GOOD AFTERNOON. I THINK I MIGHT BE THE FIRST STUDENT TO SPEAK HERE AT THE CONFERENCE. [LAUGHTER] AT THE VERY LEAST, I WOULD LIKE TO SAY IT IS AN HONOR TO REPRESENT ARIZONA STATE UNIVERSITY AT THE CONFERENCE AND IT IS HUMBLING TO BE REMINDED HOW LONG THE ROAD IS FOR THE KNOWLEDGE AND EXPERIENCE -- THAT BEING SAID, MY NAME IS GARRET LABOVE. I AM WORKING WITH PROFESSOR KORY HEDMAN. I WILL BE DISCUSSING STOCHASTIC UNIT COMMITMENT IMPROVED THROUGH USE DYNAMIC RESERVE. THERE IS MORE INFORMATION THAN I HAVE TIME. I WILL BE SPEED THROUGH SOME PARTS OF THE LITERATURE AVAILABLE. WITH PROGRESSIVE HEDGING, FOR EXAMPLE, AND PARTS OF THE DYNAMIC RESERVE SECTION. EXISTING RESERVE REQUIREMENTS, BASED ON THE LARGEST CONTINGENCY. HOWEVER, THAT DOES NOT REALLY ADDRESS THE ISSUE OF DELIVERABILITY. WHENEVER WE COME TO THE REAL- TIME MARKET. THERE ARE SOME WAYS OF ADDRESSING THIS. THE DIFFERENT OUTCOMES IN STOCHASTIC PROGRAMMING. YOU MAY NOT HAVE THE TIME TO SUFFICIENTLY SOLVE. WE COULD INCREASE THE RESERVE RULES, BUT THAT IS AT A COST. PROCURING ADDITIONAL RESERVES. WHAT WE ARE PROPOSING IS WE TAKE SOME OF THE BENEFITS, THE IMPROVED RESOLUTION OF PROGRAMMING AND COUPLE IT WITH THE EFFICIENCY OF DETERMINISTIC PROGRAMMING. WE WANT TO MIMIC THE RESERVE POLICY, BUT IMPROVE THEM BY TAKING INTO ACCOUNT THAT WE EXPECT TO SEE. WE WANT TO IMPROVE THE SCALABILITY AND CONVERGENCE OF OUR APPROACH BY INCORPORATING DIFFERENT STAGES. I WILL NOT TALK TOO MUCH ABOUT PROGRESSIVE HEDGING. IT IS A HORIZONTAL DECOMPOSITION APPROACH. IT DOES NOT STEP UP THE COMPLEXITY. THERE ARE SOME IMPROVEMENTS THAT WERE MADE THAT YOU WILL LIKELY HEAR ON THIS. THE RESERVES WE PROCURE, WE WANT TO MAKE SURE WHENEVER CONTINGENCY OCCURS, THE RESERVES WE PROCURE ARE ABLE TO BE DELIVERED TO THE REGIONS THAT ARE NECESSARY. WHAT WE WANT TO DO WITH DYNAMIC RESERVE IS TO OBSERVE AND ADEQUATELY PREPARE RESERVE PROCUREMENT TO ADDRESS [INAUDIBLE] WE IMPROVE DELIVERABILITY BY ACCOUNTING FOR CONGESTION. WITH TYPICAL DAY-AHEAD SCHEDULING, IT STARTS BY SOLVING SECURITY CONSTRAINTS. RUNNING CONTINGENCY ANALYSIS AND REPORT CONSTRAINT VIOLATIONS WITH OPERATOR DIVISION. WE MANUALLY TURN ON ADDITIONAL UNITS. AT THAT POINT, WE HAVE THE REAL COST OF THE DISPATCH AND WE HAVE THE DAY-AHEAD SCHEDULE. WHERE WE SEE THIS FITTING INTO THE TYPICAL DAY-AHEAD SCHEDULE, THE TRADITIONAL PROGRESSIVE HEDGING BY TAKING A SUBSET OF THE SCENARIO AND RUNNING THROUGH THE PROGRESSIVE HEDGING ALGORITHM WERE EACH SCENARIO IS RUN INDEPENDENTLY AND AT EACH STAGE, PENALTIES ARE APPLIED TO EACH SCENARIO. WITH THE TYPICAL STOPPING CRITERIA BEING TIMED. UNLESS YOU HAVE DONE A GOOD JOB OF ASSESSING PENALTY FACTORS FOR PROGRESSIVE HEDGING, IT IS NOT LIKELY TO OUT-OF-THE-BOX RUN PROGRESSIVE HEDGING AND IT SOLVES THE PROBLEM FOR YOU. ONCE YOU REACH AN AMOUNT OF TIME, ONE WAY TO GET TO SOLVE IS THROUGH FIXING THE CONVERGED VARIABLES AND RUNNING THROUGH A SECURITY CONSTRAINT COMMITMENT AND THEN WE ARE BACK TO THE CONTINGENCY ANALYSIS PHASE OF THE DAY-AHEAD SCHEDULE. HOWEVER, WE EXPAND UPON THIS BY INSERTING PATCHES THROUGH THE ALGORITHMS WHENEVER PROGRESSIVE HEDGING STOPS IMPROVING. LOOKING AT THAT AND SEEING THAT IT HAS NOT IMPROVED AND THEN WE RUN IT THROUGH OUR DYNAMIC RESERVE MODEL TO GENERATE NEW RESERVE POLICIES. ONCE WE STOP IMPROVING, WE TAKE A LOOK AT ALL OF THE SOLUTIONS AND WE TRY TO FIND THE ONE THAT HAS THE LEAST MEASURE OF FEASIBILITY BY EXAMINING THE REMAINING SCENARIOS. WE CAN GO FORWARD THAT APPLY DYNAMIC RESERVE MODEL. WE TAKE ALL OF THE SCENARIOS TO THAT SOLUTION AND WE OBSERVE THE POWER FLOWS OCCURRING ON THE SLIDE AND THEN WE USE A SENSITIVITY INDEX TO APPLY DIFFERENT RESERVE ZONES. TO CHANGE THAT DISPATCH, TO BETTER ADDRESS BUT WE EXPECT TO BE A PROBLEM. THE STATISTICAL CLUSTERING METHOD WAS PUBLISHED BY OTHERS IN MY RESEARCH GROUP ON MAKING USE OF K-MEANS. WITH THE SCENARIO, WE LOOK AT THE AVERAGE LOADING AND THE STANDARD DEVIATION AND WE USE THAT TO USE A SIMILAR METRIC TO THE PERFORMANCE INDEX IN ORDER TO DETERMINE HOW EACH BUS IMPACTS OTHER BUSES. IN THIS WAY, WE CAN USE CLUSTERING TO GENERATE A NUMBER OF ZONES AS NECESSARY. THE SENSITIVITY INDEX THAT WE DEVELOPED RECENTLY IS BASED ON DISTRIBUTION FACTORS. THESE WERE CUSTOM GENERATED TO SIMULATE AN INTELLIGENT RE- DISPATCH OF THE PROBLEM. TO DETERMINE WHERE WE HAVE MORE SENSITIVITY AS AND MORE POSSIBLE VIOLATIONS IN ORDER TO IDENTIFY THE HOURS WHERE WE NEED MORE CENTRALIZED RESERVES. THIS IS TO SHOW THE SENSITIVITY INDEX AND HOW IT LOOKS RELATIVE TO THE FORM OF VIOLATIONS. THIS IS SHOWING -- IT TENDS TO HAVE A NICE FOLLOWING ATTRIBUTE WITH THE EXCEPTION OF THIS PEAK HERE. THROUGH USE OF THE SENSITIVITY INDEX, WE TAKE A LOOK AT AREAS WHERE WE HAVE VERY LOW SENSITIVITY AND WE SEE WE DO NOT REALLY NEED TO ADD MORE RESERVES. THIS IS CONFIRMED BY THE CONTINGENCY ANALYSIS. FOR OTHER PERIODS, IT IS MUCH MORE SENSITIVE TO THE N-1 VIOLATIONS. WE WILL LIKE TO HAVE MORE RESERVES, HYDRO RESERVES WHICH BETTER ADDRESSES THE PROBLEM. FOR THE RESULTS IN THIS PRESENTATION, IT IS A RELATIVELY SMALL TEST CASE. WE MADE USE OF DUAL INTEL. WE WERE ABLE TO TEST 32 CASES IN PARALLEL AND NEVER COME CLOSE TO THE AMOUNT OF RAM WE WERE USING. WE MADE USE OF THE WESTERN WIND INTEGRATION DATA SET. WE ARE SOLVING THROUGH BUNDLING, 32 DIFFERENT BUNDLES OF SCENARIOS AND WE MAKE USE OF SOME OF THE IMPROVEMENTS I SKIPPED OVER, PROGRESSIVE HEDGING. IN ORDER TO GAIN MORE INFORMATION. WE START MAKING USE OF MORE RELIABLE, STRONGER SOLUTIONS AS THE ALGORITHM GOES ON. WE HAVE A DIFFERENT DETERMINATION CRITERIA. WHEN WE SEND THE PROBLEM, WE FIX ALL OF THE UNITS COMMITTED. WE DO NOT FIX UNITS THAT CONVERGE TO A NONCOMMITTED STATUS. WE ONLY FIX THE UNITS TURNED OFF. THIS ALLOWS THE FORM THE FREEDOM, BUT THIS METRIC NEEDS TO BE LOOKED AT AGAIN FOR LARGER TEST CASES. FOR USING THIS METRIC BY ITSELF ON OUR TEST CASE, IT DID NOT PROVE TO BE A PROBLEM. THE COMPARISON THAT WE MADE IS FROM PURE PROGRESSIVE HEDGING. WE RUN IT FOR A CERTAIN AMOUNT OF TIME. WE EXPANDED WITH DYNAMIC RESERVE ZONES. OVER TIME, WE ARE ADDING THESE PATCHES. WE LOOK THROUGH THE SCENARIO ANALYSIS TO GENERATE OUR POWER FLOWS BASED ON HOW SENSITIVE EACH TIME PERIOD IS. WE ARE PENALIZING IT FOR TOTAL RESERVE VALUE ACROSS THE ZONES. THE REASON FOR THREE ITERATIONS, THERE IS NOTHING TETHERING TOGETHER THE INDIVIDUAL SCENARIOS. THE SECOND STAGE, THE SECOND ITERATION TENDS TO BE ALL OVER THE PLACE. IT TENDS TO HAVE WIDE VARIANCE. AFTER THREE ITERATIONS, IT TENDS TO START CALMING DOWN. THE SOLUTION HAS THE FREEDOM TO VIOLATE THOSE CONSTRAINTS IN TRYING TO PURSUE A UNIFIED CONSTRUCTION. HERE ARE SOME RESULTS. I'M GOING TO TALK FIRST ABOUT THE LEFT TWO COLUMNS. THIS IS THE RESULT AFTER THIS STAGE OF MODIFIED DAY-AHEAD SCHEDULING. AFTER WE HAVE RUN PROGRESSIVE HEDGING COMPARED TO THIS ONE PATCH, WE SEE THE NORM OF THE COMMITMENT IS A LITTLE BIT FURTHER AWAY. HOWEVER, ROUGHLY HALF OF THE OUTSTANDING BINARIES -- AFTER 20 MINUTES, THERE ARE 13 LEFT. WITH ONE PATCH, WE HAVE JUST SEVEN. WE STARTED TO ENCOURAGE CONVERSIONS. AFTER RUNNING IT WITH THE SAME RULES APPLIED, WE ARRIVED AT THE EXACT SAME SOLUTION, SAME COST, BUT AT A SLIGHTLY LESS TIME. THIS IS COMPARED TO THE EXTENSIVE FORM. IN ADDITION TO INCLUDING A RESOLUTION TO GET TO THE OPTIMAL SOLUTION ALSO INCLUDES THE IMPACT OF APPLYING NEW RESERVE ZONES TO IMPROVE THE EXPECTATION. THIS IS IN COMPARISON TO THE EXTENSIVE FORM, WHICH SHOULD NOT HAVE THE RESERVE RULES. IT IS ON A DIRECT COMPARISON, BUT WHAT WE HAVE IS AN EXPECTATION. THIS IS AN AREA WHERE WE WERE ABLE TO IMPROVE THE CONVERGENCE AND STILL GET THE SAME VALUE FOR THE SAME SOLUTION. WITH THREE PATCHES APPLIED, WE ALLOWED THE ALGORITHM TO RUN UNTIL IT STOPPED IMPROVING BY FOUR OR FIVE PERCENT, AND THEN WE RAN ONE OF THESE PATCHES AND LET IT RUN FOR FOUR ITERATIONS AND APPLIED ANOTHER SET OF PATCHES AND THEN WE COMPARED IT TO A ROUGH EQUIVALENT TIMEFRAME. THESE WERE TRIGGERED AT THE END OF A PARTICULAR ITERATION. THE DISTANCE HAS BEEN MINIMIZED. THERE ARE JUST FOUR BINARIES REMAINING. WE ARRIVED AT A BETTER SOLUTION, BUT IT DOES TAKE A BIT LONGER TO DO SO. REDUCE THE GAP FOR THE SAME AMOUNT OF TIME. IT IS IMPORTANT TO NOTE THAT AFTER 2.5 TIMES PER PROGRESSIVE HEDGING, IT DID NOT APPROPRIATELY -- IT DID NOT SIGNIFICANTLY IMPROVE THE OUTCOME OF THE PROBLEM. IT MOVED A BIT FURTHER AWAY.

WITH THIS CHEAPER SOLUTION, BECAUSE WE WERE SIMULATING WHAT THE FLOWS WERE, WE HAVE A REDUCTION IN THE EXPECTATION RELATIVE TO PURE PROGRESSIVE HEDGING. WE ARE INCORPORATING FLOWS WE EXPECT TO REALIZE AND BY USING THESE DYNAMIC RESERVES AND TIGHTENING DOWN THE PROBLEM, WE IMPROVED THE SOLUTION QUALITIES. THIS WORK NEEDS TO CONTINUE THROUGHOUT OF MARKET CORRECTIONS. WE STILL HAVE VIOLATIONS TO ADDRESS. IN CONCLUSION, DYNAMIC RESERVES CAN IMPROVE BOTH THE PROGRESSIVE HEDGING CONVERGENT RATE. THE SENSITIVITY INDEX QUICKLY IDENTIFIES TIME PERIOD SWITCH HOW CRITICAL FLOWS THAT MAY NEED QUICK ACTION. THE EXTENSIVE FORM TERMINATION PHASE CAN ACHIEVE HIGHER QUALITY SOLUTION BY NOT AGGRESSIVELY FIXING THE BINARIES, BY STEPPING BACK AND MAKING USE TO ALLOW THE FULL CAPACITY TO ACHIEVE A BETTER SOLUTION. IN THE FUTURE, IF THIS NEEDS TO BE APPLIED, IT WILL NOT CUT IT FOR THE REAL WORLD. WE NEED TO GET OUT OF MARKET ALGORITHMS TO ARRIVE AT A TRUE FINAL COST OF OUR ANALYSIS. AND TO LOOK INTO EMBEDDED NOMOGRAMS. [APPLAUSE]

QUESTIONS? OK.

HOW DID YOU DETERMINE DISTANCE?

THE POLICIES WE ARE APPLYING ARE EASY TO PUT INTO A FULL EXTENSIVE FORM. THIS GAP IS BASED ON THE LOWER BOUNDS THAT WE GET FROM THE EXTENSIVE FORM. EMBEDDED IN THIS GAP, IN ADDITION TO THE LACK OF RESOLUTION, AND IT ALSO HAS A PREMIUM ASSOCIATED THAT WE GET RELATIVE [INAUDIBLE] YOU ARE ASKING ABOUT THE CLUSTERING METHOD. THIS WAS DEVELOPED BY OTHER MEMBERS OF MY GROUP. THE CENTRALITY METRIC, IT TAKES INTO ACCOUNT HOW IT AFFECTS OTHER BUSES IN THE NETWORK. THE VALUES THAT ARE ROUGHLY EQUIVALENT HAVE STRONG IMPACTS TO EACH OTHER AND STRONG DELIVERABILITY. WE EXPAND UPON THAT BY APPLYING WEIGHT THROUGH FLOWS. THE SCENARIOS ARE WIND PRODUCTION.

I HAVE A COUPLE OF QUESTIONS.

IT IS KIND OF A LOOSE USE OF THE WORD ZONE. WE ARE APPLYING A PARTICULAR RULE. BY CLUSTERING THESE BUSES TOGETHER RELATIVE TO THE DELIVERABILITY TO EACH OTHER, WE APPLY A PARTICULAR RULE THAT IS AVAILABLE. BY CLUSTERING THESE BUSES, WE HAVE A BETTER IDEA THAT THEY ARE DELIVERABLE. THE CLUSTERS ARE FORMED THROUGH ANALYSIS OF THE POWER FLOWS. WE APPLY ALL OF THE SCENARIOS AGAIN. BY EXAMINING THE POWER FLOWS, WE USE THAT TO DETERMINE THE CLUSTER. WITH MULTIPLE PATCHES [INAUDIBLE]

YOU WERE MENTIONING --

[INAUDIBLE] THE RENEWABLE, THE INTERMITTENT POWER GENERATION THAT WE REALIZE IN THE NETWORK COULD AFFECT THE CONGESTION. THE RESERVE PLACEMENT IS IMPORTANT. .