**2. Effect of voltage magnitude on motor power losses and motor reactive loads**

Voltage magnitude has a significant and different influence on motor loads and electric energy consumption, depending on types, nominal powers and load level (*p=PPN*) of motors. Data found in classic references (Fink, 1983) are almost identical to data from older references (Linders, 1972;), although they are not accurate enough for motors made after 1970. The main reason for disagreement is higher values of no-load current and more significant dependency of core losses on voltage magnitude for newer motors (U or T shape of magnetization curve). Data for loads less than 50% are not available in Fink (1983) and Hamer et al. (1997), although more than half of motors operate in these load regimes.

The influence of voltage magnitude on energy characteristics of standard induction motors (made after 1970.) is significant, as was affirmed by the author's research and verification (Kostic, 1998). It was also ascertained that the changing of energy characteristics is more significant for smaller motors. According to newer literature, efficiency () and power factor (*cos*) dependency on voltage value is more significant than was shown in standard literature.

The paper by Hamer et al. (1997) analyses the effects of voltage magnitude only on two motors (10HP and 100HP) and loads from 50-100%, and the results, and results are illustrated in Fig. 1. Results for standard efficiency motors, given in Fig. 1, are almost equal to the author's results (Kostic, 1998, 2010). A brief theoretical approach for determining dependency of power losses and reactive loads on voltage value will be presented, as well as proceedings for calculation and analysis of power losses and reactive loads on voltage value.

**Figure 1.** Efficiency versus load for various applied voltages in percent of its 460 V rating for a standard efficiency motor (10 HP and 50 HP)

### **2.1. Dependency of power losses and reactive loads on voltage value**

In order to determine total dependence of power losses on voltage, for the load range from no-load to full load, it is necessary to determine no-load power - voltage dependency, *P0(u)* :

$$P\_0(\mu) = P\_{Cu0}(\mu) + P\_{Fe}(\mu) + P\_{fw} \tag{1}$$

Where are

128 Induction Motors – Modelling and Control

This proposed has three parts:

alike.

**loads** 

(*cos*

literature.

Unbalance voltage can occur due to the presence of larger single-phase consumers or asymmetrical capacitor banks with damage or capacitors that are switched off due to the fuse burning only in one phase. Nowadays, the presence of higher harmonics in the supply voltage is ever more frequent due to the growth of consumers who are supplied through the rectifiers and inverters: regulated actuators, electrothermical consumers and consumers

The effect of a variation in supply voltage, wave-form or frequency on the motor's efficiency and power factor characteristics depends on the individual motor design. Typical variations of current, speed, power factor and efficiency with voltage for constant output power are given in Fink (1983). The usual characteristics of induction motors within the ±10% voltage band (*Un*±10%) are well known. These are included in corresponding table for typical 30- 100 kW, 1500 or 1800 1/min motors (Linders, 1972; Fink, 1983), but the effect of saturation has been largely neglected in these tables. However, it is the author's intent to show a

1. Study of the effect of voltage magnitude on motor losses and motor reactive loads,

**2. Effect of voltage magnitude on motor power losses and motor reactive** 

Voltage magnitude has a significant and different influence on motor loads and electric

motors. Data found in classic references (Fink, 1983) are almost identical to data from older references (Linders, 1972;), although they are not accurate enough for motors made after 1970. The main reason for disagreement is higher values of no-load current and more significant dependency of core losses on voltage magnitude for newer motors (U or T shape of magnetization curve). Data for loads less than 50% are not available in Fink (1983) and Hamer et al. (1997), although more than half of motors operate in these load regimes.

The influence of voltage magnitude on energy characteristics of standard induction motors (made after 1970.) is significant, as was affirmed by the author's research and verification (Kostic, 1998). It was also ascertained that the changing of energy characteristics is more

) dependency on voltage value is more significant than was shown in standard

The paper by Hamer et al. (1997) analyses the effects of voltage magnitude only on two motors (10HP and 100HP) and loads from 50-100%, and the results, and results are illustrated in Fig. 1. Results for standard efficiency motors, given in Fig. 1, are almost equal to the author's results (Kostic, 1998, 2010). A brief theoretical approach for determining dependency of power losses

significant for smaller motors. According to newer literature, efficiency (

*PN*) of

) and power factor

energy consumption, depending on types, nominal powers and load level (*p=P*

3. analysis of the effect of non sinusoidal voltages to the efficient energy use.

correlation between motor characteristics and voltage level.

2. analysis of the effect of unbalanced voltages, and

*PCu0* copper losses in no-load,

*PFe* core losses in no-load,

*PfW* friction and windage losses in no-load.

Load losses component (PLL) depend on relative load (*pL=PL/PN*) and relative voltage values (*u=U/UN*):

$$P\_{\gamma P} = P\_{LL,N} \cdot p^2 \text{ / } \text{u}^2\tag{2}$$

where are *PLL,N PCu,S+ PCu,R+ P,ad* - a load losses in a nominal regime (*PN, UN*), and *P,ad* are additional load losses. Load losses, *PLL,N*, can also be calculated as a difference of full load power losses (*P<sup>N</sup>*) and no-load power (*P0N*):

$$P\_{LL,N} = P\_{\gamma N} - P\_{0N} \tag{3}$$

Effects of Voltage Quality on Induction Motors' Efficient Energy Usage 131

<sup>102</sup> () () / *<sup>n</sup> qu qu q p u* (12)

*<sup>N</sup>*, so *Q1(u) Q0(u)* and *q1(u) q0(u)*, (Kostic, 1998,

*QN* and

*QN = Q1N - Q0N*). For calculating the

*qN* can

), power

2 2

), slip (*sN*) and the quotient of maximum and nominal torque (*Tm /TN*), and

For motors of nominal power 3kW, value of nominal reactive power is almost equal to no-

dependency *Pγ(u)* and *Q1(u)*, according to expressions (5) and (11), it is necessary to know: - no-load characteristic *I0(u)*, *Q0(u)*, *P0(u)* and *PFe(u)*, for the analyzed voltage range, - motor catalogue data: nominal power (*PN*), nominal current (*IN*), efficiency (

**2.2. Dependency of motor input power and reactive loads on voltage values** 

power loss is notable, especially for small motors and for lower loads *PLL /PN*.

**Figure 2.** Dependencies of motor input power and reactive loads on supply voltage

Dependencies of input power (*P1 /P1N* ) and reactive loads (*Q1 /P1N* ) versus relative voltage value (*U/UN* ), for PLL /PN 25%, 50%, 75% and 100%, for motors of nominal powers 1 kW, 10 kW and 100 kW, have been determined by the procedure described in chapter A; results are illustrated in the Fig. 2, (Kostic, 1998, 2010). Influence of voltage on reactive loads and

*Q*

2010). Expressions (11) and (12) are commonly in use. Instead of *QLN* and *qLN*,

be used if they are known or if they can be calculated (

or in per unit

factor (*cos*


load power (*Q1N Q0* ), because *QLN*

or in per unit (p =P / PN, p0 =P0 / P, and pLL,N =PLL,N / PN) as:

$$p\_{LL,N} = p\_{\gamma N} - p\_{0N} \tag{4}$$

Total load losses can be calculated in absolute values as:

$$P\_{\gamma}(p\_{\prime}u) = P\_0(u) + P\_{LL,N} \cdot p^2 \;/\; u^2 \tag{5}$$

or in per unit:

$$p\_{\gamma}(p\_{\prime}u) = p\_0(u) + p\_{LL,N} \cdot p^2 \nmid u^2 \tag{6}$$

In order to ascertain reactive loads *Q(u)* dependency, it is necessary to determine no-load reactive power versus voltage, in absolute values (*Q0(u)*):

$$\mathcal{Q}\_0(\mu) = \sqrt{3} \cdot \mathcal{U}\_0 I\_0(\mu) \cdot \sin \phi\_0 \approx \sqrt{3} \mathcal{U}\_0 I\_0(\mu) \tag{7}$$

Or in per unit values (*q0 (u) =Q0 /PN*), for the load range from no-load to full load

$$\eta\_0(\mu) = \frac{\sqrt{3} \cdot \mu\_0 i\_0(\mu)}{\eta\_N \cos \phi\_N} \tag{8}$$

In the rated regime are: efficiency, ηN=PN/P1N, and power factor, cosφN= PN/(√3·UNIN). Values of reactive power in the load branch, *QLN* and *qLN* are calculated from the quotient of maximum and nominal torque *Tm /TN*, as explained in Appendix, (Kostic, 1998, 2001):

$$Q\_{LN} = 0.5 \cdot P\_N \, / \, \text{( $T\_m / T\_N$ )}\tag{9}$$

or in per unit as:

$$q\_{LN} = 0.5 \, / \, \text{(\$T\_m\$ / T\_N\$)}\tag{10}$$

Equations (9) and (10) are obtained by the procedure given in the Appendix, gained from the equivalent Г-circuit of the induction machine (Kostic, 2001, 2010). Difference of nominal reactive power and no-load reactive power is a little bit less from calculated value of *QLN* and *qLN* because of reactive power reduction on magnetization branch *(q<sup>N</sup>* (0.01-0.10)*q0N*). Total reactive load is calculated in absolute values as:

$$Q\_1(u) = Q\_0(u) + Q\_{LN} \cdot p^2 \;/\; u^2. \tag{11}$$

or in per unit

130 Induction Motors – Modelling and Control

 *PCu,S+ PCu,R+ P*

*<sup>N</sup>*) and no-load power (*P0N*):

or in per unit (p =P / PN, p0 =P0 / P, and pLL,N =PLL,N / PN) as:

*LL N N N* , <sup>0</sup> *P PP*

Total load losses can be calculated in absolute values as:

reactive power versus voltage, in absolute values (*Q0(u)*):

*,ad* - a load losses in a nominal regime (*PN, UN*), and *P*

2 2

2 2

(5)

(6)

(8)

*q*

*<sup>N</sup>* (0.01-0.10)*q0N*).

(3)

(4)

(7)

additional load losses. Load losses, *PLL,N*, can also be calculated as a difference of full load

*LL N N N* , <sup>0</sup> *p pp* 

0 , (,) () / *LL N P pu P u P p u*

0 , (,) () / *LL N p pu p u p p u*

In order to ascertain reactive loads *Q(u)* dependency, it is necessary to determine no-load

<sup>0</sup> 00 0 00 *Q u UI u UI u* ( ) 3 ( ) sin 3 ( )

3 () ( ) cos *N N ui u*

In the rated regime are: efficiency, ηN=PN/P1N, and power factor, cosφN= PN/(√3·UNIN). Values of reactive power in the load branch, *QLN* and *qLN* are calculated from the quotient of

0.5 / ( / ) *Q P TT LN N m N* (9)

0.5 / ( / ) *LN m N q TT* (10)

Equations (9) and (10) are obtained by the procedure given in the Appendix, gained from the equivalent Г-circuit of the induction machine (Kostic, 2001, 2010). Difference of nominal reactive power and no-load reactive power is a little bit less from calculated value of *QLN*

2 2

1 0 () () / . *Qu Qu Q p u LN* (11)

maximum and nominal torque *Tm /TN*, as explained in Appendix, (Kostic, 1998, 2001):

Or in per unit values (*q0 (u) =Q0 /PN*), for the load range from no-load to full load

0

and *qLN* because of reactive power reduction on magnetization branch *(*

Total reactive load is calculated in absolute values as:

*q u*

0 0

*,ad* are

where are *PLL,N*

power losses (*P*

or in per unit:

or in per unit as:

$$\sigma\_1(\mu) = q\_0(\mu) + q\_{2\text{n}} \cdot p^2 \nmid \mu^2 \tag{12}$$

For motors of nominal power 3kW, value of nominal reactive power is almost equal to noload power (*Q1N Q0* ), because *QLN Q<sup>N</sup>*, so *Q1(u) Q0(u)* and *q1(u) q0(u)*, (Kostic, 1998, 2010). Expressions (11) and (12) are commonly in use. Instead of *QLN* and *qLN*, *QN* and *qN* can be used if they are known or if they can be calculated (*QN = Q1N - Q0N*). For calculating the dependency *Pγ(u)* and *Q1(u)*, according to expressions (5) and (11), it is necessary to know:


### **2.2. Dependency of motor input power and reactive loads on voltage values**

Dependencies of input power (*P1 /P1N* ) and reactive loads (*Q1 /P1N* ) versus relative voltage value (*U/UN* ), for PLL /PN 25%, 50%, 75% and 100%, for motors of nominal powers 1 kW, 10 kW and 100 kW, have been determined by the procedure described in chapter A; results are illustrated in the Fig. 2, (Kostic, 1998, 2010). Influence of voltage on reactive loads and power loss is notable, especially for small motors and for lower loads *PLL /PN*.

**Figure 2.** Dependencies of motor input power and reactive loads on supply voltage

Results of the author's research (Kostic, 1998, 2010) confirmed that there are significant possibilities for energy savings by setting voltage values within the voltage band (*Un*±5%), because more then 80% of induction motors, especially small and medium power (1 - 30 kW), operate at partial load (70%). Dependencies of power loss *P(u)* and reactive loads *Q1(u)* for motor of nominal power 2 MW, for *P1 /PN* 0% (no-load), 25%, 50%, 75% and 100% are given in Fig. 3, (Kostic et al., 2006 and Kostic, 2010).

Effects of Voltage Quality on Induction Motors' Efficient Energy Usage 133

*UN* 0.955-1.045, i.e. for *U* 6300V-6900V (*UN* = 6 600V), Fig. 4.


for the voltage range *U*

consumption network.

**Consumption objects**

change, Kostic et al. (2006).

 *Q1(U)Q1(UN)*,

**Figure 4.** Dependency of total power losses and reactive loads for own consumption

6.8 kV (1.03 *UN*) to 6.6 kV (*UN*) or 6.5 kV (0.985 *UN*) causes reduction of:

been determined and given in Table I, (Kostic et al., 2006, and Kostic, 2010).



As was shown in Kostic et al. (2006), application of this procedure causes reduction of the electric energy own consumption. Changing voltage value (regulation at own consumption transformers 1BT and 2BT, and at common consumption transformer OBT) from

Power losses addition reduction in the own consumption network for 42.4 kW and 54.7 kW, respectively, due to of the above mentioned of reactive loads' reduction in the own

According to values of reduced power losses, reactive loads and assumed operational plan of the thermal plant (estimated 6 000 h/years), savings in active and reactive energy have

Block 1 Motors 161 3 544 966 000 21 264 000 Block 1 Network 42 - 252 000 - Block 2 Motors 213 4 559 1 278 000 27 354 000 Block 2 Network 55 - 330 000 - **Total 471 8 103 2 826 000 48 618 000**

**Active Reactive Active Energy Reactive Energy [kW] [kvar] [kWh/year] [kvarh/year]**

**Load Reduction Consumption Energy Reduction**

**Table 1.** Reduction of the active and reactive energy own consumption of Power plant by voltage

**Figure 3.** Dependencies of power losses and reactive loads on supply voltage
