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Optimization for Operation of Power Systemswith Performance Guaranteeby Gokturk PoyrazogluUniversity at Buffalo, SUNYDepartment of Electrical EngineeringElectricity Supply Chain

GenerationTransmissionDistributionConsumerOptimal Power Flow Problem

Courtesy of EDF EnergyStandard form of NLPNon-convex Feasible Region of OPFDispatch Generating Units while minimizing Total CostIn a single time period ( i.e. 1 hour)Unit Commitment Timet=1t=2t=3t=4t=5Select and Dispatch Generating Units while minimizing Total CostIn a multi time period ( i.e. 1 day or 1 week)Unit Commitment with DC ModelTimet=1t=2t=3t=4t=5Select and Dispatch Generating Units while minimizing Total CostIn a multi time period ( i.e. 1 day or 1 week)Security Constrained Unit CommitmentTimet=1t=2t=3t=4t=5Secure transaction between two consecutive periodsPower Systems Modeling

Bus2Bus1Bus3G1G2LoadQuadratic Cost functionMin and Max Capacity LimitsPower Balance EqualitiesMin and Max Voltage LimitsMax Power Flow LimitsGBusLoadTransmission Switching Simulation VS RealityBus2Bus1Bus3G1G2Load

PART IOptimal Topology Control with Physical Power Flow Constraints and N-1 Contingency Criterion

This study was partially published in the following journal and conferences.University at Buffalo, SUNYDepartment of Electrical EngineeringProblem Definition AC Optimal Power Flow:Nonlinear and nonconvex programming (NLP or QCQP) AC OPF with optimal topology control:Mixed integer nonlinear and nonconvex programming (MINLP) Same N-1 reliability consideration as the original topologyLine contingenciesLarge-scale problem10Challenges Comparison of OPF solutions among multiple topologies NLP solvers seek for a local optimum Guarantee a better topology?NLP solutions may not reflect the quality of the global solutionTherefore, comparison between two NLP solutions does not guarantee optimal topologyApproach Semi-Definite Programming (SDP) relaxes nonconvex feasible range of OPF SDP may find a feasible solution = the global solution SDP solution provides a lower bound of the global optimizer Global solution is sandwiched between an SDP and a local solutionUpper Bound by an NLP Solver : possibly a local optimizerLower Bound by an SDP Solver:possibly infeasible solutionRange for the global optimizerOptimal Power Flow (OPF) Problem

OPF problem is given in the form of Non-convex Quadratically Constrained Quadratic Programming (QCQP)

Definition of Real and Reactive Power Flows(Bi-directional flow)Real and Reactive Power BalanceReal and Reactive Generation Capacity LimitsVoltage Magnitude Reliability LimitsMaximum Power Flow Limits(bi-directional flow)Quadratic Cost function

The vector x is lifted up to a matrix W = Convex feasible region

Real and Reactive Power BalanceReal and Reactive Generation Capacity LimitsVoltage Magnitude Reliability LimitsMaximum Power Flow Limits(bi-directional flow)

&Positive Semi-definite Matrix &Reference Angle Schur Compliment of Quadratic Cost functionSDP Relaxation

Topology and (original topology) Utilize the sandwich structure of the global solutionNLP solution of < SDP solution of Global solution of A local optimizer of is better than the global optimizer of Topology Topology Aim to find such a topology in this study

SDP RelaxationSearch for a Better Topology

NLP solution to SDP solution to NLP solution to Candidate for Step I: Candidate for : Guaranteed a better topology than Step II: Check the same N-1 reliability criterion as ones for 16Parallel Algorithm AC Transmission Topology Control with N-1 Reliability Criterion

SEPERATESOLVE SDPSOLVE NLPCHECK CONDITIONSComputation Time

Modified IEEE 30 bus system6 generators39 lines + 2 tie lines Generation capacity: 360 MWPeak load: 320 MW Area 2: load pocket High cost for generators Gen 5 and Gen6 Computation with a Linux server with 24-cores @ 2.50GHz

Simulation EnvironmentOperating Cost

Up to 10% cost reductionReal Power Losses

Reduced lossesIncreased lossesConclusion Efficient algorithm to implement topology control in the restructured electricity market experiments Identified topology Guaranteed a better oneSatisfy the same reliability criterion Topology control finds a solution withDecreased system cost butLosses may increase

PART IIScheduling Maintenance for Reliable Transmission System(The SMaRTS Model)

This study will be partially published in the following journal and conferences.

University at Buffalo, SUNYDepartment of Electrical EngineeringWhat is the SMaRTS Model?Combination of studies on power economicsSecurity Constrained Unit CommitmentTransmission Topology ControlOutage CoordinationN-1 Reliability CriterionTTCN-1SCUCSMaRTSScheduling Maintenance for Reliable Transmission System

Security Constrained Unit Commitment (SCUC) Selection of generator units Minimize total operating cost Security on ramp up and ramp down of units Mixed Integer Linear Programming (MILP)

Being used widely in business

Transmission Topology Control (TTC) Selection of branches to keep in service Minimize total operating cost Security on ramp up and ramp down of units Mixed Integer Linear Programming (MILP)

No reported use in businessChallenges of Topology Control Transient Stability Concerns Switching effect Cost of Switching Who will pay? Financial Transmission Rights (FTR) Market Unwillingness of market participants

The Proposed Model : SMaRTS Transmission lines require Preventive Maintenance Schedule maintenance Optimal time Follow same procedure No stability concern No extra cost for switching No impact on FTR market

Feasible Region of SMaRTS No outage request

SMaRTS = Unit Commitment

Outage requests on all lines

SMaRTS = Topology ControlSCUCSMaRTSTTCBusiness-As-Usual VS The SMaRTS

Problem Formulation Objective Function:Cost of Generation ($)No Load Cost of Generators ($)Start-Up Cost of Generators ($)Partial MaintenanceCost ($)In per unit

Power Balance Constraints &Power Flow Definitions

Power flow definitions- Maintenance requested Lines- Other linesReference Voltage Angle

Real Power Balance Equalities

Box ConstraintsGeneration be in between capacity limitsMax. Power flow limits are enforced

The change in generation should be applicable.Maintenance Scheduling ConstraintsDefinition of maintenance start variable

Definition of approval status &Limitation on partial maintenance (optional)

Limit on maintenance duration

Complete maintenance in planning horizonUnit Commitment ConstraintsDefinition of unit commitment variables

Limit on minimum up-time

Limit on minimum down-timeNumerical Example Modified 30-bus systemIEEE Reliability Test Case DataLow power transfer between Areas

13 MWHourly Peak Data is from IEEE Reliability Test Case - A summer weekdayOutage RequestsLine IDFrom BusTo Bus154121074612181215896763882833124259

Line IDRequested Maintenance Starting Period15Hour 87Hour 618Hour 129Hour 1538Hour 2031Hour 9Business-as-Usual ModelTransmission Owner submit TIMEResultsTotal Operating Cost ($)Approved Line ID(s)053,051.83---152,807.707252,725.157, 18352,722.567, 18, 9452,722.477, 18, 9, 31552,723.997, 18, 9, 31, 38652,841.17All

The Optimal SolutionTotal Operating Cost ($)Approved Line ID(s)053,051.83----153,054.7538253,062.7238, 9353,094.9738, 9, 7453,204.1538, 9, 7, 18554,264.1338, 9, 7, 18, 31655,030.72All

Business-as-Usual ModelThe SMaRTS ModelDecision SupportTotal Operating Cost ($)Approved Line ID(s)053,051.83----153,054.7538253,062.7238, 9353,094.9738, 9, 7453,204.1538, 9, 7, 18554,264.1338, 9, 7, 18, 31655,030.72All

Total Operating Cost ($)Approved Line ID(s)053,051.83---152,807.707252,725.157, 18352,722.567, 18, 9452,722.477, 18, 9, 31552,723.997, 18, 9, 31, 38652,841.17All

BUSINESS-AS-USUAL MODELTHE SMaRTS MODELSMaRTS

The SMaRTS Modelwith N-1 ReliabilityUniversity at Buffalo, SUNYDepartment of Electrical EngineeringN-1 Reliability CriterionABC132GGDLoss of Transmission LinesLoss of GeneratorsBC132GGDAC132GGDAB132GGDABC132GDABC132GD

Status of Transmission Line at time tStatus of Transmission Line at contingency c

Proposed N-1 Reliability The 3rd indexABC132GGDStatus of Transmission LinesTimeContingency ElementsTime t & Contingency czk, t, c : status of Line kPkij, t, c : power flow on Line kPg, t, c : power generation at Gen gDiscarding 3rd index by Physical PropertyABC132GGDLoss of Transmission LinesBC132GGDTime t & Contingency czk, t, c : status of Line kPkij, t, c : power flow on Line kPg, t, c : power generation at Gen gAC132GGDUtilizing Physical Meaning

Enforce the flow to be ZEROEnforce the generation to be ZEROGeneration ContingencyTransmission Line ContingencyDiscard 3rd index &a variableNumerical Example Modified 30-bus systemIEEE Reliability Test Case DataLow power transfer between Areas

Hourly Peak Data is from IEEE Reliability Test Case - A summer weekday

Tie lines Radial LinesOutage RequestsLine IDFrom BusTo Bus154121074612181215896763882833124259

Line IDRequested Maintenance Starting Period15Hour 87Hour 618Hour 129Hour 1538Hour 2031Hour 9Business-as-Usual ModelTransmission Owner submit TIMEResultsTotal Operating Cost ($)Approved Line ID(s)053,781.71---153,756.477253,753.677, 18353,736.757, 18, 31453,736.757, 18, 31, 385Infeasible-6infeasible-

Total Operating Cost ($)Approved Line ID(s)053,781.71----153,783.7238253,795.8938, 7353,842.8738, 7, 18454,211.4138, 7, 18, 315Infeasible-6Infeasible-

Business-as-Usual ModelThe SMaRTS Model

Total Operating Cost ($)Approved Line ID(s)053,781.71---153,772.017253,773.447, 38353,790.297, 18, 38453,833.217, 18, 31, 385Infeasible-6infeasible-The SMaRTS Model w/ no Partial Maintenance

ResultsImpact of N-1 ReliabilityConclusionPART I - SDP Based Transmission Topology ControlAC Model with physical flow limitsUp to 9% cost reductionGuaranteed to find a better topology

PART II - The SMaRTS Model A new method to utilize Transmission Switching in Outage CoordinationMethod to discard additional variable for N-1Up to 4% daily cost reductionNYISO - daily operating cost is $15 Million.

Thank you.Gokturk Poyrazoglugokturkp@buffalo.eduUniversity at Buffalo, SUNYDepartment of Electrical Engineering