Excitation &

Capability Curveof a Synchronous Generator

FB/TRAINING/E&I/GEN

Presented By: Er. Manoj Kumar Maharana [ E & I ]

Typical Configuration of a Power Plant

Excitation• The basic purpose of an excitation system is to provide direct current

to the synchronous machine field winding• The basic control function of excitation system with respect to:Generator: To supply and adjust the field current so as to maintain constant terminal voltage and respond to transient disturbance with field forcing in accordance with generator capability.Power system :To respond quickly to improve transient stability and also to modulate field to improve power system stability.

• The excitation system must have a means of measuring generator stator voltage and current.

Capability Curve of

Synchronous Generator

• The Capability Curve of a Synchronous Generator defines a boundary within which the machine can operate safely.

• It is also known as Operating Charts or Capability Charts. The permissible region of operation is restricted to the following points given below.

The MVA loading should not exceed the generator rating. This limit is determined by the armature of the stator heating by the armature current.

The MW loading should not exceed the rating of the prime mover. The field current should not be allowed to exceed a specified value

determined by the heating of the field. For steady state or stable operation, the load angle δ must be less than 90

degrees. The theoretical stability limit of the stable condition occurs when δ = 90 .⁰

GENERATOR CAPABILITY DIAGRAM

GENERATOR CAPABILITY DIAGRAM

GENERATOR CAPABILITY DIAGRAMArmature current limitField current limitPrime Mover LimitEnd region heating limit(1) Armature Current Limit/ Stator Copper Loss (stator heating): The maximum allowable

heating of the stator sets a maximum phase current IA for the machine. It’s equivalent to set a maximum apparent power for the machine. (Power factor is irrelevant).

PSCL = 3 IA2 RS

(2) Field Current Limit/ Rotor Copper Loss (rotor heating): The maximum allowable heating of the rotor sets a maximum field current IF for the machine. It’s equivalent to set a maximum EA for the machine. PRCL = IF

2 RF

(3)Prime-mover’s Power Limit: The active power output is limited by the prime mover capability to a value within the MVA rating. P =|Esinδ| The limit is related to the mechanical input and the ability of the generator to electromagnetically create a torque equal and opposite to the driving mechanical torque.

DEFINES THE OPERATING ZONE OF A SYNCHRONOUS GENERATOR IN A

P-Q PLANE

END REGION HEATING LIMIT

(4) The localized heating in the end region of the armature imposes a third limit on the operation of a synchronous machine.

This limit affects the capability of the machine in the under excited condition.

• At a given excitation, if mechanical torque increases, rotor accelerates, increasing δ and electromagnetic torque.

• This negative feedback continues until electromagnetic and mechanical torques balance.

• However, if generator is operating with δ close to 90° when rotor speeds up, δ increases past 90°, electromagnetic torque falls and positive feedback occurs, causing rotor to accelerate further, pull out of synchronism and result in zero output power and possibly catastrophic failure. The static stability limit is set at δ=90°.

GENERATOR CAPABILITY DIAGRAMPower = 3 Vph I Cos φ = 3 Vph E Sin δ/ X. The power or torque can be thought of as

cross product of two electromagnetic fields or a function of the sine of angle

between V and E.

• A capability diagram is a plot of complex power S=P+jQ • its curve can be derived back from voltage phasor diagram of the Syn.

Gen.

SYNCHRONOUS GENERATOR

• capability curve must represent power limits of generator, hence there is a need to convert the voltage phasor into power phasor.

• P=3 VφIA cosθ • Q=3 VφIA sinθ • S= 3VφIA • Reminding Pmax= 3 VφEA / Xs • The conversion factor to change scale of axes from

V VA is 3 Vφ / Xs

SYNCHRONOUS GENERATOR

• P=3 VφIA cosθ = 3 Vφ / Xs (Xs IA cosθ)• Q= 3 VφIA sinθ = 3 Vφ / Xs (Xs IA sinθ)

• On voltage phasor diagram, origin of phasor diagram is at –Vφ on horizontal axis, so origin on power diagram is:

• Q = 3Vφ /Xs (-Vφ)=-3Vφ^2/Xs • Field current ~ machine’s flux & flux ~ EA=kφω• Length corresponding to EA on power diagram:• DE=- 3 EA Vφ / Xs • IA ~ Xs IA , and length corresponding to XsIA on power

diagram is 3 Vφ IA

SYNCHRONOUS GENERATOR

FUNDAMENTALS

• The corresponding power units

SYNCHRONOUS GENERATORFUNDAMENTALS

FUNDAMENTALSThe rotor heating limit sets |E|max The stator heating limit sets |I |max.

FUNDAMENTALS

FUNDAMENTALS

The final limit is related to the mechanical input and the ability of the generatorto electromagnetically create a torque equal and opposite to the driving mechanical torque

FUNDAMENTALS

FUNDAMENTALS

• Generator capability curve a plot of P versus Q

GENERATOR CAPABILITY DIAGRAM

GENERATOR CAPABILITY DIAGRAM

Operational Limit

Capability Curve

GENERATOR CAPABILITY DIAGRAM

SYN. GENERATOR RATING

• In any balanced design, the thermal limits for the field and armature intersect at a point, which represents the machine nameplate MVA and power factor rating.

• Capability Diagram gives information about full load rotor (excitation current) & maximum rotor angle during steady state P.F.

SYNCHRONOUS GENERATORCapability Curve of KP

• A Gen. is rated 15MW, 6300V, 50 Hz, Y connected, 3000 rpm. at 18.75MVA at 0.8 PF lagging.

• It has a synchronous reactance of Xd=219.6 % per phase• The friction and windage losses are L kW, and core losses are M kW

Sketch capability curve for this generator.

Answer ?

Presented By:

Er. Manoj Kumar MaharanaHOD Electrical

Feedback Power O&M Services Ltd.