Passive Filter Aided by Shunt Compensators based on the Conservative Power Theory

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1 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE Passe Flter Aded by Shunt Compensators based on the Conserate Power Theory Tago Da Cur Busarello, José Antenor Pomlo Student Member, IEEE; Senor Member, IEEE Unersty of Campnas UNICAMP, Campnas, Brazl tago21@dsce.fee.uncamp.br; antenor@fee.uncmap.br Marcelo Godoy Smões Senor Member Colorado School of Mnes, Golden, USA mgsmoes@eee.org.br Abstract-- Passe flters are wdely used n electrcal system for power qualty mproements. Ther frst nstallatons date from 194s and ther adantages make them an attracte and standard soluton up to nowadays. Howeer, passe flters hae ther flterng characterstcs deterorated due to parameter araton, caused by agng or temperature. Addtonally, a capactor bank for power factor correcton s desgned for specfc loads and may not supply the rght amount of reacte power when loads keep beng added or changed. When these ssues make the passe flter and the capactor bank ncapable to keep the system operatng wthn acceptable leel of power qualty, an nconenence arses and a soluton must be proded. A common one s to replace both of them ether by new elements or by acte power compensators. Howeer, replacng the passe flter and the capactor bank may not be not economcally feasble because they belong to a past nestment. Ths paper presents a soluton to oercome such nconenence keepng the passe flter and the capactor bank nstalled and unchanged. It conssts of nstallng two shunt compensators specally desgned for performng what the passe flter and the capactor bank are ncapable to do. The result s a reduced processed power n the compensators. The generaton of the references s based on Conserate Power Theory. A case study s presented n order to proe the compensators effcacy and the power qualty mproement. Index Terms acte flters, power dstrbuton, power flters, power qualty. I. INTRODUCTION Power qualty n electrcal systems has been under concernng for decades. A partcular ssue noles the harmonc dstorton n the lne current. Its presence may cause conductor oerheatng, oltage dstorton, transformers malfunctons, unnecessary protecton dece trp and nterference n telecommuncaton network [1]. Seeral solutons to mproe power qualty hae been deeloped. One of the smplest and oldest solutons s the nstallaton of Tuned Passe Flter (TPF) [2]-[6]. TPF makes a low-mpedance patch at the tuned frequency. Some of the adantages of usng TPF are the low-ntal cost and the robustness. Howeer, the flterng effcacy may be deterorated due to parameter araton caused by agng or temperature. Regardng the mproement of power factor correcton for snusodal condtons, capactor banks are used due to ther low cost and desgn smplcty. Neertheless, a capactor bank s desgned for specfc amount of loads and once the loads are constantly beng added or remoed, ts performance may be backward and the power qualty deterorated. Swtched capactors appear as a soluton for load araton, but the swtch-on and off transtory behaors are ery seere to the grd [7]. Addtonally, f the load has low dsplacement factor (phase dfference between fundamental frequency current and oltage), the TPF capacte behaor at ths frequency can een reduce the power factor. The technologcal adancement allowed solutons wth more accuracy and effcency [8]-[11], such as acte compensators. These compensators can be desgned to replace the passe flters and capactor banks. Howeer, replacng them s not economcally feasble because they belong to a past nestment. Therefore, an attracte soluton s to keep nstalled the passe elements and to nstall an acte compensator, resultng n a hybrd structure. The processed power of an acte compensator s proportonal to ts output current. When a passe flter s fully replaced by an acte compensator, the last should be szed to hold all the current whch was crculatng through the passe flter. On the other hand, when a shunt compensator s nstalled and the passe flter s kept unchanged, the compensator s szed only to hold the current whch s ncapable to crculate n the passe flter. Snce the output current s lower n ths case, the processed power s expected to be lower. Smlar analyss can be found n capactor banks. Ths paper proposed two shunt compensators to ad a TPF and a capactor bank. The TPF and the capactor bank are kept nstalled and unchanged. The compensators commands are defned based on the Conserate Power Theory (CPT) [12]- [15]. One s desgned to compensate TPF detunng and also to mtgate harmonc current that s beyond the TPF bandwdth whle the other s to compensate reacte power whch s not compensated by the capactor bank, ether by ageng or connecton of new loads. Snce the proposed soluton keeps the TPF and the capactor bank, the compensator output current s expected to be reduced as well as the ts cost. II. ELECTRICAL SYSTEM PERSPECTIVE Fg. 1 presents a smplfed dagram of a typcal electrcal system. It conssts of the man generaton, dstrbuton transformers and two PCCs. There s a TPF tuned at 5 th harmonc, a capactor bank and lnear and non-lnear loads. The utlty and transformer mpedance wll be later represented by an equalent RL crcut. The non-lnear load s a sx-pulse three-phase thyrstor rectfer. The 5 th load harmonc current harmoncs s deated by the passe flter branch, composed by C5 and L5. In accordance to the IEEE recommendaton [16], the TPF should not be tuned exactly at the harmonc frequency. Instead, t s recommended a lower alue to aod the exctaton of the seres resonance by source oltage harmoncs. But the lower the tuned frequency s, the lesser effecte the TPF s (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

2 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE Man Generaton Man Generaton g L s g L s Dstrbuton Transformer 6 kva. 4.9% Dstrbuton Transformer 6 kva. 4.9% 15kVA. 6% PCC 1 1kVA.8 Lag 17kVA.89 Lag PCC 2 pcc1 pcc2 S 1 S 2 dc /2 nl dc /2 Fg. 1. Smplfed dagram of a typcal electrcal system. III. CPT BASED COMPENSATORS C bank cap PCC2 There are two compensators to support the electrcal system: () C1, connected at the PCC1, where the capactor bank s nstalled, and () C2, connected at the PCC2, where the TPF s connected. Fg. 2 presents a smlar system dagram showng the two proposed compensator. They are represented by dependent current sources. It s also presented the arable whch must be measured n order to obtan the compensator current references. A. The Conserate Power Theory The CPT s a tme-doman theory applcable to any perodc sgnal, sngle- or pol-phase system wth or wthout neutral conductor. The prncple operaton s the orthogonal decomposton of electrcal arables, resultng electrcal quanttes wth physcal meanng. Each quantty represents electrcal load characterstcs lke consumed acte power, storage energy, phase dsplacement between oltage and current, unbalancng and so on. Moreoer, the CPT does not make arable transformaton. The CPT s used n ths paper to compute electrcal quanttes at the PCC1 and PCC2. The acte and reacte powers, the harmonc content and the unbalance nformaton of them are extracted by means of the CPT. Later, the compensators 1 and 2 use these quanttes to compose ther current reference sgnals. The followng analyss s n a sngle-phase based but t s applcable to three-phase. The aerage alue of a arable x s gen by (1). 5 L 5 C 5 15kVA. 6% PCC 1 1kVA.8 Lag C1 17kVA.89 Lag C1 tot1 pcc1 PCC 2 C2 C2 pcc1 pcc2 pcc2 tot2 S 1 S 2 dc /2 nl dc /2 C bank cap PCC2 Fg. 2. The same smplfed system dagram presented n the preous fgure, but now wth the two proposed compensators. T 5 L 5 C 5 1 x x() t dt T (1) The tme-ntegral of a arable x s gen by (1). T x ( t) x( ) d (2) The unbased ntegral of a arable x s gen by (3). xˆ( t) x ( t) x ( t) (3) Where the second term of (3) s the aerage alue of (2). The unbased term means the ntegral does not contan aerage alue. The tme-derate of a arable x s gen by (4). dx() t xt () (4) dt The unbased ntegral and the tme-derate present the followng propertes: xˆ xˆ x x, x x, xˆ x, y x, y x, yˆ xˆ, y x, yˆ xˆ, y x, y where, s the nternal product. The root-mean square (RMS) alue of a arable x s (5) (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

3 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE represented by (6) Xrms For a gen oltage (t) and a current (t), the acte current for one phase s gen by (7). a x, 2 In a smlar way, the reacte current for one phase s gen by (8). r ˆ, The od current s gen by (9). 2 ˆ a r The od current contans all quanttes that do not present nether acte nor reacte behaor. The three-phase acte current s gen by (1). acte( a, b, c) 2 ( a, b, c) ( abc,, ) (6) (7) (8) (9) ( a, b, c), ( a, b, c) (1) The three-phase reacte current s gen by (11). ˆ ( a, b, c), ( a, b, c) ˆ r( a, b, c) 2 ( a, b, c) (11) ( abc,, ) The three-phase od current s gen by (12). (12) ( a, b, c) ( a, b, c) acte( a, b, c) r( a, b, c) The three-phase acte balanced current s gen by (13). aa bb cc actebal ( a, b, c) ( a, b, c) (13) a b c The three-phase reacte balanced current s gen by (14). ˆ ˆ ˆ aa bb cc ˆ rbal ( a, b, c) ( a, b, c) (14) ˆ ˆ ˆ a b c For balance compensaton, t s suffcent to add to the compensator current reference the equatons (13) and (14). B. Set-pont for Current Compensators The compensator current reference s computed based on the preous equatons. Once the compensator C2 s desgned to mtgate the harmonc currents not compensated by the TPF, ts current reference s the PCC2 od current. Therefore, the C2 current reference s gen by (15). * (15) C 2 _ pcc2 Smlarly, the compensator C1 s desgned to consder only the reacte energy, ts current reference s gen by (11). * (16) C1 r_ pcc1 Snce the compensators follow ther current reference, the power qualty n the system wll be mproed. The system presented n Fg. 2 was smulated n PSIM n order to erfy the proposed compensators effcacy. Intally, the compensators are turned off and the system s n steadystate condton. The swtch S1 and S2 are opened. Tab. I presents the system parameters used n smulaton. The TPF C5 and L5 s tuned at 5.1th harmonc n order to emulate a detunng caused by ageng. TABLE I. SYSTEM PARAMETERS USED IN THE SIMULATION Symbol Quantty Value Vg Man Generaton RMS oltage 69 kv Vpcc1 PCC1 RMS oltage 13.8 kv Vpcc2 PCC2 RMS Voltage 48 V f Frequency of the system 6 Hz IL Maxmum demand load current (fundamental frequency 3 A component) at PCC1 Sbank Capactor bank Apparent Power 5 kva Idc Rectfer DC Load Current 2 A C5 Tuned Passe Flter Capactor 3 uf L5 Tuned Passe Flter Inductor 9 uh Fg. 3 presents the PCC2 three-phase current when the compensator C2 s turned on, at t = 5 s. After that, the PCC2 current became snusodal. The spkes are due to the hgh current derate caused by the non-lnear load. The PCC2 current THD before and after the compensator began to operate are 2.9% and 9.% Ipcc2a Ipcc2b Ipcc2c Tme (s) Fg. 3. PCC2 three-phase current when the compensator C2 s turned ON. Fg. 4 depcts the TPF and the compensator C2 current for one phase when the compensator s turned ON. The C2 begns to operate wth no oscllatng behaor and the TPF current s kept unchanged. IV. CASE STUDY (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

4 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE I5a IC Tme (s) Fg. 4. TPF and the compensator C2 current for one phase when the compensator C2 s turned ON. Fg. 5 portrays the current spectra for PCC2, non-lnear load, TPF and compensator C2 currents. The fundamental components were oerlapped for better sualzaton of the remanng spectra. The non-lnear load (Inl) presents a hgh harmonc content. The TPF (I5a) presents only the fundamental and 5 th harmonc components. The fltered 5 th harmonc component s approxmately 5% of the load 5 th harmonc current due to the detunng. The compensator C2 current (IC2) contans the remanng 5 th harmonc and does not contan fundamental component. Moreoer, the compensator C2 current presents all other harmoncs equal to the non-lnear load. The resdual components n the PCC2 current are due to non-deal current dsor formed by the PCC2 and TPF mpedances. Notce that wthout the nstallaton of C2, the 5 th harmonc of the PCC2 current would be the dfference between the nonlnear load and the TPF, at 5 th harmonc. Moreoer, all the remanng harmoncs generated by the nonlnear load would crculate through the PCC2 pont upstream. 5 Ipcc2a 3 Inl 3 I5a 3 IC st 5 th 7 th 11 th 13 th 17 th 19 th 23 th Harmonc order Fg. 5. Current spectra for PCC2 (aboe), non-lnear load, TPF and compensator C2. Fg. 6 presents the spectra content for the IEEE [17] lmt, the nonlnear load (Irect), the PCC2 current when only the TPF s nstalled (Ipcc2_TPF) as well as the PCC2 current when the C2 s nstalled (Ipcc2_TPF+C2). The fundamental components were omtted for better sualzaton. The nonlnear load current components olated the IEEE leels n all analyzed harmoncs, except the 11 th. When just the TPF s nstalled as a soluton, the 5 th and the 11 th are lower than the lmt allowed by the IEEE On the other hand, when the C2 s nstalled, all harmonc components n the PCC2 current are wthn the specfed lmt. The harmonc content for the PCC1 current s not presented because such current s free of dstorton. % of the Fundamental IEEE519: 2<Isc/IL<5 Irect Ipcc2_TPF Ipcc2_TPF+C Harmonc Fg. 6. spectra content for the IEEE , the nonlnear load (Irect), the PCC2 current when only the TPF s nstalled (Ipcc2_TPF) as well as the PCC2 current when the C2 s nstalled (Ipcc2_TPF+C2). Fg. 7 shows the PCC2 current, the nonlnear current, the TPF current and the compensator C2 current when swtch S1 turns-on. Nether oscllatory nor unpredctable behaor happened n the measured arable Ipcc2a Ipcc2b Ipcc2c 2 Irecta 1 15 Ipfa IC Tme (s) Fg. 7. The PCC2 current, the TPF current and the compensator C2 current when swtch S1 turns-on. Fg. 8 shows the PCC1 current and oltage for phase A when the compensator C1 s turned ON. The compensator C2 begns to operate at t =5.2 s. The compensator makes the (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

5 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE oltage and current to be n phase. It s mportant to hghlght the fact that the most part of the PCC1 reacte energy s beng compensated by the capactor bank. The spkes found n the PCC1 current are lower those found n PCC2 current because the capactor bank acts as a hgh-pass flter. If the C1 was not nstalled, the PCC1 would operate wth dsplacement factor dfferent from one, contrbutng to the stress of the dstrbuton transformer. [A,V] Ipcc1a 4 Vpcc1a/5 compensaton. The PCC2 current s snusodal, but wth dfferent ampltudes. At t = 5.5s the unbalance compensaton turns-on. The grd current becomes balanced. Ipcc1a Ipcc1b Ipcc1c Tme (s) Fg. 1. The PCC2 current when C2 s compensatng the unbalanced load Tme (s) Fg. 8. The PCC1 current and oltage for phase A when the compensator C1 s turned ON. Fg. 9 shows the PCC1 current and oltage for phase A n an occurrence of a capactor bank fal. At t =5.24 s the capactor bank s permanently dsconnected and the compensator C1 begns to compensate all the PCC1 reacte power. The steady-state s reached after one cycle and half. The compensator C1 current s snusodal and t s 9 degree phase-shfted related to the PCC1 oltage, ndcatng that compensator processes only reacte energy. [A,V] Ipcc1a Vpcc1a/ IC1a Icapa Tme (s) Fg. 9. The PCC1 current and oltage for phase A n an occurrence of a capactor bank fal. Fg. 1 presents the PCC2 current when C2 s compensatng the unbalanced current. Intally, the swtch S2 s turned and C2 s operatng as acte flter wthout unbalance V. DISCUSSION ABOUT THE COMPENSATORS In order to analyse the compensaton strategy, the compensators are represented by controlled current sources n Fg. 2. Neertheless, n real applcatons they are power electronc conerters. Regardng the output current, the compensator 1 deals wth only fundamental component whle the compensator 2 wth fundamental and harmoncs. The fundamental s exclusely for reacte power compensaton. As the compensator 1 s nstalled at 13.8kV bus, one possble topology s the symmetrcal multleel nerter topology [18]-[2]. By usng phase-shft modulaton each cell of the multleel nerter can operate at low frequency (some hundreds of Hz), accordng to the characterstcs of the power swtches, whle the total syntheszed oltage swtchng frequency s the nddual cell commutaton frequency multpled by the number of cells. Ths way a hgh qualty, low dstorton fundamental component s produced [21]-[22]. Such behaour allows the applcaton of a current controller wth relate hgh bandwdth, a necessary condton to make the current to follow ts reference wth neglgble steady-state error. On the other hand, the compensator 2 s nstalled n low oltage. Therefore, the compensator 2 may hae the classcal H-brdge topology wth hgh frequency Pulse-Wdth Modulaton (PWM) [23]. The harmonc characterstc of the compensator 2 presents all harmonc spectrum of the nonlnear load, lmted to compensator output flter bandwdth. In the presence of TPF, the respecte harmonc components wll flow through the TPF, reducng the compensator processed power (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

6 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE VI. COST CONSIDERATIONS The quantty to represent the lfe-cycle cost of a system s defned as the total Net Present Cost (NPC) whch ncludes all costs and reenues that occur wthn the project lfetme, wth future cash flows dscounted to the present. Whereas the smulaton process models a partcular system confguraton, the optmzaton process determnes the best possble system confguraton. In a system lke the one n ths paper, the optmal system confguraton s the one that satsfes the user-specfed constrants at the lowest total NPC. In order to fnd the optmal system confguraton, one may nole decdng on the mx of components that the system should contan, the sze or quantty of each component, and the cyclng strategy the system should use. Possble decson arables (DV) mght be: DV1 - Cost of large capacte power requrements at fundamental frequency, DV2 - Power dsspated (and lost for reenues) n the TPF and any dampng, DV3 - Inestments to oercome for physcal restrctons of nstallng components, partcularly cl constructons and permts. The key physcal propertes of the study mght be ther nomnal current, ts capacty cure, ts lfetme cure, ts mnmum load, and ts round trp effcency. The cost of purchasng power from the grd can comprse an energy charge based on the amount of energy purchased n a bllng perod, and a demand charge based on the peak demand wthn the bllng perod. The conerter sze, whch s a decson arable, refers to the nerter capacty, meanng the nomnal output current. The economc propertes of the conerter are ts captal and replacement cost, ts annual Operatons & Mantenance (O&M) cost per year, and ts expected lfetme n years. Optmzaton can help the modeler fnd the optmal system confguraton out of many possbltes. Consder, for example, the task of retrofttng the shunt compensators descrbed n ths paper. In analyzng the optons for redesgnng the system, the modeler may want to consder the arrangement of components, but would not know n adance what combnaton of DV1, DV2 and DV3 aboe wll mnmze the lfe-cycle cost. These three arables would therefore be decson arables n ths analyss. A What-IF case study can be mplemented wth those arables, and many more that mght be mportant for the lfecycle cost study, for example by allowng parameters such as the number or sze of each component, the total captal cost of the system, the total net present cost, the leeled cost of energy (cost per kwh), the annual power consumpton for each soluton, and the number of hours the mantenance wll make the system not operatonal per year. A arable for whch the user has entered multple alues s called a senstty arable. Each combnaton of senstty arable alues defnes a dfferent senstty case. For example, f the user specfes sx alues for the () cost of large capacte power requrements, () power dsspated (and lost for reenues) n the TPF and three alues for nestments to oercome for physcal restrctons of nstallng components, the total number of cases s 6x6x2 = 72 for senstty analyss n dealng wth uncertanty n the optmal decson. Wth a careful spreadsheet ealuaton, a modeler can make nformed decsons despte uncertanty n mportant arables. The proposed compensator can hae renewable or nonrenewable technology as prmary source. Renewable and nonrenewable energy sources typcally hae dramatcally dfferent cost characterstcs. Renewable sources tend to hae hgh ntal captal costs and low operatng costs, whereas conentonal non-renewable sources tend to hae low captal and hgh operatng costs. In a full optmzaton process, the modeler must compare the economcs of a wde range of system confguratons comprsng aryng amounts of renewable and non-renewable energy sources. To be equtable, such comparsons must account for both captal and operatng costs. Lfe-cycle cost analyss does that by ncludng all costs that occur wthn the lfe span of the system. The total NPC condenses all the costs and reenues that occur wthn the project lfetme nto one lump sum n today s dollars, wth future cash flows dscounted back to the present usng the dscount rate. The modeler specfes the dscount rate and the project lfetme. The NPC ncludes the costs of ntal constructon, component replacements, mantenance, fuel, plus the cost of buyng power from the grd and mscellaneous costs such as penaltes resultng from pollutant emssons. Reenues nclude ncome from sellng power to the grd, plus any salage alue that occurs at the end of the project lfetme. Wth the NPC, costs are poste and reenues are negate. Ths s the opposte of the net present alue. As a result, the NPC s dfferent from net present alue only n sgn. All prces escalate at the same rate oer the project lfetme. Wth that assumpton, nflaton can be factored out of the analyss smply by usng the real (nflaton-adjusted) nterest rate rather than the nomnal nterest rate when dscountng future cash flows to the present. The modeler must use the real nterest rate, whch s roughly equal to the nomnal nterest rate mnus the nflaton rate. For each component of the system, the modeler specfes the ntal captal cost, whch occurs n year zero, the replacement cost, whch occurs each tme the component needs replacement at the end of ts lfetme, and the O&M cost whch occurs each year of the project lfetme. VII. ACKNOWLEDGMENTS The authors are grateful to the São Paulo Research Foundaton (FAPESP) (grant #212/ ) and CNPq - Brazlan Natonal Councl for Scentfc and Technologcal Deelopment (grant 3336/21-9) for supportng ths research (c) 215 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

7 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI 1.119/TIA , IEEE VIII. CONCLUSIONS Ths paper proposed two shunt compensators to ad a TPF and a capactor bank. The TPF and the capactor bank are kept nstalled and unchanged. The calculaton of the current references for the compensators s based on the Conserate Power Theory. One compensator was desgned to compensate harmonc current produced by non-lnear loads and to compensate the loss of flterng effcacy due to the TPF parameter araton. The other compensator was desgned to compensate reacte energy and load unbalance. A case study was performed to erfy the effcacy of the compensators. Accordng to the results, the power qualty was mproed and no unpredctable behaor occurred n the system durng step load and element dsconnectons. The compensators operated n combnaton wth the tuned passe flter and the capactor bank. The proposed soluton kept unchanged the already exstent passe flters, once they are a past nestment and remong them would not be good economcs or a practce that the utlty could mplement. The case study demonstrates that the compensators process lower power compared to solutons n whch passe flters are totally remoed. Therefore, the compensator szng and cost are reduced, makng the proposed soluton an attracte mplementaton for power qualty enhancements wth relate reduced costs. The smulaton fle used n ths paper s freely aalable on REFERENCES [1] F. C. de La Rosa, "Effects of harmoncs n dstrbuton systems" n Harmonc and Power Systems, 1st ed., CRC Press, 26, pp [2] Stone, P. 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