Skip to main content

METHODS OF ANALYSIS OF TRANSIENT STABILITY

MODELING

The basic concepts of transient stability 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 that 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 that 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 to 5 sec, so that simulation times need not be excessively long.

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
  • Generators stator algebraic equations
  • Generator rotor circuit differential equations
  • Swing equations
  • Excitation system differential equations
  • Prime mover and governing system differential equations
  • Transmission network algebraic equations
  • 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 largely depends on the stiffness of the system being analyzed. Implicit methods are generally better suited than explicit methods for systems in which time steps are limited by numerical stability rather than accuracy.

SIMULATION STUDIES

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

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 which quantities 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 common practice to define a limited set of parameters to be recorded.

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.

Comments

Post a Comment

Popular posts from this blog

BREAKDOWN VOLTAGE AND DIELECTRIC STRENGTH

An insulator or dielectric is a substance within which there are no mobile electrons necessary for electric conduction. However, when the voltage applied to such an insulator exceeds a certain value, then it breaks down and allows a heavy electric current (much larger than the usual leakage current) to flow through it. If the insulator is a solid medium, it gets punctured or cracked. The disruptive or breakdown voltage of an insulator is the minimum voltage required to break it down. Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down. In other words, the dielectric strength is given by the potential gradient necessary to cause breakdown of an insulator. Its unit is volt/meter (V/m) although it is usually expressed in KV/mm. For example, when we say that the dielectric strength of air is 3 KV/mm, then it means that the maximum PD which one mm thickness of ...
Read more

EQUIPMENT OF STEAM POWER STATION

A modern steam power station is highly complex and has numerous equipment and auxiliaries. However, the most important constituents of a steam power station are: 1. Steam generating equipment 2. Condenser 3. Prime mover 4. Water treatment plant 5. Electrical equipment. 1. STEAM GENERATING EQUIPMENT: This is an important part of steam power station. It is concerned with the generation of superheated steam and includes such items as boiler, boiler furnace, super heater, economizer, air pre-heater and other heat reclaiming devices. (I) BOILER : A boiler is closed vessel in which water is converted into steam by utilizing the heat of coal combustion. Steam boilers are broadly classified into the following two types: (a) Water tube boilers (b) Fire tube boilers In a water tube boiler, water flows through the tubes and the hot gases of combustion flow over these tubes. On the other hand, in a fire tube boiler, the hot products of combustion pass through the tubes surrounded by water. Wate...
Read more

TYPES OF SINGLE PHASE MOTORS

Single phase motors are manufactured in fractional kilowatt range to be operated on single phase supply and for use in numerous applications like ceiling fans, refrigerators, food mixers, hair driers, portable drills, vacuum cleaners, washing machines, sewing machines, electric shavers, office machinery etc. Single phase motors are manufactured in different types to meet the requirements of various applications. Single phase motors are classified on the basis of their construction and starting methods employed. The main types of single phase motors are: (a) Induction motors (b) Synchronous motors (c) Commutator motors The various types of motors under each class are shown as under: Repulsion, repulsion induction and reluctance start motors are not used these days, they have been largely replaced by split phase motors with special capacitors which can be designed to perform equally well as repulsion types. In addition they offer such advantages as lower cost and trouble fr...
Post a Comment
Read more

Advantages of Per Unit System in Power System Analysis | Electrical Engineering

  Advantages of Per Unit System in Power System Analysis In electrical power engineering, the per unit (p.u.) system is one of the most widely used techniques for analyzing and modeling power systems. It is a method of expressing electrical quantities — such as voltage, current, power, and impedance — as fractions of chosen base values rather than their actual numerical magnitudes. This normalization technique provides a universal language for system calculations, minimizing errors, simplifying transformer modeling, and enabling consistency across multiple voltage levels. Because of these benefits, the per unit system is essential in fault analysis, load flow studies, transformer testing, and short-circuit calculations . ⚡ What is the Per Unit System? The per unit system is defined as: Q u a n t i t y ( p u ) = A c t u a l   V a l u e B a s e   V a l u e Quantity_{(pu)} = \dfrac{Actual \ Value}{Base \ Value} Q u an t i t y ( p u ) ​ = B a se   ...
6 comments
Read more

PRIMARY SECONDARY AND TERTIARY FREQUENCY CONTROL IN POWER SYSTEMS

Primary, Secondary and Tertiary Frequency Control in Power Systems Author: Engr. Aneel Kumar Keywords: frequency control, primary frequency control, automatic generation control (AGC), tertiary control, load-frequency control, grid stability. Frequency control keeps the power grid stable by balancing generation and load. When generation and demand drift apart, system frequency moves away from its nominal value (50 or 60 Hz). Grids rely on three hierarchical control layers — Primary , Secondary (AGC), and Tertiary — to arrest frequency deviation, restore the set-point and optimize generation dispatch. Related: Power System Stability — causes & mitigation Overview of primary, secondary and tertiary frequency control in power systems. ⚡ Primary Frequency Control (Droop Control) Primary control is a fast, local response implemented by generator governors (dro...
2 comments
Read more

ELECTRIC MOTOR PRINCIPLES

The electric motor in its simplest terms is a converter of electrical energy to useful mechanical energy. The electric motor has played a leading role in the high productivity of modern industry, and it is therefore directly responsible for the high standard of living being enjoyed throughout the industrialized world. An electric motor’s principle of operation is based on the fact that a current- carrying conductor, when placed in a magnetic field, will have a force exerted on the conductor proportional to the current flowing in the conductor and to the strength of the magnetic field. In alternating current motors, the windings placed in the laminated stator core produce the magnetic field. The aluminum bars in the laminated rotor core are the current carrying conductors upon which the force acts. The resultant action is the rotary motion of the rotor and shaft, which can then be coupled to various devices to be driven and produce the output. Many types of motors are produced today. Un...
Post a Comment
Read more

FUEL INJECTION SYSTEM OF DIESEL ENGINE

Fuel injection is a system for mixing fuel with air in an internal combustion engine. A fuel injection system is designed and calibrated specifically for the type of fuel it will handle. Most fuel injection systems are for diesel applications. With the advent of electronic fuel injection (EFI), the diesel gasoline hardware has become similar. EFI’s programmable firmware has permitted common hardware to be used with different fuels. Carburetors were the predominant method used to meter fuel before the widespread use of fuel injection. A variety of injection systems have existed since the earliest usage of the internal combustion engine. The primary difference between carburetors and fuel injection is that fuel injection atomizes the fuel by forcibly pumping it through a small nozzle under high pressure, while a carburetor relies on low pressure created by intake air rushing through it to add the fuel to the air stream. The fuel injector is only a nozzle and a valve: the power to inj...
Post a Comment
Read more