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Showing papers on "AC power published in 1990"


Journal ArticleDOI
TL;DR: In this paper, an efficient method for calculating the load flow solution of weakly meshed transmission and distribution systems is presented, which uses active and reactive powers as flow variables rather than complex currents, thus simplifying the treatment of P, V buses and reducing the related computational effort.
Abstract: An efficient method for calculating the load flow solution of weakly meshed transmission and distribution systems is presented. Its essential advantages over a previous approach are the following: (1) It uses active and reactive powers as flow variables rather than complex currents, thus simplifying the treatment of P, V buses and reducing the related computational effort to half; (2) It uses an efficient tree-labeling technique which also contributes to the computational efficiency of the procedure; (3) It uses an improved solution strategy, thereby reducing the burden of mismatch calculations which is an important component of the solution process. Results of tests with 30, 243, 1380, and 4130 bus systems are given to illustrate the performance of the proposed method. >

384 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical framework is presented for the solution of the economic dispatch problem, and the application of the Dantzig-Wolfe decomposition method is emphasized to solve the problem.
Abstract: A mathematical framework is presented for the solution of the economic dispatch problem The application of the Dantzig-Wolfe decomposition method for the solution of this problem is emphasized The system's optimization problem is decomposed into several subproblems corresponding to specific areas in the power system The upper bound technique along with the decomposition method are applied to a 16-bus system and a modified IEEE 30-bus system, and numerical results are presented for larger systems The results indicate that the presented formulation of the reactive power optimization and the application of the decomposition procedure will facilitate the solution of the problem The algorithm can be applied to a large-scale power network, where its solution represents a significant reduction in the number of iterations and the required computation time >

342 citations


Journal ArticleDOI
11 Jun 1990
TL;DR: In this article, a power control system for a doubly fed wound rotor induction generator was developed, which applies a control method using a rotating reference frame fixed on the gap flux of the generator, and can control active and reactive power independently and stably.
Abstract: A power control system for a doubly fed wound rotor induction generator has been developed. This power control system applies a control method using a rotating reference frame fixed on the gap flux of the generator, and can control active and reactive power independently and stably. The characteristics of the control system have been proved by experiment. Harmonic currents fed to the rotor windings are transmitted to the stator winding changing its frequency. The transmitting characteristics of the harmonic currents have been analyzed and verified by experiments. >

296 citations


Journal ArticleDOI
TL;DR: In this paper, the authors expanded on the physical meaning of the reactive power in nonsinusoidal situations, and showed that the total reactive power Q/sub F/ is composed from four distinctive types of elementary reactive powers.
Abstract: The author expands on the physical meaning of the reactive power in nonsinusoidal situations. The sinusoidal waveform case is surveyed, viewing the active current as a component of identical waveform with the voltage. This approach, when extended to nonsinusoidal waveforms, supports Fryze's model for apparent power, S/sup 2/=p/sup 2/+Q/sup 2//sub F/. It is proved that the total reactive power Q/sub F/ is composed from four distinctive types of elementary reactive powers. Each of the basic reactive powers is identified as the amplitude of an oscillation of instantaneous power. The separation of Q/sub F/ in Q/sub 1/, the reactive power at the system frequency, and in Q/sub H/, the reactive power at harmonic frequencies, is recommended as an effective mean for monitoring filter efficacy and power-factor compensation. Two major recommendations are supported by the results of this study: abolish the power model using distortion power, and measure the active power of the system frequency separately from the active power of the harmonics. >

265 citations


Journal ArticleDOI
TL;DR: In this paper, a new definition of instantaneous reactive power is presented, which includes both the conventional instantaneous reactive powers and the instantaneous power of a zero-phase component, and a simple control algorithm for the active filter derived from the new definition is described.
Abstract: A new definition of instantaneous reactive power is presented. This definition has a clear physical meaning that includes both the conventional instantaneous reactive power and the instantaneous power of a zero-phase component. A simple control algorithm for the active filter derived from the new definition is described. Simulations verified the control algorithm. >

231 citations


Journal ArticleDOI
TL;DR: An active power filter using quad-series voltage-source pulsewidth-modulated (PWM) converters to suppress AC harmonics by injecting compensating currents into the AC system is described in this article.
Abstract: An active power filter using quad-series voltage-source pulse-width-modulated (PWM) converters to suppress AC harmonics by injecting compensating currents into the AC system is described. The circuit used to calculate the compensating current references, the compensation characteristics, and the capability of the DC capacitor are discussed theoretically and experimentally. A control circuit for the DC capacitor voltage is proposed. The discussions focus on transient states, based on the instantaneous reactive power theory. A passive LC filter is designed to remove the switching voltage and current ripples caused by the PWM converters at the AC side. Some experimental results that illustrate the details of the study are shown. >

228 citations


Journal ArticleDOI
TL;DR: In this paper, a new method for determining the voltage stability condition in a power system is presented, based on sensitivity techniques, taking into account the limits on reactive power generation capacities.
Abstract: A new method for determining the voltage stability condition in a power system is presented. The method is based on sensitivity techniques, taking into account the limits on reactive power generation capacities. A distance to voltage collapse in terms of MVAr is defined as a measure of system security. Results from calculations on a 480-bus network with 140 generators are presented. The method can be efficiently used for reactive power security evaluation in both system planning and operation. >

210 citations


Journal ArticleDOI
11 Mar 1990
TL;DR: In this paper, an adaptive frequency domain control algorithm for a PWM switched active power line conditioner (PLC) is discussed, which minimizes harmonic current in the AC line and improves power factor to unity.
Abstract: An adaptive frequency domain control algorithm for a pulse width modulation (PWM) switched active power line conditioner (PLC) is discussed. An active power line conditioner that minimizes harmonic current in the AC line and improves power factor to unity is recommended. A six switch pulse width modulated current source inverter implements the active PLC. Simulation results of the PLC adaptive frequency domain control using the PWM switching algorithm are presented. >

181 citations


Proceedings ArticleDOI
11 Jun 1990
TL;DR: In this article, the design of an active unity power factor correction circuit with variable-hysteresis control for off-line switching power supplies is described and a computer-aided design program to select the optimal circuit components is developed.
Abstract: The design of an active unity power factor correction circuit with variable-hysteresis control for off-line switching power supplies is described. Design equations relating the boost indicator current ripple to the boost inductor selection and circuit performances are developed and verified with measurements. A computer-aided design program to select the optimal circuit components is developed. Design guidelines for the low-frequency feedback network are presented using the switch model for the power factor correction circuit. Small-signal transfer functions for open and closed-loop responses are derived. >

170 citations


Patent
27 Sep 1990
TL;DR: In this article, a rectifier bridge consisting of rectifying devices (24, 25) connected to an AC source and providing a DC output to DC bus lines was proposed. But the authors did not consider the use of an external DC power source such as a battery.
Abstract: Power conversion apparatus for AC to DC to AC power conversion includes a rectifier bridge formed of rectifying devices (24,25) connected to an AC source (21) and providing a DC output to DC bus lines (27,28). A full bridge of active switching devices (30, 31, 34, 35) is connected across the DC bus lines to which a power source such as a battery (39) may also be connected. The load (36) and the AC power supply (21) share a common neutral line (33). The output of the bridge can provide AC output power to the load through a transformer (74). The power conversion apparatus allows full control of the currents on the load lines and AC input lines, even when the input and output are asynchronous. By providing an external DC power source such as a battery (39), uninterrupted power can be supplied to the load when the AC power source fails.

119 citations


Journal ArticleDOI
TL;DR: In this paper, a digital analyzer for measuring the power decomposition in a nonlinear or periodically time-variant load has been proposed, where the load is considered not as the receiver but as the source of energy.
Abstract: A nonlinear or periodically time-variant load sometimes has to be considered not as the receiver, but as the source of energy, at least for some harmonic frequencies. This can be explained in terms of its equivalent circuit, usually composed of passive elements and harmonic sources which make the power phenomena in such a circuit much more complex than in a linear circuit. The necessity of comprehension of these phenomena stems from the fact that they determine the efficiency of the power transmission and the possibility of power factor improvement. They also affect the energy accounts. A method is suggested for the apparent power decomposition into components related to current components of distinctively different physical interpretation. A digital analyzer for measuring these powers is described. >

Journal ArticleDOI
07 Oct 1990
TL;DR: In this paper, the authors proposed a parallel-resonant DC-link (PRDCL) circuit to provide zero-DC link voltage periods for PWM inverter switchings.
Abstract: A zero-voltage-switching (ZVS) three-phase pulse width modulated (PWM) inverter which uses a parallel-resonant DC-link (PRDCL) circuit proposed by J. He and N. Mohan (1989) is examined. The PRDCL circuit is aimed at both providing zero-DC link voltage periods for PWM inverter switchings and imposing minimum DC bus voltage stress to PWM inverters. A simple circuit control scheme and the design formulas are offered. To confirm the circuit theoretical analyses and results, a 50 W ZVS single-phase PWM inverter experimental prototype using the proposed PRDCL circuit was fabricated and tested. The test results have proved the proposed circuit and concept. Power device selections and device stress evaluations are described. A detailed comparison of the proposed PRDCL ZVS inverter system with conventional voltage source PWM inverters is discussed. >

Patent
25 Jun 1990
TL;DR: In this article, a portable power supply having a rechargeable battery in a housing mounted on a portable frame is used for converting DC power to AC power and for recharging the battery from an external AC source.
Abstract: A portable power supply having a rechargeable battery in a housing mounted on a portable frame An inverter/converter unit, attached to the frame, is hardwired to the battery for conversion of DC power to AC power and for recharging the battery from an external AC source Power distribution means are provided for distributing DC and AC Power Photovoltaic panels are mounted to the frame for recharging the battery

Journal ArticleDOI
TL;DR: In this paper, the performance characteristics of a cage induction machine operating as a self-excited induction generator (SEIG) in stand-alone mode are presented, where a static capacitor bank is considered to selfexcite the machine and to maintain its terminal voltage constant.
Abstract: The performance characteristics of a cage induction machine operating as a self-excited induction generator (SEIG) in stand-alone mode are presented. A static capacitor bank is considered to self-excite the machine and to maintain its terminal voltage constant. The lagging reactive power requirement of self-excited induction generator is obtained for different load values. The effect of speed on the excitation requirement of the cage machine has also been studied. An algorithm is developed to achieve these characteristics using the Newton-Raphson method and a steady-state equivalent circuit of the machine. The developed analytical technique is extended to evaluate the number of steps of switching capacitors for loading the machine up to its full load rating while maintaining the terminal voltage within desired limits. The selection of an optimum terminal voltage corresponding to the maximum output of the machine for its optimum utilization is also made using single-variable optimization. >

Journal ArticleDOI
TL;DR: In this article, it is shown that magnetic energy storage units can simultaneously operate as continuous VAr (volt-ampere reactive) controllers while performing the role of load-frequency stabilizers in electrical power systems.
Abstract: It is shown that magnetic energy storage units can simultaneously operate as continuous VAr (volt-ampere reactive) controllers while performing the role of load-frequency stabilizers in electrical power systems. This is achieved by operating the converter in the buck-boost mode with a switched capacitor bank placed across its terminals. The P versus Q modulation ranges of the 12-pulse converter depend on the source inductance, secondary voltage of the input transformers, and output current. Once the input transformer is chosen, the Q modulation range depends on the active power transfer and the current through the inductor at any instant of time. The actual reactive power consumption of the converter is varied continuously, depending on the requirements of the power system, while keeping within the Q-modulation range. Switching of the capacitor bank keeps the required Q consumption of the converter within the available range. It is shown that this mode of control improves the overall performance of the power system in P-f and Q-V loops and obviates the use of any additional VAr compensator in the power area where the SMES (superconducting magnetic energy storage) unit is located. >

Journal ArticleDOI
TL;DR: In this article, the authors present a method and the mathematical formulation for large-scale optimal power flow sensitivity analysis, which has been implemented in a computer program (OPSENS) presently in use in the Pacific Gas and Electric Company.
Abstract: The authors present a method and the mathematical formulation for large-scale optimal power flow sensitivity analysis. The method has been implemented in a computer program (OPSENS) presently in use in the Pacific Gas and Electric Company. The results of using the OPSENS program for calculating the sensitivity of system losses for a 34 bus and a 1700 bus transmission network to bus load changes are reported and compared to the results of multiple OPF (optimal power flow) studies. The effectiveness of OPSENS in this application was demonstrated. >

Journal ArticleDOI
TL;DR: In this paper, an integrated methodology for long-term VAr planning is presented that results in determining the timing (year), the location, and the amount of VAr compensation.
Abstract: An integrated methodology for long-term VAr planning is presented that results in determining the timing (year), the location, and the amount of VAr compensation. The system security and investment and operating economics are taken into account. The proposed methodology is an integration of the Newton-OPF with the generalized Benders decomposition (GBD). The total problem is decomposed into two levels: master and slave. The master level deals with the investment decision of installing discretized new VAr devices. The slave level deals with operating the existing controllers, in conjunction with the new devices solved in the master level, to maintain system feasibility and to reduce MW losses. The overall solution methodology contains numerous extensions to the basic theory. Tests performed on actual Taiwan power system data have been encouraging. Sample results are presented. >

Journal ArticleDOI
TL;DR: In this paper, a static VAr compensator (SVC) model based on state variable techniques is presented, which is capable of being interfaced to a parent (or host) electromagnetic transients program, and in particular a stable method of interfacing to the EMTDC program is described.
Abstract: A static VAr compensator (SVC) model based on state variable techniques is presented. This model is capable of being interfaced to a parent (or host) electromagnetic transients program, and, in particular a stable method of interfacing to the EMTDC program is described. The model is primarily that of a thyristor-controlled reactor. (TCR) and a thyristor-switched capacitor (TSC). Capacitor switchings within the TSC have been handled in a novel way to simplify storage and computation time requirements. During thyristor switching, the child SVC model is capable of using a smaller timestep than the one used by the parent electromagnetic transients program; after the switching, the SVC model is capable of reverting back to a (larger) timestep compatible with the one used by the parent program. Other features considered include the modeling of a phase-locked-loop-based, valve firing system. An application of this model to the simulation of a SVC controlling the AC voltage of the inverter bus of a back-to-back HVDC (high-voltage direct current) tie is presented. >

Journal ArticleDOI
11 Jun 1990
TL;DR: A novel DC/AC power converter for variable-speed AC motor drives using the zero voltage switching technique is described and the soft commutation reduces the constraints on the switches and the PWM enables simple and efficient regulation of the power flow.
Abstract: A novel DC/AC power converter for variable-speed AC motor drives using the zero voltage switching technique is described. This converter combines the advantages of soft commutated inverter and those of conventional PWM (pulse width modulation) control inverters. In the proposed scheme the soft commutation reduces the constraints on the switches and the PWM enables simple and efficient regulation of the power flow. Furthermore the zero voltage switching technique makes operation very safe, and switching bipolar transistors at 20 kHz is easily achieved without compromising the efficiency of the system. >

Journal ArticleDOI
29 Apr 1990
TL;DR: In this article, the authors considered the effect of harmonics on reactive power measurements, and presented a novel method for calculating active, reactive apparent, and residual power in nonsinusoidal conditions.
Abstract: The authors consider the effect of harmonics on reactive power measurements, and present a novel method for calculating active, reactive apparent, and residual power in nonsinusoidal conditions. The method considers common and uncommon harmonic components of voltage and current waveforms. It properly defines all power components at different harmonic frequencies, such as rotating real power, quadrature power, and the residual power (distortion). Each component is calculated correctly at different frequencies to define its physical meaning. A computer algorithm is developed to calculate all the power components for any distorted voltage and current waveforms. A numerical example is discussed. >

Patent
06 Mar 1990
TL;DR: In this article, a power conversion system is disclosed in which a direct current is taken out of an AC power supply of variable frequency and variable voltage through a PWM converter in such a manner that in a region of low source voltage, the converter input current is limited to a predetermined value to maximize the DC power taking the voltage drop of the power supply into consideration with the power factor of "1"
Abstract: A power conversion system is disclosed in which a direct current is taken out of an AC power supply of variable frequency and variable voltage through a PWM converter in such a manner that in a region of low source voltage, the converter input current is limited to a predetermined value to maximize the DC power taking the voltage drop of the power supply into consideration with the power factor of "1" of the power supply, and when the current reaches an allowable maximum, it is limited to that value. In a region of high source voltage, on the other hand, the quadrature component of the input voltage applied to the source voltage is controlled preferentially in a manner to control the converter input voltage below a predetermined value, thus making it possible to secure the maximum power available from the converter over the entire range of operation. If a battery is connected to the DC side, a cooperative operation is made possible while the battery is charged properly.

Patent
08 Jun 1990
TL;DR: In this paper, an apparatus for automatically controlling the flow of fluid in an inlet conduit that provides the water supply for a home or building so as to prevent water damage due to a failure in the water system when unattended.
Abstract: An apparatus for automatically controlling the flow of fluid in an inlet conduit that provides the water supply for a home or building so as to prevent water damage due to a failure in the water system when unattended. The apparatus comprises a power circuit for supplying a low voltage DC power output which is connectable to a standard AC power source and includes an internal battery which operates in case of AC power failure. A flow sensor and a shutoff valve are connected in the inlet conduit. A control circuit which can be preset for different operational modes, receives and processes flow status signals from the flow sensor and provides output signals that control the shutoff valve, so that if continuous flow is detected in the conduit for a time period exceeding a preselected time, the shutoff valve will automatically close.

Journal ArticleDOI
TL;DR: In this paper, a simple scheme is proposed for offline unity power factor rectification for high-frequency AC buses (20 kHz), where a bandpass filter of the series-resonant type, centered at the line frequency, is inserted between the line and the full-wave rectified load.
Abstract: A simple scheme is proposed for offline unity power factor rectification for high-frequency AC buses (20 kHz). A bandpass filter of the series-resonant type, centered at the line frequency, is inserted between the line and the full-wave rectified load. The Q=Z/sub 0//R/sub L/ formed by the load and the characteristic impedance of the tank circuit determines the power factor, the boundary between continuous and discontinuous conduction modes, the peak stresses, and the transient response of the rectifier. It is shown that for Q>2/ pi the rectifier operates in continuous conduction mode and the output voltage is independent of the load. Also, it is shown that for Q>2 the line current is nearly sinusoidal with less than 5% third-harmonic distortion and the power factor is essentially unity. An increase in Q causes an increase in the peak voltages of the tank circuit and a slower transient response of the rectifier circuit. The DC, small-signal, and transient analyses of the rectifier circuit are carried out, and the results are in good agreement with simulation and experimental results. >

Patent
13 Nov 1990
TL;DR: In this paper, a power conversion apparatus (20) is defined, which includes pairs of rectifying devices (48, 49) connected together at the first node, a pair of capacitors (50, 51) connected at the second node, and pairs of controllable switching devices (53, 54) connected in parallel by DC bus lines (58, 59).
Abstract: A power conversion apparatus (20) circuit includes pairs of rectifying devices (48,49) connected together at a first node, a pair of capacitors (50, 51) connected together at a second node, and pairs of controllable switching devices (53,54) connected together at a third node, each of the pairs being connected in parallel by DC bus lines (58,59). The AC power source (21) is connected between the first and second nodes and the output voltage to a load (22) is provided between the first and third nodes. The switching devices (53,54) are controlled to switch on and off at proper times to provide a controllable output voltage to the load (22) which is at the same frequency as the input voltage and which may be controlled from zero to substantially twice the peak-to-peak input voltage. The output voltage waveform provided to the load can be filtered to provide a substantially sinusoidal waveform to the load. The power conversion apparatus (20) can also function as an uninterruptible power system by connecting an energy storage device, such as a large capacitor (140 ) or a battery (146) across the DC bus lines (58,59), and by controlling the charging of the energy storage device when power is available for the source and discharging the storage device when the power source fails.

Patent
28 Sep 1990
TL;DR: In this paper, an electronic control system for determining the resonant frequency of and driving ultrasonic transducers in a phacoemulsification probe used for ophthalmic surgery is presented.
Abstract: An electronic control system for determining the resonant frequency of and driving ultrasonic transducers in a phacoemulsification probe used for ophthalmic surgery. The control system includes a voltage control led oscillator, power amplifier, power monitor, and automatic gain control circuit operating under the direction of command signals received from a microprocessor-based control console. The control system operates in a constant apparent power, direct drive mode with closed loop feedback maintaining the electrical power provided to the primary of a RLC transformer at the constant level requested by the command signals from the console. The frequency of the drive signal is held at the dominant resonant frequency of the ultrasonic transducer which is being driven by the control system. This resonant frequency is determined via a calibration procedure performed when the probe is first attached to the control system. During this procedure a constant voltage drive signal is swept through a range of frequencies and the electrical power consumed by the transducer is measured and stored at selected intervals such as 100 Hertz increments. The resonant frequency is also determined in part by looking for the frequency at which maximum power is consumed by the probe. The stored data is also subjected to other tests to cheok that the peak is indeed a resonant frequency and that the probe has selected output power characteristics about this resonant frequency thus helping to ensure that the probe is capable of operating satisfactorily when driven by the control system.

Journal ArticleDOI
TL;DR: In this article, a technique for planning the future reactive power requirements of a power system is presented, which reduces the dimensionality of the problem significantly, thereby allowing for more rapid calculations and more case studies to be performed.
Abstract: A technique is presented for planning the future reactive power requirements of a power system. The problem is formulated as a mathematical optimization problem based on a linearized power system model. An efficient dual simplex linear programming technique coupled with relaxation and contingency analysis is used for solution. The approach reduces the dimensionality of the problem significantly, thereby allowing for more rapid calculations and more case studies to be performed. The effectiveness of the scheme is demonstrated using the IEEE 30-bus and IEEE 188-bus systems. >

Journal ArticleDOI
01 May 1990
TL;DR: In this article, two methods are proposed for identifying the weak buses and segments in power transmission networks, based on the relative change in the bus voltages going from an initial operating state to the voltage stability limit.
Abstract: Voltage instability leading to collapse appears to be due to the inability of networks to meet a demand for reactive power at certain critical (or weak) buses. Practical control algorithms to prevent voltage collapse should identify the critical buses in the network and maintain control on voltages at these buses in particular. Two methods are proposed for identifying the weak buses and segments in power transmission networks. Both methods employ a technique presented earlier for determining the static voltage stability limit in multimachine power systems. The first method is based on the relative change in the bus voltages going from an initial operating state to the voltage stability limit. The second method is based on the sensitivity parameters computed at the voltage stability limit.

Journal ArticleDOI
01 Jan 1990
TL;DR: In this article, the authors present a physical interpretation of active, reactive, distortion, and apparent power for nonsinusoidal and sinusoidal systems with sinusoid and/or nonsinoidal voltage and current.
Abstract: Currently accepted definitions of power components are reviewed, and their disadvantages are analysed. New definitions of active, reactive, distortion, and apparent power are discussed. It is attempted to find a clear physical interpretation, and to formulate this for each power component in systems with sinusoidal and/or nonsinusoidal voltage and current. Formulas for the straightforward calculation of each power component are obtained. It is shown that (a) distortion power, as defined here consists of both active and reactive terms (b) apparent power in a nonsinusoidal system must be represented as a many-dimensional vector, and not as a vector of three dimensions as is generally accepted today. Examples are given to illustrate the application of the developed theory.

Patent
06 Nov 1990
TL;DR: In this article, an uninterrupted power supply (UPS) system is provided with a power factor correction circuit (PCC), which is operatively connected to the input and output terminals of the rectifier to cause the UPS system to exhibit substantially unity power factor to the AC utility power source.
Abstract: An uninterrupted power supply (UPS) system (10) is provided with a power factor correction circuit (30). The UPS system includes a rectifier (D1, D2) having input terminals (12, 14) for connection to an AC utility power source (32) and ouput terminals (+DC, -DC). The power factor correction circuit is operatively connected to the input and output terminals of the rectifier to cause the UPS system to exhibit substantially unity power factor to the AC utility power source.

Journal ArticleDOI
TL;DR: In this article, the behavior of grid-connected induction generators (GCIGs) driven by typical prime movers such as mini-hydro/wind turbines is investigated and some practical operational problems of such systems are identified.
Abstract: Results of an investigation dealing with the behaviour of grid-connected induction generators (GCIGs) driven by typical prime movers such as mini-hydro/wind turbines are presented. Certain practical operational problems of such systems are identified. Analytical techniques are developed to study the behavior of such systems. The system consists of the induction generator (IG) feeding a 11 kV grid through a step-up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAr are included in the study. Computer simulation was carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power, and terminal capacitance on the machine and system performance are studied. An analysis of self-excitation conditions on disconnection of supply was carried out. The behavior of a 220 kW hydel system and 55/11 kW and 22 kW wind driven system corresponding to actual field conditions is discussed. >