## Power System AnalysisIntroductionOverview of Power System Analysis : Importance of system planning and operational analysis; different models for generator, load and transmission lines based on the analysis of interest - Steady state. quasi steady state and transient analysis.Basics of Analysis and Component ModellingRepresentation : Single line diagram, per unit representation; primitive network and its matrices, bus admittance matrix formation by Two-Role method and singularity transformation method, bus impedance matrix formation by L-U factorisation of bus admittance matrix and by building algorithm. Per phase analysis of symmetrical three phase system. Symmetrical component transformation, Sequence impedances and sequence networks, equivalent circuit of transformer with off nominal-tap ratio.Power Flow AnalysisImportance of power flow analysis in planning and operation of power systems : Power flow problem : Description of the problem. Classification of buses into P-Q buses, P-V (voltage-controlled) buses and slack bus ;Power flow equations and solution :Development of Power flow model in complex variable form,Iterative solution using Gauss-Seidel method including Q-limit check for voltage-controlled buses, Flowchart.Development of Power flow model in ral variable form, Iterative solution using Newton-Raphson (N-R) method (polar form) including Q-limit check and bus switching for voltage-controlled buses, Details of expressions for Jacobian elements, Flowchart.Development of Fast Decoupled Power Flow (FDPF) model from NR-voltage updation equations, Flowchart.Comparison of the three methods with respect to reliability and speed of convergence, simplicity of programming and dependency of system size and memory requirements.Numerical solution of power flow problem of systems (not more than three buses) by G-S method and FDPF methods and systems (not more than two buses) using NR method.Power flow studies in system planning (design) and operation : Computation of transmission line / transformer flows, Transmission loss, Slack bus power, Over loaded / under loaded lines / transformers, Over voltage / under voltage buses, Contingency analysis - Simulation of single line and generator outages.Fault Analysis Need for fault analysis : Circuit breaker selection based on momentary and interrupting duties, Protective relay settings.Common approximations made in fault analysis : neglecting busloads, Shunt compensation and half-line charging.Symmetrical short circuits : Thevenin's theorem and applications, Short circuit analysis of two-bus system and numerical problems. Short circuit capacity - Fault level and circuit breaker selection : Systematic short circuit commutations - Expression for post fault voltage and currents using Thevenin's theorem.Unsymmetrical short circuits : Short-circuit analysis of unbalanced low order systems - Derivation of fault current for LG, LL, LLG short circuits and development of interconnection of sequence networks for LG, LL and LLG faults - Problems with two bus systems - Short circuit analysis of unbalanced large - Scale systems - Problem statement - Network modelling by means of sequence bus impedance matrices - Fault matrices Zf and Yf - Short circuit formulas (Derivation only). Stability AnalysisDescription of power system stability problem : Importance of stability analysis in power system planning and operation ; Classification of power system stability ; Angle and voltage stability; Classification of angle stability into small-signal and large-signal (transient) stability; classification of small-signal stability into oscillatory and non-oscillatory stability; Classification of oscillatory stability into local, inter-area, Control and torsional modes.Single Machine Infinite Bus (SMIB) system : Development of swing equation; Synchronous machine representation by classical model (constant internal voltage behind transient reactance); power-angle equation; Equal Area Criterion ; Determination of critical clearing angle and time; Algorithm for numerical solution of swing equation using modified Euler method and plotting of swing curves; Usage of numerical algorithm for determination of critical clearing time by trial and error; Small-signal stability of SMIB system ; Linearization of swing equation; Concept of synchronizing power coefficient; Determination of natural frequency of local mode of oscillation using linearized equation.Multimachine power system : Synchronous machine representation by classical model and loads by constant admittances; Algorithm for alternating solution approach through network solution using bus admittance matrix and state-equations using modified Euler method. |

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