New Approaches to Balancing Security & Economy: Risk-based security-constrained economic dispatch (RB-SCED)

Transcription

1 New Approaches to Balancing Security & Economy: Risk-based security-constrained economic dispatch (RB-SCED) Acknowledgments: Qin Wang (MISO), Xian Guo (ISU) James D. McCalley Iowa State University Tongxin Zheng and Eugene Litvinov (ISO-New England) Consortium for Electric Reliability Technology Solutions, CERTS - This research is one of the PSERC projects coordinated by CERTS w/ funding provided by US DOE Joe Eto (Lawrence Berkeley National Laboratory) Phil Overholt (US DOE Office of Electricity Delivery & Energy Reliability) PSERC Webinar January 2, 204

2 Outline. Motivation 2. SCED and RB-SCED 3. Formulation 4. RB-SCED Solution Procedure 5. Illustrative results 30 bus system 85 bus system ISO-NE system 6. Effect on LMPs 7. Corrective RB-SCED 8. Conclusions 2

3 Motivation 3 Provide new market/security software capabilities via: BETTER SECURITY & ECONOMIC PERFORMANCE: Identify a more secure operating condition at lower production costs Function Concept Outcome Risk-based securityconstrained economic dispatch (RB-SCED) Achieve economic objective while managing system security +circuit security instead of only the latter. more secure operating conditions lower costs

4 Motivation This work is about how to operate power systems under steady-state contingency constraints. 4 It suggests two changes to the way we balance security and economy in operating power systems [,2,3] (which is done by the SCED today).. Probabilistically weight the contingencies. 2. Change the nature and number of the constraints This talk focuses mainly on #2 because it is essential. [] T. Dy Liacco, Real-time Computer Control of Power Systems, Proc. of the IEEE, Vol. 62, No. 7, July 974, [2] J. Carpentier, "Differential Injections Method: A General Method for Secure and Optimal Load Flows", IEEE PICA Conference Proceedings Minneapolis, MN, pp , June 973 [3] O. Alsac and B. Stott, Optimal load flow with steady state security, IEEE Trans. on Power Apparatus and Systems, Vol. PAS-93, pp , May/June 974

5 Motivation Operating condition : contingency having post-contingency flow at 0% of its long-time emergency (LTE) limits; all other contingencies result in post-contingency flows<90% of their LTE Operating condition 2: 2 different contingencies each having 2 post-contingency flows between 95% and 00% of their LTE INSECURE SECURE 5 Yet operating condition #2 is more risky than operating condition #. Today s approach does not capture this because it does not quantify security level in terms of: heavy post-contingency flows <00% of LTE number of contingencies resulting in heavy post-contingency flows number of heavy post-contingency flows for each contingency

6 SCED and RB-SCED 6 Whereas SCED imposes re-dispatch control only for post-contingency flows exceeding its LTE as much as needed, to satisfy the (circuit) LTE RB-SCED imposes re-dispatch control for all heavy flows weighted by flow magnitude, to satisfy a (system) risk constraint

7 SCED and RB-SCED 7 Under RB-SCED, the system is dispatched under normal conditions to: Same as SCED Makes it more secure than SCED Makes it more economic than SCED ) Satisfy pre-contingency (normal) flow constraints 2) Lower post-contingency flows for circuits having post-contingency loadings above 90% of LTE flow limits 3) Satisfy post-contingency flow constraints at LTE flow limits at 05% of LTE flow limits at 20% of LTE flow limits (STE) (2) and (3) together results in more secure & more economic operating conditions.

8 SCED and RB-SCED Operating condition 3: Contingency A results in post-contingency flows of 03% and 98% Contingency B results in post-contingency flows of 95% and 93%. 8 What SCED does What RB-SCED does Weighting on Re-dispatch effort Weighting on Re-dispatch effort Cont A, Line 90% 00% 90% 00% Cont B, Line 4 Cont B, Line 3 Cont A, Line 2 Cont A, Line

9 min 0 min { f P } 0 Min ( ) st.. hp ( ) = 0 g gp ( ) g 0 0 Formulation - Optimization max g g ( P ) g, k =,..., NC k SCED max Contingency Constraints min 0 { f P0 } Min ( ) st.. hp ( ) = 0 g gp ( ) g min 0 0 max max 0 NC 0 R max PF Eqs normal constraints K g g ( P ) K g, k =,..., NC C RB-SCED k 0 Risk( g ( P ),... g ( P )) K Risk C Risk constraint PF Eqs and normal constraints are identical K C < tightens contingency constraints; K C > loosens them Risk constraint is across all contingencies K R < tightens risk constraint, K R > loosens risk constraint RB-SCED becomes SCED with K R =, K C = K R, K C enable tradeoff between system & circuit security 9

10 Risk Formulation - Risk Expression A weighted sum of normalized post-contingency flows on heavy-loaded circuits. N = C N L Sev j( g ( P NC k 0)) k= j= ( g ( P g P ) 0),..., ( 0) Prk 0 Contingency probabilities: computed using historical data & real-time information [] or assigned identical values: Pr k =/(N C +) for all k. [] F. Xiao, J. McCalley, Y. Ou, J. Adams, S. Myers, Contingency Probability Estimation Using Weather and Geographical Data for On-Line Security Assessment, Proceedings of the 9 th International Conference on Probabilistic Methods Applied to Power Systems, June -5, 2006.

11 Adaptive Emergency Transm Rates [] Lng-time emrgncy (LTE) rating, 4hrs Shrt-time emrgncy (STE) rating, 5mins Drastic action limit (DAL), immediate [] S. Maslennikov, E. Litvinov. Adaptive Emergency Transmission Rates in Power System and Market Operation, IEEE Trans. Pwr Sys, May Formulation Severity Evaluation

12 RB-SCED Solution Procedure [] Master Risk Problem (SCED) Master problem (ED) Risk Sub-problem 2 feasibility cut feasibility cut feasibility cut Feasibility Check for normal condition Contingency Feasibility Check Feasibility Check for first contingency Feasibility Check for last contingency feasibility cut optimality cut Feasibility Check of Risk Sub-problem Optimality Check of Risk Sub-problem DC power flow representation is used. Risk cannot be evaluated until flows are known. Two-level nested Benders decomposition: Master risk problem is a SCED solved by Benders SCED solution checked for feasibility & optimality in risk subproblem [] Q. Wang, J. McCalley, T. Zheng, and E. Litvinov, A Computational Strategy to Solve Preventive Risk-based Security-Constrained Optimal Power Flow, Digital Object Identifier: 0.09/TPWRS , IEEE Transactions on Power Systems, 202.

13 7 7 7 IEEE 30 bus system C5 C4 C6 C7 4 C3 C2 3 3 Results: 30-bus system Post-contingency flows represented by White Circles: SCED Blue Squares: RB-SCED with distance to center = %flow: White: Safe flow, < 90% Yellow: Heavy flow, 90-00% Red: Exceeds LTE Sectors: contingencies SCED RB-SCED Cost $45,383 $446,420 Risk

14 Results: 30-bus system Is it more secure? 4 Primary event 2 3 SCED SCOPF RB-SCED 2 RBMO 3 Level Cascading Sequence Level 2 Level 3 Level C5 C4 C6 C7 4 C3 C2 Level 5 Level Probability Severity CEI Stop Cascading Collapse Level is a second trip after initial outage, for circuits w/ flows exceeding 90%. Levels 2, 3, occur if flow>25%

15 Results: 30-bus system Is it more secure? 5 20% model, K C =.2, K R =.0 [Qmargin of RB-SCED] -[Qmargin of SCED] (MVARS) 05% model, K C =.05, K R =.0 00% model, K C =.0, K R =.0 Contingency # Post-contingency flows are more uniformly loaded, reactive losses are lower, so Qmargin is greater. AC power flow analysis indicates SCED model has more reactive losses than RB-SCED model.

16 Results: 85-bus system 6 AREA ECAR HUNTVILL NODE COLOR Blue: Generation Yellow: Load Green: Both Gen/Load HOLDEN REDBRIDG CHENAUX CHFALLS BRIGHTON STINSON PICTON NANTCOKE LINE COLOR Red: 345 kv MARTDALE Green: 38 kv AREA EAST (Control Area) LAKEVIEW CEYLON RICHVIEW HEARN Cost ($) WALDEN COBDEN MTOWN MITCHELL HANOVER KINCARD GOLDEN BVILLE JVILLE STRATFRD PARKHILL DOUGLAS WVILLE AREA WEST Risk Time R. Dai, H. Pham, Y. Wang, and J. McCalley, Long term benefits of online risk-based optimal power flow, Journal of Risk and Reliability (Part O of the Proceedings of the Institution of Mechanical Engineers): Special Issue on "Risk and reliability modeling of energy systems, Vol. 226, Issue, Feb, 202.

17 Results: 85-bus system Is it more secure? 7 Post-contingency angle separations SCED RB-SCED R. Dai, H. Pham, Y. Wang, and J. McCalley, Long term benefits of online risk-based optimal power flow, Journal of Risk and Reliability (Part O of the Proceedings of the Institution of Mechanical Engineers): Special Issue on "Risk and reliability modeling of energy systems, Vol. 226, Issue, Feb, 202.

18 Results: ISONE System ISO New England system 235 buses, 389 circuits, 250 contingencies 802,50 decision variables, 4,00,96 constraints min ( ) st.. h( P) = 0 Corrective RB-SCED { f P0 } 0 g gp ( ) g min 0 max Risk max = Risk from SCED so reference risk is no higher = C min k 0 C max than what has been acceptable in the past, then, P P P 0 k K R =0.5 K g g ( P ) K g, k,..., NC 0 Risk( g ( P ),... g ( P )) K Risk 0 NC 0 R max Solved in CPLEX on a PC laptop with inter Core 2 Duo 2.50 GHz and 3GB memory; solution time is ~20 min. SCED 00% Model (K C =, K R = 0.5) RB-SCED 05% Model (K C =.05, K R = 0.5) 20% Model (K C =.20, K R = 0.5) Cost ($/hr) 684, ,899 60,6 605,542 Risk

19 Results: ISONE System 9 Comparing SCED & RB-SCED on ISO-NE system for 0 sequential hrs (Different cases from previous slide). Social surplus ( 0 5 $) Hours Risk SCED RBED Hours Area=ISO-NE savings over 0 hrs=$2m (assume 0 during other 4 hrs) Annual cost saving: $2.0M 5 52=$520M/yr (assume 0 for weekend) And it is more secure!

20 Results: ISONE System Is it more secure? 20 Number of circuits with flows exceeding 90% of continuous limit in the normal state Number of circuits with flows exceeding 90% of LTE in all post-contingency states SCED RB-SCED 00% model 05% model 20% model

21 Traditional LMPs= Effect on LMPs Risk-based LMPs 2 LMP Energy i = λ Energy RLMPi = λ 2 + LMP + Loss i Loss = P λ i NL NC NL Congestion 0 0 k k = i µ + µ l l i l l i l= k= l= LMP ( GSF GSF ) + RLMP + Loss i Loss = 2 P λ i NL NC NL Congestion 0 0 k k = i µ + µ 2l l i 2l l i l= k= l= RLMP ( GSF GSF ) + RLMP NC NL Risk k k i = S l k l i k= l= The risk component of the LMP provides a price signal that incentivizes market participants to improve system risk. r Pr GSF τ

22 Results: Six bus system 22 B X BC = 0.25 C XBD = 0. A D XAD = 0.2 XAB = 0.2 XAE = 0.3 XED=2.97 X BE = 0.3 X BF = 0.2 E XEF = 0.3 XCF = 0. F X ED =2.97% 60 MW XCE = MW X DE = MW

23 Difference is due to RLMP s ability to distinguish between line C-E s carrying heavy post-contingency flow for 2 contingencies, with post-contingency loadings of 97.5% and 0.8%, respectively, line B-D s carrying heavy post-contingency flow for only contingency, with post-contingency loadings of 00%. 00% model 05% model 23 Some buses have higher RLMPs; some have lower, due to Risk constraint causes increase Relaxed postcontingency limits causes decrease For SCED & 00% model, investment incentives are on B-D. For 05% model, investment incentives are on C-E.

24 Results: 240 bus WECC system 24 RB-SCED 00% model 05% model 20% model R-LMP s are more uniform over space and, we think, less volatile.

25 Corrective RB-SCED [] Corrective RB-SCED allows post-contingency corrective action to relieve loadings; Formulated, coded, and tested it on 30-bus system and on ISO-NE system; Results from ISO-NE system are below. 25 [] *Q. Wang, J. McCalley, T. Zheng, and E. Litvinov, Solving Corrective Risk-based Security-Constrained OPF with Lagrangian Relaxation and Benders Decomposition, under review by IEEE Transactions on Power Systems.

26 Conclusions RB-SCED: potential to significantly enhance efficiencies of real-time electricity markets; while simultaneously increasing security levels and providing operators with a system lever for more effective control. Offers basis for identifying prices when unmanageable constraints are relaxed; No changes in market structure are required. Next step: commercialize into market SW; then gain experience side-by-side with SCED 26

27 References 27. *Q. Wang, *G. Zhang, J. McCalley, T. Zheng, and E. Litvinov, Risk-based locational marginal pricing and congestion management, under review by IEEE Transactions on Power Systems. 2. *Q. Wang, J. McCalley, T. Zheng, and E. Litvinov, Solving Corrective Risk-based Security-Constrained OPF with Lagrangian Relaxation and Benders Decomposition, under review by IEEE Transactions on Power Systems. 3. *Q. Wang and J. McCalley, Voltage instability performance of risk-based security constrained optimal power flow, under review by Electric Power Systems Research. 4. *Q. Wang, J. McCalley, and Wanning Li, Risk and N- Criteria Coordination for Real-time Operations, to appear in IEEE Transactions on Power Systems, *Q. Wang, J. McCalley, T. Zheng, and E. Litvinov, A Computational Strategy to Solve Preventive Risk-based Security-Constrained Optimal Power Flow, Digital Object Identifier: 0.09/TPWRS , IEEE Transactions on Power Systems, *R. Dai, *H. Pham, *Y. Wang, and J. McCalley, Long term benefits of online risk-based optimal power flow, Journal of Risk and Reliability (Part O of the Proceedings of the Institution of Mechanical Engineers): Special Issue on "Risk and reliability modeling of energy systems, Vol. 226, Issue, Feb, *F. Xiao and J. McCalley, Power System Risk Assessment and Control in a Multi-objective Framework, IEEE Transactions on Power Systems, Vol. 24, No., Feb. 2009, pp *F. Xiao and J. McCalley, Risk Based Security and Economy Tradeoff Analysis for Real Time Operation, IEEE Transactions on Power Systems, Volume 22, Issue 4, Nov. 2007, pp *M. Ni, J. McCalley, V. Vittal, and T. Tayyib, On-line risk-based security assessment, IEEE Transactions on Power Systems, Vol. 8., No., February, 2003, pp *M. Ni, J. McCalley, V. Vittal, S. Greene, *C. Ten, *V. Gangula, and T. Tayyib, Software Implementation of online risk-based security assessment, IEEE Transactions on Power Systems, Vol. 8, No. 3, August 2003, pp 65-72