**4.2.1 Transformers**

Transformers are used in the distribution system in order to change the levels of voltage and current in the low voltage scales. These may also include the power and instrumentation transformers and Auto-Boosters. In transformers, both the core and the wires are sensitive to the change of the power KPI. The harmonics have the following different effects on transformers.

*Transformer loss*, which is obtained as in equation 8:

$$P\_T = P\_N + P\_{\perp\perp} \tag{8}$$

In equation 8, *PN* is the "no-load" loss and *PLL* is the "full-load" loss. The no-load loss depends on the voltage and core material. The full load loss is defined as in equation 9:

$$P\_{\rm LL} = P\_{\rm DC} + P\_{\rm EC} + P\_{\rm OSl} \tag{9}$$

In equation 9, *PDC* is the DC resistance loss, *PEC* is the eddy current loss and *POSL* is the stray loss. Eddy current, which is proportional to the square of frequency, is caused by skin effect and proximity effect. Therefore, the current harmonics increase the eddy current loss dramatically. This increase results in the increase in temperature and hence reducing the transformer lifetime (Ashok).

*Lifetime* of a transformer depends on the functioning situations such as loading percentage and functioning temperature. Current harmonic components can increase the RMS value of

<sup>1</sup> Root Mean Square

Stochastic Analysis of the Effect of Using Harmonic Generators in Power Systems 203

Electronic devices including the automation or control devices and the equipments that are used for stabilizing the power systems such as PLC transmitters and RTU equipment. As the electronic devices are used for transmitting and receiving data, high frequency current can cause disorders in their functioning, such as increased noise level in communication systems. Such devices are usually installed close to power system equipment such as

Control and protection system, such as fuses, relays and circuit breakers, which control or guard the power systems. Current harmonics in the system may cause pre-heating in the fuse and problems in its function. Fuses may also be affected by the skin effect and the resulting heat may cause their malfunctioning. In circuit breakers, which work based on *di/dt*, current harmonics may cause unexpected faults. Here, the peak factor is important as well. The solenoids may also be damaged because of the harmonics. Delay in solenoid's functioning may cause sparks and damage. Vacuum circuit breakers are less sensitive to the harmonics. For relays, changes in the zero point may case improper functioning. These effects must be identified via practical experiments. Some manufacturers have presented

The consumer side equipments are classified into three different categories (Gowan, 2006):

Electric machines which are inductive devices and as confirmed by simulation using them together with electronic devices can improve the power quality indicators. The *nth* current

*n*

*n*

2 1.5 21 *n*

*<sup>T</sup> <sup>E</sup> <sup>k</sup> <sup>T</sup> S E* . *Ts* is the torque, *Er* is efficiency and *Sr* is the slippage (Schneider

The heat generated by the harmonics may cause decreasing the motor lifetime. In addition, the eddy currents can generate heat in the motors, similar to the transformers. The heat generation is almost the same in synchronous and asynchronous motors. In the case when all incandescent lamps are replaced by CFLs, the performance of induction motors will be between 5 and 15 percent (Vapopoulos, 1964). For the asynchronous motors, IEC60892

*<sup>n</sup> <sup>f</sup> <sup>L</sup>* (12)

(13)

*n*

*h nr <sup>V</sup> P P kP n V*

*<sup>V</sup> <sup>I</sup>*

In equation 12, *Vn* is the *nth* voltage harmonic and *Ln* is the inductance in *nth* harmonic (Markiewicz et al., 2004). *Ln* increases because of the skin effect. Power loss of electric

**4.2.3 Electronic devices:** 

**4.2.4 Control and protection systems** 

"harmonic adaptive" models (Ashok).

**4.3 Equipment on the consumer side** 

motors is obtained from equation 13:

*r r r*

standard is defined as in equation 14:

component of an electric machine is obtained as in equation 12:

**4.3.1 Electric machines** 

where (1 )(1 ) *<sup>s</sup>*

2010).

transformers.

the current and consequently the resistive power loss. The heat also remains in the surrounding air and affects the transformer lifetime. In the delta-wye connections in the transformers, the harmonic components of current start rotating in the wye side and cause heat generation and reduce transformer capacity. This occurs for the 3rd, 9th and 15th harmonic components. The current harmonics also cause saturation of the transformer.

In order to control the effect of current harmonics on transformers and electromotors, it is recommended not to have a current harmonic component more than 5% of the transformer's nominal current in the ANSI/IEEE C57.12.00-2000 and IEC60076 standards (Sadati et al., 2008). The K-Factor, which is defined in equation 10, identifies the relation between transformer design and increase in the electronic devices.

Fig. 8. Comparing different losses in the transformer core.

$$K - Factor = \sum\_{h=1}^{n} I\_h (ph)^2 h^2 \tag{10}$$

In equation 10, *h* is the harmonic order and *Ih* is its current component in per unit. The definition of K-Factor may be different in different standards. For example, in BS7821 standard it is defined as in equation 11.

$$K - Factor = \left[ 1 + \frac{e}{1 + e} \left( \frac{I\_1}{I} \right)^2 \sum\_{n=2} \left( n^q \left( \frac{I\_n}{I\_1} \right)^2 \right) \right]^{0.5} \tag{11}$$

#### **4.2.2 Transmission systems**

Transmission systems include power cables and wires. Transmitters are the conductors which are used in power system. Because of the skin effect (Hightech), the resistance of conductors increases with the increase of frequency. Because of the small high frequency components of the electronic devices, using these devices has a small effect on the conductors. Simulations show that the current amplitude for a sample CFL in frequencies between 1000 and 1500 Hertz (harmonics 20th to 30th) is less than 1% of the nominal value. Therefore, capacity reduction of cables and wires will be between 1% and 6% of conductor capacity in the worst case (100% replacement) (Vapopoulos, 1964).

#### **4.2.3 Electronic devices:**

202 Power Quality Harmonics Analysis and Real Measurements Data

the current and consequently the resistive power loss. The heat also remains in the surrounding air and affects the transformer lifetime. In the delta-wye connections in the transformers, the harmonic components of current start rotating in the wye side and cause heat generation and reduce transformer capacity. This occurs for the 3rd, 9th and 15th harmonic components. The current harmonics also cause saturation of the transformer. In order to control the effect of current harmonics on transformers and electromotors, it is recommended not to have a current harmonic component more than 5% of the transformer's nominal current in the ANSI/IEEE C57.12.00-2000 and IEC60076 standards (Sadati et al., 2008). The K-Factor, which is defined in equation 10, identifies the relation between

2 2

0.5 <sup>2</sup> <sup>2</sup>

*q n*

<sup>2</sup> <sup>1</sup>

(10)

(11)

1 ( ) *<sup>h</sup> <sup>h</sup>*

1

Transmission systems include power cables and wires. Transmitters are the conductors which are used in power system. Because of the skin effect (Hightech), the resistance of conductors increases with the increase of frequency. Because of the small high frequency components of the electronic devices, using these devices has a small effect on the conductors. Simulations show that the current amplitude for a sample CFL in frequencies between 1000 and 1500 Hertz (harmonics 20th to 30th) is less than 1% of the nominal value. Therefore, capacity reduction of cables and wires will be between 1% and 6% of conductor

*n*

*eI I* 

1 1

capacity in the worst case (100% replacement) (Vapopoulos, 1964).

*eI I K Factor <sup>n</sup>*

*K Factor I ph h* 

In equation 10, *h* is the harmonic order and *Ih* is its current component in per unit. The definition of K-Factor may be different in different standards. For example, in BS7821

transformer design and increase in the electronic devices.

Fig. 8. Comparing different losses in the transformer core.

standard it is defined as in equation 11.

**4.2.2 Transmission systems** 

Electronic devices including the automation or control devices and the equipments that are used for stabilizing the power systems such as PLC transmitters and RTU equipment. As the electronic devices are used for transmitting and receiving data, high frequency current can cause disorders in their functioning, such as increased noise level in communication systems. Such devices are usually installed close to power system equipment such as transformers.

#### **4.2.4 Control and protection systems**

Control and protection system, such as fuses, relays and circuit breakers, which control or guard the power systems. Current harmonics in the system may cause pre-heating in the fuse and problems in its function. Fuses may also be affected by the skin effect and the resulting heat may cause their malfunctioning. In circuit breakers, which work based on *di/dt*, current harmonics may cause unexpected faults. Here, the peak factor is important as well. The solenoids may also be damaged because of the harmonics. Delay in solenoid's functioning may cause sparks and damage. Vacuum circuit breakers are less sensitive to the harmonics. For relays, changes in the zero point may case improper functioning. These effects must be identified via practical experiments. Some manufacturers have presented "harmonic adaptive" models (Ashok).

#### **4.3 Equipment on the consumer side**

The consumer side equipments are classified into three different categories (Gowan, 2006):

#### **4.3.1 Electric machines**

Electric machines which are inductive devices and as confirmed by simulation using them together with electronic devices can improve the power quality indicators. The *nth* current component of an electric machine is obtained as in equation 12:

*n n n <sup>V</sup> <sup>I</sup> <sup>n</sup> <sup>f</sup> <sup>L</sup>* (12)

In equation 12, *Vn* is the *nth* voltage harmonic and *Ln* is the inductance in *nth* harmonic (Markiewicz et al., 2004). *Ln* increases because of the skin effect. Power loss of electric motors is obtained from equation 13:

$$P\_h = \sum P\_u = kP\_r \Sigma \left(\frac{V\_u^2}{n^{1.5} \cdot V\_1^2}\right) \tag{13}$$

where (1 )(1 ) *<sup>s</sup> r r r <sup>T</sup> <sup>E</sup> <sup>k</sup> <sup>T</sup> S E* . *Ts* is the torque, *Er* is efficiency and *Sr* is the slippage (Schneider

2010).

The heat generated by the harmonics may cause decreasing the motor lifetime. In addition, the eddy currents can generate heat in the motors, similar to the transformers. The heat generation is almost the same in synchronous and asynchronous motors. In the case when all incandescent lamps are replaced by CFLs, the performance of induction motors will be between 5 and 15 percent (Vapopoulos, 1964). For the asynchronous motors, IEC60892 standard is defined as in equation 14:

Stochastic Analysis of the Effect of Using Harmonic Generators in Power Systems 205

Fig. 9. "Home" unit with two CFLs, two lamps and induction motor.

Fig. 10. "Office room" unit with four incandescent lamps, three PCs and a single phase

Fig. 10 shows a sample commercial (office) consumer unit.

asynchronous motor.

$$HVF = \sqrt{\sum\_{h=2}^{13} \frac{II\_h}{h^2}} \le 0.02\tag{14}$$

*Uh* is the harmonic voltage of order *h*.

#### **4.3.2 Measurement devices**

Measurement devices: such as electricity meters, current transformers, voltage transformers and electronic instrumentation. The measurement transformer error is calculated as:

$$\mathbf{K}\_f = \mathbf{C}V\mathbf{K}\_r\tag{15}$$

where *C* is the ratio of real ratio to actual ratio (for current transformers), *V* is the ratio of real ratio to actual ratio (for voltage transformers) and *Kp* is angle correction coefficient (Hightech). The same as in power station transformers, high frequency current harmonics result in early saturation of transformer core and error in measurement. Electronic devices which work based on the zero crossing may also be affected by wave shape distortion. Errors may occur while calculating voltage and current *rms* values. In the inductive electricity meters (Temple, 1998) the error may be more. Changes in power factor and the THD affect the operation of these equipments.

#### **4.3.3 Communication devices**

Most communication systems are equipped with filters to reduce the noise generated by high frequency components. As the harmonics above 1500 Hz are negligible in electronic devices, they will practically not affect the communication systems. Similarly they will not affect electronic devices on the consumer side. Some malfunction of printers is reported (Abbaspour et al., 2009). Multimedia devices and televisions may be affected when used in the presence of harmonics. Distortion may be introduced by either the harmonics or the electronic ballast frequencies. All such devices are equipped with electromagnetic filters (EMC) which remove such effects. Personal Computers are sensitive to a voltage distortion of more than 5%. However, the use of harmonic generating devices does not introduce more than 0.5% voltage THD.

As the CFL ballast circuits work in 40 KHz frequency, they may affect hospital devices. Some distortions are reported in the functioning of CT devices (Abyaneh, 2004). Also because of the type of the CFL light, it is not recommended in operation rooms. The most important quality parameters which are considered here are the total power use, total harmonic distortion and transformer eddy current loss and hysteresis effect. Different measurements can explain the effect of harmonics. Total harmonic distortion (THD) is defined in equation 1 (Chapman).

### **5. Simulating of power system**

In this section, we develop individual units of consumers developed, which are a certain combination of electric device models. These units are called with terms "home" and "office". These models are obtained using statistical data about different residential regions in Iran. In the simplest case, a home is a combination of four lighting loads and one induction motor. Fig. 9 shows this consumer unit simulated in Simulink (Mathworks).

13 <sup>2</sup> <sup>2</sup>

*h*

Measurement devices: such as electricity meters, current transformers, voltage transformers

where *C* is the ratio of real ratio to actual ratio (for current transformers), *V* is the ratio of real ratio to actual ratio (for voltage transformers) and *Kp* is angle correction coefficient (Hightech). The same as in power station transformers, high frequency current harmonics result in early saturation of transformer core and error in measurement. Electronic devices which work based on the zero crossing may also be affected by wave shape distortion. Errors may occur while calculating voltage and current *rms* values. In the inductive electricity meters (Temple, 1998) the error may be more. Changes in power factor and the

Most communication systems are equipped with filters to reduce the noise generated by high frequency components. As the harmonics above 1500 Hz are negligible in electronic devices, they will practically not affect the communication systems. Similarly they will not affect electronic devices on the consumer side. Some malfunction of printers is reported (Abbaspour et al., 2009). Multimedia devices and televisions may be affected when used in the presence of harmonics. Distortion may be introduced by either the harmonics or the electronic ballast frequencies. All such devices are equipped with electromagnetic filters (EMC) which remove such effects. Personal Computers are sensitive to a voltage distortion of more than 5%. However, the use of harmonic generating devices does not introduce more

As the CFL ballast circuits work in 40 KHz frequency, they may affect hospital devices. Some distortions are reported in the functioning of CT devices (Abyaneh, 2004). Also because of the type of the CFL light, it is not recommended in operation rooms. The most important quality parameters which are considered here are the total power use, total harmonic distortion and transformer eddy current loss and hysteresis effect. Different measurements can explain the effect of harmonics. Total harmonic distortion (THD) is

In this section, we develop individual units of consumers developed, which are a certain combination of electric device models. These units are called with terms "home" and "office". These models are obtained using statistical data about different residential regions in Iran. In the simplest case, a home is a combination of four lighting loads and one induction motor. Fig. 9 shows this consumer unit simulated in Simulink (Mathworks).

and electronic instrumentation. The measurement transformer error is calculated as:

*h <sup>U</sup> HVF*

*Uh* is the harmonic voltage of order *h*.

THD affect the operation of these equipments.

**4.3.3 Communication devices** 

than 0.5% voltage THD.

defined in equation 1 (Chapman).

**5. Simulating of power system** 

**4.3.2 Measurement devices** 

0.02 *<sup>h</sup>*

(14)

*K CVK f p* (15)

Fig. 9. "Home" unit with two CFLs, two lamps and induction motor.

Fig. 10 shows a sample commercial (office) consumer unit.

Fig. 10. "Office room" unit with four incandescent lamps, three PCs and a single phase asynchronous motor.

Stochastic Analysis of the Effect of Using Harmonic Generators in Power Systems 207

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support.

**8. References** 

Eddy current loss of transformer core depends on the squares of both current and frequency (Bird). Therefore, the core loss for different experiments is compared to each other using equation 16. *fh1* and *fh2* correspond to the frequency components of the different cases in comparison.

$$\text{Relative core loss} = \frac{\sum\_{k=1}^{N} f\_{k2}^{2} I\_{k2}^{2}}{\sum\_{k=1}^{N} f\_{k1}^{2} I\_{k1}^{2}} \tag{16}$$

A similar approach is used for the hysteresis effect. However, hysteresis effect comparison is obtained using equation 17 (Bird).

$$\text{Relative hysteresis} = \frac{\sum\_{h=1}^{N} f\_{h2} I\_{h2}^{1.6}}{\sum\_{h=1}^{N} f\_{h1} I\_{h1}^{1.6}} \tag{17}$$
