ECE 692 Advanced Topics on Power System Stability 5 - Voltage Stability

Transcription

1 ECE 692 Advanced Topics on Power System Stability 5 - Voltage Stability Spring 2016 Instructor: Kai Sun 1

2 Content Basic concepts Voltage collapse and Saddle-node bifurcation P-V curve and V-Q curve Causes and prevention of voltage instability Voltage Stability Analysis (VSA) Modal analysis Continuation powerflow Measurement-based VSA 2

3 eferences Chapter 14 of Kundur s book Survey of the voltage collapse phenomenon, NEC Interconnection Dynamics Task Force eport, Aug EPI Tutorial s Chapter 6 Carson W. Taylor, Power System Voltage Stability McGraw Hil, 1994 Voltage Stability Assessment: Concepts, Practices and Tools, IEEE-PES Power Systems Stability Subcommittee Special Publication, Aug V. Ajjarapu, C. Christy, The continuation power flow: a tool for steady state voltage stability analysis, IEEE Trans Power Syst., vol. 7, no. 1, Feb, 1992 K. Vu, M.M. Begovic, D. Novosel, M.M. Saha, Use of local measurements to estimate voltage-stability margin, IEEE Trans Power Syst., vol. 14, no. 3, Aug,

4 Voltage Stability Voltage stability is concerned with the ability of a power system to maintain acceptable voltages at all buses in the system under normal conditions and after being subjected to a disturbance. A system enters a state of voltage instability (or voltage collapse) when a disturbance, e.g. increase in load demand, or change in system condition causes a progressive and uncontrollable decline in voltage The main factor causing instability is the inability of the power system to meet the demand for reactive power Voltage stability problems normally occur in heavily stressed systems. 4

5 Factors Influencing Q Transfer Q is transmitted from the high voltage side to the low voltage side. But Q cannot be transmitted over long distances because It would require a large voltage gradient to do so. An increase in Q transfer causes an increase in Q loss as well as P loss 5

6 Voltage Stability vs. otor Angle stability otor angle stability is basically stability of generators while voltage stability is basically stability of loads otor angle stability is often concerned with remote power plants connected to a large system over long transmission lines. Voltage stability is concerned with load areas and load characteristics. In a large interconnected system, voltage collapse of a load area is possible without loss of synchronism of any generators. However, transient voltage stability is usually closely associated with transient rotor angle stability. If voltage collapse at a point in a transmission system remote from loads, it is, in nature, an angle instability problem. 6

7 A simple radial system How does V change as P increases? V Z I I Z I LN LD ES Z LD P V I cos E ( Z cos Z cos ) ( Z sin Z sin ) S 2 2 LN LD LN LD Z LD decreases (assume constant Z LN ) I E Z 1 S F LN where F 2 Z LD Z LD 1 2 cos( ) ZLN ZLN Z V Z I E 1 LD LD S F ZLN P Z LD E S VI cos F ZLN 2 cos 7

8 How does voltage instability happen? Voltage stability depends on the load characteristics (dynamics and control) Under normal conditions, Z LD >> Z LN and an increase in power P is equivalent to a decrease in Z LD However, when Z LD <Z LN (heavy load conditions), a decrease in Z LD reduces P, so a control on power by varying Z LD may become unstable For instance, consider a load supplied by a transformer with automatic ULTC. The tap-changer tries to raise the load voltage (absorbing more Mvar from the primary side), which has the effect of reducing the effective Z LD and in turn lowers V further (as seen from the primary side) and may lead to a progressive reduction of voltage if the primary side is weak. Load increases (Z LD decreases) 8

9 Using an ULTC to control voltage Normally, when the turns ratio is adjusted, the Mvar flow across the transformer is also adjusted However, since a transformer absorbs Mvar to build its internal magnetic field, when its secondary voltage is raised via a tap change, its Mvar usage increases and its primary voltage often drops. The greater the tap change and the weaker the primary side, the greater the primary voltage drop. If the primary side is weak, the tap change may not necessarily increase the secondary voltage. Therefore, spare Mvar must be available for a tap change to be successful. An example: 10% / 33-position ULTC (5/16x10%= % ~ 142.3kV) (Neutral point: 0% ~ 138kV) (+10% ~ 151.8kV) 9

10 P-V Curve Z LD decreases (assume constant Z LN ) Constant P P =P Constant Z P =av 2 The critical point (also called the nose or knee point) is referred to as saddle-point bifurcation Does voltage collapse necessarily happen when the system passes the critical point? 10

11 Saddle-node bifurcation A saddle-node bifurcation is the disappearance of a system equilibrium as parameters change slowly. This is an inherently nonlinear phenomenon and cannot occur in a linear model. Bifurcation at the limit p* Two equilibriums Equilibrium disappears 11

12 Example: P-V Curve with ZIP Load E S =1.0pu, Z LN =j0.5pu, cos=0.97. Sketch the P -V curve at bus and find values of P and V at the critical point If the real power load is represented by a ZIP load mode P =P 0 (V V +4.0), where P 0 varies depending on the load level. Estimate the minimum V before voltage collapse. F 2 Z LD Z LD 1 2 cos( ) ZLN ZLN 2 2cos( ) V 1 F Z Z LD LN E S pu P Z F LD E Z S LN 2 cos pu 12

13 Normalized P-V curves ( varies) Normally, only the operating points above the critical points represent satisfactory operating conditions A sudden reduction in (increase in Q ) 13

14 V-Q Curve =V 0 o If Q I is injected by a var source at the load bus: Z LN jx LN * E S =E S Q I * ES V P j( Q QI ) VI V jx LN P =E S V sin/x LN Q Q I E V cos V X 2 S LN PX EV LN sin S ( Q Q ) X V EV 2 cos I LN S Eliminate by cos 2 +sin 2 =1 V EV Q Q P S 2 I 2 XLN XLN Q I 2 V E V P tan X X LN 2 2 S 2 LN V-Q curve for specific P and (one loading condition) P 2 Q I P increases V 14

15 Normalized V-Q curves (P varies) A V-Q curve shows sensitivity and variation of a bus voltage with respect to Q injected at the bus. It indicates the Q I required in order to maintain the bus voltage at desired value V Q I /P MAX A V-Q curve is generated by applying a fictitious var source, e.g. synchronous condenser, at the test bus, i.e. converting the bus to a PV bus with open var limits, so it can be used to examine needs for var compensation Voltage instability happens when dq I /dv <0 since All var control devices are designed to operate when an increase in Q is accompanied by an increase in V Protective devices may be activated Voltage stability limit is reached when dq I /dv =0 15

16 39-bus test system A B C P Aera 1 - V 530 Uniformly scale up the area load with constant 16

17 Probable remedial actions before the limit is reached Inject Q at Bus 530 to increase V educe load near Bus

18 Causes of voltage instability A typical scenario on the principal driving force for voltage instability: In response to a disturbance, power consumed by loads tends to be restored by motor slip adjustment, distribution voltage regulators and thermostats estored loads increase stress on the high-voltage network causing further voltage reduction Voltage instability occurs when load dynamics attempt to restore power consumption beyond the capability of the transmission network Principal causes The load on transmission lines is too high The voltage sources are too far from load centers The source voltages are too low There is insufficient load reactive compensation Contributing factors Generator reactive power and voltage control limitations Load Characteristics Distribution system voltage regulators and transformer tap-changer actions eactive power compensating device characteristics 18

19 Influence of Generation Characteristics Actions of generator AVs provide the primary sources of voltage support Under normal conditions, generator terminal voltages are maintained constant During conditions of low/high voltages, the var output of a generator may reach its limit. Consequently, the terminal voltage is not longer maintained constant Then, with constant field current, the point of constant voltage is now E q behind the synchronous reactance X S X d. That increases the network reactance significantly to further aggravate the voltage collapse condition It is important to maintain voltage control capabilities of generators The degree of voltage stability cannot be judged based only on how close the bus voltage is to the normal voltage level Voltage collapse due to the Q/current limit being reached is referred to as limitinduced bifurcation 19

20 Influence of eactive Compensator Characteristics Kundur s Example 14.1 The compensator is designed to increase compensation (Q) in order to increase voltage (V) At Point A (low compensation) The slope Q/V of the system is greater than that of the shunt capacitor With the compensation increase, A A ; V is increased at A, so compensation stops increasing Voltage is stable At Point B (high compensation) The slope Q/V of the system is smaller than that of the shunt capacitor With the compensation increase, B B ; V is decreased at B, so compensation will continue to increase (nonstop) Voltage is unstable Compensation increases 20

21 Influence of Load Characteristics When voltages drop esidential loads Active load will drop with voltage, which will in turn reduce line loading and hence the line reactive losses Industrial loads Active load will change little because of large components of induction motors. However the capacitors in the industrial area will supply less reactive power, thereby causing a net increase in the reactive load At voltages below 85-90% of the nominal value, some induction motors may stall to draw high reactive current, which brings the voltages down further. The voltage drop will cause many motors to drop out. The loss of motor loads will result in voltage recovery. However, after some time, the motors are restored to service, which may cause voltage to drop again if the original cause of the voltage problem still persists. 21

22 Load modeling for accurate analysis of voltage stability Motors and capacitors in industrial areas Load regulating devices (e.g. thermostatically controlled loads) When the distribution voltages remain low for a few minutes, they tend to restore load to the normal full voltage value in minutes, which makes distribution voltages drop further Substation transformer ULTCs and distribution voltage regulators Attempt to maintain voltage at points of consumption May have destabilizing effects during conditions of voltage collapse When the ULTCs reach the end of their tap range, distribution voltages drop 22

23 Long-Term and Short-Term Voltage Stability The time frame by which voltage instability occurs could be in the range of a few seconds (short-term) to tens of minutes (long-term) Long-term voltage instability (several minutes) Involves slower acting equipment such as transformer ULTCs, generator field current limiters and thermostatically controlled loads May be effectively studied using static analysis techniques with complementary use of dynamic analysis Short-term voltage instability (several seconds) Faults/short-circuits near loads could be important Involves dynamics of fast acting load components such as induction motors, electronically controlled loads and HVDC converters Dynamic modeling of loads are often essential; analysis requires solution of differential equations using time-domain simulations Effective countermeasures include STATCOMs, particularly smaller units connected to distribution network and fast load shedding (UVLS schemes). There is a trend of increasing short-term voltage instability due to Increasing use of low inertia compressor motors for air conditioning, heat pumps and refrigeration Growth in the use of voltage-insensitive loads with electronic power supplies Transmission network being pushed harder 23

24 A Typical Scenario of Short-Term Voltage Instability The power system is operating in a stressed condition during hot weather with a high level of air conditioning load The triggering event is a multi-phase fault near a load center Causes voltage dips at distribution buses Air conditioner compressor motors decelerate, drawing high current Following fault clearing with transmission/distribution line tripping motors draw very high current while attempting to reaccelerate. Motors stall if the power system is weak. Under-voltage load rejection may not be fast enough to be effective Loss of much of the area load and voltage collapse 24

25 4 7 Tripped by Zone 3 relay Faulty zone 3 relay GW generation tripped by SPS Loss of key hydro units Tree contact and relay mis-opt Example of Voltage Collapse - July 2 nd, 1996 Western Cascading Event 25

26 On July 3 rd, 1996, i.e. the following day, A similar chain of events happened to cause voltages in Boise area to decline. Different from the previous day, Idaho Power Company system operators noted the declining voltages and immediately took the only option available: shedding of Boise area load Then, the system returned to normal within 1 hour Lessons learned: The July 2 nd and 3 rd events in Boise, Idaho area emphasize the need for effective and sufficient, rapidly responsive dynamic Mvar reserve. The July 3 rd events illustrate the importance of system operators situational awareness and rapid responses. 26