TRENDS IN POWER FACTOR CORRECTION WITH HARMONIC FILTERING

Copyright © 1991 IEEE

MALCOLM CAMERON, MEMBER IEEE
Universal Dynamics Ltd.
900 - 1441 Creekside Dr.,
Vancouver B.C. V6J 4V3

Abstract: Most papers on power system harmonics deal with one or more specific aspects of the subject: modeling, formulas, sizing of capacitors and reactors, and IEEE Standards. This paper presents an overview of the harmonics problem, and examines how utilities are beginning to interpret and apply harmonics standards. There is a concern that some utility standards go well beyond the IEEE guidelines, to the point of being unreasonable.

INTRODUCTION

In the last 60 years, the development of the rectifier and semiconductor technology has led to a variety of applications in all industries. Major applications include static power converters and drive systems. It has long been known that this equipment produces harmonics in the ac power system. With the increased use of capacitors for power factor correction, the risk of parallel resonance also increased. In the late 1970's it became evident that standards were needed to preserve the quality of the power system and limit noise on adjacent communication systems. In 1981 the IEEE introduced Standard-519 that addressed power system concerns and distortion limits. In 1988 an update was introduced that described how the ability of a power system to absorb harmonics should be split amongst individual users.

Many utilities have since developed their own standards. Most utilities have adhered closely to the IEEE guidelines but in some cases, the guidelines have been tightened. In particular, the telephone interference parameter or I*T product has become most difficult to satisfy.

We have now come full circle. We have recognized the problem, developed standards, and designed plants to meet the new standards. It is now time to evaluate the results. Are we achieving the desired results? Is it time to revise the limits to reflect technological advances in other fields, particularly communications?

STATIC CONVERTER THEORY

It can be shown that any periodic signal f(t) with period T can be expressed as a sum of sinusoidal signals as:

where:  = fundamental frequency (2_f__
= the hth harmonic order
= dc offset
= amplitude of hth harmonic
= phase angle of hth harmonic

It can also be shown that for an ideal rectifier, where rectangular waveshapes are assumed, the sinusoidal currents flowing in the ac power system have an order and magnitude of:

h = kq ± 1
Ih = I1/h
where: h = order of harmonic
k = 1,2,3.....
q = number of pulses in rectifier circuit
I1 = amplitude of fundamental current
Ih = amplitude of harmonic current

In practice, the harmonic amplitude is affected by the commutating reactance Xc and delay angle _. In addition, due to imbalances in the electrical system and firing circuits, some non-characteristic order harmonics may be present. Hence a 12-pulse rectifier will produce some 5th, 7th, 17th and 19th order harmonics but at a much lower amplitude than an equivalent 6-pulse rectifier. Typical values for harmonic analysis are shown in Table 1.

TABLE 1
HARMONIC CURRENTS OF TYPICAL RECTIFIERS

The kq+1 harmonics described above are positive sequence currents and the kq-1 harmonics are negative sequence currents. It should be noted here that there can also be some small triple, or kq-3, harmonics present in the system. These are zero sequence currents and are much more difficult to analyze because they involve a ground return path. Analysis of these currents is beyond the scope of this paper.

CIRCUIT THEORY

A power rectifier is considered to be a source of harmonics currents and is usually modeled as a constant current source. The One Line Diagram and the equivalent circuit of a simple system are shown below. For Chlor-Alkali and Chlorate plants the plant motor load is typically about 10% of the rectifier load. To simplify the calculations the motor load is ignored in the equivalent circuit.

The basic analysis proceeds as follows:

1) Calculate the circuit inductance and capacitance parameters from nameplate ratings and utility fault capacity. These parameters include the utility source inductance, Lu and the main transformer inductance Lt.

2) Calculate the equivalent impedance of each branch as a function of frequency.

3) Successively parallel the branch impedances to an equivalent Zh as seen by the current source.

4) For each injected harmonic current compute the resulting harmonic voltage generated as Vh=Zh*Ih.

5) For each harmonic voltage compute the harmonic current in each branch as Ih(branch)=Vh/Zh(branch).

6) For each harmonic current in each branch calculate the harmonic voltage across each element in the branch.

This method of analysis can easily be implemented on a computer spreadsheet.

PROBLEMS CAUSED BY HARMONICS

Harmonics can cause problems for utilities, industry and communication systems. Utility problems include:

- overheating of synchronous machines,
- malfunction of protection and control circuits,
- metering errors.

Industry must contend with these and other problems including:

- mechanical resonance on rotating equipment,
- damage to capacitor banks.

Communication systems are susceptible to:

- inductive coupling and interference with telephone lines,
- interference with radio and TV signals,
- damage to solid state devices.

IEEE STANDARD 519-1981

In 1981 the IEEE issued Standard 519-1981 entitled "IEEE Guide for Harmonic Control and Reactive Compensation of Static Power Converters". The Standard contained guidelines and recommended practices for line notch limits, voltage distortion limits, telephone influence limits, and flicker limits. The standard dealt only with cumulative effects and did not address the question of how the ability of a system to absorb harmonics should be distributed amongst individual users. The problem was addressed in 1988 with the "Update of Harmonic Standard IEEE 519". The standard describes two criteria to evaluate harmonic distortion. The first is a limitation in the harmonic current that a user can transmit into the utility system. The second is the quality of the voltage that the utility must furnish to the user. The interrelation of these criteria shows that the harmonic problem is a system and not a site problem.

The revised standard describes limits on voltage, current and telephone interference as summarized in Tables 2 to 4.

TABLE 2
HARMONIC VOLTAGE DISTORTION LIMIT
IN PERCENT OF RATED VOLTAGE

TABLE 3
MAXIMUM HARMONIC CURRENT DISTORTION
IN PERCENT OF LOAD FUNDAMENTAL

TABLE 4
BALANCED I*T GUIDELINES

In the tables, individual harmonic distortion or ID%, is defined as the harmonic current or voltage expressed as a percentage of the fundamental. Total harmonic distortion or THD% is defined as:

and
The I*T Product is defined as:

where I1and V1 are fundamental values and Th is the Telephone Influence Factor (TIF 1960 curves).

UTILITY STANDARDS

The application of harmonic standards varies greatly between countries and utilities. The standards do, however, generally fall into two categories:

- voltage and current distortion and telephone interference limits at the customer/power system interface without setting individual limits per customer.

- voltage and current distortion and telephone interference limits at the customer/power system interface with a load proportioned fixed allowance per customer.

CONFORMANCE STRATEGY

Refer once again to the equivalent circuit in Figure 1. It is obvious that we want to limit harmonic currents flowing into the source. As we cannot prevent the harmonic currents from being injected from the current source the only practical solutions are to:

- increase the source impedance by adding a line reactor.

- provide a low impedance path or sink for the injected harmonic currents.

The first solution is rarely used because the line reactor must be current rated for the full plant load.

The second approach is more attractive because a shunt capacitor bank will be required for power factor correction of the rectifier. The usual strategy is to divide the capacitors into several banks, add series reactors and series tune each bank to a different harmonic frequency. By providing a low impedance path for each injected harmonic current, the resulting harmonic voltage is minimized.

The equivalent circuit used for harmonic analysis will then be as shown in Figure 3. The method of analysis is unchanged.

The resulting impedance Zh as seen by the harmonic current source will resemble the plot shown in Figure 4.

As expected, the impedance is at a minimum at each of the 4 tuned frequencies. Note also that for each tuned filter there is a parallel resonance, or maximum impedance, below the filter frequency but above the next lowest tuned filter. This is caused by the interaction between the tuned filter and the power system. Above the tuned frequency the filter appears inductive as is the power system. hence there is no resonance. Below the tuned frequency however the filter appears capacitive and will resonate with the power system at some point below the tuned frequency.

This shows why it is not advisable to apply filters tuned to higher order harmonics and not to the lower orders. For example if an 11th order filter is installed without a 7th order filter, and if the resulting system resonated at the 7th harmonic, then even a small injected 7th harmonic current could cause very high 7th harmonic voltages. This in turn will cause a large, 7th order, oscillating current to flow between the 11th order filter and the power system.

Note in Figure 4 that not all the harmonic currents will be picked off by the 4 filters. There are two reasons for this:

- the tuned filters are usually tuned slightly below the harmonic frequency to ensure that the parallel resonance remains below the harmonic frequency. This is to guard against the tuned frequency and associated parallel resonant frequency shifting upward due to loss of capacitance resulting from blown fuses, manufacturing tolerances of capacitors and reactors, or an increase in power system fault capacity. This design precaution results in at least some of the lower order harmonics flowing into the power system.

- injected harmonic currents beyond the tuned filter frequencies will divide between the tuned filters and the power system depending on the relative impedances.

CASE STUDIES

The following three case studies are examples of application of the standards by selected utilities and industries. The examples have been chosen to illustrate some of the recent trends and consequences in the field of harmonic analysis.

Case 1: This case involves the design of harmonic filtering for a new Chlorate plant. The plant One Line Diagram is shown in Figure 5. The rectifier was a 12 pulse unit rated at 38 MVA with an 86% power factor. The motor load was approximately 3 MVA with an 80% power factor. Based on these loads a capacitor bank with an effective value of 9.9 MVAR was needed to raise the plant power factor to 95%. It was decided to distribute the capacitors among 4 filters tuned to the 5th, 7th, and 11th harmonics. The anticipated harmonic current characteristic of the rectifier is shown in Table 1.

This configuration easily satisfied the required harmonic voltage and current limits but could not meet the I*T limit established by the power utility. It was decided to increase the capacitor bank to 11.3 MVAR (96% power factor) and to add a fourth filter at the 13th harmonic. This design also failed to meet the utility limit for I*T. In view of the increasing cost of conformance, and the prospect of causing other problems with a power factor that was uncomfortably high, the owner finally managed to negotiate a slightly relaxed I*T level with the utility. When pressed for an explanation the utility simply pointed to other countries apparently using similar standards. Tables 5 to 7 compare recommended IEEE levels, utility limits, and actual levels achieved..

TABLE 5
HARMONIC VOLTAGE DISTORTION
IN PERCENT OF RATED VOLTAGE OF 138 kV

TABLE 6
MAXIMUM HARMONIC CURRENT DISTORTION
IN PERCENT OF LOAD FUNDAMENTAL AT 138 kV

TABLE 7
BALANCED I*T LEVELS
CATEGORY I

Case 2: This case involved the design of a new Chlorate Plant on an existing industrial site. To reduce capital cost, the rectifiers were specified with a 69 kV incoming voltage as shown on the One Line Diagram in Figure 6. In order to provide power factor correction a 13.8 kV tertiary winding was provided in the transformer portion of the rectifier. Plant auxiliary power was provided from an existing 13.8 kV service within the plant. The utility guidelines specified a maximum voltage THD of 1.5% and a balanced I*T product of 5000.

A normal design would call for the insertion of a reactor in series with the capacitor bank to tune the branch to the desired harmonic. With a three winding transformer, however, there is already a reactance in series with the capacitor bank. Refer to the partial equivalent circuit shown in Figure 7. In this case the reactance was large enough to tune the branch to well below the 5th harmonic. It was therefore impossible to provide filters at the desired harmonic frequency.

Without tuned filters this installation was able to meet the utility limits for voltage distortion. The calculated I*T product, however, was about 20,000. As this level is still in the gray area of the IEEE standards, the utility approved the installation on condition that the owner mitigate any problems that may occur as a result of the high I*T product. If mitigation is required, the owner will install a 69 kV line reactor.

Case 3: This case involves the operation of two Chlorate plants on the same site, each with their own harmonic filtering. Refer to the One Line Diagram shown in Figure 8 and the equivalent circuit for analysis shown in Figure 9.

During re-energization following a plant outage, it was noticed that several fuses were blown on the 1.5 MVAR capacitor bank that was tuned to the 5th harmonic. In order to test the capacitors and replace the fuses, the plant electrician decided to disconnect the 5th filter and energize the 5th and 11th filters only. A few hours later the reactor on the 11th filter began to visibly overheat. Suspecting a serious problem, the electrician decided to de-energize the rectifier and its associated filter bank and refer the problem to an electrical engineer.

The preliminary investigation revealed that by removing the 5th filter bank, the parallel resonance of the system, as seen by the rectifier current source, was shifted to almost exactly the 5th harmonic. Refer to Figure 10. The resulting 5th harmonic voltage caused large 5th harmonic currents to flow in the 7th and 11th filters. The 11th filter suffered more damage because it was the larger of the two banks and its impedance to the 5th harmonic voltage was less than that of the 7th filter.

This case illustrates the complexity of the harmonic problem where there are multiple harmonic current sources. The system must be analyzed for each current source in order to determine the impedance seen by the current source, and the distribution of harmonic currents injected by the source. The filter bank designer must be aware that the filter may to sink harmonic currents from remote, as well as local current sources. The case also illustrates the inter-dependence of the harmonic problem. Changes in one part of the system may affect the operation of the other.

In this case the detailed investigation did not indicate a harmonic problem. The subsequent installation of a harmonic analyzer confirmed this finding. It was concluded that the original damage to the 5th filter was caused by a poorly maintained breaker which allowed restriking to occur during opening. Following a breaker overhaul and reactor replacement the system was re-energized without further incident.

CONCLUSIONS

1) Utilities are beginning to apply harmonic limits which are much lower than the IEEE guidelines. The notion that a single set of standards should apply to all customers unnecessarily penalizes large industrial plants. In most cases the voltage and current distortion factors are easily satisfied but the I*T product is almost impossible to satisfy. In view of the recent technological advances in the communications field it is time to reassess the problem of telephone interference. Mitigation costs on the power side are rising while those on the communication side are falling.

2) Some utilities have taken a more reasonable approach whereby a potential problem involving telephone interference is identified but mitigation is applied only if the level of communication service is, in fact, deteriorated.

3) Rectifiers fed at high primary voltage and those containing three-winding transformers may present special problems with respect to harmonics.

4) The harmonic problem is a dynamic one that should be re-examined whenever a major change occurs to the system. Plant personnel should be better educated regarding the principles and potential problems associated with harmonics.

REFERENCES

[1] IEEE Guide for Harmonic Control and Reactive Compensation for Static Power Converters, IEEE Standard 519-1981, New York, 1981.

[2] C. K. Duffey and R. P. Stratford, "Update of Harmonic Standard IEEE-519, IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems", Conference Record IAS/IEEE, PCIC, 1988, pp. 249-256.

[3] D. A. Gonzalez and John C. McCall, "Design of Filters to Reduce Harmonic Distortion in Industrial Power Systems", Conference Record IAS/IEEE, 1985, pp. 361-368.

[4] D. F. Miller, "Application Guide for Shunt Capacitors on Industrial Distribution Systems at Medium Voltage Levels", IEEE Transactions on Industry Applications, Vol. IA-12, No. 5, September/October 1976, pp. 444-459.

[5] A. H. Moore, "Application of Power Capacitors to Electrochemical Rectifier Systems", IEEE Transactions on Industry Applications, Vol. IA-13, No. 5, September/October 1977, pp. 399-406.

[6] R. P. Stratford, "Analysis and Control of Harmonic Current in Systems with Static Power Converters", IEEE Transactions on Industry Applications, Vol. IA-17, No. 1, January/February 1981, pp. 71-81.

[7] Canadian Electrical Association, "Report No. 415 U 474, Power System Harmonics - A Review and Assessment of Problems", Vol. 1, Montreal, Quebec, 1986.