Optimization for Operation of Power Systems with Performance Guarantee by Gokturk Poyrazoglu University at Buffalo, SUNY Department of Electrical Engineering

Electricity Supply Chain Consumer Distribution Transmission Generation

Optimal Power Flow Problem Dispatch Generating Units while minimizing Total Cost In a single time period ( i.e. 1 hour) Standard form of NLP min 𝑥 𝑓 𝑥 subject to 𝑔 𝑥 =0 ℎ 𝑥 ≤0 𝑥 𝑚𝑖𝑛 ≤𝑥≤ 𝑥 𝑚𝑎𝑥 Non-convex Feasible Region of OPF Courtesy of EDF Energy

Unit Commitment t=5 t=4 t=3 t=2 Time t=1 Select and Dispatch Generating Units while minimizing Total Cost In a multi time period ( i.e. 1 day or 1 week) t=5 t=4 t=3 t=2 Time t=1

Unit Commitment with DC Model Select and Dispatch Generating Units while minimizing Total Cost In a multi time period ( i.e. 1 day or 1 week) t=5 t=4 t=3 t=2 Time t=1

Security Constrained Unit Commitment Secure transaction between two consecutive periods 𝑥 3 𝑥 1 ∗ 𝑥 5 ∗ 𝑥 2 ∗ 𝑥 4 ∗ 𝑥 3 ∗ t=5 t=4 t=3 t=2 Time t=1

Power Systems Modeling Quadratic Cost function Min and Max Capacity Limits Bus2 Bus1 Bus3 G1 G2 Load Max Power Flow Limits Power Balance Equalities Min and Max Voltage Limits Bus G Load

Transmission Switching Simulation VS Reality Bus2 Bus1 Bus3 G1 G2 Load

University at Buffalo, SUNY Department of Electrical Engineering PART I Optimal 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, SUNY Department of Electrical Engineering

Problem Definition AC OPF with optimal topology control: 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 topology Line contingencies Large-scale problem

Challenges 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 solution Therefore, comparison between two NLP solutions does not guarantee optimal topology

Range for the global optimizer Approach 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 solution Upper Bound by an NLP Solver : possibly a local optimizer Range for the global optimizer Lower Bound by an SDP Solver: possibly infeasible solution

Optimal Power Flow (OPF) Problem Quadratic Cost function Definition of Real and Reactive Power Flows (Bi-directional flow) Voltage Magnitude Reliability Limits Real and Reactive Power Balance Maximum Power Flow Limits (bi-directional flow) Real and Reactive Generation Capacity Limits The vector x is lifted up to a matrix W = Convex feasible region OPF problem is given in the form of Non-convex Quadratically Constrained Quadratic Programming (QCQP)

SDP Relaxation Real and Reactive Real and Reactive Generation Capacity Power Balance Real and Reactive Generation Capacity Limits & Voltage Magnitude Reliability Limits Maximum Power Flow Limits(bi-directional flow) Schur Compliment of Quadratic Cost function Positive Semi-definite Matrix & Reference Angle

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

Search for a Better Topology NLP solution to Υ SDP solution to Υ NLP solution to Χ  Candidate for Χ Step I: Candidate for Χ: Guaranteed a better topology than Υ Step II: Check the same N-1 reliability criterion as ones for Υ

Parallel Algorithm AC Transmission Topology Control with N-1 Reliability Criterion SOLVE NLP SEPERATE CHECK CONDITIONS SOLVE SDP

Computation Time

Simulation Environment Modified IEEE 30 bus system 6 generators 39 lines + 2 tie lines Generation capacity: 360 MW Peak 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

Operating Cost Up to 10% cost reduction

Real Power Losses Reduced losses Increased losses

Conclusion Efficient algorithm to implement topology control in the restructured electricity market experiments Identified topology Guaranteed a better one Satisfy the same reliability criterion Topology control finds a solution with Decreased system cost but Losses may increase

University at Buffalo, SUNY Department of Electrical Engineering PART II Scheduling Maintenance for Reliable Transmission System (The SMaRTS Model) This study will be partially published in the following journal and conferences. University at Buffalo, SUNY Department of Electrical Engineering

What is the SMaRTS Model? Scheduling Maintenance for Reliable Transmission System Combination of studies on power economics Security Constrained Unit Commitment Transmission Topology Control Outage Coordination N-1 Reliability Criterion TTC N-1 SCUC SMaRTS

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 business

Challenges 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 Control SMaRTS SCUC TTC

Business-As-Usual VS The SMaRTS

Problem Formulation Objective Function: No Load Cost of Generators ($) Generation ($) No Load Cost of Generators ($) min 𝜃, 𝑃 𝐺 , 𝑃 𝑘 ,𝑢 𝑠,ℎ,𝑧,𝑚,𝑎 𝑡 𝑔∈Γ 𝐶 𝑔 𝑃 𝑔,𝑡 𝐺 𝛽 + 𝑔∈Γ 𝑁𝐿 𝑔 𝑢 𝑔,𝑡 + 𝑔∈Γ 𝑆𝑈 𝑔 𝑠 𝑔,𝑡 + 𝑘∈Ψ 𝑃𝑀 𝑘 𝑡 𝑚 𝑘,𝑡 − 𝑎 𝑘 In per unit Start-Up Cost of Generators ($) Partial Maintenance Cost ($)

Power Balance Constraints & Power Flow Definitions 𝑃 𝑘𝑖𝑗,𝑡 ≤ 𝐵 𝑘 𝜃 𝑖,𝑡 − 𝜃 𝑗,𝑡 + 1− 𝑧 𝑘,𝑡 𝑀 , ∀𝑡, 𝑘∈Ψ 𝑃 𝑘𝑖𝑗,𝑡 ≥ 𝐵 𝑘 𝜃 𝑖,𝑡 − 𝜃 𝑗,𝑡 − 1− 𝑧 𝑘,𝑡 𝑀 , ∀𝑡, 𝑘∈Ψ 𝑃 𝑘𝑖𝑗,𝑡 = 𝐵 𝑘 𝜃 𝑖,𝑡 − 𝜃 𝑗,𝑡 , ∀𝑡, 𝑘∈Ψ θ 𝑟𝑒𝑓,𝑡 =0 , ∀𝑡 𝑔∈Γ 𝑃 𝑔 𝑖 ,𝑡 𝐺 − 𝑃 𝑖,𝑡 𝐷 = 𝑘∈ 𝑖,∗ 𝑘∈Ω 𝑃 𝑘𝑖𝑗,𝑡 − 𝑘∈ ∗,𝑖 𝑘∈Ω 𝑃 𝑘𝑖𝑗,𝑡 , ∀𝑡, 𝑖∈ Φ 𝐺 − 𝑃 𝑖,𝑡 𝐷 = 𝑘∈ 𝑖,∗ 𝑘∈Ω 𝑃 𝑘𝑖𝑗,𝑡 − 𝑘∈ ∗,𝑖 𝑘∈Ω 𝑃 𝑘𝑖𝑗,𝑡 , ∀𝑡, 𝑖∈ Φ/Φ 𝐺 Power flow definitions - Maintenance requested Lines - Other lines Reference Voltage Angle Real Power Balance Equalities

Box Constraints Generation be in between capacity limits 𝑃 𝑔 𝐺,𝑚𝑖𝑛 𝑢 𝑔,𝑡 ≤ 𝑃 𝑔,𝑡 𝐺 ≤ 𝑢 𝑔,𝑡 𝑃 𝑔 𝐺,𝑚𝑎𝑥 , ∀𝑡, 𝑔∈Γ −𝑃 𝑘 𝑚𝑎𝑥 𝑧 𝑘,𝑡 ≤ 𝑃 𝑘𝑖𝑗,𝑡 ≤ 𝑧 𝑘,𝑡 𝑃 𝑘 𝑚𝑎𝑥 , ∀𝑡, 𝑘∈Ψ −𝑃 𝑘 𝑚𝑎𝑥 ≤ 𝑃 𝑘𝑖𝑗,𝑡 ≤ 𝑃 𝑘 𝑚𝑎𝑥 , ∀𝑡, 𝑘∈ Ω Ψ −𝑅 𝑔 ≤ 𝑃 𝑔,𝑡 𝐺 − 𝑃 𝑔, 𝑡−1 𝐺 ≤ 𝑅 𝑔 , ∀𝑡, 𝑔∈Γ Generation be in between capacity limits Max. Power flow limits are enforced The change in generation should be applicable.

Maintenance Scheduling Constraints Definition of maintenance start variable Definition of approval status & Limitation on partial maintenance (optional) Limit on maintenance duration Complete maintenance in planning horizon

Unit Commitment Constraints 𝑠 𝑔,𝑡 − ℎ 𝑔,𝑡 = 𝑢 𝑔,𝑡 − 𝑢 𝑔, 𝑡−1 , ∀𝑡, 𝑔∈Γ 𝜏=𝑡− 𝑝 𝑔 +1 𝑇 𝑠 𝑔,𝜏 ≤ 𝑢 𝑔,𝑡 , ∀𝑡, 𝑔∈Γ 𝜏=𝑡− 𝑤 𝑔 +1 𝑇 ℎ 𝑔,𝜏 ≤1− 𝑢 𝑔,𝑡 , ∀𝑡, 𝑔∈Γ Definition of unit commitment variables Limit on minimum up-time Limit on minimum down-time

Numerical Example Modified 30-bus system IEEE Reliability Test Case Data Low power transfer between Areas 13 MW Hourly Peak Data is from IEEE Reliability Test Case - A summer weekday

Requested Maintenance Starting Period Outage Requests Line ID From Bus To Bus 15 4 12 10 7 6 18 8 9 38 28 3 31 24 25 Business-as-Usual Model Transmission Owner submit TIME Line ID Requested Maintenance Starting Period 15 Hour 8 7 Hour 6 18 Hour 12 9 Hour 15 38 Hour 20 31 Hour 9

Total Operating Cost ($) Total Operating Cost ($) Results The Optimal Solution The SMaRTS Model Business-as-Usual Model Total Operating Cost ($) Approved Line ID(s) 53,051.83 --- 1 52,807.70 7 2 52,725.15 7, 18 3 52,722.56 7, 18, 9 4 52,722.47 7, 18, 9, 31 5 52,723.99 7, 18, 9, 31, 38 6 52,841.17 All Total Operating Cost ($) Approved Line ID(s) 53,051.83 ---- 1 53,054.75 38 2 53,062.72 38, 9 3 53,094.97 38, 9, 7 4 53,204.15 38, 9, 7, 18 5 54,264.13 38, 9, 7, 18, 31 6 55,030.72 All

Total Operating Cost ($) Total Operating Cost ($) Decision Support BUSINESS-AS-USUAL MODEL Total Operating Cost ($) Approved Line ID(s) 53,051.83 ---- 1 53,054.75 38 2 53,062.72 38, 9 3 53,094.97 38, 9, 7 4 53,204.15 38, 9, 7, 18 5 54,264.13 38, 9, 7, 18, 31 6 55,030.72 All SMaRTS THE SMaRTS MODEL Total Operating Cost ($) Approved Line ID(s) 53,051.83 --- 1 52,807.70 7 2 52,725.15 7, 18 3 52,722.56 7, 18, 9 4 52,722.47 7, 18, 9, 31 5 52,723.99 7, 18, 9, 31, 38 6 52,841.17 All

The SMaRTS Model with N-1 Reliability University at Buffalo, SUNY Department of Electrical Engineering

N-1 Reliability Criterion 3 2 G D Loss of Transmission Lines Loss of Generators B C 1 3 2 G D A C 1 3 2 G D A B 1 3 2 G D A B C 1 3 2 G D A B C 1 3 2 G D Status of Transmission Line at time t Status of Transmission Line at contingency c

Proposed N-1 Reliability The 3rd index C 1 3 2 G D Time t & Contingency c zk, t, c : status of Line k Pkij, t, c : power flow on Line k Pg, t, c : power generation at Gen g Contingency Elements Status of Transmission Lines Time

Discarding 3rd index by Physical Property 1 3 2 G D Time t & Contingency c zk, t, c : status of Line k Pkij, t, c : power flow on Line k Pg, t, c : power generation at Gen g Loss of Transmission Lines B C 1 3 2 G D A C 1 3 2 G D zk, t, A = zk, t, 0 ,∀k – A zk, t, A = zk, t, 0 , k = A Pkij, t, A ≠ Pkij, t, 0 ,∀k Pg, t, A ≠ Pg, t, 0 ,∀k zk, t, B = zk, t, 0 ,∀k – B zk, t, B = zk, t, 0 , k = B Pkij, t, B ≠ Pkij, t, 0 ,∀k Pg, t, B ≠ Pg, t, 0 ,∀k

Utilizing Physical Meaning Discard 3rd index & a variable Transmission Line Contingency Enforce the flow to be ZERO Generation Contingency Enforce the generation to be ZERO

Numerical Example Modified 30-bus system IEEE Reliability Test Case Data Low power transfer between Areas Hourly Peak Data is from IEEE Reliability Test Case - A summer weekday Tie lines Radial Lines

Requested Maintenance Starting Period Outage Requests Line ID From Bus To Bus 15 4 12 10 7 6 18 8 9 38 28 3 31 24 25 Business-as-Usual Model Transmission Owner submit TIME Line ID Requested Maintenance Starting Period 15 Hour 8 7 Hour 6 18 Hour 12 9 Hour 15 38 Hour 20 31 Hour 9

Results Business-as-Usual Model The SMaRTS Model Total Operating Cost ($) Approved Line ID(s) 53,781.71 --- 1 53,756.47 7 2 53,753.67 7, 18 3 53,736.75 7, 18, 31 4 7, 18, 31, 38 5 Infeasible - 6 infeasible Total Operating Cost ($) Approved Line ID(s) 53,781.71 ---- 1 53,783.72 38 2 53,795.89 38, 7 3 53,842.87 38, 7, 18 4 54,211.41 38, 7, 18, 31 5 Infeasible - 6 The SMaRTS Model w/ no Partial Maintenance Total Operating Cost ($) Approved Line ID(s) 53,781.71 --- 1 53,772.01 7 2 53,773.44 7, 38 3 53,790.29 7, 18, 38 4 53,833.21 7, 18, 31, 38 5 Infeasible - 6 infeasible

Results

Impact of N-1 Reliability

PART I - SDP Based Transmission Topology Control Conclusion PART I - SDP Based Transmission Topology Control AC Model with physical flow limits Up to 9% cost reduction Guaranteed to find a better topology PART II - The SMaRTS Model A new method to utilize Transmission Switching in Outage Coordination Method to discard additional variable for N-1 Up to 4% daily cost reduction NYISO - daily operating cost is $15 Million.

Gokturk Poyrazoglu gokturkp@buffalo.edu Thank you. Gokturk Poyrazoglu gokturkp@buffalo.edu University at Buffalo, SUNY Department of Electrical Engineering