Fast Computation of Steady-State. State Stability Limits for Real-time and Off-line Applications. Savu C. Savulescu

Transcription

1 Fast Computation of Steady-State State Stability Limits for Real-time and Off-line Applications presented at the 7th International Workshop on Electric Power Control Centers, May 25-28, 28, 2003, Ortisei, Italy by Savu C. Savulescu EC IEnergy Concepts International, Inc.

2 Summary How the electric industry works now Need for fast maximum loadability predictors TTC vs. stability envelope Two-Step Steady-State State Stability Limit Evaluation Paradigm Paul Dimo's Simplified Steady-State State Stability Approach Practical implementation

3 How the Industry Works Now In the past, networks were dispatched to follow pre-planned planned scenarios ƒgeneration scheduled to meet forecasted load ƒnetwork security assessed off-line and in real-time stability conditions were predictable broad range of applicability of off-line operating guidelines Today, networks are dispatched to accommodate short-term term and spot energy transactions ƒdriven by demand, price and availability ƒbetween parties across multi-area networks

4 Need for Fast Maximum Loadability Predictors Open Access Transmission mandated by law ƒbut but transmission providers can (and do) ) curtail transactions that may impact the operating reliability transfer limits computed off-line may be very different from the actual system capability need to recalculate limits as often as possible A A mechanism is needed to predict danger ƒinstability phenomena develop rapidly no time to react units out of synchronism and voltage collapse ƒhow how far from instability is the current system state? High computational speed is a must ƒallow allow time for remedial action if not far from blackout

5 TTC vs. Stability Envelope Steady-State State Stability Limit (SSSL) ƒconcept concept well understood (see next slide) ƒthe the "limit" is given by the amount of MW (internal generation + imports) such that, for any loading smaller than SSSL, the system is "stable" in the sense of small signal stability ƒmaximum MW transfer, voltage instability and steady- state instability occur at the same point singularity of the "dynamic state" Jacobian Operating states near this point are not safe ƒnerc NERC defines the Total Transfer Capability (TTC) as a safe operating limit ƒno violations of any kind

6 E V MW X SSSL = Maximum Power Transfer Capability = E V X TSL TTC - Total Transfer Capability Safe Operating Limit (Stability Envelope) Average Normal Operation δ

7 TTC vs. Stability Envelope (cont'd) Transient Stability Limit (TSL) or TTC (NERC) ƒa a "limit" in the sense defined above is difficult, if not impossible to determine it would require examining every possible mix of generation, load and voltages for a succession of increased MW levels until the system becomes unstable ƒttc TTC (TSL) is an elusive target ƒhowever, intuitively, it can be asserted that TSL is always smaller than SSSL when SSSL increases / decreases, so does TSL probably some % level, e.g. TSL < 0.8 SSSL steady-state state stability reserve

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9 TTC vs. Stability Envelope (cont'd) Instead of attempting to compute TTC... Define a stability envelope as follows: ƒfirst, first, calculate the maximum power transfer limit then, for a given x% security margin (stability reserve) ƒdetermine the safe system MW loading limit that corresponds to the current operating state How to... ƒdetailed detailed analysis -- good for off-line studies, but not (or... not yet) ) suitable for fast simulations ƒfast fast approximate methods -- useful for quick decision making but the speed must be predicated on solid theoretical ground

10 Two-Step Steady-State State Stability Limit Evaluation Paradigm Step 1: run a quick stability check ƒdetermine "how far from instability" ƒidentify "stability envelope" based on a user-defined "x% security margin" ƒwhen evaluating MW transactions across multi-area systems, run stability checks on specific areas within larger networks interchange interfaces between areas Step 2: if needed, go to full analysis ƒcases situated outside the stability envelope may need to be evaluated in detail

11 Paul Dimo's Simplified Steady-State State Stability Approach Field-proven -- published in RGE in November 1961 ƒused used in production-grade studies for many years ƒprix Prix Montefiore in 1981 Predicated on ƒshort-circuit currents radial network of short-circuit admittances ƒpractical steady-state state stability criteria simple algebraic computations instead of eigenvalues ƒsimplified representation of generators all the machines are modeled -- constant e.m.f. behind x'd ƒfictitious load-center - Zero Power Balance Network Felix Wu (1978) identified theoretical conditions for correctness ƒ case case worsening procedure instead of successive load-flows

12 Short-Circuit Currents Barbier & Barret (1980) ƒused used short-circuit currents to develop critical voltage and maximum power transfer formulae Paul Dimo (1961) ƒused used short-circuit currents to formulate the dq/dv criterion for steady-state state stability Next slides illustrate the concept of "short-circuit currents" - the system "as seen" from a load bus ƒphysically, the currents flow from generators to load ƒmathematically, generators are connected to each load bus through short-circuit admittances Ieq Iload = Ish-c - Ysh-c Vload = Ish-c - Ish-c c no-load (Barbier-Barret) Barret) (Dimo)

13 Sample Power System 1 L1 G 2 L2

14 Sample System Replaced with the Short-Circuit Currents System "seen" from L1 System "seen" from L2 2 1 G 1 2 G L1 L2

15 Another View of the Short-Circuit Currents Model -- the REI Net m m 1 1 G G i i Ii = Σ Yim Em - Yii Vi Yii = Σ Yim + Yio Ishc-noload Iload Ii = Σ Yim Em - (Σ Yii + Yio) Vi Ii = Ii-sc - Ii-o

16 The Zero Power Balance Network Concept adding a network without losses to obtain a Single Load Center i j Y o-j Loads Synchronous Machines Fictitious Ground O' Other Injections Y FL I' FL V FL Single Load Center Ground I FL S FL

17 Steady-State State Stability Criteria steady-state state stability criteria ƒexact exact -- eigenvalues of the characteristic equation ƒalgebraic -- singularity of the Jacobian matrix (J) for the "dynamic state equations" ƒpractical -- dq/dv, dp/dδ and dp/dv Venikov, Dimo: under certain conditions, the dq/dv and J criteria a are equivalent suitable for the short-circuit currents model Suggested reading: V. Venikov, "Transient Processes in Electrical Power Systems", MIR M Publishers, Moscow, 1977 Barbier, C., Barret, J.P., "An Analysis of Phenomena of Voltage Collapse on a Transmission System", RGE, Paris, Vol. 89, 10, Dimo, Paul, "Etude de la Stabilite Statique et du Reglage de Tension", Revue Generale de l'electricite RGE, Paris, 1961, Vol. 70, 11,

18 Steady-State State Stability Criteria (cont'd) For m generators connected radially to a load bus through short- circuit admittances, dq/dv can be computed with the formula dq/dv = Σ(YmEm/cosδm) - 2(ΣYm 2( + Y + Yload)V Yload Em δm Ym V = QloadQ load/vv/vv = e.m.f. behind transient or synchronous reactance of the machine m = internal angle of machine m = admittance between machine m and the single-load load bus = voltage magnitude at the single-load load bus

19 Practical Implementation

20 Near-Blackout Event August 22, 2002 ETESA, Panama 15:14:37 hours - lighting strike on 220 kv circuit -- permanent short-circuit 15:15:00 hours -- loss of generation 15:18:43 hours -- three more units are lost load shedding request not honored by DisCos severe reduction of MVAr 15:26:00 to 15:27:00 hours three units come back on line voltage starts to improve

21 1950s Practical Steady-State Stability Criteria - Venikov, Markovici, Moscow, USSR 1961 Short-Circuit Currents Method Steady-State Stability Analysis - Dimo, RGE, Paris 1980 Short-Circuit Currents Method Voltage Stability Analysis - Barret, Barbier, RGE, Paris Steady-State Stability Monitor Prototype - EPRI, Palo Alto, CA Sponsorship from Southern Company Services, Birmingham, AL 1993 Method Presented at IEEE Winter Power Meeting, New York, NY 1994 QuickStab announcement -- first experimental installations at Southern Company Services, Birmingham, AL IREQ HydroQuebec, Montreal, Canada QuickStab -- production-grade off-line and real-time CPTEE, Sao Paulo, Brazil (Off-line and Real-time) OPSIS, Caracas, Venezuela (Real-time on Compaq Unix) Southern Company Services (Windows NT & SUN Solaris) TTI, Guatemala (Off-line on Windows 98) MultiArea QuickStab (MultiArea Transfer Capability Analyzer) ETESA, Panama: Off-line on Windows 2000 Real-time on Compaq Unix MultiArea QuickStab on the Web ETESA, Panama -- TRANSELECTRICA, Romania QuickStab Professional