Of the different analysis schemes by which large-scale dynamic analysis of interconnected power systems might be implemented, that developed in the paper is one in which the differential and nondifferential equations for solution are combined into a single nonlinear vector-differential equation set for the complete system analysed. In the development of the model, Kron's synchronously rotating frame of reference is used for the stator circuits of all machines, synchronous and asynchronous, and for the network system that interconnects them, while separate rotor frames are used for the rotor circuits of each machine. Explicit forms of plant matrices for this formulation are given, and the derivation of a complete system model from them is developed. In conjunction with a compact storage scheme, a solution sequence is derived by which near-minimal storage requirements in solution are achieved, and to which both single-and multiple-step integration routines may be directly adapted. Study results from trial analyses are included, and an assessment of the principal computing requirements in using the model developed in more general applications is made. LEST OF PRINCIPAL SYMBOLSSymbols common to generators and to induction motors: T e = electromagnetic torque w r = angular velocity of rotor V(j,Vq = components of stator terminal voltage in d and q axes, respectively id>iq = components of stator terminal current in d and q axes, respectively vt = terminal voltage i|/ = flux linkage = inertia constant,kWs/kVA = H/irf = vector of derived axis voltages = diagonal matrix of winding resistances = inductance matrix = torque matrix = machine-impedance and machine-admittance matrices, respectively = derived coefficient matrices = matrix in machine-voltage equations H M Vi R L G z m> Y m Generators: * L fd d> L d» L q= torque input to generator rotor = stator resistance = field-winding resistance and total inductance, respectively = d-axis damper-winding resistance and total inductance, respectively = total inductance of d-and q-axis stator windings, respectively .= rotor-stator mutual inductance in d and q axes, respectively = field voltage and current, respectively = d-and q-axis damper-winding current, respectively = angle between d axis of frame of reference attached to generator rotor and d axis of independently rotating frame of reference Induction motors: R SS ,R ss» iV rr J m = load torque on motor shaft = stator and rotor resistance, respectively = total inductance of stator and rotor windings, respectively = mutual inductance between rotor and stator = derived reactance Automatic-excitation control-system representation: V R = equivalent reference signal corresponding to setting of error-detecting circuit K 2 ,K e = equivalent gain constants of amplifiers and main excitation system, respectively K 3 = constant of stabilising loop T 2 , r e = time constants of amplifiers and excitation system, respectively T 3 = time constant of stablising loop V 2' v fd = signal output from amplifiers and generator field voltage, resp...
Prior to instrumented site tests being carried out on a group of power-station auxiliary motors, computer studies of the site-test conditions were undertaken, and the paper reports the analytical methods developed for the pretest dynamic analyses, together with the correlation achieved between site-test and computed results. For the purposes of the tests, the motors were isolated from the turbogenerator for which they normally function as auxiliaries, and supplied from a neighbouring power station. To assess their recovery to, or divergence from, steady running conditions subsequent to disturbances in the system from which they are supplied, controlled-duration faults were applied at the power station supplying the induction-motor group. In the pretest analyses, 12 subgroups, of a total of 23 motors tested, were independently represented, as was the turbogenerator unit at the neighbouring power station. Central to the analysis is Kron's concept of a synchronously rotating frame of reference, into which the equations of all machines in the group are transformed. It is shown, in the paper, that, after transformation, the machine equations may be arranged in a form particularly suitable for multimachine-system analysis by computer. The overall method of analysis is developed in detail, and its validity is checked by comparisons, made in the paper, of site-test recordings of the principal machine variables, and solutions obtained for them in the pretest computer studies. [Z'] = transient-impedance matrix [C,] [Z] [C]ixi f = angular velocity of synchronously rotating frame of reference . . . d . . p = derivative operator -, time in secondsIn the general formulation of Section 3, suffix b denotes a system-branch quantity and suffix m denotes a machine quantity. In the derivation of the reduced forms of motor and generator representation, suffix s denotes a stator quantity and suffix r denotes a rotor quantity, i.e. for both motor and generator for a generator and l fd kd Jkq. JqrJ for a motorIn. the motor and generator representations, the term total inductance is used for the sum of the magnetising and leakage inductances.
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