ASSUMPTIONS HERE. WE ASSUME THAT WE KNOW THE WIND OUTPUT. UNIT COMMITMENT AND SECURITY REQUIREMENTS ARE IGNORED FOR NOW. AT THIS BEGINNING STAGE OF OUR STUDIES WE WANT TO KEEP THE PROBLEM AS SIMPLE AS POSSIBLE. FROM THE SCENARIO I DESCRIBED, THIS IS ACE -- A TWO-STAGE DECISION-MAKING PROCESS. THE FIRST AGES TRANSMISSION SWITCHING. THE SECOND STAGE IS TO FIND POWER FROM EITHER THERMAL OR WIND. YOU PREDICT UNCERTAIN WIND. THIS IS THE OPTIMIZING MODEL. WHY IS THE FIRST STAGE OF VARIABLE? YOU FIND THE SECOND STAGE. SO FAR [INAUDIBLE] A CONSERVATIVE REQUIREMENT IS THAT WE REQUIRE THAT THIS POWER IS ALWAYS VISIBLE. WHEN YOU GET A VERY HIGH AMOUNT OF WIND MOTHER IS NO WAY --, THERE IS NO WAY [INAUDIBLE] . MY SOLUTION IS VISIBLE. THIS IS A TWO-STAGE CHANCE CONSTRAINED MODEL. THIS IS NOT THE CLASSIC TWO- STAGE STOCHASTIC MODEL. IF I HAVE TIME, I WOULD CHOOSE WHY WE -- I WILL EXPLAIN WHY WE CHOSE THIS. [INAUDIBLE] WHEN YOU GET A RANDOM NUMBER HERE, THE QUESTION YOU ASK [INAUDIBLE] IF YOU WANT THIS TO BE TRUE, THEN YOU PUT A SMALL NUMBER HERE. IT IS VERY HARD TO DESCRIBE. WE JUST NEED A GOOD APPROXIMATION. ONE OF THEM IS CALLED THE SAMPLE AVERAGE APPROXIMATION. YOU PLUG YOUR SOLUTION IN AND YOU COUNT HOW MANY ARE VISIBLE. IF THE NUMBER OF PROBLEMS VISIBLE DIVIDED BY -- IS EQUAL TO SOME NUMBER [INAUDIBLE] THIS IS THE BASIC IDEA OF SAA. LET'S GO TO THE MODEL. THIS IS THE PRODUCTION COST CURVE. THESE ARE THE TRANSMISSIONS WHICH -- TRANSIMMISSION SWITCH. WE ARE LIMITING THE NUMBER OF LINES THAT CAN BE OPEN. THESE ARE THE VARIABLES FOR WIND PRODUCTION. EACH TIME PERIOD IS GREATER OR EQUAL TO [INAUDIBLE] I NEED TO USE MORE THAN 80% OF THE WIND I HAVE TODAY. USING THE SAMPLE AVERAGE FORMATION, WHEN THEY ARE EQUAL TO ZERO -- WHEN THE EQUAL TO ONE [INAUDIBLE] WE LEAVE OUT SOME OTHERS. THIS IS RTS96. WE CONNECT TO THE NETWORK RANDOMLY. WE SET UP THE DATA SUCH THAT -- WE REQUIRE THAT WIND POWER CANNOT BE MORE THAN 15%. THE RISK LEVEL IS 0.1. HERE IS THE SOLUTION WITH NO MORE THAN FIVE LINES OFF. WE CAN SEE THAT THE PRODUCTION COST GOES DOWN MORE THAN 10%. THE LOST LOADS ARE REDUCED TO ZERO. THE AVERAGE CURTAILMENT LEVEL GOES DOWN. THIS COST REDUCTION IS DUE TO TWO THINGS. YOUR ORIGINAL GENERATION BECOMES GREATER. LET'S VARY THE NUMBER OF LINES THAT CAN BE SWITCHED OFF. IF YOU GET ONLINE SWITCHED OFF AND YOU GET BETTER SOLUTIONS. LET'S TALK ABOUT THE COMPUTATION. THIS TRANSMITS ENTRENCHING -- TRANSMISSION SWITCHING IS PART OF SAA. IT YIELDS A BIG-M. [INAUDIBLE] WE EXPERIMENT ON A SEPARATE CLASS OF INEQUALITIES. FIRST, THIS IS A SAA FORMULATION. WE REWRITE THE VARIABLE AND THAT COMES CLEANER. WE REDUCE THIS EXPRESSION TO THE FOLLOWING ONE. THIS HAS BEEN CITED BY A LOT OF PEOPLE. THE INEQUALITIES CAN BE SEPARATED. ONCE YOU HAVE THIS, YOU DON'T HAVE TO WORRY ABOUT SAR. WE WANT TO LOOK AT THE STRUCTURE OF SWITCHING AND MIRCHOFF'S LAW. [INAUDIBLE] THESE ARE TWO LINE SEGMENTS. THE ENDPOINT IS DECIDED. UNFORTUNATELY, THE CONVEX HUKLL OF THESE TWO LINES -- THAT PARTIALLY EXPLAINS WHY IT IS SO IMPORTANT TO EXPLAIN THE VARIABLE. WE WANT TO LOOK AT THIS FIXED CHARGE NETWORK STRUCTURE. GIVEN A DIRECTED GRAPH, YOU SELECT -- THIS IS SUPPLY AND THIS IS THE MAN. YOU SELECT A SET OF ARCS SO THAT THE CONSTRUCTION COST AND FLOW COST IS MINIMIZED. YOU HAVE A LOW CONSERVATION. THE DIFFERENCE IS THAT THE POWER FLOW IS KIRCHOFF'S LAW. ONCE THE INPUT AND OUTPUT IS DECIDED -- THAT IS THE FUNDAMENTAL DIFFERENCE. THROUGH THE THE FORMULATION, IT IS BOUND ON THE FLOW. THIS IS A FAMILY OF FLOW COVER INEQUALITIES. THEY ARE EXPONENTIAL. ANOTHER FAMILY, YOU CAN SELECT AND AGGREGATE THEM AND IT BECOMES A DOMINO. THIS IS CALLED A NUMIXED DICUT INEQUALITY. RIGHT NOW WE HAD ALL THESE CUTS TO THE ROOT NODE. [INAUDIBLE] THE REASON IS THAT WE IGNORED KIRCHOFF'S LAW. ALSO THE SWITCHING COST AND POWERFUL COST IS NOT IN THE OBJECTIVE. ALSO WE HAD ALL THE COST -- CUTS TO THE ROOT NODE. [INAUDIBLE] WHAT WE ARE WORKING ON RIGHT NOW IS TRYING TO USE THIS IMPLEMENTATION OF KIRCHOFF'S LAW TO STRENGTHEN FLOW COVER INEQUALITY. WE HAD CUTS ONLY AS NEEDED. THIS IS WHAT I WANT TO TALK ABOUT. THAT IS ALL. .