scispace - formally typeset
Search or ask a question

Showing papers on "AC power published in 1985"


Journal ArticleDOI
TL;DR: In this article, a unified method for optimal real and reactive power dispatch for the economic operation of power systems is presented, where the problem is decomposed into a P-optimization module and a Q-optimisation module, but in this method both modules use the same generation cost-objective function.
Abstract: This paper presents a unified method for optimal real and reactive power dispatch for the economic operation of power systems. As in other methods, the problem is decomposed into a P-optimization module and a Q-optimization module, but in this method both modules use the same generation cost-objective function. The control variables are generator real power outputs for the real power module; and generator reactive power outputs, shunt capacitors/reactors, and transformer tap settings for the reactive power module. The constraints are the operating limits of the control variables, power line flows, and bus voltages. The optimization problem is solved using the gradient projection method (GPM) which is used for the first time in the power systems study. The GPM allows the use of functional constraints without the need of penalty functions or Lagrange multipliers among other advantages. Mathematical models are developed to represent the sensitivity tivity relationships between dependent and control variables for both, real and reactive power, optimization modules, and thus eliminate the use of B-coefficients. Results of two test systems are presented and compared with conventional methods.

559 citations



Journal ArticleDOI
01 Dec 1985
TL;DR: In this paper, the authors provide a critical review of the Lyapunov direct method of transient stability analysis of power systems and propose on-line criteria suitable for online implementation.
Abstract: Transient stability analysis of a power system is concerned with the system's ability to remain in synchronism following a disturbance In utility planning, transient stability is studied by numerical simulation The long CPU run times for simulation preclude their use for on-line security analysis Interest has therefore shifted toward the Lyapunov direct method of stability analysis This paper provides a critical review of research on direct methods since 1970 Considerable progress has been made on both theoretical properties of energy functions and on criteria suitable for on-line implementation Current theory provides a satisfactory treatment of voltage-dependent reactive power demand, transfer conductances, and flux decay However, it cannot incorporate the exciter control Proposed on-line criteria appear to work very well on sample examples; but, they still lack rigorous justification Finally, recent work has shown that power systems can exhibit chaotic behavior This surprising fact demonstrates that our understanding of the dynamics of power systems remains incomplete

300 citations


Journal ArticleDOI
TL;DR: In this article, the problem of volt/var control on general radial distribution systems is formulated, simplified and solved, where the objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions.
Abstract: In this paper (Part I) and two companion papers (Part II and Part III) the problem of volt/var control on general radial distribution systems is formulated, simplified and solved. The objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions. The decision variables to be optimally determined are (i) the locations, sizes and the real-time control of the specified number of ON/OFF switched and fixed capacitors and (ii) the locations and real-time control of the minimum number of voltage regulators. It is shown in this paper (Part I) that the regulator (volt) and the capacitor (var) problem may be treated as two decoupled problems. Part II of this set of three papers, conjoined with Part 1. provides the analytical tools by which optimal solutions for both problems may be determined. Application of the theory to representative radial systems is shown in Part III whhich also illustrates the economic benefits and numerical results achievable through both regulation and compensation schemes.

220 citations


Journal ArticleDOI
TL;DR: A 30 MJ (8.4 kWh) superconducting magnetic energy storage (SMES) unit with a 10 MW converter has been installed and commissioned at the Bonneville Power Administration (BPA) substation in Tacoma, Washington as discussed by the authors.
Abstract: A 30 MJ (8.4 kWh) Superconducting Magnetic Energy Storage (SMES) unit with a 10 MW converter has been installed and commissioned at the Bonneville Power Administration (BPA) substation in Tacoma, Washington. This is the first large-scale application in the US of superconductivity in an electric utility system. The unit, which is capable of absorbing and releasing up to 10 MJ of energy at a frequency of 0.35 Hz, was designed to damp the dominant power swing mode of the Pacific AC Intertie. This paper describes the electrical characteristics of the magnetic energy storage unit, its modes of operation, results of device tests, means for controlling real and reactive power, and some initial power system response tests. A short summary of the operating history of the unit over the first eleven months is also presented.

171 citations


Journal ArticleDOI
TL;DR: In this article, an algebraic nonlinear analysis of the switched reluctance drive system is described, which is intended to provide an understanding of the factors that determine the kVA requirements of the electronic power converter and to determine the fundamental nature of the torque/speed characteristics.
Abstract: An algebraic nonlinear analysis of the switched reluctance drive system is described. The analysis is intended to provide an understanding of the factors that determine the kVA requirements of the electronic power converter and to determine the fundamental nature of the torque/speed characteristics. The effect of saturation is given special attention. It is shown that saturation has the two main effects of increasing the motor size required for a given torque, and at the same time decreasing the kVA per horsepower (i.e., increasing the effective power factor by analogy with an ac machine). The kVA per horsepower is lower than predicted by simple linear analysis that neglects saturation. Necessary conditions are also developed for a flat-topped current waveform by correctly determining the motor back-EMF. The reason why it is desirable to allow the phase current to continue (though with much reduced magnitude) even after the poles have passed the aligned position is explained. The theory provides a formula for determining the required commutation angle for the phase current. The basis is provided for an estimation of the kVA requirements of the switched reluctance (SR) drive. These requirements have been measured and also calculated by a computer simulation program.

164 citations


Journal ArticleDOI
TL;DR: In this article, three PWM control techniques that yield substantial filter size reduction for three-phase (self-commutated) rectifiers are presented and analyzed, and it is shown that in addition to filter minimization two of the proposed three control techniques improve substantially the rectifier total input power factor.
Abstract: Minimization of input/output filters is an essential step towards manufacturing compact low-cost static power supplies. Three PWM control techniques that yield substantial filter size reduction for three-phase (self-commutated) rectifiers are presented and analyzed. Filters required by typical line-commutated rectifiers are used as the basis for comparison. Moreover, it is shown that in addition to filter minimization two of the proposed three control techniques improve substantially the rectifier total input power factor.

93 citations


Journal ArticleDOI
TL;DR: In this paper, a novel Switch-Mode-Rectifier (SMR) structure is proposed and analyzed, which employs a high-frequency sine PWM cycloconverter to provide highfrequency ohmic isolation between the source and the load.
Abstract: A novel Switch-Mode-Rectifier (SMR) structure is proposed and analyzed in this paper The proposed converter structure employs a high-frequency sine PWM cycloconverter to provide high-frequency ohmic isolation between the source and the load Furthermore, it draws high-quality current from the ac source thus requiring only small input reactive components Consequently, the proposed converter structure exhibits high power density and has low implementation cost

84 citations


Patent
29 Jul 1985
TL;DR: In this paper, at least two active conditioners are connected in series with a common DC source, and are mounted as a unit between two pairs of AC terminals to act either as a tie-in link between two AC power sources, as a buck/boost regulator between one AC power source and its load, or as VAR compensator as well as active power conditioner between phases of a multiphase AC option.
Abstract: At least two active conditioners are connected in series with a common DC source, and are mounted as a unit between two pairs of AC terminals to act either as a tie-in link between two AC power sources, as a buck/boost regulator between one AC power source and its load, or as VAR compensator as well as active power conditioner between phases of a multiphase AC option.

81 citations


Journal ArticleDOI
TL;DR: In this article, the optimal solutions of the following two decoupled problems are given on the basis of the model presented in Part I. The objective in both problems is to minimize the peak power and the energy losses and to provide smooth voltage profile along the distribution system with lateral branches.
Abstract: In this paper the optimal solutions of the following two decoupled problems are given on the basis of the model presented in Part I:(i) The capacitor (var) problem: determination of the locations, sizes and the real-time control of n ON/OFF switched and fixed shunt capacitors, (ii) The regulator (volt) problem: determination of the locations and real-time control of minimum number of voltage regulators. The objective in both problems is to minimize the peak power and the energy losses and to provide smooth voltage profile along the distribution system with lateral branches. For the first time, the nonlinear costs of installation of the capacitors are incorporated into the capacitor problem.

78 citations


Journal ArticleDOI
TL;DR: In this paper, an adaptive power factor controller for three-phase inducti on generators and also for motors is proposed, which senses the reactive current drawn by the machine and accordingly provides the needed reactive power to improve the power factor to as close to unity as possible.
Abstract: An adaptive power factor controllerfor three-phase inducti on generators (and also for motors) is proposed in this paper. The controller senses the reactive current drawn by the machine and accordingly provides the needed reactive power to improve the power factor to as close to unity as possible. The controller is a modular, low-cost, harmonic free device. It does not create any transients in line current. It is designed to eliminate the self-excitation problems associated with induction generators. The controller is tested on an induction generator, which is being used in wind energy and similar applications.

Patent
04 Oct 1985
TL;DR: In this article, a static var compensator connected to a line node in a power transmission system and having a capacitor and a first reactor for producing and absorbing reactive power, respectively, and a second reactor connected between the line node and the common node of the first reactor and the capacitor for providing, in combination with the capacitor, a maximum leading reactive capacity so as to effectively reduce the capacities of the elements and for compensating for changes in reactive power resulting from a current fluctuation in response to a load fluctuation.
Abstract: A static var compensator connected to a line node in a power transmission system and having a capacitor and a first reactor for producing and absorbing reactive power, respectively, and a second reactor connected between the line node and the common node of the first reactor and the capacitor for providing, in combination with the capacitor and the first reactor, a maximum leading reactive capacity so as to effectively reduce the capacities of the elements and for compensating for changes in reactive power resulting from a current fluctuation in response to a load fluctuation. The second reactor increases the reactive power produced by the capacitor when the reactive power absorbed by the first reactor is low and decreases the reactive power produced by the capacitor when the reactive power absorbed by the first reactor is high.

Journal ArticleDOI
TL;DR: In this article, a two-level hierarchical approach for optimum allocation of reactive volt ampere (VAR) sources in large scale power system planning is presented, which takes advantage of the natural distinction between var dispatch in system operation and var allocation in system planning.
Abstract: A two-level hierarchical approach for optimum allocation of reactive volt ampere (VAR) sources in large scale power system planning is presented in this paper. The approach takes advantage of the natural distinction between var dispatch in system operation (Level 1) and var allocation in system planning (Level 2). The two levels are related together using the Generalized Benders Decomposition. The methodology has been implemented in the form of a prototype computer program which can be applied to large scale power systems with up to 1500 buses. The results of testing the package with practical power systems of different sizes and characteristics indicate that the technique is a valuable tool for reactive source allocation.

Journal ArticleDOI
TL;DR: A mathematical analysis of shunt capacitor application for the reductions of peak power loss and energy loss for a uniform feeder with an end-load condition is presented in this paper, where the optimum location and the rating of the capacitor banks on feeders with uniformly distributed loads and endload injection are developed.
Abstract: The flow of the reactive power in utility systems produces losses which utility engineers attempt to keep at a minimum level by the installation of capacitor banks. Previous work focussed on obtaining the optimal conditions for a fixed load level. The present paper deals with the conditions of fixed load, growth in the load and the presence of end-load in the feeder. A mathematical analysis of shunt capacitor application for the reductions of peak power loss and energy loss for a uniform feeder with an end-load condition is presented. Generalized equations for calculating the reductions of peak power and energy losses in a feeder are derived. The optimum location and the rating of the capacitor banks on feeders with uniformly distributed loads and end-load injection are developed. A method to assess the economical effectiveness of whether or not to install capacitor banks in a condition of load growth is also given. The method is applied to a test case of a practical system.

Patent
02 Oct 1985
TL;DR: In this paper, an energy-saving system for feeding an electric induction motor serving as a load, which is operated from a 3-phase voltage power line, and in conjunction with feeding conductors for the motor, is presented.
Abstract: An energy-saving system for feeding an electric induction motor serving as a load, and which is operated from a 3-phase voltage power line, and in conjunction with feeding conductors for the motor includes a power-delivery sub-system operating in a magnetically linear region and coupled to the 3-phase voltage power line for providing variable feeding voltages to the induction motor, a sensing device coupled to the induction motor for generating a signal indicative of the derivatives of active power consumed by the induction motor with respect to the voltage of at least one phase provided to the induction motor, and a control apparatus coupled to the sensing device and to the power-delivery sub-system for regulating at least one of the feeding voltages, so that the derivative of the active power with respect to the voltage of that at least one phase is always substantially zero; thus for a given mechanical power output the power consumption of the induction motor is optimized, while concurrently losses in the feeding conductors are being minimized.

Journal ArticleDOI
TL;DR: A textured model which assembles local groups of buses into a multi-leaf structure which is ideally suited for parallel processing and should prove to be a valuable tool for on line computations in the course of reactive power control and management.
Abstract: The texture of the power system which govern, the interplay of reactive power and voltage is emulated by a textured model which assembles local groups of buses into a multi-leaf structure. Groups on the same leaf of the model are not coupled with each other, groups on different leaves overlap partially and are thus coupled. The paths of computational information are organized in an efficient manner and inefficient computation and information paths are eliminated, yet the computation converges to the exact solution, not an approximate one. The resulting model is ideally suited for parallel processing especially since there is no sequential component in the computation no computation overhead and (if the size of the groups and their numbers per leaf are uniform) there is no waiting time. Computation time savings of as much as 100÷1 (i.e. a hundred fold saving) were observed in experiments on steepest descent algorithms with systems of around 100 buses. Computation times also favorably compare with existing speed up techniques such as block pivoting. Computation times for common algorithms (like matrix manipulations, Newton-Raphson, linear and nonlinear programming) increase with the system size at a fast non- linear rate. The computation times remain essentially constant for the textured model in parallel processing. Thus very large computation time savings are implied on larger systems. Consequently this new model should prove to be a valuable tool for on line computations in the course of reactive power control and management.

Patent
04 Jan 1985
TL;DR: In this paper, the reactive power of an induction machine is compensated by providing fixed capacitors on each phase line for the minimum compensation required, sensing the current on one line at the time its voltage crosses zero to determine the actual compensation required for each phase, and selecting switched capacitors at each line to provide the balance of the compensation required.
Abstract: The reactive power of an induction machine is compensated by providing fixed capacitors on each phase line for the minimum compensation required, sensing the current on one line at the time its voltage crosses zero to determine the actual compensation required for each phase, and selecting switched capacitors on each line to provide the balance of the compensation required.

Patent
21 May 1985
TL;DR: In this paper, a control circuit is provided for automatically re-applying starting torque to a single phase AC induction motor by reconnecting the auxiliary or starting winding (2) to the AC power source (3) if the motor has not accelerated to a given cut-out speed, or otherwise begins to stall.
Abstract: A control circuit (10) is provided for automatically re-applying starting torque to a single phase AC induction motor by reconnecting the auxiliary or starting winding (2) to the AC power source (3) if the motor has not accelerated to a given cut-out speed, or otherwise begins to stall. Multiple reconnections of the auxiliary winding (2) are automatically provided as needed, without external intervention, to provide multiple bumping action. The auxiliary winding (2) is connected to the AC source (3) during initial energization of the motor, and is disconnected after a given starting interval. Induced voltage in the auxiliary winding (2) is sensed and compared against a reference voltage (17) for reconnecting the auxiliary winding (2) when the sensed auxiliary winding voltage drops below a given value relative to the reference voltage. The disconnecting, sensing and reconnecting functions are accomplished with a minimum number of components.

Patent
09 Sep 1985
TL;DR: In this article, a speed sensitive, load sensitive and AC line voltage fluctuation insensitive, motor starting system is provided for an AC motor having a main winding (1) and an auxiliary winding (2) both connectable across an AC power source.
Abstract: A speed sensitive, load sensitive and AC line voltage fluctuation insensitive, motor starting system is provided for an AC motor having a main winding (1) and an auxiliary winding (2) both connectable across an AC power source (3). Relative magnitudes of main and auxiliary winding voltages are sensed and compared. The auxiliary winding is disconnected (5) from the AC source when the auxiliary winding voltage, including the components from the AC source and from rotationally induced voltage, rises above a predetermined value relative to the main winding voltage as a function of motor speed. After starting, when the motor is in a run mode and the auxiliary winding is disconnected from the AC source, only the rotationally induced auxiliary winding voltage is sensed. The auxiliary winding is reconnected to the AC source when the rotationally induced auxiliary winding voltage decreases below a given value relative to the main winding voltage corresponding to a given stall condition, to automatically restart the motor.

Journal ArticleDOI
TL;DR: The 30 MJ superconducting magnetic energy storage (SMES) system was installed in the Bonneville Power Administration (BPA) Tacoma Substation in 1982-83 as mentioned in this paper.
Abstract: The 30 MJ superconducting magnetic energy storage (SMES) system was installed in the Bonneville Power Administration (BPA) Tacoma Substation in 1982-83. Operation of the unit since that time has been for over 1200 hours. Specific tests to explore the SMES system's thermal and electrical characteristics and the control functions were conducted. The coil heat load with current modulation was determined. A converter with two 6-pulse bridges interfaces the superconducting coil to the power bus. Equal bridge voltage amplitude and constant reactive power modes of operation of the system were run with computer control of the SCR bridge firing angles. Coil energy dump tests were performed. Electrical grid system response to SMES modulation was observed, and full power SMES modulation was undertaken.

Patent
23 Dec 1985
TL;DR: In this paper, an electrical circuit is disclosed which provides the capability of starting up an unattended computer or similar device either from a remote location or at a predetermined date and time.
Abstract: An electrical circuit is disclosed which provides the capability of starting up an unattended computer or similar device either from a remote location or at a predetermined date and time. The circuit includes an electrical energy storage device which, when a telephone ring signal is detected, initiates start-up of the computer. Alternatively, an interrupt from a date timer may initiate start-up of the computer using the energy storage device. Once start-up of the computer is initiated, its power supply provides the necessary voltage which, in conjunction with a latching transistor, maintains the electrical circuit providing AC power to the power supply and computer and recharges the electrical energy storage device. Finally, an electrical signal to power-down the computer may be initiated either remotely or through software instruction.

Patent
28 May 1985
TL;DR: In this paper, a stator current sampling arrangement and a motor current demodulator are proposed to achieve a preferred magnitude of motor starting current under rated load conditions and achieve near-optimum motor operating efficiency during start-up and subsequent running with reduced loads and associated motor protection.
Abstract: A standard, unmodified induction motor (11) starts with reduced input current, energy consumption and mechanical stress and is further protected from AC power source "phase loss", excessively low or high voltage or a locked-rotor condition during start-up or any subsequent moment while running when its stator winding (13,14,15) is energized from a sine wave source (300) thrkough a signal-responsive wave modifier EET-IC operative to control the portion of each cycle of the sine wave which is coupled from said source to the stator winding. A stator current sampling arrangement (6, 7, 8), and a motor current demodulator responsive to the first few hundred microseconds of stator winding initial inrush current each time said current increases from zero cooperate under certain conditions to produce signals for controlling associated wave modifier means, thereby to achieve a preferred magnitude of motor starting current under rated load conditions and achieve near-optimum motor operating efficiency during start-up and subsequent running with reduced loads and associated motor protection means (4) which inhibits said wave modifier means thereby to de- energise said stator winding under locked-rotor conditions that occur when motor start-up is attempted or later when the motor is running, or an AC power source anomaly occurs which would otherwise cause start-up stalling, excessive motor running current or motor stalling under rated loads.

Patent
06 Jun 1985
TL;DR: In this paper, a power converter that drives an AC motor includes a main circuit and a control circuit such that the main circuit includes a forward conversion circuit that forwardly converts AC power from an input AC power source into DC power, and an inverter circuit that inversely converts the thus forwardly converted and smoothed DC power into AC power of a specified voltage and frequency.
Abstract: A power converter that drives an AC motor includes a main circuit and a control circuit such that the main circuit includes a forward conversion circuit that forwardly converts AC power from an input AC power source into DC power, and an inverter circuit that inversely converts the thus forwardly converted and smoothed DC power into AC power of a specified voltage and frequency; the control circuit includes a calculation device that calculates a torque current component of the AC motor, a detection device that detects occurrence of an instantaneous interruption in the AC power source, a command device that commands a frequency to be fed into the AC motor, a control device that receives a signal relative to an output signal of the command device, so as to control a terminal voltage of the AC motor, and a compensation device that adjusts the output signal of the command device so that the output signal of the calculation device is caused to be substantially zero in response to the output signal of the detection device.

Patent
13 Sep 1985
TL;DR: A snubber circuit (26, 28) for protecting power switches (Q1, Q2) which modulate the flow of power through an inductive element (12) in a power converter, such as a main primary winding (12a, 12b) of a transformer (12), includes a snubbing capacitor (C1 or C2) and a first switch (S1 or S3) which is operable to connect the snubbin capacitor to a power switch.
Abstract: A snubber circuit (26, 28) for protecting power switches (Q1, Q2) which modulate the flow of power through an inductive element (12) in a power converter, such as a main primary winding (12a, 12b) of a transformer (12), includes a snubbing capacitor (C1 or C2) and a first switch (S1 or S3) which is operable to connect the snubbing capacitor (C1 or C3) to a power switch (Q1 or Q3). A second switch (S2 or S4) is operable to connect the snubbing capacitor (C1 or C3) to an auxiliary primary winding (12d or 12e) of the transformer (12). The first (S1 or S3) and second (S2 or S4) switches are operated so that immediately prior to turn-off of the power switch (Q1 or Q2), the capacitor (C1 or C2) is connected thereto to store the turn-off reactive power caused by turn-off of the power switch (Q1 or Q2). The first switch (S1 or S3) is then opened and the second switch (S2 or S4) closed to couple the reactive power to the auxiliary primary winding (12d or 12e) to improve the efficieny of the converter.

Journal ArticleDOI
TL;DR: In this paper, the problem of volt/var control on general radial distribution systems is formulated, simplified and solved, where the objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions.
Abstract: In this paper (Part I) and two companion papers (Part II and Part III) the problem of volt/var control on general radial distribution systems is formulated, simplified and solved. The objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions. The decision variables to be optimally determined are (i) the locations, sizes and the real-time control of the specified number of ON/OFF switched and fixed capacitors and (ii) the locations and real-time control of the minimum number of voltage regulators. It is shown in this paper (Part I) that the regulator (volt) and the capacitor (var) problem may be treated as two decoupled problems. Part II of this set of three papers, conjoined with part I, provides the analytical tools by which optimal solutions for both problems may be determined. Application of the theory to representative radial systems is shown in Part III which also illustrates the ecomonic benefits and numerical results achievable through both regulation and compensation schemes.

Journal ArticleDOI
TL;DR: In this paper, the adaptive tuning of the critical converter control system parameters in function of an estimate of the net commutation resistances is proposed to improve the dc system dynamic response.
Abstract: The transient performance of High Voltage Direct Current (HVdc) power transmission systems depends heavily on the current regulators associated to the converter control systems. The tuning of these current regulators is a function of the converters short-circuit ratio, or equivalently of all the net converter commutation resistances. These resistances vary with the network operating conditions and they are affected by AC system contingencies. This paper concerns the adaptive tuning of the critical converter control system parameters in function of an estimate of the net commutation resistances. Compared to regulators with constant gains, the proposed control and estimation algorithms improve the dc system dynamic response. This is demonstrated by a computer simulation of a typical HVdc system.

Journal ArticleDOI
TL;DR: In this paper, the steady-state voltage stability of power systems is investigated via linearized dynamical equations of on-load tap changers and steady state decoupled reactive power flow equations.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a DC link controller which, in the presence of major disturbances in the AC system, modulates the active and reactive power of the converters and improves the transient stability of the integrated system.
Abstract: Active power modulation has been successfully used to improve the dynamic performance of interconnected AC/DC systems. This, however, results in uncoordinated reactive power modulation which, in the case of weak systems, reduces the effectiveness of the method. The paper presents the basic design of a DC link controller which, in the presence of major disturbances in the AC system, modulates the active and reactive power of the converters and improves the transient stability of the integrated system. The proposed control method was tested using dynamic simulation techniques and the results obtained are presented in the paper. These results show that the application of the method, under certain conditions, leads to significant improvement of the transient performance of the interconnected AC/DC system.

Journal ArticleDOI
TL;DR: In this article, a fixed capacitor-thyristor controlled reactor (FC-TCR) type of power factor compensator with thyristor-controlled series R-L load is analyzed using an approximate and also a more exact circuit.
Abstract: A fixed capacitor-thyristor controlled reactor (FC-TCR) type of power factor compensator with thyristor-controlled series R-L load is analysed using an approximate and also a more exact circuit. The variation of power and power factor before and after compensation is examined for both cases. It is shown that considerable power factor improvement can be achieved in the circuit for low values of load thyristor firing- angle. However, for higher values of firing-angle, any improvement is obtained at the expense of additional. power losses.

Journal ArticleDOI
TL;DR: In this paper, a no-gain theorem for electric power systems is presented using the S-E model based decoupled active power-phase angle P -theta network, in which each transmission element consists of two branches, representing transmitted power and loss power.
Abstract: In this paper a no-gain theorem for electric power systems is presented using the S- E model based decoupled active power-phase angle P - \theta network, in which each transmission element consists of two branches, representing transmitted power and loss power. The theorem gives necessary and sufficient conditions such that if a power system is perturbed from its normal operating point then the magnitude of the change in active power through either branch of a given transmission line S- E graph is not greater than the sum of the magnitudes of the changes in active power through the sources. These conditions are given as a region of allowable perturbations, which are derived as a set of inequalities. Based on this result we present a proof, valid for systems with losses, of localized steady state response. Specifically, we prove that the effects of a single fault in a given power system diminish as one moves away from the fault, subject only to the constraint that the operating point of the system remains within the allowable regions given by the no-gain theorem. This result is often assumed without proof to be valid in the entire operating region.