Energy Efficiency in Vector Controlled Variable Speed Drives VSD Goran Rafajlovski and Krste Najdenkoski
Abstract: Today 40% of all energy consumption is in electrical energy and will grown to 60% by 2040. On the other side, the share of electrical energy which will be controlled by power electronics e.g. in variable speed drives will increase from 40% in 2000 to 80% in 2015.The ZVEI shows that a saving of 22.3TWh per year is possible by applying VSD in the German industry. The design challenge is to provide control in a simple way and to do it cost effectively. In most cases the smart use of power electronics and control techniques even can lead to significant cost savings with return on investment in a few months. The ongoing trend to replace analog with digital, standard U/f scalar control techniques with modern vector oriented control in VSD application is motivated not only by lower energy consumption but also better functionality and reliability of control, and reduced wear out of the complete e.g. drive system. Keywords: variable-speed drive (VSDs), motor energy efficiency, scalar control, vector control, direct torque control
Introduction Insistent demand for energy-saving industrial and home appliances has recently escalated because of energy and environmental matter and the necessity to comply with new energy consumption regulations. These regulations force the development of energy-efficient motors for appliances such as washing machines, air conditioner compressor systems and fans [5]. Industrial motors and drives are estimated to consume 610 TWh or 64% of all electricity in industrial applications. Studies accomplished by the Electric Power Research Institute say that over 60% of industrial motors are operating under of their rated load capacity. By using VSDs a potential reduction of energy consumption of 20-30% is achievable [5]. The study concluded that 180 TWh is the potential to save energy using variable speed drives (VSDs), which accounts for 80 Mtons of CO2 reduction . The function of a variable-speed drive (VSDs) is to convert electrical energy to mechanical energy and vice versa. This is currently achieved almost exclusively via a magnetic field. Until today none new processes of energy conversion are known that may replace this in the next century. Until a few years ago, the induction machine was mainly used for constant-speed application. With recent improvements in semiconductor technology, power electronics and control techniques, the induction machine is seeing wider use in variable-speed application for increased efficiency. One of the key challenges to
increased efficiency of electrical drive is to extend the application areas of variable-speed drives using modern control techniques. This paper discuss how these challenges related to the induction machine are overcome to effect torque and speed control with that of the DC machine. The discussion focuses around various VSDs systems and their characteristics, as well as the domain of their application. The first section involves what is termed volts-per-hertz, or scalar control. The rest of the paper will present vector-controlled methods applied to the induction machine. These methods are aimed at bringing about independent control of the machine torque- and flux- producing stator currents. The goal of vector-controlled methods is to make the induction motor emulate the DC motor by transforming the stator currents to a specific coordinate system where one coordinate is related to the torque production and the other to the rotor flux. This so called field oriented control method (FOC) provides excellent dynamic response matching that of the DC machine [3], [4]. The main disadvantage is the computational overhead required in the coordinate transformation. With the advanced using the dynamic machine model, vector-controlled VSDs exhibit far better dynamic performance and better energy efficiency than VSDs with scalar control. Direct Torque Control or DTC is the most advanced VSDs technology developed in the world [3]. With this control technology, field orientation is achieved without feedback using advanced motor theory to calculate the motor torque directly and without modulation. The controlling variables are motor magnetising flux an motor torque. DTC drives do not need a tachometer or encoder to monitor motor shaft speed or position in order to achieve the fastest torque response ever from an AC drive which saves initial cost. With a DTC controlled bridge harmonics can be significantly reduced [2], the low level current distortion is usually less than a conventional 6-pulse or 12-pulse configuration and power factor can be as high as 0.99.
Scalar control Scalar control method is derived from the steady state machine model and is satisfactory for many lowperformance low - energy efficiency industrial and commercial application. The block diagram for the scalarcontrolled induction drive is shown in Fig.1. The inverter DC-link voltage is obtained through rectification of the AC line voltage needed to drive the induction machine to implement frequency control. The drive uses a simple pulsewidth-modulated (PWM) inverter whose time-average
output voltages follow a reference-balanced three-phase set, the frequency and amplitude of which are provided by the speed controller. The drive shown here uses an active speed controller based on a proportional integral derivative (PID), or other type of controller. The input to the speed controller is the error between a reference speed signal and the shaft speed of the machine. An encoder or other speed-sensing device is required to ascertain the shaft speed. The drive can be operated in the open-loop mode as well; however, the speed accuracy will be highly reduced.
Fig.1 Scalar control of induction machine
Induction machine torque control is possible by varying the magnitude of the applied stator voltage. Speed control is accomplished by adjusting the input voltage until the machine torque for a given slip matches the load torque. However, the developed torque decreases as the square of the input voltage, but the rotor current decreases linearly with the input voltage [3]. This operation is inefficient and requires that the load torque decrease with decreasing machine speed to prevent overheating. In addition, the breakdown torque of the machine decreases as the square of the input voltage. Fans and pumps are appropriate loads for this type of speed control because the torque required to drive them varies linearly or quadratically with their speed.
resistance. The relationship (2) is usually a piecewise linear function with several breakpoints in a standard scalarcontrolled drive. This allows the user to tailor the drive response characteristic to a given application in order to achieve the better energy efficiency.
Field oriented control FOC The field oriented control FOC techniques bring overall improvements in drive performance over scalar control, with the advantages like higher efficiency, full torque control, decoupled control of flux and torque and improved dynamics. The basic idea of the FOC algorithm is to decompose a stator current into flux and torque producing components. Both components can be controlled separately after decomposition. The structure of the motor controller is then as simple as that for a separately excited DC motor. The microcomputer-based principled block structure of a field oriented vector control system is shown on fig 2. The control system is principally divided in three sections. One of them represents the object of control, i.e. the dynamic nonlinear and multi-variable mathematical model of the induction motor. The second section is the inverter, i.e. its discrete mathematical model with a variable structure, and the third section represents the DSP (Digital Signal Processor) which is to perform the function of the entire control in the closed control system. It implements the controlling algorithms, the acquisition and estimation of valid data, transformation of the coordinates, as well as the synthesis algorithms of control circuit.
One remaining complication is the fact that the magnetizing reactance changes linearly with excitation frequency.
Therefore, with constant input voltage, the input current increases as the input frequency decreases. In addition, the stator leakage magnitude increases as well, possibly saturating the machine. To prevent this from happening, the input voltage must be varied in proportion to the excitation frequency. If the input voltage and frequency are proportional with proportionality constant K f , the electrical torque developed by the machine is uniform throughout the full speed range and can be expressed as: 2
(1) Te =
3 ⋅ Vin ⋅ s ns ⋅ R2
3 ⋅ Vin ⋅ (ns − nr ) 2
=
n ⋅ R2 2 s
=
3 ⋅ K 2f R2
⋅ (ns − nr )
where ns and nr are synchronous frequency and machine shaft speed both in electrical radians per second. Practical scalar-controlled drives have additional functionality, some of which is added for the convenience of the user. In a practical drive, the relationship between the input voltage magnitude and frequency takes the form (2) Vin = K f ⋅ ns + Voffset where Voffset is a constant. The purpose of this offset voltage is to overcome the voltage drop created by the stator series
Figure 2. Principled block structure of vector control
Accordingly, vector control is a method for dynamic control of the speed and the torque of the induction motor through permanent control of the intensity and the angle of the space vectors of the electromagnetic variables. One of the most important benefits of this control is energy saving, because the vector control enables dynamic control of the factor of power. The vector oriented techniques can bring overall improvements in drive performance over scalar control. Main advantages of FOC are higher efficiency, full torque control, decoupled control of flux / torque and improved dynamics (fig 4.).
With all this in mind, it can be easy to explain the common tendency of the world’s highly developed countries to accept vector control as a universal method for controlling VSDs drives. M
M 3Hz 10Hz 20Hz 30Hz 40Hz 50Hz 30Hz
40Hz
50Hz
20Hz
150%
150%
10Hz 100%
100%
3Hz
n
n
Fig.3 Torque-speed characteristic for U/f and FOC Control
A basic, common characteristic to all approaches toward the different types of vector control is the dynamic equivalent scheme of the induction machine (Fig.3) by the help of which the dynamic non-linear structure of the induction motor is transformed or approximated to the model of a DC engine with independent excitation. This results in the possibility of four-quadrant work-mode of the induction motor with full response and torque dynamics, as well as good performances of the drive down to zero-speeds.
i1
R1
dΨ 1 dt
u
X 2σ
X1σ
X
m
R2
i2
dΨ2 dt
R1 ⎡ ⎢ −σ⋅X 1 ⎡Ψ ⎤ ⎢ ⎢ •1x ⎥ ⎢ ⎢Ψ ⎥ ⎢ − n k ⎢ •1 y ⎥ = ⎢ ⎢Ψ ⎥ ⎢ R1 ⋅ X m ⎢ •2 x ⎥ ⎢ σ ⋅ X 1 ⋅ X 2 ⎢⎣Ψ2 y ⎥⎦ ⎢ ⎢ 0 ⎢⎣
R1 ⋅ X m
nk
•
−
σ ⋅ X1 ⋅ X 2
R1
0
σ ⋅ X1 −
0 R1 ⋅ X m σ ⋅ X1 ⋅ X 2
R2 σ ⋅ X2
− ( n k − n)
⎤ ⎥ ⎥ R1 ⋅ X m ⎥ σ ⋅ X1 ⋅ X 2 ⎥ ⎥⋅ nk − n ⎥ ⎥ R2 ⎥ ⎥ − σ ⋅ X 2 ⎥⎦ 0
⎡ Ψ1x ⎤ ⎡1 0⎤ ⎢ ⎥ ⎢ ⎥ (3) ⎢ Ψ1 y ⎥ ⎢0 1⎥ ⎡U 1x ⎤ + ⋅ ⎢ Ψ2 x ⎥ ⎢0 0⎥ ⎢⎣U 1 y ⎥⎦ ⎢ ⎥ ⎢ ⎥ ⎣Ψ2 y ⎦ ⎣0 0⎦ Or in short matrix form: •
(4) Ψ ( t ) = A ⋅ Ψ ( t ) + B ⋅ U ( t ) (5) ⎡ 1 ⎡i1x ⎤ ⎢ σ ⋅ X 1 ⎢i ⎥ = ⎢ ⎣ 1y ⎦ ⎢ 0 ⎢⎣
0
−
Xm σ ⋅ X1 ⋅ X 2
1
0
σ ⋅ X1
⎤ ⎡ Ψ1x ⎤ ⎥ ⎢ Ψ1 y ⎥ ⎥ ⎥⋅⎢ Xm ⎢ Ψ2 x ⎥ ⎥ − σ ⋅ X 1 ⋅ X 2 ⎥⎦ ⎢Ψ2 y ⎥ ⎣ ⎦ 0
in short form as: (6) I 1 ( t ) = C ⋅ Ψ ( t ) , where underline denotes matrix variable. Similarly, the equation for the torque balance can be jΨ2( nk n ) represented as: •
(7) n = jΨ n
1 k
Figure 4. Dynamic equivalent scheme of the IM
According to [5], the state equations for the induction r r motorψ 1 − ψ 2 dynamic model in matrix form can be expressed as follows:
1 TA
⎡ Xm ⎤ ⋅ Ψ2 x ⋅ Ψ1 y − Ψ2 y ⋅ Ψ1x − M t ⎥ ⎢ ⎣σ ⋅ X 1 ⋅ X 2 ⎦
(
)
In (3), (5) and (7) indexes x, y denotes freely chosen frame of reference that rotate with angular speed nk . The system matrix A, regulation matrix B, and resulting matrix C contain the parameters of the control system, i.e. induction motor. Basically, there are two field oriented vector control techniques: indirect control- and direct control method (fig 5).
Fig.5 FOC of induction machine
The indirect vector FOC control method uses the mathematical model of the induction motor, i.e. for rotor flux-oriented control it uses the corresponding slipping relation and is very dependant on the change of the machine’s parameters. This control method do not estimate or measure the space vector of the rotor flux, but use the slipping relation to calculate the output signals of the stator current’s space vector (at vector control with a current inverter), or correspondingly the output signals of the stator’s voltage space vector (at vector control with a voltage inverter). The basic idea of the FOC algorithm is to decompose a stator current into flux and torque producing components. Both components can be controlled separately after decomposition. The structure of the motor controller is then as simple as that for a separately excited DC motor. Direct vector FOC control system is based on measurement, acquisition and (or) estimation of the space angle of the rotor’s flux. In order to avoid rotor flux acquisition problems, the recent general tendency is to leave the approach of measuring the flux through additionally embedded coils or Hall’s probes, and to acquire the flux through appropriately adapted mathematical models for this purpose [4]. The measurement of the rotor flux mainly has disadvantages connected with the loss of machine’s simplicity due to installing additional measurement elements in the course of constructing the machine and to extra expenses for additional signal processing equipment [3], [4], thus increasing the price and reducing the need to apply such control drives. The model-based acquisition of the rotor flux has a disadvantage related to the heating sensitivity of the parameters, which is closely related to the drive’s state of the motor. In this sense, long-term researches have been implemented and many models in different coordinate systems for rotor flux acquisition have been developed, as well as qualitative-quantitative evaluation and compensation of the error which is due to the temperature and magnetic variability of the parameters.
Direct torque control According to the needs for an ever greater automation of the manufacturing processes, the servo systems most often operated by induction motors are becoming increasingly necessary for different applications, both in the field of robotics and the field of the numerically controlled machine tools. In recent years, especially in the highly developed industrial countries, a much intensified development of various concepts for VSDs field-oriented control can be noticed which, in a control sense, enables approximation of the induction torque to the DC motor. The latest development in VSDs control with high efficiency is the Direct Torque Control (DTC) method. Unlike the control system which is oriented to r the space vector of the rotor’s flux ψ 2 , on the r r i1 − ψ 2 dynamic model in a d-q coordinate system of IM and PWM of the voltage inverter, thereby using linear control technique and linear controllers, the direct torque
control systems have a different concept for vector control. These DTC systems are based on the space angle of the stator flux, on the model of the induction motor in a stationary frame of reference and on the space-vector modulation of the inverter. Thereby, this concept uses non-linear control techniques and non-linear controllers (Fig. 6).
Fig.6 Power circuit of inverter fed IM and line voltage
The orientation of the control system to the space r vector ψ 1 , greatly reduces the control structure’s dependence on the temperature variations of the parameters of the equivalent induction motor scheme [6]. In contrast to FOC control systems in which the precision r in the estimation of the space angle of the rotor’s flux ψ 2 is directly dependent on the motor’s parameters which determine the rotor’s time-constant, in this vector control concept, there is no need to acquire the space angle of the r rotor flux ψ 2 . The orientation of the control structure to r r the ψ 1 − ψ 2 model of the induction motor in a stationary α − β coordinate system avoids the need of coordinates transformation.. Space-vector modulation enables optimum use of the inverter’s dynamics, easy and simple optimization of the on-off switching frequency regarding the quality of the expected response of the controlled variables (flux, speed and torque.). In fig.6 the power circuit of inverter fed IM and corresponding line voltage are presented. Ideally inverter can be considered as three 2-way switches connected between the two DC-busses. Thus the inverter could be characterised as a source of voltage pulses with constant amplitude 2/3 U d and controllable direction takeing 2 3 = 8 different states. Six of these 1(001), 2(010), 3(011), 4(100), 5 (101) 6(110) correspondent to active
voltages with the same amplitude 2/3 U d , while the two others are null-voltage vectors 0(000), 7(111). Output voltage space vector of the inverter is:
r r r r 2 (8) u1 ( t ) = U d ⋅ 1 ⋅ Sa ( t ) + a ⋅ Sb ( t ) + a 2 ⋅ Sc ( t ) 3 2π j r Where ra = e 3 is a complex operator. Primary flux
vector ψ 1 is calculated as integral of the inverter output r voltage vector u1 according to the relation:
r
(9)ψ 1 =
∫ (u
T
r
1
r − R1 ⋅ i1 )dt
{
}[
r r r r r r r r (11) M = ψ × i = Im i ⋅ψ = Reψ ⋅ Im i − Imψ ⋅ Re i 1 1 1 1 1 1 1 1
]
Despite its control simplicity, the DTC method provides possibly the best dynamic response and energy efficiency of any of the methods (fig.7). The average switching frequency of the drive is lower as well, reducing switching loss, enhancing the energy efficiency, as compared with the FOC drive. Since the control basis is the stator flux linkage, the DTC drive is capable of advanced function such as performing “flying starts” and “flux braking”.
o
2π 4π ⎡ ⎤ j⋅ j⋅ ⋅ ⎢ S a (t ) + S b (t ) ⋅ e 3 + S c (t ) ⋅ e 3 ⎥ ⋅ t ⎢⎣ ⎥⎦ Considering that the voltage drop in the winding is neglected the trajectory of stator flux moves in direction to the inverter output voltage vector.r When output is one of the nonzero voltage vectors, ψ 1 moves with the constant velocity which is proportional to the output voltage. In the case of the zero voltage vector the velocity is very small and considered to be approximately zero because of the small value of the voltage drop ( R1 ⋅ i1). Therefore, byr selecting these vectors appropriately, the trajectory of ψ 1 can follow up to the specified locus. By
r 2 (10) ψ 1 (t ) = ⋅ U d 3
selecting adequate voltage vectors, module
r
ψ r1 ψ1
can be
kept constant and the rotating speed of can be controlled by changing the output ratio between zero and non zero vectors. Developed electrical torque can be express as:
Fig.7 Torque response for DTC drive
With the feature called motor flux optimisation, the energy efficiency of the total drive (that is controller and motor) is greatly improved in fan and pump applications. For example, with 25% load there is up to 10% total energy efficiency improvement. At 50% load there can be 2% total efficiency improvement [2]. This directly impacts on operating costs. This feature also significantly reduces the motor noise compared to that generated by the switching frequency of a traditional FOC-PWM drive.
Fig.8 DTC of induction machine - Torque and appropriate space voltage vector
Savings Potential The largest potential for energy savings with variable speeds drive are generally in variable torque applications, like centrifugal pumps and fans, where the power
requirements changes as the cubes of speed. The estimated motor electricity consumption in the EU by 2015 is 721 TWh in industry and 224 TWh in the tertiary/commercial sector [5]. For the assessment of electricity savings potential with the application of VSDs,
two different scenarios [1] have been analyzed: the technical savings potential and economic savings potential assuming constant VSD prices. In general, VSDs are not cost effective in the lower power ranges. In data given in Table 1, only the power ranges with a cost of saved electricity (CSE) lower than the average price of kilowatt hours in the sector of application are considered. It is assumed there are no economic restrictions in the technical potential of VSDs. Furthermore Table I summarizes the technical and economic savings potential in the industrial and in the tertiary sector with the application of VSDs [1],[5]. Table 1 EU Saving potential with application of VSDs by 2015
Industry (TWh per year) Tertiary (TWh per year) Total (TWh per year) Savings (Mton CO 2 /year)
Technical potential 62 22 84 33
Economical potential 39 8 47 19
Savings (10²€ year) 5600 2050 The estimated economic electricity savings potential (assuming VSD constant prices) with the application of VSDs, by 2015, would translate into 19 Mton CO 2 savings, contributing to the goal of reducing the greenhouse gas emissions in the EU. Table I also shows the technical and economic potential CO 2 and Euro savings, considering average generated CO 2 emission of 0.4kg CO 2 /kWh and considering average price of 0.05 and 0.1 Euro/kWh in industry and tertiary sector, respectively, with the application of VSDs, by 2015.
Conclusion VSDs with choosing appropriate control (U/f control, vector control, DTC), with the fast development of the power semi-conducting components, and with the development of hybrid digital signal processing systems are a very relevant growing market, although only 25% of new motors are equipped with VSDs . They allow one to control with precision the speed and torque of induction motors, increasing its application spectrum having significant economical and technical advantages. Huge energy savings (it’s been evaluated that around 10% of the generated energy can be saved), and the associated reduction in environmental emissions, are possible through the massive application of VSDs in a wide variety of loads in the different sectors of the industry. VSDs may introduce problems related to the motor efficiency and reliability, power quality, and EMI. Causes and cures for line interference, harmonics and motor damage must be considered in almost any VSDs application. They are discussed in detail in the IEEE 519 and NEMA MG1 Part 31 specifications, but the best defence is an experienced application engineer who is familiar with operating plant and different control techniques.
In future, wider application of the DTC, (using fuzzy logic an artificial neural network based controllers) in application of VSDs is expected. However, there are several barriers, both technical and non-technical, which prevent a larger scale adoption of VSDs. Because of lack of knowledge of the VSDs economical and technical advantages in industrial and commercial sectors, actions to promote awareness of those advantages should be implemented.
References [1] Anfbal T.de Almeida;Fernando J.T.E.Ferreira, and Dick Both: Technical and Economical Consideration in the Application of Variable-Speed Drives with Electric Motor Systems, IEEE Trans. on Industry Application Vol. 41, No1, Jan/Feb. 2005 [2] ABB Industry Drives: Direct torque Control The world’s most advanced AC drive technology [3] Bocker, Joachim; Mathapati, Shashidhar: State of the Art of Induction Motor Control, IEMDC-IEEEElectrical Machines & Drives Conference, 2007, Volume 2 Issue, 3-5 May 2007 pp.1459-64 [4] B. Bose, Power Electronics and Variable Frequency Drives. New York: IEEE Press, 1996. [5] ECPE Position Paper Energy Efficiency – the Role of Power Electronics, Nürnberg, March 2007 [6] Goran Rafajlovski, Krste Najdenkoski: Modelling of Circuit Parameter Variation in Vector Controlled Induction Motor Drives, OPTIM`06, 10-th International Conference on Optimization of Electrical and electronic equipments, Romania Brasov, 2006, pp.1234-1241
Biographies Goran Rafajlovski was born in Skopje, Macedonia, on May 2, 1963. He graduated from the University - Skopje, received Master degree from University Zagreb Croatia in 1991 and Doctor degree from University of Skopje 1996. He is a Member of IEEE Power Engineering Society. His field of interest includes electrical machines and drives, power electronics and energy efficiency control techniques. He is today a associate Professor in the Faculty of Electrical Engineering and Information Technologies of the Ss. Cyril and Methodius University, Karpos II b.b. 1000 Skopje, Macedonia (email:
[email protected] ) Krste Najdenkoski, received his Ph.D. degree in Electrical Engineering from Faculty of Electrical Engineering -Skopje in 2003. His area of interest are electrical machines, power transformers, power quality, energy efficiency systems and wind energy systems. He is a Member of IEEE Power Engineering Society and CIGRE Paris. Currently he is a Assistant Professor at the Faculty of Electrical Engineering and Information Technologies, "Ss. Cyril and Methodius University" - Skopje, Republic of Macedonia (e-mail:
[email protected] )
