Steady State Stability in Power Systems: Definition, Causes, and Improvement Methods

Definition of Steady State Stability

Steady state stability is defined as the capability of an electric power system to sustain its initial operating condition following a small disturbance, or to converge to a state closely approximating the initial condition when the disturbance persists. This concept holds critical significance in power system planning and design, the development of specialized automatic control devices, the commissioning of new system components, and the adjustment of operating conditions.

The assessment of the steady state stability limit is essential for power system analysis, which encompasses verifying the system’s performance under specified steady state conditions, determining stability limits, qualitatively evaluating transient processes, and evaluating factors such as the type of excitation system and its controls, control modes, and parameters of excitation and automation systems.

Stability requirements are determined by the stability limit, the quality of electrical energy under steady state conditions, and transient performance. The steady state stability limit refers to the maximum power flow through a specific point in the system that can be maintained without triggering instability when power is gradually increased.

In power system analysis, all machines within a single segment are treated as a single large machine connected at that point—even if they are not directly linked to the same bus and are separated by significant reactances. Large-scale systems are typically assumed to have a constant voltage and are modeled as an infinite bus.

Consider a system comprising a generator (G), a transmission line, and a synchronous motor (M) functioning as the load.

The expression shown below gives a power developed by a generator G and synchronous motor M.

The expression below gives the maximum power generated by the generator G and synchronous motor M

Here, A, B, and D represent the generalized constants of the two-terminal machine. The above expression yields power in watts, calculated per phase—provided that the voltages used are phase voltages in volts.

Reasons for System Instability

Consider a synchronous motor connected to an infinite busbar, operating at a constant speed. Its input power equals the output power plus losses. If the smallest increment of shaft load is added to the motor, the motor’s output power increases while its input power remains unchanged. This creates a net retarding torque, causing the motor’s speed to drop temporarily.

As the retarding torque reduces the motor speed, the phase angle between the motor’s internal voltage and the system voltage increases until the electrical input power equals the output power plus losses.

During this transient interval, since the motor’s electrical input power is less than the mechanical load, the excess power required is drawn from the stored energy in the rotating system. The motor oscillates around the equilibrium point and may eventually either come to a halt or lose synchronism.

A system also loses stability when a large load is applied or when a load is applied too suddenly to the machine.

The equation below describes the maximum power a motor can develop. This maximum load is achievable only when the power angle (δ) equals the load angle (β). The load can increase until this condition is met; beyond this point, any further load rise will cause the machine to lose synchronism due to insufficient power output.

The deficit power will then be supplied by the stored energy of the rotating system, leading to a drop in speed. As the power deficit grows larger, the angle gradually decreases until the motor comes to a stop.

For any given δ, the difference between the power developed by the motor and the generator equals the line losses. If the line’s resistance and shunt admittance are negligible, the power transferred between the alternator and the motor can be expressed as follows:

Where, X – line reactance

• V_G – voltage of generator

• V_M – voltage of motor

• δ – Load Angle

• P_M – Power of motor

• P_G – Power of motor

• P_max – maximum power

Methods for Improving the Steady-State Stability Limit

The maximum power transferred between an alternator and a motor is directly proportional to the product of their internal electromotive forces (EMFs) and inversely proportional to the line reactance. The steady-state stability limit can be increased through two primary approaches:

• Increasing the excitation of the generator, motor, or both
  Enhancing excitation raises the internal EMF of the machines, which in turn increases the maximum power transferred between them. Additionally, higher internal EMFs reduce the load angle (δ).

• Reducing the transfer reactance
  Transfer reactance can be lowered by:

• Adding parallel transmission lines between the connection points;

• Using bundled conductors, which reduce line reactance;

• Incorporating series capacitors in the line.

Series capacitors are primarily used in extra-high-voltage (EHV) lines to boost power transfer efficiency and are more economically viable for distances exceeding 350 km.