**3. Voltage sag statistical indices**

For many years, electricity companies have used sustained interruption indices as indicators describing the quality and reliability of the services they provide. In order to compare power quality in different networks, regulators need to have common, standardised quality indices. The number of these indices should be kept at a minimum, easy to assess, and be representative of the disturbance they characterise. This section briefly discusses various voltage sag indices proposed by electrical association organisations and indices suggested by recent researchers. These indices are used to characterise any voltage sag, according to the individual index point of view. The procedure to evaluate the quality of supply, reference to non-rectangular events and equipment compatibility issues are also discussed.

#### **3.1 Types of indices**

Any available voltage sag index can be classified within the following three categories (Bollen, 2000).


Power Quality and Voltage Sag Indices in Electrical Power Systems 143

Canadian utilities have retained 2-min heating time constant to assess the factor related to overvoltages and undervoltages. This factor is measured over 10 min intervals (5x2 min). The most-commonly used single event indices for voltage dips are ''retained voltage'' and ''duration''. It is recommended to only use the rms voltage as a function of time, or the magnitude of the characteristic voltage for three-phase measurements, to calculate the duration. Using the characteristic voltage magnitude versus time, the retained voltage and

The basic measurement of a voltage dip and swell is URMS (1/2) on each measurement channel. Where URMS (1/2) is defined as the value of the RMS voltage measured over one

A voltage sag begins when the URMS (1/2) voltage falls below the dip threshold, and ends when the URMS (1/2) voltage is equal to or above the dip threshold plus the hysterisis voltage(Polycarpou, A. et al., 2004). The retained voltage is the smallest URMS (1/2) value

The duration of a voltage dip is the time difference between the beginning and the end. Voltage sags may not be rectangular. Thus, for a given voltage sag, the duration is

The user can define the sag threshold value either as a percentage of the nominal, rated voltage, or as a percentage of pre-event voltage. For measurements close to equipment terminals and at distribution voltage levels, it is recommended to use the nominal value (Bollen, 2001). At transmission voltages, the pre-event voltage may be used as a

The choice of threshold obviously affects the retained voltage in per cent or per unit. The choice of threshold may also affect the measurement of the duration for voltage dips with a slow recovery. These events occur due to motor starting, transformer energizing, post-fault

The voltage sag starts when the RMS voltage URMS (1/2) , drops below the threshold in at least one of the channels, and ends when the RMS voltage recovers above the threshold in all channels. The retained voltage for a multi-channel measurement is the lowest RMS

Several methods have been investigated leading to a single index for each event. Although this leads to higher loss of information, it simplifies the comparison of events, sites and systems. The general drawback of any single-index method is that the result no longer

directly relates to equipment behaviour. Single indices are briefly described below.

The loss of voltage "LV" is defined as the integral of the voltage drop during the event.

The loss of energy "LE" is defined as the integral of the drop in energy during the event:

{1 ( )} *L v t dt <sup>V</sup>* = − (1)

c. Electrical apparatus with a heating time constant exceeding 24 min.

cycle and refreshed each half cycle (Polycarpou et al., 2004).

duration can be obtained as follows.

**3.3.1 For single-phase measurements** 

dependent on a predefined threshold sag value.

motor recovery, and post-fault transformer saturation.

**3.3.2 For multi-channel three phase measurement** 

measured during the dip.

voltage in any of the channels.

Loss of Voltage:

Loss of Energy:

reference.

The procedure to evaluate the power systems performance regarding voltage sag is as follows (Bollen, 2000).


Each step mentioned above is discussed in the following parts of this chapter, with more detail given on the steps involving the various index types. Step 1 is not discussed at all since it simply represents the procedure to obtain voltage samples for every event with a certain sampling rate and resolution.

#### **3.2 Event characteristics**

From the sampled voltages, the characteristic voltage magnitude as a function of time can be obtained. Methods to accomplish this, using three phase measurements are (Bollen & Styvaktakis, 2000):


#### **3.3 Single event indices**

From the event characteristics as a function of time, a number of indices are determined that describe the event. For some applications the phase angle at which the sag begins is important and called 'point on wave of dip initiation'. Using the concept of point on wave the exact beginning of the voltage dip can be identified (Bollen, 2001). In addition the point on wave of voltage recovery allows precise calculation of the sag duration. The maximum phase shift can be obtained from the voltage characteristic versus time and can be used for accurate phase-angle jump calculation. The maximum slew rate, and zero sequence voltage are mentioned as potential single event indices. The Canadian electrical association uses two approved quality indices: RMS Overvoltage (RMSO) and Undervoltage (RMSU) (Bergeron,R., 1998). The indices are assessed over intervals equal to the time needed for equipment to reach its steady-state temperature. The heating time constant, which varies with the size and nature of the equipment, has been divided into three classes:


c. Electrical apparatus with a heating time constant exceeding 24 min.

Canadian utilities have retained 2-min heating time constant to assess the factor related to overvoltages and undervoltages. This factor is measured over 10 min intervals (5x2 min).

The most-commonly used single event indices for voltage dips are ''retained voltage'' and ''duration''. It is recommended to only use the rms voltage as a function of time, or the magnitude of the characteristic voltage for three-phase measurements, to calculate the duration. Using the characteristic voltage magnitude versus time, the retained voltage and duration can be obtained as follows.

The basic measurement of a voltage dip and swell is URMS (1/2) on each measurement channel. Where URMS (1/2) is defined as the value of the RMS voltage measured over one cycle and refreshed each half cycle (Polycarpou et al., 2004).

### **3.3.1 For single-phase measurements**

142 Electrical Generation and Distribution Systems and Power Quality Disturbances

The procedure to evaluate the power systems performance regarding voltage sag is as

b. Step 2- Calculate event characteristics as a function of time, from the sampled voltages.

d. Step 4- Calculate site indices from the single-event indices of all events measured

e. Step 5- Calculate system indices from the site indices for all sites within a certain power

Each step mentioned above is discussed in the following parts of this chapter, with more detail given on the steps involving the various index types. Step 1 is not discussed at all since it simply represents the procedure to obtain voltage samples for every event with a

From the sampled voltages, the characteristic voltage magnitude as a function of time can be obtained. Methods to accomplish this, using three phase measurements are (Bollen &

a. Method of Symmetrical components: From the voltage magnitude and phase angle, a sag type is obtained along with the characteristic voltage, and Zero sequence voltage. The characteristic magnitude (the absolute value of the characteristic complex voltage) can be used to characterize three-phase unbalanced dips without loss of essential information. Using the characteristic magnitude and duration for three-phase unbalanced dips, corresponds to the existing classification (through magnitude and

b. Method based on six rms voltages: The procedure used in this method is to calculate the zero sequence component of the voltage and remove it from the phase voltages. The new phase to phase voltages can then be calculated. From the phase to phase voltages and the three phase voltages, the rms values can be calculated. The characteristic

From the event characteristics as a function of time, a number of indices are determined that describe the event. For some applications the phase angle at which the sag begins is important and called 'point on wave of dip initiation'. Using the concept of point on wave the exact beginning of the voltage dip can be identified (Bollen, 2001). In addition the point on wave of voltage recovery allows precise calculation of the sag duration. The maximum phase shift can be obtained from the voltage characteristic versus time and can be used for accurate phase-angle jump calculation. The maximum slew rate, and zero sequence voltage are mentioned as potential single event indices. The Canadian electrical association uses two approved quality indices: RMS Overvoltage (RMSO) and Undervoltage (RMSU) (Bergeron,R., 1998). The indices are assessed over intervals equal to the time needed for equipment to reach its steady-state temperature. The heating time constant, which varies

magnitude would then be the lowest of the six rms voltages.

with the size and nature of the equipment, has been divided into three classes:

b. Varistors and power electronics with a 2-min heating time constant.

a. Highly sensitive electronic systems with a heating time constant of less than 600 ms.

a. Step 1- Obtain sampled voltages with a certain sampling rate and resolution.

c. Step 3- Calculate single event indices from the event characteristics.

follows (Bollen, 2000).

system.

during a certain period of time.

certain sampling rate and resolution.

duration) for single-phase equipment.

**3.2 Event characteristics** 

**3.3 Single event indices** 

Styvaktakis, 2000):

A voltage sag begins when the URMS (1/2) voltage falls below the dip threshold, and ends when the URMS (1/2) voltage is equal to or above the dip threshold plus the hysterisis voltage(Polycarpou, A. et al., 2004). The retained voltage is the smallest URMS (1/2) value measured during the dip.

The duration of a voltage dip is the time difference between the beginning and the end. Voltage sags may not be rectangular. Thus, for a given voltage sag, the duration is dependent on a predefined threshold sag value.

The user can define the sag threshold value either as a percentage of the nominal, rated voltage, or as a percentage of pre-event voltage. For measurements close to equipment terminals and at distribution voltage levels, it is recommended to use the nominal value (Bollen, 2001). At transmission voltages, the pre-event voltage may be used as a reference.

The choice of threshold obviously affects the retained voltage in per cent or per unit. The choice of threshold may also affect the measurement of the duration for voltage dips with a slow recovery. These events occur due to motor starting, transformer energizing, post-fault motor recovery, and post-fault transformer saturation.

#### **3.3.2 For multi-channel three phase measurement**

The voltage sag starts when the RMS voltage URMS (1/2) , drops below the threshold in at least one of the channels, and ends when the RMS voltage recovers above the threshold in all channels. The retained voltage for a multi-channel measurement is the lowest RMS voltage in any of the channels.

Several methods have been investigated leading to a single index for each event. Although this leads to higher loss of information, it simplifies the comparison of events, sites and systems. The general drawback of any single-index method is that the result no longer directly relates to equipment behaviour. Single indices are briefly described below. Loss of Voltage:

The loss of voltage "LV" is defined as the integral of the voltage drop during the event.

$$L\_{\vee} = \int \{1 - \upsilon(t)\} dt \tag{1}$$

Loss of Energy:

The loss of energy "LE" is defined as the integral of the drop in energy during the event:

$$L\_{\mathbb{E}} = \int \{1 - \upsilon(t)^2\} dt \tag{2}$$

Power Quality and Voltage Sag Indices in Electrical Power Systems 145

**Event Number Magnitude (pu) Duration (s)**

The values of the table above are used with various types of scatter plot to illustrate the use

The CBEMA chart presents a scatter plot of the voltage magnitude and event duration for each RMS variation. The CBEMA group created the chart as a means to predict equipment mis-operation due to rms variations. An RMS variation event with a magnitude and duration that lies within the upper and lower limit of the CBEMA curve, has a high probability to cause mis-operation of the equipment connected to the monitored source. Observing Figure 1, the number of events which are below the lower limit of the CBEMA

Total Events: 12

**0.001 0.01 0.1 1 10 100 1000 Duration (seconds)**

Events Violating CBEMA Low er Curve: 7 Events Violating CBEMA Upper Curve: 0

**0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8**

**Voltage Magnitude (pu)**

Table 1. Voltage sag event characteristics

**a. CBEMA curve Scatter Plot** 

Fig. 1. The CBEMA curve scatter plot

of known curves in equipment compatibility studies.

curve is seven, giving a SAFRI-CBEMA of seven events.

1 0.694 0.25 2 0.459 0.1 3 0.772 0.033 4 0.47 0.133 5 0.545 0.483 6 0.831 0.067 7 0.828 0.05 8 0.891 0.067 9 0.008 0.067 10 0.721 0.067 11 0.684 0.033 12 0.763 0.033

Method proposed by R. S. Thalam, 2000, defines the energy of voltage sag as:

$$E\_{\mathbb{V}s} = (1 - V\_{\mu u})^2 \times t \tag{3}$$

Where t is the sag duration.

Method proposed by Thallam & Heydt, 2000: The concept of ''lost energy in a sag event'' is introduced, in such a way that the lost energy for events on the Computer Business Equipment Manufacturers Association (CBEMA) curve is constant for three-phase measurements. The lost energy is added for the three phases:

$$\mathcal{W}\_{\boldsymbol{a}} = \{1 - \frac{V\_{\boldsymbol{a}}}{V\_{\boldsymbol{a}} \text{nominal}}\}^{3.14} \times t \tag{4}$$

To include non-rectangular events an integral expression may again be used. The event severity index 'Se' is calculated from the event magnitude (in pu) and the event duration. Also essential for the method is the definition of a reference Curve.

$$S\_c = \frac{1 - V}{1 - V\_{ref}(d)}\tag{5}$$

Where ( ) *V d ref* is the event magnitude value of the reference curve for the same event duration. This method is illustrated by the use of the CBEMA and Information Technology Industry Council (ITIC) curves as reference curves. However the method is equally applicable with other curves.

#### **3.4 Site indices**

Usually the site indices have as inputs the retained voltage and duration of all sags recorded at a site over a given period. Available RMS Variation Indices for Single Sites are described below.

#### **3.4.1 SAFRI related index and curves**

The **SAFRI** index (System Average RMS Variation Frequency Index) relates how often the magnitude of a voltage sag is below a specified threshold. It is a power quality index which provides a rate of incidents, in this case voltage sags, for a system (Sabin, 2000).

**SARFI-X** corresponds to a count or rate of voltage sags, swell and interruptions below a voltage threshold. It is used to assess short duration rms variation events only.

**SARFI-Curve** corresponds to a rate of voltage sags below an equipment compatibility curve. For example **SARFI-CBEMA** considers voltage sags and interruptions that are not within the compatible region of the CBEMA curve.

Since curves like CBEMA do not limit the duration of a RMS variation event to 60 seconds, the SARFI-CBEMA curve is valid for events with a duration greater than ½ cycle. To demonstrate the use of this method the following table is assumed for a given site (Polycarpou et al., 2004).


Table 1. Voltage sag event characteristics

The values of the table above are used with various types of scatter plot to illustrate the use of known curves in equipment compatibility studies.

#### **a. CBEMA curve Scatter Plot**

144 Electrical Generation and Distribution Systems and Power Quality Disturbances

Method proposed by Thallam & Heydt, 2000: The concept of ''lost energy in a sag event'' is introduced, in such a way that the lost energy for events on the Computer Business Equipment Manufacturers Association (CBEMA) curve is constant for three-phase

> 3.14 {1 } nominal *a*

To include non-rectangular events an integral expression may again be used. The event severity index 'Se' is calculated from the event magnitude (in pu) and the event duration.

> 1 1 () *<sup>e</sup> ref*

Where ( ) *V d ref* is the event magnitude value of the reference curve for the same event duration. This method is illustrated by the use of the CBEMA and Information Technology Industry Council (ITIC) curves as reference curves. However the method is equally

Usually the site indices have as inputs the retained voltage and duration of all sags recorded at a site over a given period. Available RMS Variation Indices for Single Sites are described

The **SAFRI** index (System Average RMS Variation Frequency Index) relates how often the magnitude of a voltage sag is below a specified threshold. It is a power quality index which provides a rate of incidents, in this case voltage sags, for a system (Sabin,

**SARFI-X** corresponds to a count or rate of voltage sags, swell and interruptions below a

**SARFI-Curve** corresponds to a rate of voltage sags below an equipment compatibility curve. For example **SARFI-CBEMA** considers voltage sags and interruptions that are not

Since curves like CBEMA do not limit the duration of a RMS variation event to 60 seconds, the SARFI-CBEMA curve is valid for events with a duration greater than ½ cycle. To demonstrate the use of this method the following table is assumed for a given site

voltage threshold. It is used to assess short duration rms variation events only.

*V d*

*<sup>V</sup> <sup>S</sup>*

*a <sup>V</sup> W t*

Method proposed by R. S. Thalam, 2000, defines the energy of voltage sag as:

measurements. The lost energy is added for the three phases:

*a*

Also essential for the method is the definition of a reference Curve.

Where t is the sag duration.

applicable with other curves.

(Polycarpou et al., 2004).

**3.4.1 SAFRI related index and curves** 

within the compatible region of the CBEMA curve.

**3.4 Site indices** 

below.

2000).

<sup>2</sup> {1 ( ) } *L v t dt <sup>E</sup>* = − (2)

<sup>2</sup> (1 ) *E Vt Vs* =− × *pu* (3)

*<sup>V</sup>* = − <sup>×</sup> (4)

<sup>−</sup> <sup>=</sup> <sup>−</sup> (5)

The CBEMA chart presents a scatter plot of the voltage magnitude and event duration for each RMS variation. The CBEMA group created the chart as a means to predict equipment mis-operation due to rms variations. An RMS variation event with a magnitude and duration that lies within the upper and lower limit of the CBEMA curve, has a high probability to cause mis-operation of the equipment connected to the monitored source. Observing Figure 1, the number of events which are below the lower limit of the CBEMA curve is seven, giving a SAFRI-CBEMA of seven events.

Fig. 1. The CBEMA curve scatter plot

Power Quality and Voltage Sag Indices in Electrical Power Systems 147

severity. Observing the graph shown in Figure 4, there are 5 events per year where the voltage drops below 40% of nominal Voltage for 0.1 s or longer. Equally there are 5 events

device B

90% 80% 70% 60% 50% 40% 30% 20% 10%

**Voltage (pu)**

*VVV abc <sup>S</sup>* + + = − (6)

*VSEI* = Ε (7)

= Ε (8)

0s 0.2s 0.4s 0.6s 0.8s

**Sag duration (s)**

The advantage of this method is that equipment behavior can be directly compared with system performance, for a wide range of equipment. The disadvantage of the method is that a two-dimensional function is needed to describe the site. For comparison of different sites a

The method calculates a "sag score" from the voltage magnitudes in the three phases (Sabin,

This sag score is equal to the average voltage drop in the three phases. The larger the sag

A number of site indices can be calculated from the "voltage sag energy" (Thallam, 2000). The "Voltage Sag Energy Index" (VSEI) is the sum of the voltage sag energies for all events

The "Average Voltage Sag Energy Index" (AVSEI) is the average of the voltage sag energies

*AVSEI*

*i*

*N* <sup>=</sup>

3

*VS i* \_ *i*

\_ 1 1 *<sup>N</sup>*

*VS i*

1

per year where the voltage drops below 70% magnitude and 250 ms duration.

device A

5

smaller number of indices would be preferred.

score, the more severe the event is considered to be.

measured at a given site during a given period:

for all events measured at a given site during a given period:

10

**Number of Events**

Fig. 4. Voltage sag co-ordination chart

**3.4.2 Calculation methods** 

2000).

**a. Method used by Detroit Edison** 

**b. Method proposed by Thallam** 

25 15 20
