A Filtering Scheme for Reducing Harmonics Penetration into Transmission Systems (V1.0)

Transcription

1 A Filtering Sceme for Reducing Harmonics Penetration into Systems (V.) J. W. Hagge, Senior Member, IEEE, and L. L. Grigsby, Fellow, IEEE Abstract--Tis paper presents a novel sceme to reduce armonics penetration into transmission systems. Te sceme utilizes te tertiary winding of te substation transformer to construct a low impedance pat to trap armonics at tuned fruencies. Tis is acieved by inserting capacitors and inductors into te delta loop of te tertiary winding for zero-suence armonics filtering and by connecting sunt capacitors and inductors to te tertiary winding for non-zero-suence armonics filtering. Te proposed topology is capable of trapping two zero-suence armonics and tree non-zero-suence armonics simultaneously. Design procedure is given in details. Simulations conducted on a detailed modeled distribution system ave demonstrated te effectiveness of te tertiary winding. In addition, economic analysis furter confirms tat te proposed tertiary winding is a muc more costeffective solution compared to medium-voltage L filter package. H Index Terms Power quality, armonics, filter. I. INTRODUTION ARMONI distortion is one of te main power quality concerns for utility companies. Traditional approaces for managing armonic distortions are to limit te armonic currents injected by customers into te power supply systems. An example is te IEEE Std. 9 []. Te approac as been very effective in mitigating te armonic distortions caused by large, concentrated armonic sources suc as industry facilities wit variable fruency drives. Wit te wide spread adoption of standards suc as te IEEE Std. 9, armonics generated by large industries and commercial facilities are no longer a major concern to utility companies. In recent years, te proliferation of energy efficient but armonic-producing ome appliances and consumer electronic devices as resulted in anoter type of armonic distortions in power distribution systems. Tese new armonic sources ave comparable sizes and are distributed all over a network. Altoug tey produce insignificant amount armonic currents individually, te collective effect of a large number of suc loads can be substantial. Several power quality concerns ave been identified due to suc distributed armonic sources. One of tem is tat residential feeders ave become significant armonic sources, injecting unnegligible armonic currents into power transmission systems. Te consuences could be te overloading of transmission capacitors and transmission level armonic resonances etc []. Tis work was supported by te Natural Sciences and Engineering Researc ouncil of anada and Alberta Power Industry onsortium. Te autors are wit te department of Electrical and omputer Engineering, University of Alberta, Edmonton, A T6G V, anada ( wxu@ualberta.ca). Two types of solutions ave been proposed to address tis emerging armonic issue so far. One solution is to reduce te armonic emission from individual electronic devices. IE 6 - as been establised for tis purpose []. Te second solution is to reduce te armonic distortions in power distribution systems troug, for example, medium and low voltage filters []. ot solutions can reduce te amount of armonic currents injected into te transmission systems. Te penetration of armonics from distribution systems into transmission systems is a sensitive issue since transmission and distribution systems often ave different owners. ot types of companies will, terefore, benefit from a solution tat is dedicated to preventing distribution system armonics from penetrating into te transmission systems. Distribution system owners may use te solution to meet te interconnection ruirements of te transmission system regardless te armonic distortion levels inside te distribution systems. Te transmission owner can easily verify te effectiveness of te solution in meeting its ruirements. Te objective of tis paper is to investigate scemes tat can reduce te armonic injection from distribution systems into transmission systems. A novel filtering sceme, called te tertiary winding filter, is proposed and its advantages and effectiveness are demonstrated troug simulation studies. Economic analysis furter confirms tat te proposed filter sceme is a cost-effective solution. Tis paper is organized as follows: Section II reviews te tecniques tat are applicable to reduce armonic injections into transmission systems. Section III presents te proposed tertiary winding filter and explains its principles. Te design metod for te proposed tertiary winding filter is given in Section IV. Section V demonstrates te effectiveness of te proposed sceme troug computer simulation studies and investigates te overall system performance wen a few tertiary winding filters are installed. Economic comparison is conducted in Section VI. II. REVIEW OF APPLIALE HARMONI MITIGATION SHEMES Altoug little researc work as been done in te area of preventing armonics from entering transmission systems, tecniques tat can be adopted for te purpose do exist. Tese tecniques can be classified into two types. One is to prevent or reduce te injection of zero suence armonics into te transmission system. Te oter type is to deal wit te nonzero suence armonics.

2 A. Zero Suence Harmonic Mitigation Tecniques Zero Suence (ZS) armonics are tose armonic components wose are in zero suence according to te definition of symmetrical components. ZS components are dominant in te rd, 9t, t and oter triple-order armonics. Single pase non-linear loads suc as energy efficient ome appliances are te most significant source of ZS armonics. It is quite common to observe ig levels of ZS armonics in a distribution substation feeding residential loads tese days. ) onnection For multi-grounded neutral (MGN) configuration widely adopted in Nort America distribution systems, te secondary side windings of te substation transformer are connected as grounded Wye, wile te primary side windings' connection may vary according to corresponding ruirements of te transmission systems. Te simplest way to prevent ZS armonics' propagation into transmission systems is to modify te primary side windings' of substation transformer connection as ungrounded Wye as sown in Fig.. For suc a connection, tere is no patway for ZS armonic currents to pass troug from te secondary side to te primary side of te substation transformer. Tus no ZS armonics could propagate from distribution systems to transmission systems. System HV us H X MV us Distribution Feeders and Loads ) Sunt Passive ZS Filter A sunt filter installed at te secondary side of te substation transformer can also reduce te injection of distribution system armonics into te transmission system. Sunt passive ZS filters create sunt low ZS impedance to trap te ZS armonics. Tey ave various topologies (as sown in Fig. ) and can be broadly classified into two types. Te first type is te L ZS filter wic only consists of capacitors and inductors. It as positive/negative suence impedance so it affects te flow of non-zs armonics. A representative example of suc filters is te star-connected capacitors grounded troug an inductor (Fig. (a)) wic is tuned to create a low ZS impedance. Te main attractive caracteristic of tis topology is tat by adding a tree-pase inductor (Fig. (b)), te capacitors can be tuned to filter positive and negative suence armonics as well. Te downside of tis filter is tat it can affect te fundamental fruency power flow and can lead to positive or negative suence resonances at oter fruencies. Te second type of ZS filter is te transformer based ZS filter. It is developed based on te concept of grounding transformer. Suc a filter beaves as open circuit at positive and negative suences so it as no impact on normal power system operation and on non-zero-suence armonics. One of te examples is te zig-zag transformer based filter (Fig. (c)). A drawback of tis filter is tat it needs a nonstandard transformer. Anoter example consists of a Yg/delta transformer wit tuned capacitors and inductors inserted into te delta loop (Fig. (d) (e)). y proper selection of te capacitors and inductors, a ZS impedance as low as te transformer s resistance could be acieved at desired armonic fruencies. Tis leads to attractive ZS filter topologies witout using non-standard transformers. A A (a) L Fitler (b) L Filter A A A Grounding Fig. transformer connection tat can prevent ZS armonics' propagation into transmission systems. For cases were te primary side must be grounded, a grounding transformer may be installed at te primary bus as sown in Fig. wit te dotted connection. Te most common grounding transformer is te unloaded Yg/Delta transformer wit Yg side connected to te primary bus. (c) Zig-zag Single Tuned Filter (d) -based Fig. Topologies of ZS sunt filters. (e) -based Double Tuned Filter It sould be noted tat te ZS filter can be installed at te eiter side of te substation transformer teoretically. However, because of ig voltage, te primary side sceme is uneconomic and ard to implement. Te practical implementation, terefore, is to install te ZS filter at te secondary side (as sown in Fig. ). System HV us H Fig. ZS filter installation location. X MV us ZS Filter Distribution Feeders and Loads. Non Zero Suence Harmonic Mitigation Tecnique Non Zero Suence (non-zs) armonics are tose armonic components wose are in positive suence or negative suence according te definition of symmetrical components. Non-ZS components are dominant in te t, 7t, t and oter non-triple order armonics. All te non-linear loads including te single pase non-linear load, te two pase non-

3 linear load and te tree pase non-linear loads generate non- ZS components. Tis results in tat te non-zs armonic distortion level is usually more serious tan te ZS armonic distortion level in te system. onsidering te connection types of te substation transformer ave no impacts on te non-zs armonic currents flow pat, te only effective way to prevent te non-zs armonics' propagation into te transmission system is by installing filters. Active filters sound attractive to be applied for te MV application due to its great flexibility. In terms of cost and reliability, owever, tey still could not compete wit te passive filters of similar filtering performance. Similar to tat in ZS armonics mitigation tecniques, passive filters are also playing a leading role in non-zs armonics mitigation tecniques. Among all passive filters, sunt passive filters wic are designed to be connected in parallel wit te load are te most widely used in te MV level because of teir lower installation and maintenance cost and iger operation reliability. Sunt passive filters could be furter categorized as L non-zs filter, L ZS filter and transformer based ZS filter. Wile L ZS filter and transformer based ZS filter ave been discussed in te former section, Fig. gives te topologies of some commonly used L non-zs filter. It sould be noted tat tese topologies could be used for te L ZS filter as well, as long as te tree pase filter brances are connected in delta or grounded Wye. L L (a)l Filter (b)l Filter (c)l Filter Fig. Topologies of L non-zs filters. As sown in Fig., similar to te ZS filter installation location, te practical sceme to trap non-zs armonics also install te filter at te secondary side of te substation transformer, instead of te primary side considering te ig cost and implementation difficulty of ig voltage filter. R L R A ombined Filter Fig. 6 Topology of te combined filter. Te generic teory of te combined filter is based on te Yg/delta transformer and te tuned filter. It utilizes te leakage inductance of te transformer to create a low impedance pat to trap armonic current at tuned fruencies. Tis is acieved by inserting capacitors and inductors into te delta loop of secondary windings for ZS armonic filtering and by connecting sunt capacitor and inductors to te secondary winding for non-zs suence armonic filtering. Similar to oter tuned filters, at tuned fruencies, te combined filter s impedance will only contain te resistive component (i.e. te transformer sort circuit resistance) since te reactive component of te combined filter will be canceled out by te tuning capacitor. If tis impedance is lower tan te upstream uivalent armonic impedance (i.e. te transmission system uivalent armonic impedance plus te substation transformer uivalent armonic impedance), armonics originated from te distribution system will be trapped by te combined filter. Tis filter is very compact and could reduce costs by using low voltage L components. However, as mentioned above, for tis filter to effectively reduce te armonics penetrating into transmission systems, te transformer sort circuit resistance sould be less tan te upstream uivalent armonic impedance, wic means a large transformer comparable to te substation transformer is needed. D. Summary urrent available tecniques for preventing armonics propagation into transmission systems are summarized as sown in Fig. 7. HV us MV us System H X Distribution Feeders and Loads Filter Fig. Non-ZS filter installation location.. ombined Filter Depending on te ruirements of transmission companies, bot types of filters may be ruired at a substation. It is possible to combine te two types of filters into one unit for cost savings. One possible solution is te combined filter sown in Fig. 6. Fig. 7 Applicable tecniques for preventing armonics' propagation into transmission systems. To prevent te armonics from distribution systems (wic usually as a wide spectrum) from entering transmission systems, bot Zero Suence armonic mitigation tecniques and

4 Filter Impedanece( ) non-zero Suence armonic mitigation tecniques sould be used. Among all combinations, te most compact one is to install a combined filter at te secondary side of te substation transformer. However, tis sceme ruires a large transformer to work effectively. And oter scemes wit transformer based filters also ave te same problem. onsidering te ig cost of a large transformer, all tese scemes are not optimal options. ompared to te sceme of te combination of te L ZS filter and te L non-zs filter, te sceme wit ungrounded primary windings and L non-zs filter is of less cost because of te absence of te L ZS filter. Neverteless, for te cases tat te grounding at te transmission side is a must, expensive ig voltage grounding transformer sould be incorporated into tis sceme (as sown in Fig. ) and tis will make tis sceme loose its cost advantage. Actually, te primary side winding connections of te substation transformer is usually fixed and could not be canged arbitrarily wic furter render te applicability of te ungrounding sceme. It sould be furter noted tat tree winding transformers are widely used by utility companies as distribution substation transformer and teir common connection is Yg/yg/delta wit no loads served by te delta connected tertiary windings. Te above situation naturally leads to te researc on oter feasible passive solutions to prevent armonics' propagation into te transmission system for te substation wit Yg/yg/delta configured substation transformer besides te sceme using te combination of L ZS filter and L non-zs filter. III. PROPOSED TERTIARY WINDING FILTER As reviewed in te previous section, several options are available to reduce te injection of distribution system armonics. Eac option as its advantages and limitations. Te transformer based filters ave several attractive features. However, tey ruire a transformer wit small sort-circuit impedance. In view tat many substation transformers ave a tertiary winding, it may be possible to utilize te substation transformer as a filtering transformer on top of its power transmission function. Te need for a dedicated transformer is tus eliminated. Tis reasoning as led us to propose a new filtering sceme called Tertiary Winding Filter. A. asic Principle of te Tertiary Winding Filter Similar to te combined filter, te basic idea of te tertiary winding filter is to utilize te leakage inductance of te tertiary winding to create a low impedance pat to trap armonic currents at tuned fruencies. Tis is acieved by inserting capacitors and inductors into te delta loop of te tertiary winding for ZS armonic filtering and by connecting sunt capacitors and inductors to te tertiary winding for non-zs armonic filtering. Topology of te filter is depicted in Fig. 8. Fruency response of a sample tertiary winding filter tuned to te rd and 9 t ZS armonics and t, 7 t and t non-zs armonics is sown in Fig. 9. System VSA VS VS Zup # # # Tertiary Winding Filter us Fig. 8 Topology of te proposed tertiary winding filter A N Distribution Feeders and Loads Zero suence Positive/Negative suence Harmonic Order Fig. 9 Fruency response of a sample tertiary winding filter. Te system uivalent circuit at tese tuned fruencies seen from te secondary side of te substation transformer is sown in Fig.. System Z ( ) Up / / # # R Xfrm _ j L R Xfrm _ Xfrm _ j LXfrm _ # R Xfrm _ us Distribution Feeders and Loads () ZDown / / I () Down / / Fig. Equivalent circuit of te tertiary winding filter at tuned fruencies. Were R Xfrm _ and L represent te resistance and leakage Xfrm _ inductance of te substation transformer's primary winding (referred to te secondary side) R Xfrm _ and Xfrm _ L represent te resistance and leakage inductance of te substation transformer's secondary winding Xfrm _ R represent te resistance of te substation transformer's tertiary winding (referred to te secondary side)

5 Z Z I Up ( ) / / represents uivalent transmission system armonic impedance seen at te primary side of te substation transformer (but referred to te secondary side) Down Down ( ) / / represents uivalent armonic impedance of distribution feeders and loads ( ) / / represents uivalent armonic current source of distribution feeders and loads It can be seen tat te tertiary winding s impedance only contains te resistive component since te reactive component as been canceled out by te tuning capacitor. As a result, a low impedance pat separates te transmission and distribution systems. Harmonics originated from te distribution system will be bypassed by te tertiary winding before it can reac te transmission system. In addition, typical voltage of a substation tertiary winding is.6kv to.8kv. Low voltage L components can be used to construct te filter, wic results in cost savings.. Equivalent ircuits of Tertiary Winding Filter As sown in Fig. 8, te tertiary winding filter is composed of two parts, i.e., te delta connection part (te delta loop) and te star connection part (te sunt components at te tertiary side). Since for ZS armonics, te star connected sunt components at te tertiary side beaves as open circuit, te tertiary winding filter ZS uivalent circuit only consists of te delta connection parts (see Fig. (a)). For non-zs armonics, te star connected sunt components at te tertiary side beave as normal loads. Tus te tertiary winding filter non-zs uivalent circuit consists of bot te delta connection part and te star connection part (see Fig. (b)). ased on te above caracteristics of te tertiary filter's uivalent circuit, te delta connection part is designed to form a double tuned filter for te ZS armonics and te delta connection part and te star connection part togeter are designed to form a triple tuned filter for te non-zs armonics. Since te delta connection part is essentially te same as te conventional double tuned filter, its components selection can use te existing approac directly. Te selection of star connection part components can be illustrated intuitively by Fig.. As sown in Fig., te delta connection part as a fruency response wit two series resonant tuned points (at te two designed ZS armonic orders and ), and one parallel resonant point (between te two designed ZS armonic orders). Te desired tree non-zs armonic orders to filter determine te crossing points of te delta connection part fruency response and te star connection part. Tus te roug sape of te star connection part fruency response is determined. According to tis, te components size of te star connection part could be obtained based on rigorous matematical uations described in Section IV. a R /a Xfrm _ L /a Xfrm _ L /a a Delta connection part L /a a a / R /a Xfrm _ L /a Xfrm _ L /a a L /a L / a L / a a / Delta connection part Star connection part (a) Equivalent ZS circuit (b) Equivalent non-zs circuit Fig. Equivalent circuit of te tertiary winding filter. Fig. Fruency response of delta connection part and star connection part of te tertiary winding filter.. Performance Analysis Tis subsection is to compare te relative size of te primary impedance versus tuned tertiary impedance and sow tat most armonics will enter te tertiary pat. According to Fig., for te tertiary winding filter to be effective, te uivalent impedance of te tertiary winding filter sould be less tan te transmission system impedance plus substation transformer primary side winding's impedance at corresponding fruencies. Tis is an easily satisfied condition. Intuitively, te minimum impedance of te tertiary winding filter at tuned armonic orders could be acieved as te substation transformer tertiary winding resistance referred to te secondary side by proper selection of te capacitors and inductors. According to te typical parameters of tree winding transformer, te tertiary winding resistance is comparable to te primary winding resistance. And for a substation transformer, its reactance resistance ratio is usually very ig wic L R. means Xfrm _ Xfrm _ Tus R R j L ' Xfrm _ Xfrm _ Xfrm _ R ( ) Xfrm _ j L Xfrm _ ZUp / / wic means te impedance of te tertiary winding filter is far smaller tan upstream system impedance. In tis way, armonics at tuned fruencies will be trapped into te tertiary side ()

6 6 rater tan propagating into te transmission system. A roug estimation of te percentage of te armonic current tat will be trapped by te tertiary winding filter could be obtained by te following uation: L Xfrm _ Ratio R L ' Xfrm _ Xfrm _ were is te tuned armonic order. To sow te performance of te tertiary winding filter, some of te typical sizes of te tree winding transformers used by te utility company are listed in Table I. Te percentage of te tird armonic current tat will be trapped by te tertiary winding filter is provided in te last column. For iger tuned order armonics, larger percentage will be trapped by te tertiary winding filter. TALE I: TRAPPED RATIO FOR DIFFERENT SIZES OF THREE WINDING TRANSFORMERS Rated apacity a (MVA) Rated Voltage b (kv) // //6. //8 //.8 //. //6. //6.7 //.8 Sort ircuit Impedance () H-M. H-L 8 M-L 6. H-M. H-L 8 M-L 6. H-M. H-L 7 M-L 6. H-M. H-L 8 M-L 6. a Te rated capacity of eac winding. b Te nominal line-to-line voltage (LL-rms) On-Load Loss (kw) IV. TERTIARY WINDING FILTER DESIGN Trapped Ratio () Similar to te design of te transformer based double tuned ZS filter [], te design of te tertiary winding filter is also an iterative process based on te system armonic load flow study and components loading assessment. However te tertiary winding filter design does not need to select te transformer size, since te size of te distribution substation transformer is primarily determined by te loads served by te substation. Te tertiary winding filter design is just te proper selection of L components to coordinate te transformer to trap corresponding armonics into its tertiary windings. Te flowcart of design procedure for te tertiary winding filter is sown as Fig.. A. L omponents' Size Determination As sown in Fig., te determination of components size consists of two steps. Te first step is to determine te delta connection part components size. As seen from Fig. (a), te delta connection part is actually te same to te conventional double tuned filter. Terefore, te proper component sizes of te delta connection part can be derived by using te same matematical approac derived for te conventional double () tuned filter. According to [] [6], te component sizes of te delta connection part can be determined by te following uation set ().. No No Set, L L Xfrm _ alculate te delta connection part components parameters Are te delta connection part components parameters reasonable? L L Xfrm _ alculate te star connection part components parameters Are te star connection part components parameters reasonable? Perform HLF to examine te filter performance in te system an te filter mitigate te problem effectively? Overloading of te transformer winding (TLL>)? No Overloading in capacitors? No Te Final Filter Design No. Increase te capacitor rating and Kvar witout canging its capacitance (uf) Fig. Flowcart of design procedure for te tertiary winding filter. i j i j ( i j ) ( i j) ( LXfrm _ L )( i j ) L ( i j) i i ( LXfrm _ L ) j j ( LXfrm _ L ) were i and j represent te ZS tuned order of te tertiary winding filter. Once, and L are determined, te star connection part components parameter could be determined by te following way. Te non-zs impedance of te tertiary winding filter at armonic order could be expressed as f( ) ( ) Z Xfrm _ / ( ) / a RXfrm _ j g () ()

7 7 were f ( ) ( L L L Xfrm _ ) ( L ) L ( L ) ( L )( L ) () g( ) ( L )( L ) (6) Since te filter is tuned to ave tree tuned positive/negative fruencies, ten f()= at corresponding armonic orders, and, i.e., f( ) f( ) f( ) y solving uations set (7),, and L are determined. It is important to note tat two compensation inductors L and L are used in te tertiary winding filter, due to te leakage inductance of te transformer wic is usually small may result in extremely large capacitance needed. y adjusting te compensation ratios α and β (sown in Fig. ), tertiary winding filter wit capacitors and inductors of acievable parameters could be obtained and te reactive power compensated by te filter could also be set to be te ruired value.. omponents Loading Assessment omponents are susceptible to failures and even breakdown if te voltages across tem or te currents flowing troug tem exceed a certain degree during a certain period of time []. Tus te components loading assessment is an important part of te filter design. ) Loading Assessment Te transformer loading condition is evaluated by te index TLL ( Loading Level) wic is developed in []. Te TLL is defined as follows: TLL P P (7) TLL (8) TLL rated were P TLL represents te winding total load loss during filter operation, te winding maximum permissible loading capacity is represented by P TLL-rated, wic is te winding loading loss under a rated sinusoidal current. Terefore, as long as TLL of eac winding does not exceed pu, te transformer operates safely witout overeating. If te TLL of one winding exceeds pu (indicating te winding is overloaded), te compensation ratio sould be adjusted. ) apacitor Loading Assessment For assessing te loading of te capacitors, te uivalent loading index based on researc findings of partial-discarge caused capacitor aging is used. Tis uivalent loading index is described by te following uation. were n p, n rms and n f K p, were V p Krms and K f n n p rms f p nrms f V ( K ) ( K ) ( K ) (9) are coefficients tat describe te significance of eac factor. Teir values are dependent on te type of films used in te capacitor. are indices describing te waveform experienced by te capacitor, as follows K K K p rms Vp () V * p V () V rms * rms N V p V () is te peak value of te distorted voltage * V is te peak value of te rated fundamental fruency p voltage V is te rms value of te distorted voltage rms * V is te rms value of te rated fundamental fruency rms voltage V is te armonic order is te order armonic voltage. Te pysical meaning of tis index is tat it represents a normalized composite or uivalent voltage applied to a capacitor. If te voltage is above one, te capacitor is considered as overloaded and its life will be sortened. If te value is less tan one, te capacitor is considered as operating witin its design limits. ) Inductor Loading Assessment As for te inductor, te current flowing troug it sould be less tan its current rated rms value. Tus te loading level of te inductor could be defined as I I () I rms * rms were I is te rms value of te distorted current rms * I is te rms value of te rated fundamental fruency rms current. V. SIMULATION STUDIES Two test systems are selected to verify te proposed tertiary winding filter and its design procedure as well as to examine

8 8 its system performance. A. Simulation Studies on Distribution System Tis subsection conducts te simulation studies on test system # a generic distribution system supplying residential loads wic are evenly distributed along five feeders. Fig. depicts te network configuration of test system #, in wic eac section block consists of tree service transformers wic are connected to te secondary system serving residential ouses. System VSA VS VS Zup # # # A N Line Section Rg S S Feeder S Feeder S S7 S7 8 6 TDD -- Witout Tertiary Winding Filter Pase A Pase Pase Time () (a) 8 6 TDD -- Wit Tertiary Winding Filter Pase A Pase Pase Time () (b) Fig. TDD variation of te currents propagating into te transmission system. IDD Spectrum -- Witout Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order (a) IDD Spectrum -- Wit Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order (b) Fig. 6 Typical IDD spectrum of te currents propagating into te transmission system. S Feeder S S7 THD -- Witout Tertiary Winding Filter Pase A Pase Pase THD -- Wit Tertiary Winding Filter Pase A Pase Pase Fig. Network configuration of test system #. Primary System ) Tertiary Winding Filter Design Results Te introduced iterative process (Fig. ) was employed to determine te final filter design. Table II presents te components size of te designed tertiary winding filter. TALE II: DESIGNED OMPONENTS SIZE OF THE TERTIARY WINDING FILTER L None Delta connection part 6.kvar (.6 kv) a.mh(79a) b L L L 9.kvar (.6kV).9mH(79A).kvar(.6kV) Star connection part.7mh(79a) 67.8kvar (.6kV) a Te voltage in te bracket is te capacitor rated voltage. b Te current in te bracket is te inductor rated current, te inductor rated voltage is 6.kV. ) Simulation Results All te developed models are employed in a multipase armonic power flow program to perform te simulation studies. As te residential loads are time-varying during a day, time-varying simulation results are obtained. In order to establis a sound understanding of te proposed tertiary winding filter performance, te simulation results for bot te case witout tertiary winding filter and te case wit tertiary winding filter are sown in Fig. to Fig. 8. As seen from Fig. to Fig. 8, bot te armonic currents propagating into te transmission system and te armonic voltages at te primary side of te substation transformer ave been greatly reduced, wic demonstrates te effectiveness of te proposed filter Time () (a) Time () (b) Fig. 7 THD variation of te voltages at te primary side of te substation transformer. IHD Spectrum -- Witout Tertiary Winding Filter. Positive suence Negative suence Zero suence Harmonic Order (a)... IHD Spectrum -- Wit Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order (b) Fig. 8 Typical IHD spectrum of te voltages at te primary side of te substation transformer.. Simulation Studies on System Tis subsection conducts several simulation studies on test system # an extension of te IEEE bus transmission system proposed in [] aiming to furter examine: Will te distribution armonic loads at oter bus lead to te tertiary winding filter overloading? Is it essential to uip all te buses wit distribution armonic loads wit te tertiary winding filter? Fig. 9 presents te network configuration of test system #. ) Influence of Distribution Harmonic Loads at Oter uses In te previous sections, te tertiary winding filter was torougly examined in te distribution system. However in te tertiary winding filter design, loading assessment was conducted witout considering te influence of distribution armonic loads at oter buses. Will tis be an issue for te tertiary

9 9 winding filter if tere are multiple distribution armonic loads at oter buses in te transmission system? To answer tis question, eigt sets of cases are studied. Eac set of cases consists of two cases: ) for te first case tere is no oter distribution armonic load at oter buses except were te tertiary winding filter is installed; ) for te second case all te load buses are modified as distribution armonic loads. Te detailed description of tese cases is follows: ase Set G G ase Filter Placement Distribution Harmonic Loads Location i us us ii us us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us i us 9 us 9 ii us 9 us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us i us us ii us us, us, us 9, us, us, us, us, us G Fig. 9 Network configuration of test system # 6 9 SV onverter 7 8 Loading assessment for all eigt case sets sow tat te distribution armonic loads at oter buses do ave influence on te loading level of te tertiary winding filter. ut te influence is different for te tertiary winding filter at different locations. According to ase Set, and 6, te tertiary winding filter designed based on te distribution armonic load information at its own bus will be overloaded by distribution armonic loads at oter buses. Tus if multiple distribution armonic loads exist, te transmission system armonic power flow sould be incorporated into te tertiary winding filter loading assessment and components of larger size sould be adopted wen overloading issues are identified. ) Installation Density Study Tis subsection presents te sensitivity study to assess te influence of te installation density of te tertiary winding filter on te overall transmission system armonic distortion level. Simulation results for te following cases are compared in Table IV and Table V. i. Test system # wit te loads at bus, bus, bus 9, bus, bus, bus, bus and bus all modified as a distribution armonic load. ii. ased on i, install one tertiary winding filter at any one of te buses wit distribution armonic loads. iii. ased on i, install one tertiary winding filter at any two of te buses wit distribution armonic loads respectively. iv. ased on i, install one tertiary winding filter at any tree of te buses wit distribution armonic loads respectively. ix. ased on i, install one tertiary winding filter at all buses wit distribution armonic loads respectively. In Table III, te average voltage THD for kv buses, kv buses and te overall system is given, wile in Table IV te average current TDD for kv lines, kv lines, transmission transformers and te overall system is given. As sown in tese two tables, te more te tertiary winding filter installed te lower te overall transmission system armonic distortion level is in terms of bot te bus voltage THD and transmission uipment TDD. TALE III: VOLTAGE DISTORTION LEVEL Average Voltage THD () ase kv kv uses uses Overall System i ii iii iv v vi vii.8.. viii... ix TALE IV: URRENT DISTORTION LEVEL Average urrent TDD () ase Overall kv Lines kv Lines s System i ii iii iv v vi vii viii ix

10 Fig. depicts te average and minimum voltage distortion level and current distortion level for eac filter installation density. Fig. Average minimum armonic distortion level for different cases Table V furter gives te filter placement wic results te minimum armonic distortion level for case ii ~ case viii and te corresponding overall system voltage distortion level and current distortion level wit suc placement. TALE V: OPTIMUM FILTER PLAEMENT FOR DIFFERENT ASES Overall System ase Optimum Filter Placement Harmonic Distortion Voltage urrent TDD * THD * () () ii us 9 6.7(8.6).(.9) iii us 9, us.6(8.7).9(.) iv us 9, us, us.9(7.8).9(.98) v us 9, us, us, us.86(6.7) 8.8(.) vi us 9, us, us, us, us.9(.6) 8.7(.9) vii us 9, us, us, us, us, us.(.) 8.(.6) viii us 9, us, us, us, us, us, us.(.) 7.87(8.88) *Figure in te bracket is te average value for eac case. As indicated by Fig. and Table V, wit optimum filter placement, better armonic mitigation effects can be acieved. Anoter useful information could be extracted from Table V is te distribution armonic loads at us 9 ave te largest impacts on te overall system distortion level since for all te optimum filter placement one tertiary winding filter sould be placed at us 9. Possible explanation for tis is tat te transfer impedance between us 9 and oter buses are muc larger tan tat between oter buses. Furter fruency scan studies are needed to confirm tis. VI. OMPARATIVE EONOMI ANALYSIS Te cost of te proposed tertiary winding filter as been investigated using te test system #. It is also compared wit te cost of te MV L filter package. To obtain a meaningful comparison, te MV L filter package is designed to acieve te same armonic distortion reduction wit te tertiary winding filter specified by Table II. Te designed MV L filter package sown as Fig. consists of two inductor grounded single tuned L filters wic are tuned to filter te rd, t and 9t and t armonics respectively and one directly grounded single tuned L filter wic is tuned to filter te 7t armonic. Te designed components size of te MV L filter package is given in Table VI. TALE VI: DESIGNED OMPONENT SIZE OF MV L FILTER PAKAGE Filter Tuned Harmonic omponent Size Design Order L 6.mH (8A) Filter, 87.8kvar (.kv) L.69mH (6A) L 8.7mH (69A) Filter kvar (.9kV) L.8mH (69A) Filter 9, 9.8kvar (.9kV) L.88mH (69A) Te voltage in te bracket is te capacitor rated voltage. Te current in te bracket is te inductor rated current, te inductor rated voltage is.kv. For te cost estimation, te data collected from [] and te internet are used. Table VII to Table X sow te approximate expenses wit filter components and installation. TALE VII: OST OF APAITORS Rated voltage <kv kv~kv kv~kv kv~kv ost $/kvar $/kvar $/kvar $6/kvar Rated urrent TALE VIII: OST OF INDUTORS Voltage Level kv~kv kv~kv <A $ $8 A~A $7 $ A~A $9 $8 TALE IX: OST OF OTHER OMPONENTS kv~kv kv~kv Switcing Device $7, $, Protection Device $, $7, TALE X: ESTIMATED OST FOR FILTER INSTALLATION ivil $7, Engineering & Design $8, Labor ost a $, a Labor cost is based on: persons * 8our/day *days *$/our y te above set of information, te overall cost of te tertiary winding filter and MV L filter package is estimated as presented in Table XI. As seen from Table XI, te tertiary winding filter is found be muc more economical. TALE XI: OVERALL ESTIMATED OST Tertiary Winding Filter MV L Filter Package omponents ost $9, $7,9 Installation ost $,7 $,7 Total ost $89,8 $98,6 VII. ONLUSIONS Tis paper presented a novel and effective filter to prevent armonic currents propagating into te transmission system. Te design issues of te proposed filters are fully investigated. Te main findings and contributions of tis paper could be summarized as follows. Te proposed tertiary winding filter could trap two ZS armonics and tree non-zs armonics simultaneously. It becomes a very desirable metod to mitigate armonic currents wit a wide spectrum.

11 Te proposed filter and its design metod ave been tested troug two compreensive test systems. Te results ave demonstrated te effectiveness of te filter and also reveal proper placement could acieve te same reduction of te overall system armonic distortion level wit fewer filters. ompared to oter transformer based filters, te most important benefit of te proposed tertiary filter is tat it utilizes te existing substation transformer wic greatly reduces te filter cost. Furtermore, actually tree winding transformers are widely used by utility companies in anada as distribution substation transformer and teir common connection is Yg/yg/delta wit no loads served by te delta connected tertiary windings. Tis means te proposed tertiary filter as a brigt application prospect. Economic analysis furter confirmed tat te proposed tertiary winding filter is a cost effective solution for preventing armonics' propagation from te distribution system into te transmission system. Tianyu Ding (S') obtained te.sc. degree in electrical engineering from Sandong University, Jinan, ina, in. urrently, e is pursuing is P.D. degree in Electrical and omputer Engineering at te University of Alberta, Edmonton, A, anada. His main researc interest is power quality. VIII. REFERENES [] "IEEE Recommended Practices and Ruirements for Harmonic ontrol in Electrical Power Systems," IEEE Std 9-99, pp. -, 99. [] J. Aririllaga, D. A. radley, P. S. odger, Power System Harmonics: Jon Wiley & Sons Ltd, 98. [] IE Standard 6--: Electromagnetic compatibility (EM) Part - : Limits - Limits for armonic current emissions (uipment input current 6A per pase), 9. [] A.. Nassif, X. Wilsun, and W. Freitas, "An Investigation on te Selection of Filter Topologies for Passive Filter Applications," Power Delivery, IEEE Transactions on, vol., pp. 7-78, 9. [] P. ageri, "Metods to mitigate armonics in residential power distribution systems," M. Sc. dissertation, Dept. Elect. omput. Eng., Univ. Alberta, Edmonton, A, anada,. [6] P. ageri and W. Xu, "A Tecnique to Mitigate Zero-Suence Harmonics in Power Distribution Systems," IEEE Trans. Power Del., vol. 9, pp. -, Feb.. [7] D. Salles, J. en, W. Xu, W. Freitas, and H. E. Mazin, "Assessing te ollective Harmonic Impact of Modern Residential Loads - Part I Metodology," IEEE Trans. Power Del., vol. 7, pp , Oct.. [8] J. en, D. Salles, W. Xu, and W. Freitas, "Assessing te ollective Harmonic Impact of Modern Residential Loads - Part II: Application," IEEE Trans. Power Del., vol. 7, pp. 97-9, Oct.. [9] W. Xu, J. R. Marti, and H. W. Dommel, "A multipase armonic load flow solution tecnique," Power Systems, IEEE Transactions on, vol. 6, pp. 7-8, 99. [] R. Abu-Hasim, R. urc, G. ang, M. Grady, E. Gunter, M. Halpin, et al., "Test systems for armonics modeling and simulation," Power Delivery, IEEE Transactions on, vol., pp , 999. Pooya ageri obtained te.sc. degree in electrical engineering from Sarif University of Tecnology, Teran, Iran, in and te M.Sc. degree in electrical engineering from te University of Alberta, Edmonton, A, anada, in. urrently, e is wit te Electrical Engineering Department, Oil & Gas segment, Stantec onsulting Ltd., Edmonton, A, anada. His researc interests are power quality and power distribution systems. Wilsun Xu (M 9-SM 9-F ) obtained te P.D. degree from te University of ritis olumbia, Vancouver, in 989. urrently, e is a NSER/iORE Industrial Researc air Professor at te University of Alberta. His current main researc interests are power quality and power disturbance analytics.

12 A Filtering Sceme to Reduce te Penetration of Harmonics into Systems (Final) Tianyu Ding, Student Member, IEEE, and Wilsun Xu, Fellow, IEEE Abstract Te widespread adoption of energy efficient but armonic-producing loads in residential omes as led to increased injection of armonic currents into transmission systems. In response to tis situation, a novel filtering sceme tat can reduce te armonic penetration into transmission systems is proposed. Te sceme utilizes te tertiary winding of a substation transformer to construct a tuned low impedance pat for te armonic currents. Te proposed sceme is capable of trapping two zero-suence armonics and tree non-zero-suence armonics simultaneously. Design procedure as been developed. Performance of te sceme is evaluated and demonstrated troug simulation studies. In addition, economic analysis reveals tat te sceme is a cost-effective solution in comparison wit oter applicable metods. I Index Terms Power quality, armonics, passive filter. I. INTRODUTION N recent years, te proliferation of energy efficient but armonic-producing ome appliances and consumer electronic devices as resulted in a new type of armonic distortions in power distribution systems. Tese new armonic sources ave comparable sizes and are distributed all over a network. Altoug tey produce insignificant amount armonic currents individually, te collective effect of a large number of suc loads can be substantial [-6]. Several power quality concerns ave been identified due to suc distributed armonic sources [-, -9]. One of tem is tat distribution systems are injecting significant amount of armonic currents into transmission systems [, 6]. Te consuences include overloading of transmission capacitors, tripping of HVD filters, and increased incidents of transmission armonic resonances [-]. It is common nowadays tat transmission and distribution systems are owned by different owners due to electricity market deregulation. Te penetration of armonic currents from distribution systems into transmission systems is becoming a sensitive issue. For example, several jurisdictions ave imposed limits on suc armonics [-]. Terefore, bot types of companies will benefit from a solution tat can prevent distribution system armonics from penetrating into te transmission systems. Distribution system owners may use te solution to meet te interconnection ruirements regardless te armonic distortion levels inside te distribution systems. Te Tis work was supported by te Natural Sciences and Engineering Researc ouncil of anada and Alberta Power Industry onsortium. Te autors are wit te department of Electrical and omputer Engineering, University of Alberta, Edmonton, A T6G V, anada ( wxu@ualberta.ca). transmission owner can easily recognize te solution taken by te distribution company and verify its effectiveness. Motivated by te above considerations, tis paper presents a novel filtering sceme tat can reduce te armonic injection from distribution systems into transmission systems. Te basic idea is to utilize te tertiary winding of te substation transformer to create a tuned low impedance pat for te armonics. Te proposed filtering sceme is terefore called tertiary winding filter. In te following sections, subjects suc as filter topology, design metod, performance assessment and cost analysis are presented. II. REVIEW OF APPLIALE MITIGATION SHEMES Altoug little researc work as been done in te direction of preventing armonics from entering transmission systems, tecniques tat can be adopted for te purpose do exist. Tese tecniques can be classified into two types. One is to prevent or reduce te injection of zero-suence (ZS) armonics into te transmission system. Te oter type is to deal wit te positive and negative armonics. Tese armonics are collected termed as non-zero-suence (NZS) armonics in tis paper. A. Zero-Suence Harmonic Mitigation Tecniques ZS components are dominant in te rd, 9 t and oter tripleorder armonics. Single pase non-linear loads suc as energy efficient ome appliances are te most significant source of ZS armonics. It is quite common to observe ig levels of ZS armonics in a distribution substation feeding residential loads tese days [,, 9]. ) onnection Te simplest way to prevent ZS armonics' propagation into transmission systems is to configure te substation transformer s primary side into delta or ungrounded Wye connection. For suc connections, tere are pats for te ZS armonic currents to flow into te primary side. For cases were te primary side must be grounded, a grounding transformer [] may be installed at te primary bus to serve as te grounding point. ) Passive Zero-Suence Filter Sunt passive ZS filters create low ZS impedance to trap te ZS armonics. Tey ave various topologies and can be broadly classified into two types. Te first type is te L filter. A representative example of suc filters is te star-connected capacitors grounded troug an inductor [6]. Tis filter as positive/negative suence impedance so it affects te flow of NZS armonics. Te second type is te transformer based ZS

13 filter wic is derived from te grounding transformer. Tis type as no impact on te normal power system operation and on NZS armonics since tey beave as open circuit at positive and negative suences. Examples include te zig-zag transformer based filter [7] and te Yg/delta transformer based single tuned ZS filter [8] and double tuned ZS filter [9].. Non-Zero-Suence Harmonic Mitigation Tecnique NZS components are dominant in te t, 7 t and oter nontriple order armonics. All non-linear loads generate NZS armonics. As a result, NZS armonic distortion level is usually iger tan te ZS armonic distortion level. At present, te only known metod to mitigate NZS armonic in mediumvoltage (MV) or ig-voltage (HV) systems is te passive sunt filters. ommonly used L NZS filters include te tuned filter, damped filter and te type filter [-]. Tese filters can be installed in te secondary side of te substation, creating a low impedance pat to trap te armonics originated from te distribution systems.. Summary It can be seen tat te options to prevent te armonics from entering transmission systems are limited. Some of tem are adopted from te metods developed for oter applications. It is, terefore, wortwile to investigate solutions tat are dedicated to addressing te problem and, tus, can take advantages of te specific caracteristics of te substation configurations. III. PROPOSED TERTIARY WINDING FILTER In view tat many substation transformers ave a tertiary winding [], it may be possible to utilize te substation transformer as a filtering transformer on top of its power transmission function. Te need for a dedicated filtering transformer is tus eliminated. Tis reasoning as led us to propose a new filtering sceme called Tertiary Winding Filter. A. asic Principle of te Tertiary Winding Filter Te basic idea of te tertiary winding filter is to utilize te leakage inductance of te tertiary winding to create a low impedance pat to trap armonic currents at tuned fruencies. Tis is acieved by inserting capacitors and inductors into te delta loop of te tertiary winding for ZS armonic filtering and by connecting sunt capacitors and inductors to te tertiary winding for NZS armonic filtering. Topology of te filter is depicted in Fig.. Te system uivalent circuit at tese tuned fruencies seen from te secondary side of te substation transformer is sown in Fig.. In Fig., R Xfrm _ and L Xfrm _ represent te leakage resistance and leakage inductance of te substation transformer's primary winding (referred to te secondary side), R Xfrm _ and L Xfrm _ represent te leakage resistance and leakage inductance of te substation transformer's secondary winding, R Xfrm _ represents te leakage resistance of te substation transformer's tertiary winding (referred to te secondary side), Z ( ) Up / / represents uivalent transmission system armonic impedance seen at te primary side of te substation transformer (but referred to te secondary side), Z ( ) Down / / and I ( ) Down / / represent uivalent armonic impedance and armonic current source of distribution feeders and loads. System V SA V S V S Z up # # # us Fig. Topology of te proposed tertiary winding filter. System Z ( ) Up / / # # R Xfrm _ j L R Xfrm _ Xfrm _ j LXfrm _ # R Xfrm _ A N Distribution Feeders and Loads Tertiary Winding Filter us Distribution Feeders and Loads Z () Down / / I () Down / / Fig. Equivalent circuit of te tertiary winding filter at tuned fruencies. It can be seen tat te tertiary winding s impedance only contains te resistive component, i.e. te leakage resistance of te tertiary winding, since te reactive component as been canceled out by te tuning capacitors. As a result, a low impedance pat separates te transmission and distribution systems. Harmonics originated from te distribution system will be bypassed by te tertiary winding before it can reac te transmission system. In addition, typical voltage of a substation transformer tertiary winding is.6kv to.8kv. Low voltage L components can be used to construct te filter, wic results in cost savings.. Equivalent ircuits of Tertiary Winding Filter As sown in Fig., te tertiary winding filter is composed of two parts, i.e., te delta connection part (te delta loop) and te star connection part (te sunt components at te tertiary side). Since for ZS armonics, te star connected sunt components at te tertiary side beaves as open circuit, te tertiary winding filter ZS uivalent circuit only consists of te delta connection parts (see Fig. (a)). For NZS armonics, te star

14 connected sunt components at te tertiary side beave as normal loads. Tus te tertiary winding filter NZS uivalent circuit consists of bot te delta connection part and te star connection part (see Fig. (b)). It sould be noted tat in Fig., a represents te tertiary winding to secondary winding turn ratio. Delta connection part a R /a Xfrm _ L /a Xfrm _ L /a a L /a (a) Equivalent ZS circuit a a / Fig. Equivalent circuit of te tertiary winding filter. R /a Xfrm _ L /a Xfrm _ L /a a L /a L / a Delta connection part L / a Star connection part a / (b) Equivalent NZS circuit ased on te above caracteristics of te tertiary winding filter's uivalent circuit, te delta connection part is designed to form a double tuned filter for te ZS armonics and te delta connection part and te star connection part togeter are designed to form a triple tuned filter for te NZS armonics.. Feasibility Analysis Tis subsection is to compare te relative size of te primary impedance versus tuned tertiary impedance and to sow tat most armonics will enter te tertiary pat. According to Fig., for te tertiary winding filter to be effective, te uivalent impedance of te tertiary winding filter sould be less tan te transmission system impedance plus substation transformer primary side winding's impedance at corresponding fruencies. Tis is an easily satisfied condition. Intuitively, te minimum impedance of te tertiary winding filter at tuned armonic orders could be acieved as te substation transformer tertiary winding resistance referred to te secondary side by proper selection of te capacitors and inductors. According to te typical parameters of tree winding transformer, te tertiary winding resistance is comparable to te primary winding resistance. And for a substation transformer, its reactance resistance ratio is usually very ig [] wic means L Xfrm _ R Xfrm _. Tus R R j L ' Xfrm _ Xfrm _ Xfrm _ R ( ) Xfrm _ j L Xfrm _ ZUp / / () smaller tan upstream system impedance. In tis way, armonics at tuned fruencies will be trapped into te tertiary side rater tan propagating into te transmission system. A roug estimation of te percentage of te armonic current tat will be trapped by te tertiary winding filter could be obtained by te following uation: L Xfrm _ Ratio R L ' Xfrm _ Xfrm _ were is te tuned armonic order. To sow te performance of te tertiary winding filter, some of te typical sizes of te tree winding transformers used by te utility company are listed in Table I. Te percentage of te tird armonic current tat will be trapped by te tertiary winding filter is provided in te last column. For iger tuned order armonics, larger percentage will be trapped by te tertiary winding filter. TALE I: TRAPPED RATIO FOR DIFFERENT THREE WINDING TRANSFORMERS Parameter Trapped Rated Rated Sort ircuit On-Load Ratio apacity a Voltage b Impedance Loss () (MVA) (kv) () (kw) H-M. // //6. H-L M-L 6. H-M. //8 //.8 H-L M-L 6. H-M. //6 //.6 H-L M-L 6. H-M. //. //6. H-L M-L 6. H-M. //6.7 //.8 H-L M-L 6. a Te rated capacity of eac winding. b Te nominal line-to-line voltage (LL-rms) IV. TERTIARY WINDING FILTER DESIGN Te design of te tertiary winding filter is an iterative process based on te system armonic load flow study and components loading assessment. Te design objective is to determine proper L component parameters based on te transformer parameters. Te flowcart of design procedure is sown as Fig.. A. L omponents' Size Determination As sown in Fig., te determination of components size consists of two steps. Te first step is to determine te delta connection part components size. As seen from Fig. (a), te delta connection part is actually te same to te double tuned filter. ased on analytical derivations, te component parameters of te delta connection part can be determined by te uation set (). () wic means te impedance of te tertiary winding filter is far

15 . No Increase te inductor rated current and kvar Set, L L Xfrm _ Size delta connection part components Are te parameters reasonable? L L / Xfrm _ Size star connection part components Are te parameters reasonable? Overloading in transformer windings? No Overloading in capacitors? No Overloading in inductors? No Final Filter Design Fig. Flowcart of design procedure for te tertiary winding filter. i j i j ( i j ) ( i j) ( LXfrm _ L )( i j ) L ( i j) i i ( LXfrm _ L ) j j ( LXfrm _ L ) No. Increase te capacitor rated voltage and kvar were i and j represent te ZS tuned order of te tertiary winding filter. Once, and L are determined, te star connection part components parameter could be determined by te following way. Te NZS impedance of te tertiary winding filter at armonic order could be expressed as were f( ) a ( ) Z Xfrm _ / ( ) RXfrm _ j g () () f ( ) ( L L L Xfrm _ ) ( L ) L ( L ) ( L )( L ) () g( ) ( L )( L ) (6) Since te filter is tuned to tree NZS fruencies, ten f()= at corresponding armonic orders, and, i.e., f ( ),,, (7) y solving uations set (7),, and L are determined. It is important to note tat two compensation inductors L and L are used in te tertiary winding filter, due to te leakage inductance of te transformer wic is usually small may result in extremely large capacitance needed. y adjusting te compensation ratios α and β (sown in Fig. ), tertiary winding filter wit capacitors and inductors of acievable parameters could be obtained and te reactive power compensated by te filter could also be set to be te ruired value.. omponents Loading Assessment omponents are susceptible to failures and even breakdown if te voltages across tem or te currents flowing troug tem exceed a certain degree during a certain period of time []. Tus te components loading assessment is an important part of te filter design. In te tertiary winding filter design, te transformer loading condition is evaluated by te index TLL ( Loading Level) wic is developed in [9]. For assessing te loading of te capacitors, te uivalent loading index based on researc findings of partial-discarge caused capacitor aging is used []. As for te inductor, its loading level is evaluated by te current flowing troug it normalized by its current rated rms value []. As long as te components overloading is identified, corresponding adjustments sould be made as sown in Fig.. V. SIMULATION STUDIES Two test systems are selected to verify te proposed tertiary winding filter and its design procedure as well as to examine its system performance. A. Simulation Studies on Distribution System Tis subsection conducts te simulation studies on test system # a generic distribution system supplying residential loads wic are evenly distributed along five feeders mainly in support of te effectiveness of te proposed tertiary winding filter and its design procedure. Table II gives te main parameters of test system #. Fig. depicts its network configuration, in wic eac section block consists of tree service transformers wic connects secondary systems serving residential ouses.

16 System V SA V S V S Z up # # # A N Line Feeder Section S Rg Feeder S S7 S7 propagating into te transmission system and te armonic voltages at te primary side of te substation transformer ave been greatly reduced wen te tertiary winding filter is installed, wic demonstrates te effectiveness of te tertiary winding filter. 8 6 TDD -- Witout Tertiary Winding Filter Pase A Pase Pase 8 6 TDD -- Wit Tertiary Winding Filter Pase A Pase Pase Fig. Network configuration of test system #. Primary System TALE II: MAIN PARAMETERS OF TEST SYSTEM # System Parameters Values Voltage level (LL-rms) kv Z System Equivalent impedance +/-=.8+j.9 Ω Z =.+j.6 Ω Rated apacity MVA/MVA/MVA Rated Voltage (LL-rms) kv/kv/6.kv onnection Type Yg/yg/delta H-M. Sort ircuit Impedance H-L 8 M-L 6. On-Load Loss 6.kW Number of Feeders Power Line Type Overead line Main Trunk # of Sections per Feeder 7 Lengt of Eac Section.km Grounding Span m Grounding Resistance (R g) Ω ) Tertiary Winding Filter Design Results Te introduced iterative process (Fig. ) was employed to determine te final filter design. Table III presents te component size of te designed tertiary winding filter. TALE III: DESIGNED OMPONENTS SIZE OF THE TERTIARY WINDING FILTER omponent Parameters Values L None 6.kvar (.6 kv) a Delta connection part.mh(79a) b L L L 9.kvar (.6kV).9mH(79A).kvar(.6kV) Star connection part.7mh(79a) 67.8kvar (.6kV) a Te voltage in te bracket is te capacitor rated voltage. b Te current in te bracket is te inductor rated current, te inductor rated voltage is 6.kV. ) Simulation Results All te developed models are employed in a multipase armonic power flow program [] to perform te simulation studies. As te residential loads are time-varying during a day, time-varying simulation results are obtained. In order to establis a sound understanding of te proposed tertiary winding filter performance, te simulation results for bot te case witout tertiary winding filter and te case wit tertiary winding filter are sown in Fig. 6 to Fig. 9. As seen from Fig. 6 to Fig. 9, bot te armonic currents Time () Time () (a) (b) Fig. 6 TDD variation of currents propagating into transmission system. IDD Spectrum -- Witout Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order IDD Spectrum -- Wit Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order (a) (b) Fig. 7 Typical IDD spectra of currents propagating into transmission system. THD -- Witout Tertiary Winding Filter Pase A Pase Pase Time () THD -- Wit Tertiary Winding Filter Pase A Pase Pase Time () (a) (b) Fig. 8 THD variation of voltages at primary side of substation transformer. IHD Spectrum -- Witout Tertiary Winding Filter. Positive suence Negative suence Zero suence Harmonic Order... IHD Spectrum -- Wit Tertiary Winding Filter Positive suence Negative suence Zero suence 7 9 Harmonic Order (a) (b) Fig. 9 Typical IHD spectra of voltages at primary side of substation transformer.. Simulation Studies on System Tis subsection conducts several simulation studies on test system # (see Fig. ) an extension of te IEEE bus transmission system proposed in [6] aiming to furter examine: Will te distribution armonic loads at oter bus lead to te tertiary winding filter overloading? Is it essential to uip all te buses wit distribution armonic loads wit te tertiary winding filter?

17 6 G G G Fig. Network configuration of test system #. 6 9 SV onverter Te major difference of test system # from IEEE bus transmission system includes: All components in te system are modeled in pase domain. Te loads at us, us, us 9, us, us, us, us and us are selected to be modified as distribution system loads as test system #. To reduce te complexity, te aggregated distribution system load model (see Fig. ) is adopted. It sould be noted tat te total fundamental fruency loads at us, us, us 9, us, us, us, us and us keep te same wit tat in te IEEE bus transmission system, wile teir armonic caracteristic parameters wic include te armonic current spectrum of eac pase and armonic impedance matrix are derived from test system # at peak load instant. To simplify te analysis, te armonic currents injected by HVD and SV are neglected. A HV us MV us A A # # HV us # PA jqa P jq P jq (a) Fundamental fruency model # # # MV us A I ( ) A I( ) I ( ) (b) Harmonic fruency model Fig. Aggregated distribution system load model. Z {} ) Influence of Distribution Harmonic Loads at Oter uses In te previous sections, te tertiary winding filter was torougly examined in te distribution system. However in te tertiary winding filter design, loading assessment was conducted witout considering te influence of distribution armonic loads at oter buses. Will tis be an issue for te tertiary winding filter if tere are multiple distribution armonic loads 7 8 at oter buses in te transmission system? To answer tis question, eigt sets of cases are studied. Eac set of cases consists of two cases: i) tere is no distribution armonic loads at oter buses except were te tertiary winding filter is installed; ii) all te load buses (us, us, us 9, us, us, us, us, us ) are modified as distribution armonic loads. Te detailed description of tese case sets and overloaded components for different cases are given in Table IV. Loading assessment for all eigt case sets sow tat te distribution armonic loads at oter buses do ave influence on te loading level of te tertiary winding filter. ut te influence is different for te tertiary winding filter at different locations. According to Table IV, indicated by ase Set, and 6, te tertiary winding filter designed based on te distribution armonic load information at its own bus will be overloaded by distribution armonic loads at oter buses. Tus if multiple distribution armonic loads exist, te transmission system armonic power flow sould be incorporated into te tertiary winding filter loading assessment and components of larger size sould be adopted wen overloading issues are identified. ase Set TALE IV: LOADING ASSESSMENT RESULT ase Filter Distribution Harmonic Overloaded Placement Loads Location omponents i us us None ii us All load buses None i us us None ii us All load buses None i us 9 us 9 None ii us 9 All load buses None i us us None ii us All load buses i us us None ii us All load buses i us us None ii us All load buses i us us None ii us All load buses None i us us None ii us All load buses None ) Installation Density Study Tis subsection presents te sensitivity study to assess te influence of te installation density of te tertiary winding filter on te overall transmission system armonic distortion level. Simulation results for te following case sets are compared in Fig.. i. Test system # wit te loads at bus, bus, bus 9, bus, bus, bus, bus and bus all modified as a distribution armonic load. ii~ix, based on i, install one tertiary winding filter at any one, any two,, all of te buses wit distribution armonic loads. In Fig., te average voltage THD is te voltage THD average over all buses under eac cases for eac case set and te average current TDD is te current TDD average over all transmission lines and transmission transformers under eac cases for eac case set, wile minimum voltage THD is te minimum voltage THD average over all buses for eac case set

18 7 and minimum current TDD is te minimum current TDD average over all transmission lines and transmission transformers for eac case set. As sown in Fig., te more te tertiary winding filter installed te lower te overall transmission system armonic distortion level is in terms of bot te bus voltage THD and transmission uipment TDD. =, =7 =9, A A A L L L L L L L L L L L Fig. MV L filter package. Fig. Average minimum armonic distortion level for different cases. Table V furter gives te filter placement wic results te minimum armonic distortion level for ase Set ii ~ viii and te corresponding overall system voltage distortion level and current distortion level wit suc placement. TALE V: OPTIMUM FILTER PLAEMENT FOR DIFFERENT ASES Overall System ase Optimum Filter Harmonic Distortion Placement Voltage urrent THD * () TDD * () ii us 9 6.7(8.6).(.9) iii us 9, us.6(8.7).9(.) iv us 9, us, us.9(7.8).9(.98) v us 9, us, us, us.86(6.7) 8.8(.) vi us 9, us, us, us, us.9(.6) 8.7(.9) vii us 9, us, us, us, us, us.(.) 8.(.6) viii us 9, us, us, us, us, us, us.(.) 7.87(8.88) *Figure in te bracket is te average value for eac case set. As indicated by Fig. and Table V, wit optimum filter placement, better armonic mitigation effects can be acieved. Anoter useful information could be extracted from Table V is te distribution armonic load at us 9 as te largest impacts on te overall system distortion level since for all te optimum filter placement one tertiary winding filter sould be placed at us 9. VI. OMPARATIVE EONOMI ANALYSIS Te cost of te proposed tertiary winding filter as been investigated using test system #. It is also compared wit te cost of te MV L filter package. To obtain a meaningful comparison, te MV L filter package is designed to acieve te same armonic distortion reduction wit te tertiary winding filter specified by Table III. Te designed MV L filter package sown as Fig. consists of two inductor grounded single tuned L filters wic are tuned to filter te rd, t and 9 t and t armonics respectively and one directly grounded single tuned L filter wic is tuned to filter te 7 t armonic. Te designed components size of te MV L filter package is given in Table VI. TALE VI: DESIGNED OMPONENT SIZE OF MV L FILTER PAKAGE Filter Tuned Harmonic omponent Size Design Order L 6.mH (8A) Filter, 87.8kvar (.kv) L.69mH (6A) L 8.7mH (69A) Filter kvar (.9kV) L.8mH (69A) Filter 9, 9.8kvar (.9kV) L.88mH (69A) Te voltage in te bracket is te capacitor rated voltage. Te current in te bracket is te inductor rated current, te inductor rated voltage is.kv. For te cost estimation, te data collected from [7] and te Internet are used. Table VII sows te approximate expenses for filter components. TALE VII: ESTIMATED OST OF OMPONENTS apacitor Rated Voltage <kv kv~kv kv~kv kv~kv ost $/kvar $/kvar $/kvar $6/kvar Inductor Voltage Level kv~kv kv~kv <A $ $8 Rated A~A $7 $ urrent A~A $9 $8 Oter omponents kv~kv kv~kv Switcing Device $7, $, Protection Device $, $7, y te mentioned information, te overall cost of te tertiary winding filter and MV L filter package is estimated as presented in Table VIII. As seen from Table VIII, te tertiary winding filter is found to be muc more economical. TALE VIII: OVERALL ESTIMATED OST Tertiary Winding Filter MV L Filter Package Total ost $9, $7,9 VII. APPLIATION ONSIDERATIONS Most substation transformers are custom made and ave tertiary windings. It is relatively easy to make te six terminals of te tertiary windings available for te proposed application. Terefore, utility companies could order suc a transformer for new substations. Te tertiary winding filter can ten be implemented by connecting corresponding L components. Te same applies to te existing substations were six terminals of te tertiary windings are accessible.