Reactive Power

Laws of Reactive PhysicsSystem load is comprised of resistive current (such as lights, space heaters) and reactive current (induction motor reactance, etc.).Total current IT has two components.IR resistive currentIQ reactive currentIT is the vector sum of IR & IQ IT = IR + jIQ ITIRIQNorth American Electric Reliability Corporation

Laws of Reactive PhysicsComplex Power called Volt Amperes (VA) is comprised of resistive current IR and reactive current IQ times the voltage.VA = VIT* = V (IR jIQ) = P + jQ

Power Factor (PF) = Cosine of angle between P and VAP = VA times PFSystem LossesPloss = IT2 R (Watts)Qloss = IT2 X (VARs)

VAPQNorth American Electric Reliability Corporation

Reactive Physics VAR lossEvery component with reactance, X: VAR loss = IT2 XZ is comprised of resistance R and reactance XOn 138kV lines, X = 2 to 5 times larger than R.One 230kV lines, X = 5 to 10 times larger than R.On 500kV lines, X = 25 times larger than R.R decreases when conductor diameter increases. X increases as the required geometry of phase to phase spacing increases.VAR lossIncreases in proportion to the square of the total current.Is approximately 2 to 25 times larger than Watt loss.North American Electric Reliability Corporation

Reactive Power for Voltage SupportReactive LoadsVARs flow from High voltage to Low voltage; import of VARs indicate reactive power deficit

Reactive Power Management/CompensationWhat is Reactive Power Compensation?

Effectively balancing of capacitive and inductive components of a power system to provide sufficient voltage support.Static and dynamic reactive power

Essential for reliable operation of power system prevention of voltage collapse/blackout

Benefits of Reactive Power Compensation:

Improves efficiency of power delivery/reduction of losses.Improves utilization of transmission assets/transmission capacity.Reduces congestion and increases power transfer capability.Enhances grid reliability/security.

Static and Dynamic VAR SupportStatic Reactive Power DevicesCannot quickly change the reactive power level as long as the voltage level remains constant.Reactive power production level drops when the voltage level drops.Examples include capacitors and inductors.

Dynamic Reactive Power DevicesCan quickly change the MVAR level independent of the voltage level.Reactive power production level increases when the voltage level drops.Examples include static VAR compensators (SVC), synchronous condensers, and generators.

Voltage Stability

Common DefinitionsVoltage stability - ability of a power system to maintain steady voltages at all the buses in the system after disturbance.

Voltage collapse - A condition of a blackout or abnormally low voltages in significant part of the power system.

Short term voltage stability - involves the dynamics of fast acting load components such as induction motors, electronically controlled loads, and HVDC converters.

Long term voltage stability - involves slower acting equipments such as tap-changing transformer, thermostatically controlled loads, and generator limiters.

What is Voltage Instability/Collapse?A power system undergoes voltage collapse if post-disturbance voltages are below acceptable limitsvoltage collapse may be due to voltage or angular instabilityMain factor causing voltage instability is the inability of the power systems to maintain a proper balance of reactive power and voltage control

Voltage Instability/Collapse

The driving force for voltage instability is usually the loadThe possible outcome of voltage instability:loss of loads loss of integrity of the power systemVoltage stability timeframe:transient voltage instability: 0 to 10 secslong-term voltage stability: 1 10 mins

Voltage stability causes and analysis

Causes of voltage instability Increase in loading

Generators, synchronous condensers, or SVCs reaching reactive power limits

Tap-changing transformer action

Load recovery dynamics

Tripping of heavily loaded lines, generators

Methods of voltage stability analysis Static analysis methods Algebraic equations, bulk system studies, power flow or continuation power flow methodsDynamic analysis methodsDifferential as well as algebraic equations, dynamic modeling of power system components required

MWStator Winding Heating LimitTurbine Limit- Per unit MVAR (Q) +0.8 pf lineUnder-excitation LimitLagging (Over-excited)Leading (Under-excited)Normal Excitation (Q = 0, pF = 1)Over-excitation LimitStability LimitGenerator Capability Curve

P-V Curve

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