INVESTIGATION OF DYNAMIC BRAKING OF ELECTRIC VEHICLES POWERED BY PERMANENT MAGNET DC MOTOR L. Joni Polili School of Electrical & Electronic Engineering Nayang Technological University Hall 7 #40-1-746 Nanyang Link, Singapore 637717 e-mail: H722663@ntu.edu.sg Keywords: dynamic braking, two-quadrant chopper, simulink model, speed-up time and braking time. Abstract Electric vehicle has become the major interest to replace gasoline powered vehicle because the problem of ever decreasing gasoline resources. Simulink (one of Matlab toolboxes) was used to model EV system. Permanent magnet DC motor dynamic model was derived. Two-quadrant chopper model was developed. After combining both models, simulation was conducted. Speed and current waveforms were discussed. Control scheme was then designed and implemented to the system, starting with current controller and following with speed controller. Optimization of controllers following with verification would complete the overall model. Dynamic braking was presented by simulation and waveform results were discussed. Reference speed and load torque were varied and simulated. Speed-up time and braking time were discussed. Conclusions were drawn at the end of the paper. 1 Introduction Facing the dilemma of decreasing of gasoline sources in the world, scientists and researchers have been trying very hard to find a new alternative energy source for vehicles. Between 1832 and 1839, Robert Anderson of Scotland invented the first crude electric carriage. These two inventions started a new era of Electric Vehicle (EV). EV is clean, emission free and environment friendly. These facts are the major factor for automakers around the world to invest large amount of effort and capital in developing a new technologies for EV. Nowadays, EVs have been used widely in USA, but with limited production. In Singapore, EV is predicted to be an ideal market because of its geographic size and climate that support efficient performance of the batteries. In this project, a popular simulation tool, Simulink (one of the MATLAB toolboxes), will be used to design and analyst the model for research objectives. Simulink is menu driven, userfriendly simulation tool. Simulink is mostly used for simulating dynamic systems. Its library provides all the functional blocks for simulating different type of dynamic systems. The very beginning step for using the simulink is to model the system by either using mathematical expression or circuit representation. In this project, both ways were used complimentary to assist the design of the model. 2 Objectives One of the technical issues in the EV design is the dynamic braking. In gasoline vehicles, mechanical brakes are used to reduce the speed of the vehicle, resulting in a significant power loss. However, the EVs can be designed such that power loss due to braking can be converted to electric energy and then returned to the battery. In order to provide reverse current to flow back to the battery, known as charging process, a power electronic converter will be required. A twoquadrant chopper will be a good choice to serve this purpose; hence an effective and efficient dynamic braking will be achieved. The research focus will be on developing a control scheme for an effective dynamic braking. 3 Contributions In modelling of permanent magnet DC Motor, it is clearly shown that a Simulink model of DC motor was derived. This model is more suitable for Simulink analysis of system with power electronic library block used. Furthermore, it is simpler and easier to understand than the model provided in the library of Simulink under Additional Machines subfolder. Moreover, it combines the method of mathematical expression and circuit representation when modelling DC motor. After system model was completed, it was proven that larger the reference speed larger the time taken to reach the required speed. In addition, different type of speed response was figured out for different type of load characteristic. During braking (sudden drop of reference speed), it was clearly seen that current was flowing back to the DC source (battery) by observing current waveform. This enables some form of recharging process in regenerating mode. Speed response during braking was faster because the ability of two-
quadrant chopper to let the current reach negative value in the system. For constant torque characteristic, the larger the load torque, the faster the speed response during braking. 4. Methodology 4.1 Modelling of Permanent Magnet DC Motor In steady state, DC motor can be represented as shown below: Figure 1 DC motor dynamic model. From the above model, equations can be derived as shown: i a e 1/ ra = sl / r + 1 T = k v AA I a a ( Va kvωr ) (1) (2) 1 ω r = ( Te TL ) (3) Js + Bm L AF k v = V f (4) R f From equations (1) to (4), model of shunt DC motor can be derived. Equation (1) was replaced by real circuit model to provide current to flow in two way direction. Simulink model was then derived as shown in the following figure: percentage of time in one period where the current is allowed to flow into the load or the voltage is supply to the load. For example, 50% of duty cycle will supply an average of half the dc supply level. Chopper is commonly divided into four types: step down chopper, step up chopper, two-quadrant chopper and fourquadrant chopper. Two-quadrant chopper would be used in the research. It is basically combination of step down and step up chopper. It is operated in two mode of operation. When current is flowing to the load (positive), it acts as a step down chopper. When current is flowing back to the supply (negative), it acts as a step up chopper. In the research, two-quadrant dc to dc converter will be used. The configuration of basic dc to dc converter is shown below: Figure 3 Circuit configuration of two-quadrant chopper. There are two switches S1 and S2 connected across a dc voltage source ES. The switches open and close alternately in such a way that when S1 is closed, S2 is open and vice versa. S1 and S2 turn on time contribute to one period of switching. Diode connected parallel with the switch would block the current to flow downward but provided flowing upward. The following figure shows the Simulink model of the chopper: Figure 2 Shunt DC motor Simulink model. The parameters of DC motor were chosen from design specification given such that it delivered required power for the motor to run at required speed. Additional parameters required for simulation purpose were derived using equations (1) to (4). 4.2 Modelling of DC to DC Converter DC to DC switching converter, sometimes called chopper, makes use of parameter called duty cycle to vary dc supply level and therefore output speed. Duty cycle is defined as the Figure 4 Two-quadrant chopper Simulink model. IGBT and diode connected in parallel can be simplified and represented as a single bidirectional ideal switch. IGBT provides the current to flow downward while diode provides the current to flow upward. Turn on voltage for diode is small enough to be neglected. Hence, a bidirectional ideal switch was chosen to model IGBT and diode in parallel. From block diagram of Simulink library, ideal switch block diagram was found and therefore used in the model. The two switch used in two-quadrant chopper were controlled by a gating signal supply to the switch. This gating signal is either on or off in a periodical manner. To serve this purpose, pulse generator block was used. Since the two switches were
turned on alternatively. It is more efficient to use only one gating circuit, means one pulse generator. An inverter was designed to invert the gating signal supplied for second switch. 4.3 Modelling of System Upon completion of motor and DC to DC converter, the open loop system was simulated. The open loop system was shown in the figure below: Figure 7 Model of PI controller Using classical method of control system design, proportional constant and integrator constant were set. Further tuning was made until overshoot was low enough (< 5% overshoot). The following figure shows the overall system after speed output and current output were fed back to the system: Figure 5 Model for open loop system with linear load torque. Two-quadrant chopper and DC motor model were grouped into one subsystem and represented as a box shown above. Input of two-quadrant chopper was gating signal and DC source. Pulse generator was still used for open loop model. Output of two-quadrant chopper was then connected to input (armature field) of DC motor. Load torque input was then connected to speed output. This was a model for linear torque characteristic. Value of constant chosen was slope of linear torque characteristic, i.e. 1.1106. DC supply voltage was set to 1 pu and gating signal was set to 50% duty cycle. Switching frequency was also set to 3 khz. Simulation was run and the waveform of armature current, developed torque and rotor speed were observed. Gating circuit was designed to accept control input replacing pulse generator as shown in the figure below: Figure 6 Model of gating circuit. Input of the gating would be an integer in order to match with the output of PI controller. A range of 0~10 was chosen. This range was used to specify the parameter of repeating sequence block used in this model. Input was then compared to triangular waveform with upper limit 10, lower limit 0 and frequency 3 khz. This will create a square wave. Hence, for different integer value, different duty cycle resulted in the output. Before passing through the gating circuit, it would be going through a PI controller. The controller was then modeled as shown below: Figure 8 Model of close loop system with current and speed controller. Using practical rules of thumb that time constant for outer loop is 10 times greater than inner loop, speed controller constants were defined. Further tuning was made for optimization purpose and final value of proportional and integral constant were defined. 4.4 Implementing Different Torque Characteristic to the System Besides linear torque characteristic, there are two others torque characteristic, i.e. constant torque characteristic and fan/pump torque characteristic. Torque input in the system was changed to constant torque. Simulation was run and speed output was then observed. The same procedures were done for fan/pump torque characteristic. 4.5 Application of Dynamic Braking in the System To observed application of dynamic braking, reference input was changed to timer block from Simulink library. This block can be set to different value at different simulation time. Timer was set to 10% of reference speed after 0.5 second. Simulation was conducted and output waveform was then observed. Simulation was also conducted for different torque characteristics with different reference speed. Waveform of speed output was then observed. 5. Simulation Result
5.1 Open Loop System The result of open loop system simulation was shown below: After optimisation, proportional constant and integral constant of current controller were found to be 10 and 0.1. During speed controller optimization, three different type of response was observed as shown in the figure below: Figure 10 Slow Response of speed output waveform. Figure 11 Critically damped response of speed output waveform. Figure 9 Armature current (A), torque developed (Nm) and speed (rad/s) waveforms. It was understood from the waveform above that current and torque waveform has ripple. This was due to supply voltage passing through two-quadrant chopper with very fast switching frequency. The current was forced to be increasing and decreasing as fast as the switching speed. Since armature current and developed torque is linearly proportional to each other, developed torque would have the same ripple characteristic as armature current waveform would have. Another phenomenon appeared in the observation of current waveform was that it went through a very large overshoot before stabilized. Armature current went through some overshoot before it stabilized at 1 pu. Maximum overshoot were calculated and it was 606%. This was unacceptable since it will damage the motor. In order to overcome this problem, it was necessary to provide a feedback loop accompanied by a controller to achieve a stable and reliable system. 5.2 Close Loop System Figure 12 Under damped response of speed output waveform. From three different responses, critically damped system was chosen in order to have precise speed output and faster response. The values of controller constants for this response are 100 (proportional constant) and 15.45 (integral constant). 5.3 Load Torque Characteristic Linear torque characteristic simulation has been shown in figure 17 above. With same reference speed, constant torque simulation result was shown in figure 18 and fan/pump torque simulation was also shown in the next figure.
Figure 13 Speed response of constant torque system with ω r *=50 rad/s. Figure 14 Speed response of fan/pump torque system with ω r *=50 rad/s. It was shown that speed response was faster for fan/pump torque system because speed was squared and input to the load torque. While for constant torque, load torque would stay constant during simulation. 5.4 Dynamic Braking The result of simulation (armature current and rotor speed) was shown in the following figure: Figure 15 Current waveform for linear torque system with ω r *=50 rad/s and braking at 0.3s. After reference speed was reached, current would decrease to a certain value such that speed can be maintained. This value would be different for different torque characteristic and different reference speed. Higher reference speed would have higher value. Once brake was applied and reference speed was reduced to 10%, current would suddenly decrease very sharp to the lowest value it could reach. At this point of time, saturation block would take a role in limiting the lowest value of armature current can reach. But, without two-quadrant chopper, armature current would not be able to flow in negative direction. Hence, by means of two-quadrant chopper, some energy would be saved and braking response would be faster. For different reference speed, different braking time was observed. Higher reference speed before braking would result in longer braking time. Longer braking time would mean higher energy saved and therefore recharge back to the battery. For simulation result shown in figure 19 above, energy saved can be calculated as shown below. Esaved = Power t brake = I a 2 Ra 0.8s = (177A) 2 0.0415Ω 0.8s = 1040.1228 J. After braking speed was reached, current would go back to certain value in order to maintain braking speed. If braking speed was zero, current would go back to zero and motor would then stop rotating. 5.5 Reference Speed Variation For linear torque characteristic, current and speed waveform were shown below for different reference speed. Figure 16 Reference speed and speed output waveforms with waveform for linear torque system. During the increase of speed, current input to the motor was at highest value. This is to ensure fast increase of speed. It would stay at the limit as speed increased. This limiting current was resulted from application of saturation block in the controller. If no limit was implemented, current would have increased uncontrollably and therefore damaged the motor. Figure 17 Output waveform of linear torque system with different reference speed. There were three phenomenon observed from the above figures: [1] Speed-up time was slower for increase of reference speed, [2] Steady state current was higher for increase of reference speed, [3] Braking time was slower for increase of reference speed.
For constant torque and fan/pump torque characteristics, the same phenomenon appeared. 5.6 Different Load Torque value in Constant Torque System. For constant torque characteristic, load torque can be varied and the output waveforms were shown below: (current before braking), it would have larger amount of reduce current. Hence, the braking response would be faster. This would not be very significant compared to one-quadrant chopper. If one-quadrant chopper were implemented in the system, lower limit of armature current would be zero since no negative current would be able to flow. It would have reduced the amount of reduced current by more than 50% and the braking response would be very slow. Speed response for different type of load torque implemented in DC motor was presented in this research. Basically, three common type of load torque characteristic would share almost the same speed response. Fan/pump load torque characteristic would have a little bit faster speed-up response. This was due to non-linear relationship between speed and load torque. It was also shown in the research that braking time would also depend on reference speed before braking happened. In other words, to brake from higher speed would take longer time. References Figure 18 Output waveform of constant torque system with different load torque. From figure above, although reference speed was same, speed-up time was slower for bigger load torque, but brake time was a bit faster for bigger load torque. This was due to higher moment of inertia for big load torque. 6 Conclusions EV has become more and more popular alternative for nongasoline powered vehicles. One of its technical issues in the EV design is the electronic dynamic braking. EV system has been successfully modelled using Simulink and dynamic braking was investigated. As model in the system, dynamic braking was introduced by a sudden reduce in the reference speed. This would alter the DC motor to operate as a generator. The electric power generated was actually the power loss during mechanical brake. By means of twoquadrant chopper, electric power generated was returned back to the source. The source was actually a rechargeable battery therefore electric power generated was charged back to the battery. It was also shown that the time for the speed to reduce to the desired speed was very fast (around 0.1 second for 50% rated speed). This can be achieved because two-quadrant chopper provides a negative current to flow back to the battery. The speed of braking actually depends on how large the armature current can reduce and it was limited by lower limit of rated current the DC motor can take. For higher steady state current [1] Bausiere, R., Labrique, L., Seguier, G. 1993. Power electronic converters : DC-DC conversion. Berlin : Springer-Verlag. [2] Krause, P.C. 1986. Analysis of Electric Machinery. New York : McGraw-Hill. [3] MathWorks, Inc. 1998. The student edition of Simulink : dynamic system simulation for MATLAB : user's guide. Upper Saddle River, N.J. : Prentice Hall. [4] Mosćinśki, J. 1995. Advanced Control with MATLAB and SIMULINK. New York : E. Horwood. [5] Ogata, K. 2002. Modern Control Engineering. Upper Saddle River, N.J. : Prentice Hall, Inc. [6] Ong, Chee-Mun. 1998. Dynamic simulation of electric machinery : using MATLAB/SIMULINK. Upper Saddle River, N.J. : Prentice Hall PTR. [7] Slemon, G.R. 1992. Electric Machines and Drives. Reading, Mass. : Addison-Wesley Pub. Co. [8] Slemon, G.R. Straunghen, A. 1984. Power semiconductor drives. New York : Wiley. [9] Wildi, T. 2002. Electric Machines, Drives, and Power Systems. Upper Saddle River, N.J. : Prentice Hall. [10] Websites: http://inventors.about.com/library/weekly/aacarselectrica. htm The history of electric vehicles