A dynamic system, in general, would necessarily entail a detailed study of some concepts interrelated to each other. Particularly, in system planning these concepts are system reliability, security and stability. Definitions of these concepts may help in understanding the relationships and differences between them.

The synchronous machine considered in this chapter has six magnetically coupled windings: three stator `armature' windings and three rotor windings, `one for the field circuit and two for the damper circuits' as demonstrated. The field circuit and one of the two damper circuits are located on the same axis called the direct or d-axis. The second damper circuit is located on an axis lagging the d-axis by 900 elec. and is called the quadrature or q-axis. The d-axis defines the rotor position in space at some instant of time to be at angle q elec. with respect to a fixed reference position. In the case of a larger number of damper windings, the same methodology of derivation, as derived here for one damper winding on each of the two axes, can be applied to model the synchronous machine. The modelling process is based on considering a uniformly distributed sinusoidal mmf in the air gap and without harmonics. It commences, for simplicity, with neglecting the magnetic saturation that will be represented later.

Moreover, each synchronous machine in the power system is equipped with an excitation control system and its prime mover is controlled by a governor control system. These controllers decide the values of vf and Tm and may be involved in the machine equations that are written in this chapter in pu using base phase quantities (the alternative per unit/normalising system is given in Appendix I, Section I.3). These features are presented in this chapter.

Generation, transmission and distribution are the main three parts that comprise a power system. Each part has its own function for electric power: generation part to generate the electric power commonly at medium voltage level by using synchronous generators, transmission part to transmit this power through high voltage or extra-high voltage transmission lines and finally distribution part to distribute the electric power to feed the consumers' loads at medium voltage or low voltage levels. The interconnections between these three parts that operate at different voltages necessitate use of transformers, e.g. step-up/step-down power transformers, distribution transformers, autotransformers. Accordingly, to start the stability studies it is essential to model all elements - generators, transformers, transmission lines and loads - in a manner that is convenient for this purpose. Modelling of synchronous generator has been explained in Chapters 2 and 3, and this chapter deals with the modelling of the rest of the elements.

Models of the individual components of the electric power system are described in Part I. The purpose of this chapter is to study mathematical relations between individual components to develop a model for the overall power system network, which is made of an interconnection of the various components. This model showing the currents, voltages, real power and reactive power flows at each bus in the network is known as Power Flow or Load Flow model. It is found that all relationships - between voltage and current at each bus, between the real and reactive power demand at a load bus or the generated real power and scheduled voltage magnitude at a generator bus - are non-linear. Therefore, power flow calculation implies the solution of a set of non-linear equations to give the electrical response of the transmission system to a particular set of loads and generator power outputs. In practice, the distribution system is not represented in power flow studies of bulk transmission systems and the loads are represented at substation levels. In addition, some assumptions regarding component modelling are made depending on the operating condition, whether it is in steady state or under a contingency, and should be consistent with the time period and purpose of study. A single-phase equivalent representation of the power network is used in power flow studies as the system is generally assumed to be balanced. Section 5.1 is focused on the general concepts of AC power flow calculation methods using bus admittance matrix because of its relevance to the needs of the stability studies. In particular, Newton-Raphson and fast-decoupled methods have been explained with illustrative examples because of their accuracy and fast convergence.

One of the important tools for power system planning and operation is the optimal power flow (OPF). It is a power flow problem in which some control variables are adjusted to minimise or maximise an objective function, while satisfying physical and operating limits as constraints on various controls, dependent variables and functions of variables.

Analysing the power system with a goal of determining its stability is based on models of system components encompassing adequate assumptions to formulate an appropriate mathematical model in the time scale that properly describes the phenomenon under study.

The objective of transient stability study is to determine whether the system generators remain in synchronism when subjected to large disturbances. The transient stability is evaluated by studying the system dynamic response during the transient period that usually lasts up to a few seconds taking into account the rapid change of electrical variables, including relative swinging between generators. A longer transient period may be covered in the study when the behaviour of some controls is of interest. Because of the nature of transient disturbances, the non-linear system equations cannot be linearised and must be solved in stability evaluation. Significant simplifications are required to obtain analytical solutions. Therefore, numerical integration techniques are applied. To form the system equations, adequate models of system components are needed to implement stability study with the desired accuracy. Models of system components, such as synchronous generators with associated controls, excitation system and prime mover, transformers, transmission lines and loads, have been discussed in Part I. It is to be noted that the most important component is the synchronous generator with its associated controls. On the other hand, in stability analysis, load frequency controllers and prime mover models are often neglected without loss of accuracy. Per unit equations of current or flux linkage models given in Chapter 3 completely describe the dynamic performance of a synchronous machine. However, these equations cannot be used directly for system transient stability studies. Some simplifications and approximations are required to represent the synchronous machine in stability studies.

The key idea that the alternative method is based on is to specify a certain function by which the system transient energy at the end of the disturbance period can be calculated. The calculated value is compared with a critical energy value to assess the transient stability, as the difference between the two values gives an indication of stability.

Traditional analytic and time analysis approaches may not easily handle online real-time applications for large systems due to computational time requirements. In particular, the power systems being non-linear and time varying, application of traditional approaches to a power system for the purpose of identifying its parameters, controlling the operation to maintain stability and damping oscillations following disturbances is not suitable for online monitoring. They are more suitable for offline design and investigations. Advent of artificial intelligence (AI) techniques based on logic mathematics has encouraged power system engineers, planners and designers to employ these techniques with the goal of reducing computation time and designing fast algorithms that are adequate for power system online applications. Many AI and computational intelligence techniques, such as artificial neural network (ANN), fuzzy logic (FL), neuro-FL (NFL), particle swarm optimisation (PSO), genetic algorithms, exist. The basics of ANN, FL and NFL as well as the adaptive neuro-fuzzy control (ANFC) are presented in this chapter as they are used, in addition to the time analysis techniques, for some applications (e.g. power system stabilisers and static var compensators) to power systems in the subsequent chapters.

PSSs based on the control algorithms described above have been studied extensively in simulation. They have also been implemented and tested in real time on physical models in the laboratory with very encouraging results. The pole-shifting control algorithm-based APSS has also been tested on a multi-machine physical model, on a 400-MW thermal machine under fully loaded conditions connected to the system, and is now in regular service in a hydro power station after extensive testing in the field. These studies have shown clearly the advantages of the advanced control techniques and intelligent systems. Very satisfactory adaptive controllers can be developed and implemented using a number of approaches, i.e. purely analytical, purely AI techniques or by amalgamating the analytical and AI approaches. Which approach to use depends on the expertise of the designer and the developer of the controller, and the confidence that they or the client have in a particular technology.

This chapter focuses on the series compensation of transmission network and its benefits, in particular, the system stability improvement.

Shunt compensation is applied by using shunt capacitors and shunt reactors that are permanently connected to the network or switched on and off according to operating conditions. Shunt capacitors help increase the system load ability and reduce the voltage drop in the line by improving the power factor. Shunt reactors are used to limit voltage rise under both open line and light load conditions.

A UPFC can regulate the active and reactive power simultaneously. In general, it has three control variables and can be operated in different modes. The shunt-connected converter regulates the voltage of bus i, and the series-connected converter regulates the active and reactive power or active power and the voltage at the series-connected node. In principle, a UPFC is able to perform the functions of the other FACTS devices, which have been described, namely voltage support, power flow control and improved stability.

Modern power systems have been growing in size and complexity. They are characterised by long distance bulk power transmission and wide area interconnections. Such networks have a chance to produce transmission congestion due to load increase (active and reactive power), particularly at peak periods, and also un-damped low-frequency power swings. This may cause severe problems such as reduction of power transfer capability of transmission lines, increased line losses, loss of generator synchronism. The system becomes stressed and has the risk of losing stability following a disturbance. Considerable progress has been made to overcome such problems by (i) controlling the active power of both the generators and loads; (ii) controlling the reactive power using compensators, SSSC, SVC, STATCOM, UPFC, etc.; and (iii) using fast-response excitation control and governor control on the generating units [1, 2]. The interest in applying new technologies in electric power systems is directly related to the expectation of improved performance, stability and efficiency. Some of the recently developed technologies, energy storage systems and phasor measurement devices, are presented in this chapter. Examples of the actual implementation, in particular those from the perspective of power system stability, and the trends in current research are discussed. Possible applications of energy storage in utility systems include transmission enhancement, power oscillation damping (POD), dynamic voltage stability, tie-line control, short-term spinning reserve, load levelling, reducing the need for under-frequency load shedding, allowing less stringent time limits for circuit breaker reclosing, sub-synchronous resonance damping and power quality improvement.

The appendix is about stator base quantities; synchronous machine voltage equations; alternative per unit-normalising systems; and rotor base quantities.

This appendix presents a diagram and data tables for the Nine-bus test system.

The appendix is about Euler's method; the Trapezoidal method; and Runge-Kutta methods.

This appendix presents a diagram and data tables for the 15-bus, 4-generator system.