METHODS OF ANALYSIS OF TRANSIENT STABILITY

1) MODELING:

The basic concepts of transient stability presented above are based on highly simplified models. Practical power systems consist of large numbers of generators, transmission circuits, and loads.

For stability assessment, the power system is normally represented using a positive sequence model.

The network is represented by a traditional positive sequence power flow model, which defines the transmission topology, line reactances, connected loads and generation, and pre disturbance voltage profile.

Generators can be represented with various levels of detail, selected based on such factors as length of simulation, severity of disturbance, and accuracy required. The most basic model for synchronous generators consists of a constant internal voltage behind a constant transient reactance, and the rotating inertia constant (H). This is the so-called classical representation that neglects a number of characteristics: the action of voltage regulators, variation of field flux linkage, the impact of the machine physical construction on the transient reactances for the direct and quadrature axis, the details of the prime mover or load, and saturation of the magnetic core iron. Historically, classical modeling was used to reduce computational burden associated with more detailed modeling, which is not generally a concern with today’s simulation software and computer hardware. However, it is still often used for machines that are very remote from a disturbance (particularly in very large system models) and where more detailed model data is not available.

In general, synchronous machines are represented using detailed models, which capture the effects neglected in the classical model including the influence of generator construction (damper windings, saturation, etc.), generator controls (excitation systems including power system stabilizers, etc.), the prime mover dynamics, and the mechanical load. Loads, which are most commonly represented as static voltage and frequency dependent components, may also be represented in detail by dynamic models that capture their speed torque characteristics and connected loads. There are a myriad of other devices, such as HVDC lines and controls and static VAR devices, which may require detailed representation.

Finally, system protections are often represented. Models may also be included for line protections (such as mho distance relays), out-of-step protections, loss of excitation protections, or special protection schemes.

Although power system models may be extremely large, representing thousands of generators and other devices producing systems with tens-of-thousands of system states, efficient numerical methods combined with modern computing power have made time-domain simulation readily available in many commercially available computer programs. It is also important to note that the time frame in which transient instability occurs is usually in the range of 1–5 s, so that simulation times need not be excessively long.

2) ANALYTICAL METHODS:

To accurately assess the system response following disturbances, detailed models are required for all critical elements. The complete mathematical model for the power system consists of a large number of algebraic and differential equations, including

Ø Generators stator algebraic equations
Ø Generator rotor circuit differential equations
Ø Swing equations
Ø Excitation system differential equations
Ø Prime mover and governing system differential equations
Ø Transmission network algebraic equations
Ø Load algebraic and differential equations

While considerable work has been done on direct methods of stability analysis in which stability is determined without explicitly solving the system differential equations, the most practical and flexible method of transient stability analysis is time domain simulation using step by step numerical integration of the nonlinear differential equations. A variety of numerical integration methods are used, including explicit methods (such as Euler and Runge-Kutta methods) and implicit methods (such as the trapezoidal method). The selection of the method to be used depends largely on the stiffness of the system being analyzed. In systems in which time-steps are limited by numerical stability rather than accuracy, implicit methods are generally better suited than the explicit methods.

3) SIMULATION STUDIES:

Modern simulation tools offer sophisticated modeling capabilities and advanced numerical solution methods. Although each simulation tools differs somewhat, the basic requirements and functions are the same.

i) INPUT DATA:

1. Power flow: Defines system topology and initial operating state.

2. Dynamic data: Includes model types and associated parameters for generators, motors, protections, and other dynamic devices and their controls.

3. Program control data: Specifies such items as the type of numerical integration to use and time-step.

4. Switching data: Includes the details of the disturbance to be applied. This includes the time at which the fault is applied, where the fault is applied, the type of fault and its fault impedance if required, the duration of the fault, the elements lost as a result of the fault, and the total length of the simulation.

5. System monitoring data: This specifies the quantities that are to be monitored (output) during the simulation. In general, it is not practical to monitor all quantities because system models are large, and recording all voltages, angles, flows, generator outputs, etc., at each integration time step would create an enormous volume. Therefore, it is a common practice to define a limited set of parameters to be recorded.

ii) OUTPUT DATA:

1. Simulation log: This contains a listing of the actions that occurred during the simulation. It includes a recording of the actions taken to apply the disturbance, and reports on any operation of protections or controls, or any numerical difficulty encountered.

2. Results output: This is an ASCII or binary file that contains the recording of each monitored variable over the duration of the simulation. These results are examined, usually through a graphical plotting, to determine if the system remained stable and to assess the details of the dynamic behavior of the system.