Power System Stability.pdf

POWER SYSTEM STABILITY

Power system dynamic disturbances • Because of the interconnection of various elements a large variety of dynamic interactions are possible • The prime concern: System response to change in power demand and to various types of disturbances.

Power system dynamic disturbances  These dynamic interaction vary in their speed of occurrence in the power network and cause disturbance in the operation of the network. Eg.  The fastest: Associated with the very fast wave phenomena (surges) in HV transmission lines  caused by lightning strikes or switching operation  Speed ranges from (μs - ms)

 Slower: Due to electromagnetic changes in electrical machines windings  caused by operation of the protection system or the interaction between electrical machines and the network (ms - s)

Power system dynamic disturbances  Slow: Due to electromechanical rotor oscillations Caused by oscillation of the rotating masses of generators and motors following a disturbance, operation of the protection system or voltage and prime mover control Speed ranges from (s – several seconds)

 The occurrence of these disturbances greatly affect the stability of the entire network

Power system Stability

• A power network is characterised by many generators each injecting power in the network • Its important to understand the network stability as generators interact with other system components

Power system stability; Definition  Stability: Stability is a condition of equilibrium between opposing forces!

 Power System Stability: Power system stability is the property of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance

Types of Power System Stability  Rotor angle stability: The ability of interconnected synchronous machines of a power system to remain in synchronism. (Study of electromechanical oscillations inherent to power system is required.)

 Voltage stability: The ability of a power system to maintain steady acceptable voltages at all buses in the system under normal operating conditions and after being subjected to a disturbance. (The main factor is inability of power system to meet the demand for reactive power.)

Rotor Angle Stability

Types of Rotor Angle Stability  Small-disturbance stability The ability of a power system to maintain synchronism under small disturbance

 Transient stability The ability of a power system to maintain synchronism when subjected to a severe transient disturbance

Causes of Rotor Angle Instability  Lack of synchronising torque component results in instability through an aperiodic drift in rotor angle (leads to aperiodic instabilitymachine going out of step)  Lack of damping torque component results in oscillatory instability ( i.e, growing Oscillations)

Rotor Angle Stability • The electrical power produced is a function of the synchronising and damping power/ torque. • The relating equation are as follows;

• Where; • Te = Electrical torque • TSΔδ = Synchronising torque (power) component (in phase with the rotor angle perturbation)

• TS = Synchronising torque (power) coefficient • TD∆w =Damping torque (power) component

(in phase with the rotor speed deviation) • TD = Damping torque (power) coefficient

Rotor Instability

Cases of transient instability Case 1: Stable system Case 2: Unstable system due to insufficient synchronising torque. This is also known as first swing instability. Case 3: Unstable system (insufficient damping torque)

Voltage Stability  At a given operating condition for every bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased.  Voltage instability is generally a local phenomenon.  Voltage collapse is the result of a sequence of events accompanying voltage instability leading to a lowvoltage profile in a significant part of the system

Instability subdivisions

Mathematical approach to power system stability

The Swing Equation • It describes the rotor dynamics for synchronous machines where 𝛿 is the angle of the internal voltage of the generator terminals. • This is given as;

• Where;

𝜕2 𝛿 𝜕𝑡 2

=

𝜔0 (𝑃𝑚 2𝐻

𝛿 =rotor angle, in rads 𝐻 = inertia constant in secs 𝑃𝑚 = mechancal power, pu 𝑃𝑒 = electrical power

− 𝑃𝑒 )

The Swing Equation • From the above equation, its possible to obtain the critical clearing angle and critical clearing time so that the system attains its stability level. • The concept of equal area criterion works hand in hand and is key in determining the critical clearing angle

Critical clearing Time

• When a fault aoccurs, there is a time when the fault must be cleared before the system becomes unstable. This time is known as the critical clearing time tcr. • The clearing time can be derived from the swing equation by integrating with respect to time such that;

• “Derive the expression for critical clearing time?”

Critical clearing Angle  when the fault occurs in the system the load angle curve begin to increase, and the system becomes unstable. The angle at which the fault becomes cleared and the system becomes stable is called critical clearing angle (𝛿𝑐𝑟 ).

Power curve  Consider the fig below. The electrical power delivered to the load can be determined

Power equation

 Where

V is the voltage at infinite bus. E is internal voltage of generator. X is the total reactance Taking V as ref. Voltage = V

Power Equation Phasor diagram

Such that

Power curve  When the initial load is given, then there is a critical clearing angle, and if the actual clearing angle exceeds a critical clearing angle, the system becomes unstable otherwise it is stable.  Curve A represents the power angle curve for a healthy condition;  Curve B represents the power angle curve for faulty condition and curve  Curve C represents the power angle curve after isolation of fault as shown below.

Critical clearing angle Power curves

Equal Area Criterion  The critical clearing angle can be determined using the equal area criterion

Example  Consider the network below with a 3-phase on the line as shown. Determine the clearing angle and time.

 In order to solve such a question, we need to first determine the electrical power before, during and after the fault

Before fault (Pre-Fault condition)

Before fault (Pre-Fault condition)

After fault (Post-Fault condition)

During the fault (At -Fault condition)

Using Thevenin’s theorem to solve the circuit

Power transfer before, during and after the fault

Equal Area Criterion

Critical Clearing Angle