Anders Grauers

Efficiency of three wind energy generator systems

This paper presents a method to calculate the average efficiency from the turbine shaft to the grid in wind energy converters. The average efficiency of three 500 kW systems are compared. The systems are: a conventional grid-connected four-pole induction generator equipped with a gear, a variable-speed synchronous generator equipped with a gear and a frequency converter, and a directly driven variable-speed generator equipped with a frequency converter. In this paper it is shown that a variable-speed generator system can be almost as efficient as one for constant speed, although it has much higher losses at rated load. The increased turbine efficiency that variable speed leads to has not been included in this paper. It is also found that a directly driven generator can be more efficient than a conventional four-pole generator equipped with a gear.

Optimal Sizing of a Parallel PHEV Powertrain

This paper introduces a novel method for the simultaneous optimization of energy management and powertrain component sizing of a parallel plug-in hybrid electric vehicle (PHEV). The problem is formulated as a convex optimization problem to minimize an objective function, which is a weighted sum of operational and component costs. The operational cost includes the consumed fossil fuel and electrical energy, whereas the component cost includes the cost of the battery, electric motor (EM), and internal combustion engine (ICE). The powertrain model includes quadratic losses for the powertrain components. Moreover, the combustion engine and the electric motor losses are assumed to linearly scale with respect to the size and the losses of baseline components. The result of the optimization is the variables of the global optimal energy management for every time instant and optimal component sizes. Due to the dependency of the result on the driving cycle, a long real-life cycle with its charging times is chosen to represent a general driving pattern. The method allows the study of the effect of some performance requirements, i.e., acceleration, top speed, and all-electric range, on the component sizes and total cost.

Force density limits in low-speed PM machines due to temperature and reactance

This paper discusses two of the mechanisms that limit the attainable force density in slotted low-speed permanent-magnet (PM) electric machines. Most of the interest is focused on the force density limits imposed by heating of the windings and by stator reactance. The study is based on analytical models for the force and reactance calculations and a lumped parameter thermal model. It is found that in a machine with an indirectly cooled stator, it is difficult to achieve a force density greater than 100 kN/m/sup 2/ due to temperature limits. A high force density is achieved by using deep slots, which lead to high reactance. The high reactance severely increases the converter kilovolt-ampere requirement and total system cost. It is also shown that the cost caused by the high reactance will also limit the force density reached. In machines with one slot per pole per phase, the reactance limited the useful slot depth to approximately 200 mm. However, in machines having a greater number of slots per pole per phase the reactance becomes no longer an important limiting factor for the slot depth and force density.

Force density limits in low-speed permanent-magnet machines due to saturation

This work discusses the practical limits imposed by magnetic saturation for the force density in low-speed permanent-magnet electric machines. The force density dependence on current density and slot depth is investigated with the aid of finite-element modeling. For saturation reasons, shallow slots are more favorable for achieving high force densities. However, for thermal reasons, deeper slots become favorable. Therefore, an optimum slot depth that maximizes the force density for each current density level exists. The maximum allowable slot depth range for four low-speed applications has been identified for a given maximum motor diameter.

Effect of Driving Patterns on Components Sizing of a Series PHEV

In the past decade, it has been demonstrated that Plug-in Hybrid Electric Vehicles (PHEVs) can significantly reduce petroleum consumptions. However, the extend to which these vehicles can reduce the petroleum consumption highly depends on components size and driving patterns. In other words, PHEVs show the best benefits if the components are dimensioned to match the driver’s driving behavior. In this paper, the effect of different driving patterns on the optimal sizing of three major components of series PHEVs, i.e., battery, electric motor, and engine generator unit is studied. Different driving cycles are generated stochastically from real driving data using Markov chains, to represent life-time driving patterns of different drivers. To find the optimal size of the components, the problem is formulated as a convex optimization problem. The optimization variables (the variables of component size and energy management) are obtained by minimizing a cost function which is the sum of the operational and component costs.

An iterative dynamic programming/convex optimization procedure for optimal sizing and energy management of PHEVs

This paper proposes a time-efficient method for sub-optimal design of a plug-in hybrid electric vehicle with a parallel powertrain topology. The method finds the optimal design of the vehicle by iteratively using dynamic programming (DP) and convex optimization to minimize sum of operational and component costs over a given driving cycle. In particular, DP is used to optimize energy management, gear shifting and engine on-off for given component sizes, and convex optimization is used to optimize energy management and component sizes using the gear shifting and engine on-off strategies obtained by DP. Next, DP is re-optimized with the component sizes obtained by convex optimization, and the procedure is repeated until the component sizes converge. The result of this iterative method is compared by using DP on a grid of possible component sizes. It is shown that the iterative method gives a result very close to the global optimum in a comparably short time.

Dimensioning and control of a thermally constrained double buffer plug-in HEV powertrain

This paper describes modeling steps to enable fast evaluation of performance and cost effectiveness of a plug-in hybrid electric vehicle. The paper also shows how convex optimization can be used to dimension the vehicle powertrain while simultaneously controlling the energy buffer power. The method allows for optimal control of powertrain components that are subject to thermal constraints. The studied vehicle is a city bus driven along a perfectly known bus line. The bus is equipped with an engine-generator unit and an energy buffer consisting of an ultracapacitor and a battery. The engine generator unit and the energy buffer are modeled with quadratic power losses and are sized for two different charging scenarios. In the first scenario the bus can charge for a couple of seconds while standing still at bus stops, and in the second scenario the bus can charge for a couple of minutes before starting the route. In both scenarios, the ultracapacitor temperature is kept below a certain limit.

Convex Optimization Methods for Powertrain Sizing of Electrified Vehicles by Using Different Levels of Modeling Details

This study investigates the impact of different levels of modeling details on the problem of optimizing the total cost of ownership of a fuel-cell hybrid electric vehicle. In this optimization, the objective function is a weighted sum of operational and component costs over a driving cycle. The former includes the consumed hydrogen and electrical energy, and the latter includes the sum of the battery, fuel-cell, and electric-motor costs. Three methods with different levels of modelling details are investigated; in the first method, the power split between the two power sources together with component sizes are optimized, while assuming nonlinear loss functions for the components. In the second method, the efficiencies of the components are approximated by constant values. In the third method, the problem is simplified further by considering the energy split between the battery and the fuel-cell. As shown in the results, a more detailed model gives more accurate results at the price of increased computation time. However, the simplified models can give similar results as the detailed model in most cases. In some problems though, the model simplifications lead to results that differ notably from those obtained by using the detailed model.

Valuation of contract between power supplier and electric vehicle owner

The role of EVs can range from that of passive loads with no difference compared to the traditional ones to active components highly beneficial to the modern power system. An essential part in changing EV storages from passive to active components is the contractual framework. Therefore, we present several different agreements that can be formed between a power supplier and an EV owner. These agreements establish the terms for utilization of storages when an EV is parked and connected to a household charger. We show that these benefits are significant and present a valuable economic opportunity for both EV owners and power suppliers.