Transient Stability in Power System

Electrical4u
03/22/2024

What Is Transient Stability In Power System

The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc. is referred to as the transient stability in power system. More often than not, the power generation systems are subjected to faults of this kind, and hence its extremely important for power engineers to be well-versed with the stability conditions of the system.
In general practice studies related to transient stability in the power system are done over a minimum period equal to the time required for one swing, which approximates to around 1 sec or even less. If the system is found to be stable during this first swing, its assumed that the disturbance will reduce in the subsequent swings, and the system will be stable after that as is the case. Now to mathematically determine whether a system is stable or not we need to derive the swing equation of
power system.

Swing Equation for Determining Transient Stability

swing equationIn order to determine the transient stability of a power system using swing equation, let us consider a synchronous generator supplied with input shaft power PS producing mechanical torque equal to TS as shown in the figure below. This makes the machine rotate at a speed of ω rad/sec and the output electromagnetic torque and power generated on the receiving end are expressed as TE and PE respectively.
When, the synchronous generator is fed with a supply from one end and a constant load is applied to the other, there is some relative angular displacement between the rotor axis and the stator
magnetic field, known as the load angle δ which is directly proportional to the loading of the machine. The machine at this instance is considered to be running under a stable condition.

Now if we suddenly add or remove load from the machine the rotor decelerates or accelerates accordingly with respect to the stator magnetic field. The operating condition of the machine now becomes unstable and the rotor is now said to be swinging w.r.t the stator field and the equation we so obtain giving the relative motion of the load angle δ w.r.t the stator magnetic field is known as the swing equation for transient stability of a power system.
Here for the sake of understanding, we consider the case where a synchronous generator is suddenly applied with an increased amount of electromagnetic load, which leads to instability by making PE less than PS as the rotor undergoes deceleration. Now the increased amount of the accelerating power required to bring the machine back to a stable condition is given by,

Similarly, the accelerating torque is given by,

Now we know that

(since T = current × angular acceleration)
Furthermore, angular momentum, M = Iω

But since on loading the angular displacement θ varies continuously with time, as shown in the figure below, we can write.

swing equation with angular position

Double differentiating the above equation w.r.t time, we get,

where angular acciletation

Thus we can write,

Now the electromagnetic power transmitted is given by,

Thus we can write,

This is known as the swing equation for transient stability in power system.

Statement: Respect the original, good articles worth sharing, if there is infringement please contact delete.

Electrical4u

Electrical4U is dedicated to the teaching and sharing of all things related to electrical and electronics engineering.

What is reactive power measurement?
What is reactive power measurement?
The power which exists in the circuit when the voltage and current are out of phase to each other, such type of power is known as the reactive power. The formula measures the reactive power in the circuitReactive Power Measurement & VarmetersReactive power measurement is critical as it indicates circuit power loss: low reactive power worsens load power factor, increasing system losses. Varmeters (volt-ampere reactive meters) measure reactive power and are categorized by circuit phases:Single
Edwiin
07/17/2025
What is a step voltage regulator?
What is a step voltage regulator?
Hey everyone, I'm Blue — an electrical engineer with over 20 years of experience, currently working at ABB. My career has mainly focused on circuit breaker design, transformer management, and providing power system solutions for various utility companies.Today, someone asked the question: "What is a step voltage regulator?" Let me explain it in simple but professional terms.So, a step voltage regulator is basically a device used in power distribution systems to keep the voltage stable. Think of
Master Electrician
07/11/2025
Classification of Electric Power Distribution Network Systems
Classification of Electric Power Distribution Network Systems
The typical electric power system network is categorized into three main components: generation, transmission, and distribution. Electric power is produced in power plants, which are often located far from load centers. As a result, transmission lines are employed to deliver power over long distances.To minimize transmission losses, high-voltage power is used in transmission lines, and the voltage is reduced at the load center. The distribution system then delivers this power to end-users.Types
Edwiin
06/05/2025
Why is the Ground Wire Always Positioned Above the Overhead Power Lines?
Why is the Ground Wire Always Positioned Above the Overhead Power Lines?
Ground Wire in Overhead Transmission LinesThe ground wire (also called earth wire or OPGW) installed above phase lines in overhead transmission lines acts as a key protective and safety component. It provides lightning protection, ground fault defense, and helps prevent electrical system disruptions.In overhead transmission lines, positioning the ground wire above phase lines serves specific safety and performance purposes. Referred to as a "shield wire" or "static wire," this configuration has
Edwiin
06/04/2025
Inquiry
Download
IEE-Business is dedicated to serving the personnel in the global power industry.
Join IEE-Business, not only can you discover power equipment and power knowledge, but also canhnd like - minded friends!