6- Fundamentals of Harmonics

Joint MSc in Electrical Engineering (JMEE) Program

6878- Power Quality Quality and Standard Standardss for Microgrids Microgrids

Fundamentals of Harmonics

Dr. Fouad Zaro Electric Power System Engineering Palestine Polytechnic University 

Harmonic Distortion •

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Harmonics take place in steady state and are integer multiples of the fundamental frequency. The waveform distortion that produces the harmonics is continuously present or at least for several seconds.

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load . Usually, harmonics are associated with the continuous operation of a load.

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Harmonic distortion is caused by nonlinear devices in the distribution system.

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A nonlinear device is defined as the one in which the current is not proportional to the applied voltage. In a distribution system, most nonlinearities can be found in its shunt elements, that is, loads. harmonics study, it is customary to treat these harmonic-generating loads simply generatorss as harmonic current sources, that is, harmonic current generator

Harmonics Cause •

Extra power losses in  –

distribution transformers,

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feeders,

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motors.

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Interference Interfer ence in communication circuits.

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Resonance in power systems.

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Abnormal operations of protection and control equipment.

Distribution Factors •

Total Harmonic Distortion (THD) where V h is the harmonic voltag voltage e at harmonic frequency “h” in rms V 1 is the rated fundamental voltage in rms fundamental)) h is the harmonic order ( h = 1 corresponds to the fundamental • • •

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For balanced three-phase voltages, the line-to-neutral voltage is used to find THDv. in the unbalanced case, it is necessary to calculate a different THD for each phase.

where Ih is the harmonic current at harmonic frequency “h “ h” in rms I1 is the rated fundamental current in rms • •

The rms rms volt voltage age and curren currentt

Total Demand Distortion (TDD) •

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The current THD definition causes some confusion because there is a nonlinear relationship relation ship between the magnitude magnitude of the harmonic components components and percent percent THD. a waveform with 120% does not contain twice the harmonic components of a waveform with 60% distortion. a small current may have a high THD but not be a significant threat to the system. This difficulty may be avoided by referring THD to the fundamental of the peak demand current rather than the fundamental of the present sample. This is called total demand distortion (TDD) and serves as the basis for the guidelines in IEEE Std. 519-1992. Therefore, where

I L is the maximum demand

Active (Real) and Reactive Power The real power is defined as

The average

The reactive power is defined as

Apparent Power

where S1 is the apparent power at the fundamental frequency.

Power Factor •

For purely sinusoidal voltage and current, the average power (or true average active power) θ  is

the power factor (PF) cos

For the sake of simplicity

This PF is now called the displacement power factor (DF). Also,

Power Factor For the nonsin nonsinusoid usoidal al case

Note that here, the Vh and Ih quantities are the peak quantities:

Therefore, because of harmonic distortion,

Dist Di stor orti tion on Vol Volta tamp mper eres es (D (D))

True Power Factor (TPF) •

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D represents all cross products of voltage and current at different frequencies, which yield no average power.

Since the PF is a measure of the power utilization efficiency of the load,

where  DF = P/S1 is the displacement power factor  DPF is the distortion power factor

True Power Factor (TPF) •

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The unity PF is attainable only with pure sinusoids. What is actually provide provided d is the displacement displace ment PF. PF. Power quality monitoring instruments now commonly report both the displacement factors as well as the TPFs. The displacement factor factor is typically used in determining PF adjustments on a utility bill since it is related to the displacement of the fundamental voltage and current. sizing capacitors for PF correction is no longer simple. It is not possible to get unity PF due to the distortion power presence. Capacitors basically compensate only for the fundamental frequency reactive power and cannot completely correct the TPF to unity when there are harmonics present. In fact, capacitors can make the PF worse by creating resonance conditions that magnify the harmonic distortion. distortion.

Example Based on the output of a harmonic analyzer, it has been determined that a nonlinear load has a total rms curren currentt of 75 A. It also has 38, 21, 4.6, and 3.5 A for the third, fifth, seventh, and ninth harmonic currents, respectively. The instrument used in has been programmed to present the resulting data in amps rather than in percentages. Based on the given information, determine the following: a.

The Th e fun funda dame ment ntal al cu curr rren entt in in amp ampss

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The amounts amounts of of the third, third, fifth, fifth, seven seventh, th, and ninth ninth harmon harmonic ic currents currents in in percenta percentages ges

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The am amount of of th the TH THD

Example Cont d ’

b.

Or

IEEE Std. 519

Example A 4.16 kV three-phase feeder is supplying a purely resistive load of 5400 kVA. It has been determined that there are 175 V of zero-sequence third harmonic and 75 V of negative-sequence fifth harmonic. Determine the following: a.

The Th e tot total al vo volt ltag age e dis disto tort rtio ion. n.

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Is the THD below below the the IEEE IEEE Std. Std. 519-1992 519-1992 for the 4.16 4.16 kV dist distribu ribution tion syst system? em?

Solution (a)

(b)

the THDV limit for 4.16 kV is 5%. Since the THD calculated is 4.58%, it is less than the limit of 5% recommended by IEEE Std. 519-1992 for 4.16 kV distribu distribution tion systems.

Power in Passive Elements A. Po Powe werr in a Pur Pure e Resis Resista tance nce Real (or active) power dissipated in a resistor is given by

where Rh is the resistance at the hth har harmon monic. ic.

If the resistance is assumed to be constant, that is, ignoring the skin effect, then , where

A. Power in a Pure Resistance

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Cont ’d

Alternatively, expressed in terms of current, , where

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Note that the aforemention aforementioned ed equations can be re-expressed re-expressed in pu as

where P is the total power loss in the resistance P1 is the power loss in the resistance at the fundament fundamental al frequency •

For a purely resistive resistive element  element , it can be observed from  =    1 +    =    1 +   

That

B. Power in a Pure Inductance •

Power in a pure inductance can be expressed as

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Where   is the fundamental frequency

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Thus

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So that

  = 2 ℎ   

C. Power in a Pure Capacitance •

Power in a pure capacitance can be expressed as

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The negative sign indicates that the reactive power is delivered to the load

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Thus

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Hence

Harmonic Distortion Limits •

IEEE Std. 519-1992 is entitled Recommended Practices and Requirements  for Harmonic Harmonic Control in Electric Electric Power Systems Systems.  –

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gives the recommended practice for electric power system designers to control the harmonic distortion that might otherwise determine electric power quality. a guideline in the design of power system with nonlinear loads. The limits set are for steady-state operation and are recommended for “worsecase” conditions. The underlying philosophy is that the customer should limit harmonic currents and the electric utility should limit harmonic voltages. It does not specify the highest-order harmonics to be limited. it does not differentiate between single-phase and three-phase systems. Thus, the recommended harmonic limits equally apply to both. It does also address direct current that is not a harmonic.

Voltage Distortion Limits

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The PCC is the location where another customer can be served from the system. It can be located at either the primary or the secondary of a supply transformer depending on whether or not multiple customers are supplied from the transformer.

Current Distortion Limits

Current Distortion Limits

Current Distortion Limits

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The harmonic currents from an individual customer are evaluated at the PCC where the utility can supply other customers. The limits are dependent on the customer load in relation to the system shortcircuit capacity at the PCC. Note that all current limits are expressed as a percentage of the customer ’s average maximum demand load current. The current distortion limits vary by the size of the user relative to the utility system capacity capacit y.

A procedure to determine the short-circuit ratio: ratio: Isc/IL

Determine the three-phase short-circuit duty ISC  at the PCC.

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Find the load average kilowatt kilowatt demand P D over the most recent 12 months. This can be found from billing informa information. tion. Convert the average kilowatt demand to the average demand current in amperes using the following expression:

Harmonics Evaluation at PCC

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The harmonic characteristics of the utility circuit seen from the PCC are often not known accurately. Therefore, good engineering judgment often dictated to review a case-by-case basis. However, through a judicious application of the recommended practice, the interferences between different loads and the system can be minimized.

According to IEEE 519-1992, the evaluation procedure procedure for newly installed nonlinear loads includes the following:

1. De Defi fini niti tion on of th the e PCC PCC 2. De Detter ermi mina nati tion on of of the the Isc, IL, and Isc/IL at the PCC 3. Find Finding ing the harmo harmonic nic curre current nt and curr current ent disto distortion rtion of of the nonline nonlinear ar load 4. Determi Determinati nation on of whether whether or not not the harmonic harmonic curre current nt and curre current nt distort distortions ions in step 3 satisfy IEEE 519-1992 recommendation limits 5. Taking nece necessary ssary rem remedie ediess to mee meett the guid guidelin elines es

Harmonic controls •

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Harmonic controls can be exercised at at the utility util ity and end-user sides. IEEE Std.519 attempts to establish reasonable harmonic goals for electric systems syst ems that contain nonlinear n onlinear loads.

The objectives are the following: 1) Cust Customer omerss should limit limit harmonic harmonic curren currents, ts, since since they have have contro controll over their their loads; loads; 2) Electric Electric utiliti utilities es should should limit harmoni harmonicc voltage voltages, s, since since they have have control control over over the system impedances; 3) Both parties parties share share the the responsi responsibilit bility y for for holding holding harmonic harmonic levels levels in in check. check.

Representation Represen tation of a nonlinear load •

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In power systems, the nonlinear load can be modeled as a load for the fundamental current and as a current source for the harmonic currents. The harmonic currents flow from the nonlinear load toward the power source, following the paths of least impedance

General flow of harmonic currents in a radial power system

without power capacitors

with power capacitors

Derating Transformers

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Transformers serving nonlinear loads exhibit increased eddy current losses due to harmonic currents generated by those loads. Because of this, the transfo transformer rmer rating rating is derated derated using a K -factor. -factor.

K-Factor •

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K-factor is an indication to transformer’s suitability fo forr nonsinusoid nonsinusoidal al load currents. K-factor relates transformer capability to serve varying degrees of nonlinear load without exceeding the rated temperature rise limits.

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It is based on the predicted losses of a transformer.

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In per unit , the K -factor -factor is

where Ih is the rms rms current at harmonic harmonic h, in per unit of rated rated rms load current current

K-Factor •

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Manufacturers build special K -factor -factor transformers. Standard K -factor -factor ratings are 4, 9, 13, 20, 30, 40, and 50. For linear loads, the K -factor -factor is always one. For nonlinear loads, if harmonic currents are known, the K -factor -factor is calculated and compared against the transformer’s nameplate K -factor. -factor. As long as the load K -factor -factor is equal to, or less than, the transformer K -factor, -factor, the transformer does not need to be derated.

Transformer Derating •

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For transformers, transformers, ANSI/IEEE ANSI/IEEE Std. C75.110 provides provides a method to derate the transformer capacity when supplying nonlinear loads. The transformer derating is based on additional eddy current losses due to the harmonic current and that these losses are proportional to the square of the frequency. Thus, where Pec-r is the maximum transformer per unit eddy current loss factor (typically, between 0.05 and 0.10 per units for dry-type transformers). Ih is the harmonic current, normalized by dividing it by the fundamental current. h is the harmonic order. •

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Typical Values Of Eddy Current Loss Factor Factor (Pec-r )

Example Assume that the per unit harmonic currents are 1.000, 0.016, 0.261, 0.050, 0.003, 0.089, 0.031, 0.031, 0.002, 0.002, 0.048, 0.026, 0.026, 0.001, 0.033, 0.033, and 0.021 pu A for the harmonic order of 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25, respectively. Also assume that the eddy current loss factor is 8%. Based on ANSI/IEEE Std. C75.110, determine the following: a.

The K -factor -factor of the transformer

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The tra trans nsfo form rmer er dera deratin ting g based based on the the sta standa ndard rd