TECHNO-ECONOMIC COMPARISONS OF IMPROVED SYNCHRONOUS RELUCTANCE MOTORS

E. V. Kononenko, A. S. Baturin

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

Various branches of industry have a need for synchronous motors. However, the use of synchronous motors with a power of \(0.6 \div 50\) kW is limited by the fact that domestic industry practically does not manufacture synchronous motors in the specified power range.

The Institute of Power Engineering of the Latvian Academy of Sciences has developed an experimental CO series of three-phase brushless synchronous motors (with a claw-pole rotor) with a power of \(1.5 \div 7.5\) kW, based on the stator iron of asynchronous motors of the new unified A02 series [1]. These motors, along with positive properties \((\cos \varphi = 1.0)\), have, in comparison with asynchronous squirrel-cage motors of the A02 series, substantial shortcomings. The principal ones are:

1) higher cost, due to larger overall dimensions (in the same frame sizes the power is lower by two steps of the power scale) and the complexity of manufacture (use of steel casting, difficulty of machining the bearing shields and claw-shaped rotor poles, etc.);

2) lower efficiency (at \(P_{\text{n}} = 4.0\) kW in a four-pole version \(\eta^{a} = 0.86; \eta^{c} = 0.83\));

3) lower reliability, due to a more complex design (the presence of an additional winding placed in the stator slots, an excitation winding, rectifiers, starting automation, etc.);

4) unsatisfactory starting characteristics, which permit starting synchronous motors only when operating at no load or with a small load, since the pull-in torque even in motors with improved starting characteristics is no more than 0.25 of rated torque (at 1500 rpm).

Synchronous reluctance motors (s.r.m.), owing to the absence of an excitation winding on the rotor and to the simplicity and manufacturability of their design, have certain techno-economic advantages in comparison with other types of low-power synchronous machines. However, in domestic industry up to the present time s.r.m. have found application only in low-power drives. The latter is explained by the fact that in the technical literature the opinion is widespread that s.r.m. have low energy indicators, and that the power of a three-phase s.r.m. is approximately about 40% of that of a three-phase asynchronous motor of the same frame size. This has led to the fact that in Soviet-

In the Soviet Union, until the present time, new types of synchronous reluctance motors have not been developed.

Since 1963, synchronous reluctance motors of the RS type with ratings of \(0.65 \div 7.0\ \text{kW}\), designed on the basis of A02-series induction motors, have been introduced into production [2]. These motors have the usual salient-pole rotor design and, as a result, large dimensions and low energy-performance indices. RS-type motors, in the same frame sizes as A02-series motors, have a power three steps lower on the power scale (approximately 40% of the power of the induction motor), with \(\cos\varphi_{\text{n}} = 0.30 \div 0.44\), \(\eta_{\text{n}} = 0.63 \div 0.73\).

As studies carried out at the Tomsk Polytechnic Institute have shown, by improving the rotor design within the same dimensions it is possible to increase substantially the power of a synchronous reluctance motor [3]. The improved rotor designs are made analogously to the design proposed by Prof. E. M. Goldovsky as early as 1928 [4]. To increase the power and the energy-performance indices of a synchronous reluctance motor in the same frame size, it is necessary, while keeping the magnetic conductance of the rotor along the longitudinal axis at a maximum value, to reduce substantially the magnetic conductance along the transverse axis. This is achieved by introducing into the rotor design additional nonmagnetic interlayers (gaps) along the path of the transverse magnetic flux.

One of the manufactured and tested improved synchronous reluctance motors of type SRO-41-4 has the following data: \(P_{\text{n}} = 4.0\ \text{kW}\); \(I_{\text{n}} = 10.3\ \text{A}\); \(U_{\text{n}} = 380\ \text{V}\); \(n_{\text{n}} = 1500\ \text{rpm}\); \(\eta_{\text{n}} = 0.865\); \(\cos\varphi_{\text{n}} = 0.684\); \(M_{\text{m}}/M_{\text{n}} = 1.43\). The temperature rise of the stator winding in rated operation is \(52.5^\circ\text{C}\). The motor weight is \(55\ \text{kg}\). The motor under consideration was designed on the basis of, and in the frame size of, the A02-41-4 induction motor, whose rated power is \(4.0\ \text{kW}\) and whose stator-winding temperature rise is \(58.0^\circ\text{C}\).

Thus, by improving the rotor design within the frame size of a totally enclosed fan-cooled induction motor, it is possible to make an improved synchronous reluctance motor of the same rated power.

In order to draw conclusions about the expediency of using improved synchronous reluctance motors, it is necessary to carry out techno-economic comparisons of these motors with other versions of synchronous motors.

The present work gives the results of a techno-economic analysis of an improved synchronous reluctance motor (SRO-41-4) in comparison with an ordinary synchronous reluctance motor (RS-52-4) and a brushless synchronous motor (SO-51-4). All the motors have a rated power of \(4.0\ \text{kW}\) and a rotational speed of \(1500\ \text{rpm}\).

The economic efficiency of the motors under consideration was determined on the basis of calculating annual reduced costs [5, 6]. In doing so, both capital investments and annual operating expenses were taken into account.

The cost of the SRO-41-4 motor was determined on the basis of the following data. In the improved synchronous reluctance motor SRO-41-4, all materials and parts used in the A02-41-4 motor are employed, with the exception of the rotor core. The manufacturing technology of the rotor of the improved synchronous reluctance motor is the same as that of the induction squirrel-cage motor. The rotor core is assembled from stamped sheets of electrical steel, and after pressing, the slots of the starting winding and the additional gaps are filled with aluminum under pressure. Owing to the more complex design and the increased consumption of active materials, the cost of the rotor of the improved synchronous reluctance motor proves to be higher than the cost of the rotor of a normal induction motor with a squirrel-cage rotor. In accordance with the foregoing,

the production cost of the SRO-41-4 motor increased in comparison with the production cost of the AO2-41-4 motor. This increase is explained by additional costs for manufacturing the rotor core under the following items:

1) materials—due to an increase in the consumption of electrical steel by 0.84 rubles and aluminum by 0.29 rubles;

2) wages—due to an increase in the volume of machining by 0.03 rubles and an increase in the labor input of stamping by 0.08 rubles;

3) special tooling costs increased, owing to the need to manufacture an additional die, by 0.36 rubles. Taking indirect costs into account, the production cost increased by 2.1 rubles.

Considering that the synchronous reluctance motor RS-52-4 was designed on the basis and within the overall dimensions of the AO2-52-4 asynchronous motor, and also the fact that the technology and design of these motors differ only slightly, we take their production costs to be the same.

The production costs of the AO2-41-4 and AO2-52-4 motors were determined according to [7]. The production cost of the CO-51-4 synchronous brushless motor was taken from [8].

Table 1 presents, for comparison, the technical-and-economic indices of asynchronous (AO2), improved synchronous reluctance motors (SRO), ordinary synchronous reluctance motors (RS), and synchronous motors (CO) having the same power.

Table 1

The economic analysis of the compared motors was carried out using the formula for reduced costs

$$ Z = C + E_{\mathrm{n}} K, \tag{1} $$

where $Z$ is the annual reduced costs, rubles/year;
$C$ is the annual operating expenses;
$E_{\mathrm{n}}$ is the standard coefficient of economic efficiency;
$K$ is the one-time capital investment.

The economically advantageous variant is the one having the smaller value of the reduced costs.

When comparing variants having different values of $\cos\varphi$, the motors are brought to the same $\cos\varphi$ by connecting a capacitor bank in parallel. In this case the capital investment and operating expenses of the motor with the lower $\cos\varphi$ increase by

account of the cost, depreciation, and losses of electric energy of the capacitor bank.

Annual operating expenses include: depreciation charges, the cost of electric-energy losses, maintenance and repair costs, and others. We assume that, in the compared types of motors, maintenance and repair costs differ little in magnitude; therefore, in the operating expenses only depreciation charges and the cost of electric-energy losses are taken into account.

Electric-energy losses in motors depend on the time of their operation per year, \(t\). On this basis, it is expedient to express the cost of electric-energy losses as a function of time. This makes it possible, when comparing variants, to determine from the condition of equality of annual reduced costs the operating time \(t_p\) at which the compared motors will be equally economical.

Economic comparisons of the SRO-41-4 and RS-52-4 motors

The motors being compared have different power factors (Table 1). In order for the variants to be comparable, it is necessary to increase \(\cos \varphi^{\mathrm{pc}}\) of the RS-52-4 reluctance motor to the value \(\cos \varphi^{\mathrm{cp}}\) of the improved SRO-41-4 reluctance motor by connecting a capacitor bank in parallel. The required power of the static capacitors, under the condition that the motors operate in the rated mode and that the useful powers of the compared motors are equal, is determined by the equation

\[ Q_c = P_{\mathrm{н}}^{\mathrm{pc}} \cdot \left( \frac{\operatorname{tg}\varphi_{\mathrm{н}}^{\mathrm{pc}}}{\eta_{\mathrm{н}}^{\mathrm{pc}}} - \frac{\operatorname{tg}\varphi_{\mathrm{н}}^{\mathrm{cp}}}{\eta_{\mathrm{н}}^{\mathrm{cp}}} \right) \;[\text{kvar}]. \tag{2} \]

where \(P_{\mathrm{н}}^{\mathrm{pc}}\) is the rated useful power of the RS motor;
\(\eta_{\mathrm{н}}^{\mathrm{pc}}\) and \(\eta_{\mathrm{н}}^{\mathrm{cp}}\) are the rated values of the efficiency of the RS and SRO motors.

In the case when the compared motors operate in a mode differing from the rated one, the power of the static capacitors is determined by the equation

\[ Q'_c = P_{\mathrm{н}}^{\mathrm{pc}} \cdot k_{\mathrm{э}} \cdot \left( \frac{\operatorname{tg}\varphi_{1}^{\mathrm{pc}}}{\eta_{1}^{\mathrm{pc}}} - \frac{\operatorname{tg}\varphi_{1}^{\mathrm{cp}}}{\eta_{1}^{\mathrm{cp}}} \right) \;[\text{kvar}]. \tag{3} \]

where \(k_{\mathrm{э}}\) is the coefficient of utilization of the motors with respect to power;
\(\varphi_1\) and \(\eta_1\) are the phase angles and efficiencies corresponding to the operating mode of the motors.

a) When the compared motors operate in the rated mode

Substituting the corresponding data of Table 1 into equation (2), we determine that the power of the static capacitors is equal to

\[ Q_c = 10.15\ \text{kvar}. \tag{4} \]

The annual reduced costs for the SRO-41-4 motor, in accordance with equation (1), may be represented in the form

\[ З^{\mathrm{cp}} = \frac{H_g}{100}\cdot K + \left( \frac{P_{\mathrm{н}}^{\mathrm{cp}}}{\eta_{\mathrm{н}}^{\mathrm{cp}}} - P_{\mathrm{н}}^{\mathrm{cp}} \right)\cdot t \cdot s_{\mathrm{э}} + E_{\mathrm{н}}\cdot K, \tag{5} \]

where \(H_g\) is the annual rate of depreciation charges for motors, taken to be \(10.2\%\) [9];

\[ K = C_g \cdot k_p \cdot k_t \]

— simultaneous capital investments (initial cost of the motor);

\[ C_g \]

— production cost of the motor;

\[ k_p = 1.05 \]

— coefficient taking into account the profit of the manufacturing enterprise;

\[ k_t = 1.1 \]

— coefficient taking into account installation and transportation costs;

\[ S_e = 0.01 \text{ rub}/\text{kW}\cdot\text{h} \]

— cost of 1 kW·h of energy losses [6];

\[ E_n = 0.2 \]

— normative coefficient of economic efficiency (corresponding to a payback period of 5 years) [6];

Substituting the known values of the quantities into equation (5), we find the dependence of the reduced costs as a function of time \(t\)

\[ Z^{\mathrm{sr}} = 9.48 + 0.0063\,t. \tag{6} \]

The annual reduced costs for the RS-52-4 motor, in accordance with equation (1), may be represented in the form

\[ Z^{\mathrm{rs}} = \frac{H_g}{100}K + \frac{H_k}{100}C_k + \left( \frac{P_n^{\mathrm{rs}}}{\eta_n^{\mathrm{rs}}} - P_n^{\mathrm{rs}} \right)tS_e + 0.005Q_c t S_e + E_n(K+C_k), \tag{7} \]

where

\[ C_k = Q_c s_k \]

— cost of the bank of static capacitors;

\[ s_k \]

— cost of 1 kvar of capacitors, including installation; at 380 V it is taken equal to 8.5 rub/kvar [10];

\[ H_k = 12.0\% \]

— annual depreciation rate for static capacitors [9];

\[ 0.005\ \text{kW}/\text{kvar} \]

— specific energy losses in the capacitors.

Substituting the known values of the quantities into equation (7), we find the dependence of the reduced costs as a function of time \(t\)

\[ Z^{\mathrm{rs}} = 45.1 + 0.0185\,t. \tag{8} \]

Fig. 1. Comparison of the annual calculated costs of the SRO-41-4 and RS-52-4 motors as a function of the number of operating hours per year. Solid lines correspond to operation of the motors being compared in the rated mode; dashed lines correspond to a power utilization factor \(k_z = 0.7\).

On the basis of equations (6) and (8), Fig. 1 presents the dependences of the variation of the annual calculated costs of the SRO-41-4 and

RS-52-4 as a function of time. From the relationships presented it follows that the SRO-41-4 motors, for any operating time per year, are more economical than the RS-52-4 motors. With the number of motor operating hours per year equal to \(t = 2000\) h, the annual saving proves to be

\[ \mathcal{E}=Z^{\mathrm{pc}}-Z^{\mathrm{cp}}=60.0\ \text{rubles/year}. \tag{9} \]

b) When the motors being compared operate with a utilization factor \(k_{\mathrm{e}}=0.7\)

For economic comparisons it is necessary to know the actual \(\eta\) and \(\cos\varphi\) of the motors corresponding to the specified operating mode. We assume that \(\eta\) and \(\cos\varphi\), compared with the rated mode, change only slightly, and take them equal to the rated values. Then, in accordance with equation (3), the power of the static capacitors is

\[ Q'_c=Q_c\cdot k_{\mathrm{e}}=7.1\ \text{kvar}. \tag{10} \]

When determining the annual reduced costs in this case, equations (5) and (7) may be used, taking into account that the magnitude of the energy losses in the motors decreases in proportion to \(k_{\mathrm{e}}\). Then

\[ Z^{\mathrm{cp}}_1=9.48+0.00441\,t, \]

\[ Z^{\mathrm{pc}}_1=36.8+0.0129\,t. \tag{11} \]

The relationships showing the variation of the reduced costs of the motors being compared as a function of time are presented in Fig. 1.

From an analysis of equations (11) it follows that, with a utilization factor \(k_{\mathrm{e}}=0.7\), the SRO-41-4 motors, for any operating time per year, are more economical than the RS-52-4 motors. At \(t=2000\) h the annual saving is

\[ \mathcal{E}_1=Z^{\mathrm{pc}}_1-Z^{\mathrm{cp}}_1=44.3\ \text{rubles/year}. \tag{12} \]

On the basis of the comparisons carried out, it may be concluded that it is expedient to replace ordinary synchronous reluctance motors with improved ones, since this yields a large economic effect.

Economic comparisons of SRO-41-4 and SO-51-4 motors

Since the motors being compared have different power factors, in the analysis the \(\cos\varphi^{\mathrm{cp}}\) of the SRO-41-4 synchronous reluctance motor must be increased to the value of \(\cos\varphi\) of the SO-51-4 synchronous motor.

a) When the motors being compared operate in the rated mode

The required power of the static capacitors in this case is determined by the equation

\[ Q_c=\frac{P^{\mathrm{cp}}_{\mathrm{n}}}{\eta^{\mathrm{cp}}_{\mathrm{n}}}\cdot \tg \varphi^{\mathrm{cp}}_{\mathrm{n}}=4.92\ \text{kvar}. \tag{13} \]

The annual reduced costs for the SRO-41-4 motor, in accordance with equation (1), may be represented in the form

\[ Z^{\mathrm{cp}}= \frac{H_y}{100}K+ \frac{H_k}{100}C_k+ \left( \frac{P^{\mathrm{cp}}_{\mathrm{n}}}{\eta^{\mathrm{cp}}_{\mathrm{n}}} - P^{\mathrm{cp}}_{\mathrm{n}} \right)s_{\mathrm{e}}t+ \]

\[ +\,0.005\,Q_c s_{\mathrm{e}}t+E_{\mathrm{n}}(K+C_k). \tag{14} \]

Substituting into equation (14) the values of the quantities determined above, we write the dependence of the reduced costs in the form

\[ З^{\mathrm{cp}} = 22{,}9 + 0{,}00655\,t. \tag{15} \]

The annual reduced costs for the SO-51-4 motor are determined by the equation

\[ З^{\mathrm{c}} = \frac{H_g}{100}K + \left( \frac{P^{\mathrm{c}}_{\mathrm{н}}}{\eta^{\mathrm{c}}_{\mathrm{н}}} - P^{\mathrm{c}}_{\mathrm{н}} \right)s_\mathrm{э}t + E_\mathrm{н}K, \tag{16} \]

or

\[ З^{\mathrm{c}} = 21{,}2 + 0{,}0082\,t. \tag{17} \]

Solving equations (15) and (17) jointly, we find that at \(t_p = 1030\) h the motors being compared are economically equivalent. The dependences of the annual reduced costs in accordance with equations (15), (17) are presented in Fig. 2. From the data presented it follows that, for

Fig. 2. Comparison of the annual costs of SRO-41-4 and SO-51-4 motors as a function of the number of hours of operation per year. Solid lines correspond to operation of the motors being compared in the rated mode; dashed lines correspond to a power utilization factor \(k_\mathrm{э}=0{,}7\).

a number of hours of operation per year \(t > 1030\), the improved s.r.m. are more economical in comparison with SO-51-4 motors. At \(t = 2000\) h, the annual saving is \(Э = З^{\mathrm{c}} - З^{\mathrm{cp}} = 1{,}6\) rubles/year.

b) When the motors being compared operate with a utilization factor \(k_\mathrm{э}=0{,}7\)

We assume that \(\eta\) and \(\cos\varphi\), in comparison with the rated mode, change only slightly and take them equal to the rated values. The power of the static capacitors in this case is determined by equation (13), taking into account the motor power utilization factor,

\[ Q'_c = Q_c \cdot k_\mathrm{э} = 3{,}44\ \text{kvar}. \tag{18} \]

When determining the annual reduced costs, we use equations (14) and (16), taking into account that the magnitude of energy losses in the motors decreases in proportion to \(k_\mathrm{э}\).

Then

\[ \begin{aligned} Z_{1}^{\mathrm{sr}} &= 18.7 + 0.00458\,t,\\ Z_{1}^{c} &= 21.2 + 0.00574\,t. \end{aligned} \tag{19} \]

It follows from equations (19) that, at a utilization factor \(k_{e}=0.7\), the SRO-41-4 motors are more economical than the SO-51-4 motors for any annual operating time. At \(t=2000\) h, the annual saving is \(E_{1}=Z_{1}^{c}-Z_{1}^{\mathrm{sr}}=4.8\) rubles/year. The dependences of the variation in annual reduced costs in accordance with equations (19) are presented in Fig. 2.

The economic comparisons carried out make it possible to conclude that it is expedient to use improved s.r.m. instead of synchronous motors of type SO in cases where the number of operating hours of the motors is not less than 1030 h.

Above, only economic comparisons of the motors under consideration have been carried out in monetary terms. Economic comparisons are only one of the elements of a techno-economic analysis. To choose the best solution, it is necessary to compare not only economic but also technical indicators: reliability, ease of operation, technical characteristics, etc.

Improved s.r.m. are technologically manufacturable, reliable, and as simple to operate as induction motors with a squirrel-cage rotor. At practically the same cost as induction motors, they possess the mechanical characteristics of synchronous motors; that is, their rotational speed does not depend on load and voltage, but is determined by the frequency of the supply network. The starting and start-up characteristics of s.r.m. are analogous to those of induction motors with a squirrel-cage rotor. All this indicates that improved s.r.m. can successfully compete with other types of synchronous machines in low- and medium-power drives (approximately up to 30 kW), where a synchronous rotational speed is required that is independent of load and voltage, or where several motors must rotate at identical speeds, independently of the load of each motor.

Conclusions

The techno-economic analysis carried out in this work has shown that improved s.r.m. are the most economical in comparison with ordinary s.r.m. Under certain conditions they can successfully compete with contactless synchronous motors of type SO. All this indicates the expediency of developing a series and introducing improved s.r.m. into production.

In the event that improved s.r.m. have weight and energy indicators close to those of induction motors, they will find wide application in various branches of industry.

LITERATURE

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