Journal of Power and Energy Engineering, 2014, 2, 5862 Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee http://dx.doi.org/10.4236/jpee.2014.24009 How to cite this paper: Suzdorf, V.I. and Meshkov, A.S. (2014) Improving Energy Efficiency of Smart Household Appliances and Devices. Journal of Power and Energy Engineering, 2, 5862. http://dx.doi.org/10.4236/jp ee.2014.24009 Improving Energy Efficiency of Smart Household Appliances and Devices Viktor I. Suzdorf, Aleksandr S. Meshkov KomsomolskonAmur State Technical University, Khabarovsk, Russian Federation Email: susdorf@mail.ru Received July 2013 Abstract With the everincreasing volume of applications of various kinds of electric drives in all spheres of human activity, the issues in improving the efficiency of the electromechanical converters of elec tric energy, one of the most important components of the electric drive (ED), are becoming increa singly important. Such issues include reducing their weight and size, improving the functional characteristics of these devices to increase their operational life and reducing the cost of manu facture. Taking full advantage of these opportunities relates to the AC and DC singlephase com mutator motor (SCM), which is widely used in regulated and highspeed motor drives in home ap pliances and electric hand tools. The SCM is used in machinery where the load torque has a hyperbolic dependence on the rotational speed and the need to work with a large motor overload due to the “soft” mechanical characteristics of such motors. Keywords Smart Household Appliances; Efficiency; Motor Control 1. Introduction The Efficiency of the SinglePhase Commutator Motor (SCM) Control Such motors have qualities that cause their widespread use [1]: The overload capacity is greater than that in oth er motors used in consumer electrics; the performance of the CMS is greater than that of a DC motor with sepa rate excitation; there is no need for a power supply for the field winding; the SCM is smaller for a given perfor mance than DC motors of independent and parallel excitation; reliability is increased due to the large crosssection of the field winding and the small live intertrack; reversing the motor is simple to implement with a split field winding; the loss is reduced by the same amplitude of the ripple voltage as compared to a DC motor with separate excitation, with a pulsating current; they are smaller and lighter than semiconductor electric drive (ED) systems. Expansion of the volume of applications of this class of electric motor is also largely due to the fact that the collectorbrush assemblies are highfrequency converters due to their reliability, weight, size, and cost indicators, and have prospects for further development. Typically, the control systems of the ED with SCM are adjustable, due to the process requirements imposed
V. I. Suzdorf, A. S. Meshkov on the ED. As for electric tools, and other household appliances, the workflow is at a certain optimum speed for each material. This is due to the need for optimization in terms of energy and enhanced durability. To control the speed of the drive, a chain is introduced into the semiconductor converter, producing an aver age value for the control voltage. For the motor power from a standard household circuit, the inverter may be arranged such that the DC rectifier follows the AC circuit. Obviously, the scheme’s implementation should dif fer in greater simplicity and energy efficiency. The problem of minimizing the power loss can be formulated as follows: To find the dependence of i(t) and v(t), ascertain the maximum integral , for a given value of the integral equation 22 0 (()+() ) T пex Qitk itd τ = ⋅ ∫ and communications . where i(t) and v(t) are a function of current and speed in relative units of time, respectively; a is the amount of displacement in relative units and T is the time constant of the motor; with t—time in arbitrary units; Q—amount of heat liberated in the motor in rela tive units; Q0—maximum allowable amount of heat that can be released into the armature winding during the time T, yet without leading to overheating isolation; and a constant that takes into account the heating winding. The solution of the Lagrange variational calculus is sought from the Euler equations for the intermediate functions: 20 22 (`)Fi i λ νλνµ =−⋅⋅+⋅+− ⋅Φ in general is a function: where is the constant and λ a function of τ. In the commutator motors, sequentially exciting the reaction cannot be ignored, since the magnetic flux de pends on the armature current. The formula for the optimal control output for an arbitrary relationship between the current and the magnetic flux is F = F(i). A good approximation of such a relationship between the magnetic flux and the armature current is given by: where a + b = 1 and the value q for different engines is in the range 3  7. Then the optimal control law is: () () 1 0 ( 1) 2 qq q aФbФa bqФC bq aФ λτ − ⋅ +⋅⋅+⋅⋅=−⋅ + ⋅Φ+ ⋅ For optimal control of sequentially exciting the commutator motors, the problem of the minimum loss for a given performance and time has to be considered. Equations of state for an unsaturated collector serieswound motor in relative terms is a system where: With reversible points: The coordinates of the current state of the anchor chain i, are speed v, angle α and the heat loss Q, and of the control parameter is the voltage u, through which the desired control law.
V. I. Suzdorf, A. S. Meshkov The optimal control problem is considered in a controlled ED, that is, when developing the increment rate in the formulation of the minimum loss: a function i(t) is found, which provides a minimum loss of Q. Then, if the set of possible optimal laws of i(t) is the simplest i(t) = i0(t) = const, then the solution is: where is the increase in velocity. When using Pontryagin’s maximum principle, in general, the solution of the problem of stabilization can be obtained as follows: *1 12 *2 if 0 *( )if if M T M i i iT ττ τµτ ττ ττ + ≤≤ = ≤≤ − ≤≤ The efficiency of energy processes is usually defined by the ratio of net power or energy expended to. With out causing difficulties in the simplest cases, this rate is inconvenient in some situations, such as when there is a channel in the power transducer elements and a wide range of changes in the shaft servomotor. Imperfection of the criterion of efficiency of energy conversion results in a significant reduction in the effectiveness of technical measures aimed at saving electricity, making it difficult to obtain objective assessments of the quality of differ ent technical solutions. As a criterion for evaluation of energy efficiency, largely free of the disadvantages presented, we can offer dynamic efficiency, which is defined by: () () () дин P tdt W WW P tdtP tdt η = = +∆ +∆ ∫ ∫∫ where W is the energy consumed by the motor during the period of work, W∙h; ΔW is the loss of energy during work, W∙h, P(t) is the motor power for the period of work, W, △ P(t) is the loss of power for the period of opera tion of the engine, W; Using this criterion enables the assessment of the energy efficiency of the system, not only in static mode, but also in a dynamic that does not allow the use of efficiency in the traditional form. The advantages of this include the following criteria: choice of the time interval for the estimate (if provided, the integral equation is defined) and the presence of a nonnegative power value, thus maintaining the criterion point for any energy flow direc tions. Consumption values and power output are determined according to: ( )( )( ) ; elgrid motor Рt UtIt= ⋅ ( )( )( ) ; mechmotor motor РtМtt ω = ⋅ where Ugrid(t) is rms voltage motor, V; Imotor(t) is the rms current of the motor armature, A; Мmotor(t) is the mean value of the electromagnetic torque of the motor, N m; ωmotor(t) is the rms value of the circular engine speed, 1/s; The energy consumed by the system is determined by the time integration of power consumption. As a result of the integration of the energy, a balance equation is obtained [2]: 2 222 22 2 2 2 121 11 1 () ()() 22 ttt L ttt II Uti tdtMdtJRitdtL ωω ω −− ⋅=+⋅+ ⋅+⋅ ∫∫ ∫ or EL МЕCHKIN H M ААЕА Е=+ ++
V. I. Suzdorf, A. S. Meshkov where, t1, t2 is the start and end of the integration step; ω1, I1 is the speed and motor current at the beginning of the integration area; ω2, I2 is the speed and motor current at the end of the integration range; and АEL, АMECH, ЕKIN, АH and ЕM are electrical, mechanical, kinetic, thermal and magnetic energy, respectively. For the serieswound motor with a linear or close to it, depending on the current, the flow of the excitation energy efficiency of the engine is determined by the expression [3]: where T is a time constant of the SCM. Dependence of the dynamic efficiency of the supply voltage and the time is extreme. Therefore, the surface being located in the space of “dynamic efficiencyvoltageelectromagnetic torque”, will have a certain maxi mum. Thus, driving the motor to the point of extreme, when the shaft torque is through the formation of the de sired signal control PWM converter, provides high energysaving effects. Among the requirements for the engine speed before the other dominated by those who brought the process. Processes require that the appliance chooses stable speeds for performance and the quality of processing. Thus, the obvious is the need to maintain the frequency of rotation at a constant level regardless of the func tion of the load torque. To determine the management criterion, consider the structure “controlled converter—the serieswound motor” in relative terms: 2 ; ;;; ;; ; NN NN N arm L CM NMN N IM U i iu IM U JR MtT MTMR ω µµν ω ω µτ ρ = ===== ⋅ = === Then the basic equation of motion in the EP relative units is as follows: In optimal control theory, there are two types of drives: acceleration and position. The EDelectric instrument is in the first group and the optimal control of the ED can be summarized as follows: to change the speed of the motor of the value of v1 to v2 so that, for any time of the transition, the energy consumed by the inverter is mi nimal it is necessary to ensure maximum dynamic efficiency: ( ) () () c c vd v Pd µτ ητ µτ ⋅⋅ =⋅ +∆⋅ ∫ ∫ where ΔP is this loss in ED: electrical and mechanica: ΔPEL ΔP_meх. The exploration and development of motor control systems must take into account the limitations imposed by the basic coordinates in the process: • Current limiting • Heating restriction; • Speed limit; • Limited voltage value; • Limited acceleration a=amax; • Limit on the jerk j=jmax; It is obvious that maximum functionality will be provided under the following condition: 2 min L MECH u v Pd µτ ρ ⋅ ++∆→ ∫
V. I. Suzdorf, A. S. Meshkov Expressing the equation of motion dτ and replacing the limits of integration, we get: 2 22 01 tp v LMECHLMECH L v uu dv v PdvP τ µ τµ ρρ µµ ⋅+ +∆=⋅+ +∆⋅ − ∫∫ In those cases where μL is velocity, the function does not depend explicitly on the time and route; at least a definite integral is achieved with the proviso that at each speed range v1v2 of the motor a minimum integrand is provided: 2 0 L MECH L u vP d d µρ µ µµ ⋅ ++∆ = − Then, at a constant speed and ignoring mechanical losses, the solution is: MECH uvP a ρµ ρµ =±⋅ ⋅+ ⋅∆=±⋅ It should be noted that this control law can also be derived without the use of optimal control methods, and the definition of efficiency. As already mentioned, the efficiency—the ratio of useful power supplied—and the motor current is proportional to the square root of the electrodynamic motor torque. Then, the relative efficiency of the units is determined by the expression: Expressing voltage, we get the expression: Assuming that the speed is constant, that is, it is stabilizing, and that efficiency is maintained at a constant level, such as its maximum level, then the voltage takes a function of one variable—the electromagnetic torque. The last expression confirms the previously derived management characteristic in order to maintain maximum efficiency in the management of singlephase commutator serieswound motors. References [1] Emadi, A. (2004) EnergyEfficient Electric Motors, Third Edition, Revised and Expanded. Illinois Institute of Tech nology, Chicago. [2] Krause, P.C., Wasynczuk, O. and Sudhoff, S.D. (2002) Analysis of Electric Machinery and Drive Systems. Wiley IEEE Press. http://dx.doi.org/10.1109/9780470544167 [3] Meshkov, A. and Suzdorf, D. (2010) Improving the Energy Efficiency Factor of Low Power Electric Drives. http://www.rusnauka.com
