style="font-size:15px;"> 4 4. https://www.energy.gov/sites/prod/files/2014/02/f8/Motor%20Energy%20Savings%20Potential%20Report%202013‐12‐4.pdf5 5. https://sciamble.com
6 6. Clark, K., Miller, N. W., and Sanchez‐Gasca, J. J. (2009). Modeling of GE wind turbine‐generators for grid studies. GE Energy Report, Version 4.4, 9 September 2009.
7 7. Johnson, K. E. (2004). Adaptive torque control of variable speed wind turbines. NREL Technical Report, August 2004.
FURTHER READING
1 Mohan, N. (1981). Techniques for energy conservation in AC motor driven systems. Electric Power Research Institute Final Report EM‐2037, Project 1201‐1213, September 1981.
2 Mohan, N. and Ramsey, J. (1986). Comparative study of adjustable‐speed drives for heat pumps. Electric Power Research Institute Final Report EM‐4704, Project 2033‐4, August 1986.
PROBLEMS
1 1‐1. A US Department of Energy report estimates that over 100 billion kWh/year can be saved in the United States by various energy conservation techniques applied to the pump‐driven systems. Calculate (a) how many 1000‐MW generating plants running constantly supply this wasted energy and (b) the annual savings in dollars if the cost of electricity is 0.10$/kWh.
2 1‐2. Visit your local machine‐tool shop and make a list of various electric drive types, applications, and speed/torque ranges.
3 1‐3. Repeat Problem 1-2 for automobiles.
4 1‐4. Repeat Problem 1-2 for household appliances.
5 1‐5. In wind turbines, the ratio (Pshaft/Pwind) of the power available at the shaft to the power in the wind is called the coefficient of performance, Cp, which is a unit‐less quantity. For informational purpose, the plot of this coefficient, as a function of λ, is shown in Fig. P1-5 [6] for various values of the blades pitch‐angle θ, where λ is a constant times the ratio of the blade‐tip speed and the wind speed.The rated power is produced at the wind speed of 12 m/s where the rotational speed of the blades is 20 rpm. The cut‐in wind speed is 4 m/s. Calculate the range over which the blade speed should be varied, between the cut‐in and the rated wind speeds, to harness the maximum power from the wind. In this range of wind speeds, the blade’s pitch‐angle θ is kept at nearly zero. Note: this simple problem shows the benefit of varying the speed of wind turbines, by means of a variable‐speed drive, for maximizing the harnessed energy.Fig. P1-5 Plot of Cp as a function of λ [6].
6 1‐6. Read the report in Appendix 1‐A in the accompanying website “Adaptive Torque Control of Variable Speed Wind Turbines” by Kathryn E. Johnson, National Renewable Energy Laboratory [7].
7 1‐7. In wind turbines, describe the Standard Region 2 Control and describe how it works in your own words.
8 1‐8. Read the report in Appendix 1‐B in the accompanying website “Final Report on Assessment of Motor Technologies for Traction Drives of Hybrid and Electric Vehicles” and answer the following questions for HEV/EV applications:What are the types of machines considered?What type of motor is the most popular choice?What are the alternatives if NdFeB magnets are not available?What are the advantages and disadvantages of SR motors?
9 1‐9. Read the report in Appendix 1‐C in the accompanying website “Evaluation of the 2010 Toyota Prius Hybrid Synergy Drive System” and answer the following questions:What are ECVT, P, CU, and ICE?What type of motor is used in this application?
10 1‐10. Read the report in Appendix 1‐D and summarize the possibility of using SR motors in HEV/EV applications.
Note
1 (Adapted from chapter 1 of Electric Machines and Drives: A First Course ISBN: 978‐1‐118‐07481‐7 by Ned Mohan, January 2012 and from chapter 1 of Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink ISBN: 978‐1‐118‐48548‐4 by Ned Mohan, August 2014)
2
Understanding Mechanical System Requirements for Electric Drives
2‐1 INTRODUCTION
Electric drives are an interface between an electrical system and a mechanical system, as Fig. 2-1 shows. They themselves consist of an electric machine and a power electronic converter. In subsequent chapters of this book, we will look at the power electronic converter and its role, as well as analyze electric machines and how they can be controlled, given the desired speed and position of the mechanical system.
Fig. 2-1 Block diagram of adjustable speed drives.
In electric drives, the power flow may be in either direction. For example, in an electric vehicle in driving mode, power flows from the electric source, a battery, to the electric motor, a mechanical system, through a power electronic converter. On the other hand, while slowing down the vehicle, the roles are reversed. The kinetic energy of the moving vehicle energy is extracted (called regenerative braking), and power flows from the electric motor to the battery, again through a power electronic converter.
Electric drives must satisfy the requirements of torque and speed imposed by mechanical loads connected to them. The load in Fig. 2-2, for example, may require a trapezoidal profile for the angular speed, as a function of time. In this chapter, we will briefly review the basic principles of mechanics for understanding the requirements imposed by mechanical systems on electric drives. This understanding is necessary for selecting an appropriate electric drive for a given application.
Fig. 2-2 (a) Electric drive system and (b) example of a load‐speed profile requirement.
This analysis equally applies when the load becomes the source of power, as in a wind turbine, and the electric drive generates and transfers power to the utility grid, an electric system.
2‐2 SYSTEMS WITH LINEAR MOTION
We will begin by applying physical laws of motion in their simplest form, starting with linear systems. In Fig. 2-3a, a load of a constant mass M is acted upon by an external force fe that causes it to move in the linear direction x at speed u = dx/dt.
