Chapter 13
Harmonic Summation for Multiple Arc
Furnaces
J. Wikston
13.1 Introduction
The IEEE Std. 519-1992 establishes limits for harmonic voltage and current levels at the
Point of Common Coupling (PCC). When estimating compliance to these limits for new or
expanding facilities with multiple time varying harmonic loads such as Electric Arc Furnaces
(EAFs) the summation of harmonics from the time varying loads becomes an important issue.
This chapter examines existing harmonic summation methods defined in IEC 61000-3-6 and
illustrates the application of these methods based on measured data from various EAF sites.
The science of harmonic simulation has advanced a great deal in the past two to three
decades. The problem of how to represent multiple harmonic sources and background harmonics
so that future levels can be predicted when expanding an existing facility or building a new
facility still represents a difficult task. When the loads are time varying loads such as Electric
Arc Furnaces (EAFs) the representation becomes even more complex. There are a few methods
of combining multiple sources:
1) Linear
2) Vector Sum
3) Root Sum of Squares (RSS)
4) Vector Sum Randomly Varying Phase
5) Linear Randomly Varying Magnitude
6) Vector Sum Random Phase & Magnitude
A linear combination gives the most pessimistic results of voltage distortion since you
assume that the current injections from multiple sources are all in phase. A vector sum is the
ideal method but requires information on the phase of the harmonics with respect to each other,
which is usually difficult to obtain. The RSS only requires magnitude information but assume
the square law correctly defines the combination due to phase angle differences, which is
sometimes conservative and sometimes pessimistic. The other three methods are statistical
methods that try to account for the phase angle and magnitude variations when not all the
information is known.
In the IEEE Std. 519-1992 “Recommended Practices and Requirements for Harmonic
Control in Electrical Power Systems” [1] there are tables for harmonic voltage and current limits
for recommended practices for utilities and consumers. However there is little guidance on how
to apply these limits in particular with regards to the method used for determining the harmonic
levels. If, for example, the loads did not vary with time and the system background harmonics
were constant then this would be a non-issue; however that is far from practical. Most loads vary
with time, and background harmonics also vary but to a lesser degree than some of the more
severe loads like EAFs. In The IEEE Std. 519-1992 a reference is made to “the values in the
table maybe exceeded for a one-hour period” even though it is not stated it can be assumed that
this is one hour per day. With this assumption the tables can then be viewed as values not to be
exceeded 95% of the time (23/24  95%). We round to 95% because IEC standards also refer to
values not exceeded 95% of the time to evaluate harmonic emissions. Also in Std. 519, there is a
cumulative probability function (CPF) illustrating the time varying nature of harmonic sources.
This CPF example introduced the concept of having to apply the tables against a value not to
exceed a certain percentage of the time. The other complication in applying the Std. 519 tables
is how to do the measurements: do you measure one cycle at a time or do you measure multiple
cycles? In [2] a measurement philosophy is described which overcomes this problem. The
measurement philosophy uses multiple cycles which allows inter-harmonics to be identified.
The technique has four different measurement intervals on which to evaluate harmonics; 200
milliseconds, 3 seconds, 10 minutes or 2 hours, with each interval being related by the following
equations:
H3s =  [( 1/15)*( H2200ms)]
H10min =  [( 1/200)*( H23s)]
H2hr =  [( 1/12)*( H210min)]
The IEC standards use the 10-minute interval for comparing the 95% CPF value as well
as the 3-second interval. The use of harmonic snapshots whether 200ms or 1 cycle to compare
to the CPF value is also commonly applied. In this chapter we focus on the combination of
harmonic currents from EAFs for instantaneous and the 10-minute intervals.
13.2 Harmonic Limits Used by IEC Standards
Figure 13.1 illustrates a disturbance immunity planning and compatibility level graph. In
the graph all disturbances are represented by a probability density function. Another, slightly
overlapping, probability density function represents equipment/user immunity levels.
As
illustrated in the graph, in a generic sense, some disturbances exceed the defined compatibility
level and some of the environment (equipment, people etc) may not be immune even at the
defined planning level. The defined planning and compatibility levels are chosen such that the
system is not over designed and to make best use of the economical investment in the system.
Figure 13.1
Compatibility levels for voltage harmonics in [3] are defined to be a THD of 5%, 8%, and
10% for equipment Class 1, 2, and 3 respectively. Class 1 applies to protected supplies and has
compatibility levels lower than public network. Class 2 applies to public networks. Class 3
applies to a point of common couple inside a facility, which meets certain requirements. These
compatibility values refer to continuous levels; time varying components may have higher
values. Reference [4] gives the following guidelines on how to apply the compatibility levels to
time varying harmonics.

The greatest 95% probability daily value of Vh,vs (rms value of the individual
harmonic component over “very short” 3s periods) should not exceed the planning
level.

The maximum weekly value of Vh,sh (rms value of the individual harmonic component
over “short” 10m periods) should not exceed the planning level.

The maximum weekly value of Vh,vs should not exceed 1.5 to 2 times the planning
level.
13.3 Harmonic Summation Techniques Used by IEC Standards
In [4] two methods for harmonic summation are presented. The first is a simple linear
combination of the magnitudes with a diversity factor.
This is used for the new voltage
distortion when connecting a new load and the existing background distortion is known. The
diversity factors depend on:

Type of load

Harmonic order

Size of the load versus system strength

Phase angle of background and new load
The second more generic law for both harmonic voltages and currents is as follows:
HTOTAL = (  Hmindividual )(1/m)
This equation is applied to each harmonic component of interest.
The following values for m are given in [4] for 95% non-exceeding probability values.
SUMMATION EXPONENTS FOR HARMONICS
M
Harmonic Order
1
h<5
1.4
5 < h < 10
2
h > 10
Note – When it is known that the harmonics are
likely to be in phase (i.e. phase angle difference
less than 90), then an exponent m = 1 should
be used for order 5 and above.
The exponent m depends mainly on two (2) factors:

The chosen value of the probability for the actual value not to exceed

The degree to which individual harmonic voltages/currents vary randomly in terms of
magnitude
13.4 Empirical Exponent Values for Multiply EAFs
The second law of harmonic summation for currents from EAF loads is the focus of this
chapter. The following tables illustrate the exponent, ratio of exponents, and ratio of values for
the 95% & 99% CPF values for snapshots and the 10-minute evaluation interval.
From Table 13.1-13.2, it can be seen that the recommended exponent value of 1.0 for orders less
than the fifth will result in too high of an estimate for harmonic current combination from
multiple EAFs.
TABLE 13.1 EXPONENTS AND RATIOS FOR HARMONIC SNAPSHOTS
Harmonic Order
2
4
6
3
5
7
Site 1
1.4
1.4
1.5
1.5
1.5
1.4
Exponent Site 2
1.5
1.4
1.5
1.5
1.3
1.3
95%
Site 3
1.7
1.6
1.5
1.5
1.3
1.2
Site 4
1.6
1.5
1.7
1.7
1.5
1.6
Average
1.5
1.5
1.5
1.5
1.4
1.4
Site 1
1.6
1.7
1.8
1.7
1.9
1.6
Exponent Site 2
1.8
1.9
2.0
1.8
1.3
1.4
99%
Site 3
2.0
1.9
1.6
1.7
1.5
1.4
Site 4
2.2
2.7
2.5
2.2
1.4
1.4
Average
1.9
2.0
2.0
1.8
1.5
1.4
Site 1
1.3
1.3
1.4
1.4
1.4
1.4
Ratio
Site 2
1.5
1.7
1.7
1.4
1.2
1.2
99%
Site 3
1.4
1.4
1.6
1.3
1.2
1.2
to
Site 4
1.6
1.6
1.6
1.4
1.3
1.3
95%
Average
1.5
1.5
1.6
1.4
1.3
1.3
Ratio
Site 1
1.1
1.2
1.2
1.1
1.3
1.2
Exponent Site 2
1.3
1.4
1.5
1.2
1.0
1.0
99%
Site 3
1.2
1.1
1.0
1.1
1.2
1.1
to
Site 4
1.3
1.8
1.7
1.3
0.9
0.9
95%
Average
1.2
1.3
1.3
1.2
1.1
1.1
TABLE 13.2 EXPONENTS AND RATIOS FOR HARMONIC 10-MINUTE INTERVAL
Harmonic Order
2
4
6
3
5
7
Site 1
1.4 1.4 1.6 1.4
1.5
1.3
Exponent Site 2
1.8 1.6 1.7 1.4
1.2
1.2
95%
Site 3
1.5 1.4 2.0 1.4
1.1
1.4
Site 4
2.4 2.0 1.8 1.7
1.3
1.4
Average
1.8 1.6 1.8 1.5
1.3
1.3
Site 1
1.4 1.4 1.6 1.7
1.9
1.5
Exponent Site 2
1.8 2.2 1.8 1.4
1.1
1.2
99%
Site 3
1.7 1.7 2.0 1.2
1.2
1.5
Site 4
1.8 2.9 2.4 1.5
1.1
1.2
Average
1.7 2.0 1.9 1.4
1.3
1.3
Site 1
1.2 1.1 1.1 1.2
1.2
1.2
Ratio
Site 2
1.2 1.3 1.3 1.1
1.1
1.1
99%
Site 3
1.0 1.1 1.1 1.1
1.0
1.0
to
Site 4
1.3 1.2 1.2 1.3
1.2
1.2
95%
Average
1.2 1.2 1.2 1.2
1.1
1.1
Ratio
Site 1
1.0 1.0 1.0 1.2
1.2
1.2
Exponent Site 2
1.0 1.4 1.1 1.0
0.9
1.0
99%
Site 3
1.1 1.2 1.0 0.9
1.0
1.0
to
Site 4
0.8 1.5 1.3 0.9
0.9
0.8
95%
Average
1.0 1.3 1.1 1.0
1.0
1.0
The values in the tables show that even harmonic components are less likely to combine
with an average exponent of 1.5, 1.7, 2.0, and 1.9 as compared to the odd order harmonic
components which had an average exponent of 1.4, 1.4, 1.6, and 1.4 for the 95% snapshot, 95%
10-minute, 99% snapshot, and 99% 10-minute respectively.
For the even harmonic components at 95% the 10 minute value are less likely to combine
than the snapshot values, since the 10 minute exponents have a higher average. For the odd
harmonic components the snapshot and 10 minute values have approximately the same average
exponent value.
For the even harmonic components at 99% the 10-minute and the snapshot have
approximately the same exponent value. For the odd harmonic components at 99% the snapshot
values are less likely to combine than the 10-minute values since the average exponent value is
higher.
The ratio of 99% to 95% values is high for even harmonic components as compared to
odd harmonic components with an average of 1.5 compared to 1.3 for the snapshot values and
1.2 compared to 1.1 for the 10-minute values.
13.5 Conclusions
The generic summation law is extremely useful since information about harmonic phase
angles is not required. The calibration of the exponents for different percentiles, measurement
intervals, odd/even components, and component order is required for loads with unique profiles
such as EAFs.
13.6 References
[1] IEEE Std. 519-1992 “Recommended Practices and Requirements for Harmonic Control in
Electrical Power Systems”
[2] IEC 61000-4-7, “Electromagnetic compatibility (EMC) – Part 4: Testing and measurement
techniques – Section 7: General guide on harmonics and interharmonics measurements and
instrumentation, for power supply systems and equipment connect thereto”, 1991-08. (Work
in Progress IEC 61000-4-7 Ed. 2.0 Stage Code CCDV).
[3] IEC 61000-2-4, “Environment – Section 4: Compatibility levels in industrial plants for low
frequency conducted disturbances”, 1994-02
[4] IEC 61000-3-6, “Limits – Section 6: Assessment of emission limits for distorting loads in
MV and HV power systems – Basic EMC publication”, 1996-10