SM36 V and Inverted V Curves of alternator

Name: SM36 V and Inverted V Curves of alternator
Uploaded: 2019-11-19T05:00:03.000Z
Duration: 36 min 56 s

What Happens When an Alternator is Connected to an Infinite Bus Bar?

Introduction to Infinite Bus Bar

The discussion begins with the concept of connecting an alternator to an infinite bus bar, which consists of multiple alternators connected in parallel.

It is explained that changing the excitation or mechanical input of one generator does not affect terminal voltage and frequency, as the infinite bus bar acts like a voltage source with zero internal impedance.

Characteristics of Infinite Bus Bar

The zero internal impedance ensures constant voltage and frequency due to infinite mechanical inertia, meaning speed cannot change.

Power equations are introduced: P = EV/X_ex sin delta and Q = V/X_ex (E cos delta - V) , highlighting how reactive power behaves under different conditions.

Reactive Power Dynamics

If E cos delta = V, then reactive power Q = 0, indicating no consumption or delivery of reactive power.

When E cos delta > V, Q becomes positive, indicating delivery of reactive power; conversely, if E cos delta < V, then Q is negative, indicating absorption.

Resultant Flux and Its Implications

The resultant flux responsible for terminal voltage can be expressed as dependent on constants related to voltage and frequency.

Under no-load conditions, it’s established that when losses are neglected ( delta = 0), both active and reactive powers equal zero since current also equals zero.

Effects of Over-excitation

In over-excitation scenarios where excitation increases ( E > V), this leads to a lagging current behind the voltage.

Understanding Reactive Power and Excitation in Electrical Systems

The Concept of Reactive Power

Reactive power is defined as the product of voltage (V) and armature current (IA), indicating that it can be positive when supplying power.

Under-Excitation Effects

Decreasing excitation leads to a reduction in magnetic flux, necessitating an adjustment in armature current to maintain constant resultant flux.

When the electromotive force (E) is less than voltage (V), the armature current flows in a direction that compensates for this difference, resulting in negative reactive power absorption.

Magnetizing vs. Demagnetizing Conditions

Under-excitation results in magnetizing effects, while over-excitation causes demagnetization to keep resultant flux constant.

The total magnetic field strength remains constant by balancing contributions from both main field MMF and armature MMF.

Power Calculations under Different Conditions

In loaded conditions, active power (P) can be expressed as P = E/X_s sin(delta) , which relates to voltage and armature current through cosine relationships.

Changes in excitation affect reactive power calculations; with mechanical input held constant, only excitation changes impact system behavior.

Proportional Relationships and System Behavior

Active power remains proportional to E sin(delta) , while also being related to IA cos(phi).

As excitation increases, induced EMF rises, affecting delta values and leading to shifts in system parameters.

Observations on Armature Current and Power Factor

With normal excitation conditions established, any increase or decrease alters the relationship between E and V significantly impacting reactive power dynamics.

Increasing excitation raises both armature current and overall current levels but decreases the power factor due to changes in cos(φ).

Summary of Key Effects from Increased Excitation

As excitation increases:

Armature current rises alongside overall system currents.

The value of delta decreases consistently throughout these adjustments.

Effects of Excitation on Machine Performance

Overview of Excitation Changes

As excitation increases, the value of delta decreases, while armature current and reactive power (Q) supplied increase. This is observed when moving from normal to under-excitation conditions.

Impact of Decreasing Excitation

When excitation is decreased, the electromotive force (E) also decreases, leading to changes in delta and armature current values. The new value of E can be represented as E2, with corresponding changes in Ia (armature current).

With decreased excitation, delta increases while armature current also rises. Consequently, the angle phi between current and voltage increases, resulting in a decrease in cos phi.

Reactive Power Dynamics

As excitation decreases further, Q becomes negative and continues to increase negatively. This trend is consistent whether excitation is increased or decreased from normal levels; both scenarios lead to an increase in armature current but a decline in power factor.

V and Inverted V Curves

The V and inverted V curves can only be accurately drawn for an alternator operating at constant frequency and voltage—specifically applicable to infinite bus systems. These curves cannot be applied when voltage or frequency varies during excitation adjustments.

Power Factor Behavior

Under normal excitation at unity power factor, increasing or decreasing excitation leads to a falling power factor represented by an inverted V shape on the graph. In under-excitation regions, the power factor is leading due to the current leading voltage; conversely, over-excitation results in lagging power factors where Q is positive and increasing.

Summary of Key Observations