unbalanced conditions typical during faults. The results of fault analyses are used to size and apply syster protective devices(breakers, relays, etc. Fault analysis is discussed in more detail in Section 61.5. Transient Stability Analysis Transient stability analysis, unlike the analyses previously discussed, assesses the systems performance over a period of time. The system model for transient stability analysis typically includes not only the transmission network parameters, but also the dynamics data for the generators. Transient stability analysis is most often used to determine if individual generating units will maintain synchronism with the power system following a disturbance(typically a fault) Extended Stability analysis Extended stability analysis deals with system stability beyond the generating units' first swing. "In addition to the generator data required for transient stability analysis, extended stability analysis requires excitation system, d governor, and prime mover dynamic data. Often, extended stability analysis will also include dynamics data for control devices such as tap changing transformers, switched capacitors, and relays. The addition of these elements to the system model complicates the analysis, but provides comprehensive simulation of nearly all major system components and controls. Extended stability analyses complement small signal stability analyses by verifying the existence of persistent oscillations and establishing the magnitudes of power and/or Small Signal Stability Analysis Small signal stability assesses the stability of the power system when subjected to"small"perturbations. Small ignal stability uses a linearized model of the power system which includes generator, prime mover, and control device dynamics data. The system of nonlinear equations describing the system are linearized about a specific operating point and eigenvalues and eigenvectors of the linearized system found. The imaginary part of each eigenvalue indicates the frequency of the oscillations associated with the eigenvalue; the real part indicate damping of the oscillation. Usually, small signal stability analysis attempts to find disturbances and/or system conditions that can lead to sustained oscillations(indicated by small damping factors)in the power system. Small signal stability analysis does not provide oscillation magnitude information because the eigenvalues only indicate oscillation frequency and damping. Additionally, the controllability matrices(based on the linearized system)and the eigenvectors can be used to identify candidate generating units for application of new or improved controls(i.e, power system stabilizers and new or improved excitation systems) Transient analysis involves the analysis of the system (or at least several components of the system)when subjected to"fast"transients(i. e, lightning and switching transients). Transient analysis requires detailed component information which is often not readily available. Typically only system components in the immediate vicinity of the area of interest are modeled in transient analyses. Specialized software packages(most notably EMTP)are used to perform transient analyses perational analyses Several additional analyses used in the day-to-day operation of power systems are based on the results of the nalyses described above. Economic dispatch analyses determine the most economic real power output for each generating unit based on cost of generation for each unit and the system losses. Security or contingency analyses assess the systems ability to withstand the sudden loss of one or more major elements without overloading the remaining system. State estimation determines the"best"estimate of the real-time system state based on a redundant set of syster Im measuremen The power flow problem Power flow analysis is fundamental to the study of power systems. In fact, power flow forms the core of power system analysis. a power flow study is valuable for many reasons. For example, power flow analyses play a key role in the planning of additions or expansions to transmission and generation facilities. a power flow solution e 2000 by CRC Press LLC© 2000 by CRC Press LLC unbalanced conditions typical during faults. The results of fault analyses are used to size and apply system protective devices (breakers, relays, etc.) Fault analysis is discussed in more detail in Section 61.5. Transient Stability Analysis Transient stability analysis, unlike the analyses previously discussed, assesses the system’s performance over a period of time. The system model for transient stability analysis typically includes not only the transmission network parameters, but also the dynamics data for the generators. Transient stability analysis is most often used to determine if individual generating units will maintain synchronism with the power system following a disturbance (typically a fault). Extended Stability Analysis Extended stability analysis deals with system stability beyond the generating units’ “first swing.” In addition to the generator data required for transient stability analysis, extended stability analysis requires excitation system, speed governor, and prime mover dynamic data. Often, extended stability analysis will also include dynamics data for control devices such as tap changing transformers, switched capacitors, and relays. The addition of these elements to the system model complicates the analysis, but provides comprehensive simulation of nearly all major system components and controls. Extended stability analyses complement small signal stability analyses by verifying the existence of persistent oscillations and establishing the magnitudes of power and/or voltage oscillations. Small Signal Stability Analysis Small signal stability assesses the stability of the power system when subjected to “small” perturbations. Small signal stability uses a linearized model of the power system which includes generator, prime mover, and control device dynamics data. The system of nonlinear equations describing the system are linearized about a specific operating point and eigenvalues and eigenvectors of the linearized system found. The imaginary part of each eigenvalue indicates the frequency of the oscillations associated with the eigenvalue; the real part indicates damping of the oscillation. Usually, small signal stability analysis attempts to find disturbances and/or system conditions that can lead to sustained oscillations (indicated by small damping factors) in the power system. Small signal stability analysis does not provide oscillation magnitude information because the eigenvalues only indicate oscillation frequency and damping. Additionally, the controllability matrices (based on the linearized system) and the eigenvectors can be used to identify candidate generating units for application of new or improved controls (i.e., power system stabilizers and new or improved excitation systems). Transient Analysis Transient analysis involves the analysis of the system (or at least several components of the system) when subjected to “fast” transients (i.e., lightning and switching transients). Transient analysis requires detailed component information which is often not readily available. Typically only system components in the immediate vicinity of the area of interest are modeled in transient analyses. Specialized software packages (most notably EMTP) are used to perform transient analyses. Operational Analyses Several additional analyses used in the day-to-day operation of power systems are based on the results of the analyses described above. Economic dispatch analyses determine the most economic real power output for each generating unit based on cost of generation for each unit and the system losses. Security or contingency analyses assess the system’s ability to withstand the sudden loss of one or more major elements without overloading the remaining system. State estimation determines the “best” estimate of the real-time system state based on a redundant set of system measurements. The Power Flow Problem Power flow analysis is fundamental to the study of power systems. In fact, power flow forms the core of power system analysis. A power flow study is valuable for many reasons. For example, power flow analyses play a key role in the planning of additions or expansions to transmission and generation facilities. A power flow solution