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Showing papers on "Maximum power principle published in 1999"


Journal ArticleDOI
TL;DR: In this paper, a broadband spatial power-combining system implemented in a standard X-band waveguide environment is presented, using 24 off-the-shelf GaAs monolithic-microwave integrated-circuit (MMIC) power amplifiers integrated with tapered-slot antenna arrays.
Abstract: In this paper, we present new results in the development of a broad-band spatial power-combining system implemented in a standard X-band waveguide environment. Using 24 off-the-shelf GaAs monolithic-microwave integrated-circuit (MMIC) power amplifiers integrated with tapered-slot antenna arrays, the new combining circuit produced up to 126-W maximum power output with a gain variation of /spl plusmn/1.9 dB within the band of interest (8-11 GHz). This hybrid circuit combiner is transparent to the device technology, and also provides an excellent heat-sinking capacity, sustaining as much as 415 W of dc power consumed by the MMIC amplifiers. The modular architecture allows easy maintenance, variable output power level, and modular assembly. Results on graceful degradation are also presented, showing superb tolerance to device failure.

169 citations


Journal ArticleDOI
01 Sep 1999
TL;DR: In this paper, the authors describe the analysis, modelling and implementation of a fuzzy based photovoltaic peak power tracking system, which is implemented by an inexpensive RISC microcontroller.
Abstract: The authors describe the analysis, modelling and implementation of a fuzzy based photovoltaic peak power tracking system. The maximum power of a photovoltaic system changes with temperature, solar intensity and load. An analytical model is built for the solar cell on the basis of the manufacturer's characteristics. The solar panel is integrated with the converter model and a fuzzy algorithm is developed, so as to perform an online search procedure to track the maximum power continuously. The system is implemented by an inexpensive RISC microcontroller. Experimental results have shown excellent performance, robustness with parameter variation and modularity for parallel operation at higher power. The system is ready and easy to fit into existing installations.

118 citations


Journal ArticleDOI
TL;DR: The hypothesis that the power curve may not in fact exist, in the sense that the cost of flight may not be perceived by a bird as a continuous smooth function of air speed, is advanced and is considered together with evidence from variation in flight behaviour, wingbeat kinematics and flight gait with speed.
Abstract: The power required for flight in any flying animal is a function of flight speed. The power curve that describes this function has become an icon of studies of flight mechanics and physiology because it encapsulates the accessible animal's flight performance. The mechanical or aerodynamic power curve, describing the increase in kinetic energy of the air due to the passage of the bird, is necessarily U-shaped, for aerodynamic reasons, and can be estimated adequately by lifting-line theory. Predictions from this and related models agree well with measured mechanical work in flight and with results from flow visualization experiments. The total or metabolic power curve also includes energy released by the animal as heat, and is more variable in shape. These curves may be J-shaped for smaller birds and bats, but are difficult to predict theoretically owing to uncertainty about internal physiological processes and the efficiency of the flight muscles. The limitations of some existing models aiming to predict metabolic power curves are considered. The metabolic power curve can be measured for birds or bats flying in wind tunnels at controlled speeds. Simultaneous determination in European starlings Sturnus vulgaris of oxygen uptake, total metabolic rate (using labelled isotopes), aerodynamic power output and heat released (using digital video thermography) enable power curves to be determined with confidence; flight muscle efficiency is surprisingly low (averaging 15-18 %) and increases moderately with flight speed, so that the metabolic power curve is shallower than predicted by models. Accurate knowledge of the power curve is essential since extensive predictions of flight behaviour have been based upon it. The hypothesis that the power curve may not in fact exist, in the sense that the cost of flight may not be perceived by a bird as a continuous smooth function of air speed, is advanced but has not yet formally been tested. This hypothesis is considered together with evidence from variation in flight behaviour, wingbeat kinematics and flight gait with speed. Possible constraints on flight behaviour can be modelled by the power curves: these include the effect of a maximum power output and a constraint on maximum speed determined by downstroke wingbeat geometry and the relationship between thrust and lift.

113 citations


Proceedings ArticleDOI
29 Nov 1999
TL;DR: In this paper, the authors proposed a novel maximum power point controller, which not only can track the maximum power of an array quickly without perturbation and observation process but also can be implemented easily.
Abstract: In this paper, the authors proposed a novel maximum power point controller, which not only can track the maximum power of an array quickly without perturbation and observation process but also can be implemented easily. The main idea is based on the graphical interpretation of the maximum power point as the intersecting point of two curves on the phase plane corresponding to the solution of two algebraic equations. In other words, the operating point is the intersecting point of the PV-array characteristic curve and the maximum power line. A circuit is constructed based on a boost circuit and a three phase full bridge inverter.

102 citations


Patent
Shigefumi Odaohhara1, Arimasa Naitoh1
07 Dec 1999
TL;DR: In this article, a method and apparatus for controlling power consumption of the PC, which is provided with base loads comprising a plurality of components, as well as a CPU including operation modes of “throttling” and “clock-down”, is presented.
Abstract: Disclosed is a method and apparatus for controlling power consumption of the PC, which is provided with base loads comprising a plurality of components, as well as a CPU including operation modes of “throttling” and “clock-down”. Actual power consumption 103 of the CPU in a certain operation mode varies heavily or widely within a range of maximum power consumption of the CPU. A variation of actual power consumption 101 of the base loads is relatively gentle or mild. Predicted maximum power consumption (Pmax) of the PC is obtained from actual power consumption of the base loads and maximum power consumption in the current operation mode of the CPU. Reference power vales 121, 123, 125 are set up such that they are compared with the Pmax for changing an operation mode to another operation mode. When the Pmax exceeds a reference power vale, the operation mode of the CPU is changed for controlling actual power consumption of the PC.

94 citations


Journal ArticleDOI
TL;DR: A distributed fixed-step power control algorithm is presented and it is shown by simulation that blocking a new call is more probable than dropping any existing calls, if the capacity is exceeded.
Abstract: A distributed fixed-step power control algorithm is presented. It is a simple feedback adjustment algorithm using only local information. In the ideal case where there is no power constraint, it is guaranteed that existing users will not be dropped due to admission of new users. If it is infeasible to accommodate all of them, the new user will be blocked. When the constraint on the maximum power is imposed, it is shown by simulation that blocking a new call is more probable than dropping any existing calls, if the capacity is exceeded. Besides, its convergence property is demonstrated. The convergence rate, which depends on the step size, is studied through simulation. In addition, the issue of power quantization is addressed.

90 citations


Proceedings ArticleDOI
29 Nov 1999
TL;DR: In this paper, a transformer-less single phase inverter for a photovoltaic (PV) power system is presented, which consists of two sets of a PV array and buck-boost type chopper circuit.
Abstract: This paper presents a newly developed transformer-less single phase inverter for a photovoltaic (PV) power system. The proposed system consists of two sets of a PV array and buck-boost type chopper circuit. However, it is afraid that the system has lower "using rate" of PV energy than that of the ordinary PV system, as each PV array is only operated in the half duration of the AC power frequency. In this paper, it is also discussed how to increase this "using rate" by varying the connected capacitor between PV array terminals. The perturbation and observation method is adapted to the maximum power tracking in our PV systems. We adopt the wavelet transform to detect a power outage. The experimental data shows that this new inverter can supply AC power to the utility grid line with the power factor nearly unity.

82 citations


Proceedings ArticleDOI
01 Jan 1999
TL;DR: This design calls for a pilot module to track the maximum power point voltage by changing the duty cycle of a step-down chopper, which is controlled by a software P voltage controller.
Abstract: A design of an inexpensive and efficient maximum power point tracker is presented. This design calls for a pilot module to track the maximum power point voltage (V/sub m/). The tracking is done by changing the duty cycle of a step-down chopper, which is controlled by a software P voltage controller. The controlled voltage of the tracker (V/sub m/) is obtained by measuring the open circuit voltage (V/sub oc/) and searching in the look-up table stored in the computer for (V/sub m/) versus the measured (V/sub oc/). This table is obtained from theoretical calculations for maximum power points locus of the solar cell array (SCA) used. For the difference between the theoretical and experimental locus of the maximum power points, for temperature effect, degradation of the (SCA) and dust effect, the oscillation about the theoretical point is used to determine the actual point. It is also used for the (power-voltage) curve of the SCA.

71 citations


Journal ArticleDOI
TL;DR: In this article, the Hartmann model is used to describe the flow of an electrically-conducting incompressible fluid in an MHD induction machine and an optimum magnetic field strength (i.e., Hartmann number) is found based on the maximum overall efficiency.
Abstract: Magnetohydrodynamic (MHD) induction devices such as electromagnetic pumps or electric generators are analysed within the approach of entropy generation. The flow of an electrically-conducting incompressible fluid in an MHD induction machine is described through the well known Hartmann model. Irreversibilities in the system due to ohmic dissipation, flow friction and heat flow are included in the entropy-generation rate. This quantity is used to define an overall efficiency for the induction machine that considers the total loss caused by process irreversibility. For an MHD generator working at maximum power output with walls at constant temperature, an optimum magnetic field strength (i.e. Hartmann number) is found based on the maximum overall efficiency.

54 citations


Patent
20 Aug 1999
TL;DR: In this paper, a maximum power control circuit was proposed to accelerate the following to maximum power of a solar battery and to accurately and stably execute control near maximum output by performing the maximum power controlling of changing a reference operating voltage based on the output of the solar battery in an area where the operating voltage of the battery is less than the changeover solar voltage.
Abstract: PROBLEM TO BE SOLVED: To accelerate following to maximum power of a solar battery and to accurately and stably execute control near maximum output by performing the maximum power control of changing a reference operating voltage based on the output of the solar battery in an area where the operating voltage of the solar battery is less than the changeover solar voltage. SOLUTION: A maximum power control circuit 23 sets the operating point voltage of the solar battery 10 to be the open voltage and reduces the reference operating voltage in a prescribed sampling cycle by a relatively large change width. At the time, the operating voltage and the predetermined changeover solar voltage are compared and the monotonous control of monotonously reducing the reference operating voltage is performed when the operating voltage is larger. When the operating voltage outputted from the solar battery 10 falls below the changeover solar voltage, the maximum power control of substantially reducing the change width of the reference operating voltage compare to the time of the monotonous control based on the output of the solar battery and searching the maximum output of the solar battery 10 is performed. That is, in the area where the operating voltage is less than the changeover solar voltage, the change width of the reference operating voltage is reduced and the climbing control is performed.

50 citations


Patent
12 Nov 1999
TL;DR: In this paper, the maximum power level for transmissions over a local loop of a digital subscriber line is determined based on a response of the local loop to a test signal to allow a different loop in the binder group to have a different maximum power levels to reduce potential for crosstalk.
Abstract: A method for controlling transmission power from a customer premise equipment device over a local loop of a digital subscriber line involves determinating a maximum power level for transmissions over the local loop. The maximum power level is based on a response of the local loop to a test signal to allow a different loop in the binder group to have a different maximum power level to reduce potential for crosstalk in the binder group.

Patent
Robert A. Lacy1
24 Aug 1999
TL;DR: In this paper, a system consisting of a fuel cell subsystem, switches and a controller is adapted to determine the power that is consumed by the residential loads and based on the determined power, operate the switches to selectively regulate electrical connections between the residential load and the fuel cell to keep the power approximately below the first power threshold.
Abstract: A system includes a fuel cell subsystem, switches and a controller. The fuel cell subsystem is adapted to provide power that is capable of being consumed by residential loads, and the fuel cell subsystem is sized to provide power up to a first power threshold that is less than a maximum power threshold that is capable of being consumed by the residential loads. The controller is adapted to determine the power that is consumed by the residential loads and based on the determined power, operate the switches to selectively regulate electrical connections between the residential loads and the fuel cell subsystem to keep the power approximately below the first power threshold.

Patent
04 Feb 1999
TL;DR: In this article, a control method using calculation of the power characteristic (B) from a quasi-continuous current characteristic (A) of a sensor of similar type and charge to the solar generator, which is isolated from the latter, with provision of a setting parameter for the generator transducer in dependence on the maximum power point (MPP) of power characteristic.
Abstract: The control method uses calculation of the power characteristic (B) from a quasi- continuous current characteristic (A) of a sensor of similar type and charge to the solar generator, which is isolated from the latter, with provision of a setting parameter for the solar generator transducer in dependence on the maximum power point (MPP) of the power characteristic. An Independent claim for a maximum power point control circuit is also included.

Journal ArticleDOI
TL;DR: In this article, it was shown that a general property of endoreversible Curzon-Ahlborn-Novikov (CAN) cycles can be extended for non-endoreversible CAN-cycles.
Abstract: In this work it is shown that a general property of endoreversible Curzon-Ahlborn-Novikov (CAN) cycles previously demonstrated can be extended for non-endoreversible CAN-cycles. This general property is based on the fact that at the so-called maximum ecological regime the efficiency is the average of the Carnot and the maximum-power efficiencies, and that in such a regime the power output is 75% of the maximum power of the CAN-cycle and the entropy produced is only 25% of that produced in the maximum power point. This property is independent of the heat transfer law.

Patent
30 Mar 1999
TL;DR: In this article, a method and apparatus for power throttling to manage the temperature of an IC is presented. Butler et al. use a temperature sensor to generate an output in response to junction temperature of the IC components.
Abstract: A method and apparatus for power throttling to manage the temperature of an IC. A temperature sensor is manufactured on the same die as the IC components. The temperature sensor generates an output in response to junction temperature of the IC components. A state machine is coupled to receive the output of the temperature sensor and to provide power reduction functions in response to the temperature sensor output exceeding a maximum thermal value. The maximum thermal value is less than the maximum allowable temperature of the IC corresponding to maximum power consumption. Thus, the invention reduces power consumption at a thermal value lower that a potentially catastrophic value rather than shutting down the IC when catastrophic failure is imminent.

Patent
02 Apr 1999
TL;DR: In this paper, the authors proposed a solution to avoid irregular power feeding and power generation of a metal material to realize save power consumption using only the power feeding circuit to supply non-contact power even when a metal materials other than the regular power receiving coil is arranged in the opposing positions of power transmitting coil.
Abstract: PROBLEM TO BE SOLVED: To avoid irregular power feeding and power generation of a metal material to realize save power consumption using only the power feeding circuit to supply non-contact power even when a metal material other than the regular power receiving coil is arranged in the opposing positions of power transmitting coil. SOLUTION: A substance coupled by magnetic inductance effect with an LC parallel resonance circuit 14 in the power transmitting side is detected a resonance frequency generated by a frequency follow-up circuit 18 of a mutual inductance detector 17. As a result, when a load detecting circuit 19 has detected the maximum power transmission amount, a regular power receiving side LC parallel resonance circuit 21 is determined to be arranged and the oscillation circuit 16 continuously oscillates the transmission frequency for transmitting the power. On the other hand, the oscillating circuit 16 oscillates intermittently in other cases and also oscillates the frequency other than the transmission frequency and thereby power of the resonance frequency for reducing the power transmission amount can be saved by a power transmitting side voltage control circuit 12 or a current limiting resistor 13.

Proceedings ArticleDOI
01 Jan 1999
TL;DR: Experimental results showed an average of 70.7% tighter peak power bounds for large sequential benchmark circuits was achieved in short execution times, and genetic spot expansion and optimization is proposed in this paper.
Abstract: Estimating peak power involves optimization of the circuit's switching function. We propose genetic spot expansion and optimization in this paper to estimate tight peak power bounds for large sequential circuits. The optimization spot shifts and expands dynamically based on the maximum power potential (MPP) of the nodes under optimization. Four genetic spot optimization heuristics are studied for sequential circuits. Experimental results showed an average of 70.7% tighter peak power bounds for large sequential benchmark circuits was achieved in short execution times.

Proceedings ArticleDOI
07 Nov 1999
TL;DR: This paper relates the voltage-scaling power optimization to the maximal weighted independent set (MWIS) problem, which is polynomial-time solvable on a transitive graph, and develops a provably good lower-bound algorithm based on MWIS to generate the lower bound of the power consumption.
Abstract: The dual-voltage approach has emerged as an effective and practical technique for power reduction. In this paper, we explore power optimization with dual supply voltages under given timing constraints. By analyzing the relations among the timing slack, delay and power consumption in a given circuit, we relate the voltage-scaling power optimization to the maximal weighted independent set (MWIS) problem, which is polynomial-time solvable on a transitive graph. Then we develop a provably good lower-bound algorithm based on MWIS to generate the lower bound of the power consumption. Also, we propose a fast approach to predict the optimum supply voltages. The maximum power reduction is obtained by using a modified lower-bound algorithm with optimum voltages. Experimental results show that the resulting lower bound is tight for most circuits and that the estimated optimum supply voltage is exactly, or very close to, the best choice of actual voltages.

Journal ArticleDOI
TL;DR: In this article, the performance of an isothermal combined-cycle chemical engine with mass leak was analyzed and the relation between the optimal power output and the maximum energy efficiency was derived.
Abstract: The performance of an isothermal combined-cycle chemical engine with mass leak is analyzed in this paper. The relation between optimal power output and ef®ciency, the maximum power output and the corresponding ef®ciency, as well as the maximum ef®ciency and the corresponding power output are derived.

01 Jan 1999
TL;DR: In this paper, the photovoltaic (PV) voltage varies nonlinearily with temperature and isolation level, but is directly proportional to the PV cell open circuit voltage.
Abstract: It is shown that at maximum power, the Photovoltaic (PV) voltage varies nonlinearily with temperature and isolation level, but is directly proportional to the PV cell open circuit voltage The proportionality voltage-factor is fixed for a given PV generator regardless of temperature, isolation and panel configuration, but depends on cell material and manufacturing This remarkable property is used to achieve temperature and insolation independent maximum power point tracking of satellite’s solar cells with a simple and reliable technique The open circuit voltage is continuously measured by a microcontroller and is used to estimate the maximum power operating point of the system

Journal ArticleDOI
TL;DR: In this paper, the authors extended the endoreversible thermodynamic theory of heat engines to fluid flow power converters and derived the relation between power output and efficiency, which involves the maximum (reversible) efficiency (with zero power output) as well as the maximum power and the corresponding efficiency bound, based on the nonlinear flow resistance relations.
Abstract: The endoreversible thermodynamic theory of heat engines is extended to fluid flow power converters. The relation between power output and efficiency, which involves the maximum (reversible) efficiency (with zero power output) as well as the maximum power and the corresponding efficiency bound, is derived based on the nonlinear flow resistance relations. Some modification to the results from recent literature is performed, and a theory of generalized thermodynamic optimization is provided.

Proceedings ArticleDOI
09 May 1999
TL;DR: A new hysteresis maximum power tracking scheme, which is independent of wind turbine or turbine generator characteristics, is proposed and investigated and some field test waveforms are presented.
Abstract: A new hysteresis maximum power tracking scheme, which is independent of wind turbine or turbine generator characteristics, is proposed and investigated in this paper. As a comparison, two other wind energy conversion control schemes, namely DC-link voltage based linear control and hill-climb maximum power tracking, are studied. A simplified wind turbine model using MATLAB/SIMULINK is given in this paper as well. Simulations for these schemes have been conducted. Some field test waveforms are also presented.

Journal ArticleDOI
TL;DR: In this paper, a finite-time thermodynamic optimization based on the maximum power density criterion for an irreversible combined Carnot heat engine model has been carried out, and the effects of the finite-rate heat transfer, internal irreversibility and heat leak are considered in the analysis.
Abstract: A finite-time thermodynamic optimization based on the maximum power density criterion for an irreversible combined Carnot heat engine model has been carried out. The effects of the finite-rate heat transfer, internal irreversibility and heat leak are considered in the analysis. The obtained results are compared with those results obtained by using the maximum power criterion. The design parameters under the optimal conditions were derived analytically and the effects of irreversibilities on the general and the optimal performances are investigated.

Proceedings ArticleDOI
P. Ide1, N. Froehleke, H. Grotstollen, W. Korb, B. Margaritis 
29 Nov 1999
TL;DR: In this article, a boost-type 3-level topology for switched mode rectifiers is inspected towards its application at wide input voltage range and power line distorted conditions including single-phase supply.
Abstract: A prominent boost-type 3-level topology, which is proved to represent a cost effective and highly efficient solution for switched mode rectifiers is inspected towards its application at wide input voltage range and power line distorted conditions including single-phase supply. Supplementary measures for a low cost control scheme are described to facilitate the operation under these unfavorable conditions. Shutdown of e.g. telecommunication plants can thus be avoided, if a maximum power limitation is observed. The inherent adaptation of the control scheme to the largely varying supply conditions supports the high yielding efficiency at high output voltage, even when supplied out of two phases. Simulation and measurement results prove the maturity of this rectifier scheme.

Proceedings ArticleDOI
10 Mar 1999
TL;DR: In this article, an upper theoretical limit for the efficiency of thermophotovoltaic (TPV) devices as a function of optical band gap, in the ideal case where radiative recombination is dominant and where the source is taken as a black body, was derived.
Abstract: Using the thermodynamic model of Shockley and Queisser we compute an upper theoretical limit for the efficiency of thermophotovoltaic (TPV) devices as a function of optical band gap, in the ideal case where radiative recombination is dominant and where the source is taken as a black body. We obtain for TPV diodes with black body source temperatures Ts=12000 K–2500 K: optimum bandgaps, Eg in the range 0.2–0.5 eV, maximum conversion efficiencies between 30 and 35%, and maximum output powers between 5 and 80 Watts/cm2. We compare this fundamental calculation of the maximum power output and efficiency with recent projections for the same quantities for TPV devices derived from semiempirical device modeling of a TPV diode under black body radiation. In contrast to the fundamental calculation, these models give for Ts=120 K–2500 K, optimum bandgaps Eg in the range 0.4–0.7 eV and maximum output powers and maximum conversion efficiencies of the order of one half of the obtained in the fundamental calculation.

Proceedings ArticleDOI
29 Nov 1999
TL;DR: A fuzzy logic control has been proposed based on the wind speed estimation in order to get maximum power and stability of the system.
Abstract: In this paper a system to evaluate a variable speed and pitch angle wind turbine by fuzzy logic techniques is described. A fuzzy logic control has been proposed based on the wind speed estimation in order to get maximum power and stability of the system. An 11 kW prototype system using two inverters connected by a DC-link capacitor has been used: the first one works as a controlled rectifier implementing vector control and the second one handles the power injected into the utility grid. Experimental result of an 11 kW generator are shown.

Journal ArticleDOI
TL;DR: In this article, the effects of internal irreversibilities on the power output and thermal efficiency of the cycle have been determined using the finite-time thermodynamics, with the objective of having a more efficient small-sized engine.

Patent
09 Mar 1999
TL;DR: In this paper, a power-consumption control system composed of devices 300, 400 and of a centralized control device 100 which controls them is presented, which can clarify various pieces of information on respective devices.
Abstract: PROBLEM TO BE SOLVED: To provide a power-consumption control system which can clarify various pieces of information on respective devices. SOLUTION: A system is composed of devices 300, 400 and of a centralized control device 100 which controls them. The centralized control device 100 is provided with a maximum-power-consumption-value holding means 110, which holds an allowable maximum power consumption value based on a contract power value with an electric power company, with a power-consumption holding means 111 which totals power consumption values in respective devices so as to hold their total value, with a power- consumption-value comparison means 112 which compares the total value with the allowable maximum power consumption value and with a display means 120 which displays the compared result of the power-consumption-value comparison means 112. The devices 300, 400 are provided with respective power-consumption-information holding means 301 which hold information regarding their own power consumption and with respective power-request reporting means 302 which report the necessity degree of the supply of electric power to the centralized control device 100 via respective communication means 101. In addition, the communication means 101 which communicates with the respective devices 300, 400 and with the centralized control device 100 are provided at the respective devices 300, 400 and at the centralized control device 100.

Patent
25 Jun 1999
TL;DR: In this paper, it is disclosed a power amplifier includes an in-phase power splitter generating two split signals from an input signal, and two amplifiers capable of operating in different modes.
Abstract: There is disclosed a power amplifier includes an in-phase power splitter generating two split signals from an input signal, and two amplifiers capable of operating in different modes. The split signals are provided as respective inputs to the two amplifiers which are coupled through transmission lines such that as the first amplifier approaches the maximum power it can produce, the output from the second amplifier begins to contribute to the power amplifier output and supplements and modifies the power provided by the first amplifier thereby extending the range of input power over which the power amplifier delivers output power.

Journal ArticleDOI
TL;DR: In this paper, the effects of inefficiencies in the compression, expansion and regeneration processes on engine performance have been evaluated theoretically for a Stirling heat engine operating in a closed regenerative thermodynamic cycle.
Abstract: The effects of inefficiencies in the compression, expansion and regeneration processes on engine performance have been evaluated theoretically for a Stirling heat engine operating in a closed regenerative thermodynamic cycle. The irreversible cycle has been optimized by using the maximum power density technique. Maximized power and maximized power density are obtained for different n ex , τ, α c , α h , η c , η ex and η reg values. The maximum efficiencies have been found very close to the values corresponding to the maximum power density conditions but far from the values at maximum power. It has been found that the engines designed by considering the maximum power density have high efficiencies and small sizes under the same prescribed conditions.