Test Case: Power System Voltage Stability Mats Larsson Corporate Research Mats Larsson / 2002-02-18 / 1 2002 Corporate Research Ltd, Baden, Switzerland
Preview The People from Characteristics of Power Systems Voltage Stability Corrective Measures The Platform for Corrective Control What do we need from CC? The Power Grid Test Case Conclusion Corporate Research Mats Larsson / 07.10.2001 / 2 2001 Corporate Research Ltd, Baden, Switzerland
People Involved From Eduardo Gallestey Mats Larsson PhD in Mathemathics 1998 University of Bremen Optimal and robust control, Corporate optimization Research etc. Mats Larsson / 07.10.2001 / 3 PhD Industrial Automation 2001 Lund University 2001 Corporate Research Ltd, Baden, Switzerland Control and stability of power systems
Characteristics of Power Systems Large-scale Substantial nonlinearity Wide span of time-scales Uncertainty Changing operating point Mix of continuous and discrete control variables Embedded Controllers System model has differentialalgebraic structure A good example of a complex system! Corporate Research Mats Larsson / 07.10.2001 / 4 2001 Corporate Research Ltd, Baden, Switzerland
Control of Power Systems Global control problem extremely difficult Decomposition, Controller hierarchies Some stability concerns in PS Frequency stability Simple linear decentralized control Transient stability -- Energy functions, Lyapunov Small-disturbance stability Linear analysis, H_inf etc. Voltage stability Model Predictive Control etc. Corporate Research Mats Larsson / 07.10.2001 / 5 2001 Corporate Research Ltd, Baden, Switzerland
System collapse due to Voltage Instability Date Location Time to Collapse 860413 Winnipeg, Canada, Nelson River HVDC link 1 s 861130 SE Brazil, Paraguay, Itaipu HVDC link 2 s 850517 S Florida, USA 4 s 870822 W Tennessee, USA 10 s 960702 Western USA 35 s 831227 Sweden 55 s 820902 Florida, USA 1-3 min 821126 Florida, USA 1-3 min 821228 Florida, USA 1-3 min 821230 Florida, USA 1-3 min 770922 Jacksonville, Florida minutes 820804 Belgium 4-5 min 870112 Western France 6-7 min 651209 Bretagne, France minutes 761110 Bretagne, France minutes 870723 Tokyo, Japan 20 min Corporate Research 781219 France 26 min Mats Larsson / 07.10.2001 / 6 2001 Corporate Research Ltd, Baden, Switzerland 700822 Japan 30 min
Voltage Stability 1p.u j1 p.u. => 1 j1 V L + I R v = load voltage p = load power g = load admittance I v 1 = VL = R + j1 1 = VL = 2 1+ g RI = R R + j1 1 = 1+ jg 1 v crit v g p = 2 gv p max p Maximum transfer: p = p Corporate Research max at Mats Larsson / 07.10.2001 / 7 v = v crit 2001 Corporate Research Ltd, Baden, Switzerland
Stability analyis Load constant power behavior: dg T dt v = = p 0 1 1+ g gv 2 2 (increase g if consumption too low) => f dg 1 g ( g) = = ( p0 ) 2 dt T 1+ g Stationary points given by: * 1 1 f ( g) = 0 => g = ± 2 2 p 4 p v 0 g 0 1 p p p 0 0 0 < 0.5 - two equilibrium points = 0.5 - the two equilibrium points coalesce > 0.5 - no equilibrium points v crit p Corporate p 0 Research Mats Larsson / 07.10.2001 / 8 p max Unstable if: 2001 Corporate Research Ltd, Baden, Switzerland p > p or < 0 max v v crit
Simulation Results Small Step in p0 (a) stable case, (b) unstable case Corporate Research Mats Larsson / 07.10.2001 / 9 2001 Corporate Research Ltd, Baden, Switzerland
Tap Changer Control R generation transmission 130/50 kv R R 50/20 kv 20/10 kv 1.08 1.04 130 kv Voltage 50 kv Voltage Used to control customer voltage Relay control Time delay + Deadband 1 0.96 0 6 12 18 24 hours Uses a local viewpoint Bad for System Stability! Corporate Research Mats Larsson / 07.10.2001 / 10 2001 Corporate Research Ltd, Baden, Switzerland
Generator Overload Limits Generators normally under terminal voltage control If the generator is overloaded, voltage control is lost 1.05 Tap Controlled Load Generator Voltage Overload limit reached 1 0.95 0.9 0 100 Corporate Research 200 300 400 Mats Larsson / 07.10.2001 / 11 2001 Corporate Research Ltd, Baden, Switzerland Tap Changer Control
Typical Instability Scenario 1. Line or generator outage reduces the voltage in an area 2. Temporary load reduction 3. Transfer capacity to the area is reduced 4. Load demand recovers (distribution voltage control, inherent dynamics) 5. Voltage is further reduced 6. Generator overload protection activated 7. Collapse! Time scale: seconds to several minutes Corporate Research Mats Larsson / 07.10.2001 / 12 2001 Corporate Research Ltd, Baden, Switzerland
Countermeasures against Voltage Instability Time (seconds) Load shedding Tap locking Capacitor switching Generator voltage setpoints Corporate Research Mats Larsson / 07.10.2001 / 13 2001 Corporate Research Ltd, Baden, Switzerland
Countermeasures (ctd.) Corporate Research Mats Larsson / 07.10.2001 / 14 2001 Corporate Research Ltd, Baden, Switzerland
Wide-area Protection SPC GPS Satellite PMU WAN Transmission Network PMU PMU PMU PMU Snapshot of power system topology and state every 50-250 ms Sophisticated control possible Corporate Research Mats Larsson / 07.10.2001 / 15 2001 Corporate Research Ltd, Baden, Switzerland
The Power Grid Test Case Small-scale example Discrete Step Controls Tap locking Load Shedding Capacitor Switching Hybrid Behaviour Generator overload protection Transformer Relay Control Corporate Research Mats Larsson / 07.10.2001 / 16 2001 Corporate Research Ltd, Baden, Switzerland
Collapse Scenario Line tripping (L3) after 100 s Inherent Load Recovery Tap Changer Tries to Restore Voltage Generator field limit activated at 286 s Collapse 1.05 Tap Controlled Load Generator Voltage Overload limit reached 1 0.95 Tap Changer 0.9 0 100 200 300 400 Corporate Research 2001 Corporate Research Ltd, Baden, Switzerland Mats Larsson / 07.10.2001 / 17 Control
What Do We Need from CC? Optimal Control Problem Find optimal switching sequences for our controls Observability Analysis Select a minimum but sufficient number of measurement points Controllability Select a minimum but sufficient number of control points Reachability Analysis Which are the safe operating regions? When is the last time to stabilize the system, given some set of available controls?... and other things? Corporate Research Mats Larsson / 07.10.2001 / 18 2001 Corporate Research Ltd, Baden, Switzerland
Conclusion Industrially highly relevant problem We are dealing with transmission not distribution A challenging test case: Nonlinearity Load behaviour is uncertain Hybrid behaviour Embedded relay controls Limiter logic Large Scale Present Status Now available in Modelica language, SIMULINK SimStruc T. Geyer at ETH currently works on a PWA model Later on, medium and large scale examples will be available Corporate Research Mats Larsson / 07.10.2001 / 19 2001 Corporate Research Ltd, Baden, Switzerland