LOADING OF TRANSFORMERS BEYOND NAMEPLATE RATING

Transcription

1 LOADING OF TRANSFORMERS BEYOND NAMEPLATE RATING by K. B. M. I. Perera and J. R. Lucas Abstract Te application of a load in excess of nameplate ratings, and/or an ambient temperature iger tan designed of a transformer, involves a degree of risk and accelerated ageing. A software package as been developed, based on te standard termal equations given in IEC 354: Loading guide for oil immersed power transformers, to identify te risks involved and indicate ow transformers may be loaded in excess of te nameplate rating witout adverse effects. Te software package eliminates te tedious manual calculations oterwise involved wit te practical complex load profiles. It is also sown tat accurate results are obtained wit te package not obtained wit te limited step approximations required by te manual metod. Tis ensures tat unexpected damages to te transformer are avoided. Te study also sows tat tere is no significant cange in te voltage regulation and on te efficiencies of motor loads due to te loading provided tey are kept witin te specified limits. 1. Introduction 1.1 Scope A software package as been developed to provide guidance for loading of ONAN type distribution transformers from te point of view of operating temperature and termal ageing. Tis package identifies te risks involved wit over-loading and indicates ow, witin limitations transformers may be loaded in excess of teir nameplate rating. Te package is applicable to transformers wit a maximum rating of 25 kva tree pase or 833 kva per limb single pase. Te ig voltage rating is limited to 33 kv and witout on-load tap-canging, complying wit IEC 76: Power Transformers wit normal cyclic loading of duration one day. Te package can be used to acieve two objectives, namely to select a transformer of optimum capacity for a given loading condition and to ceck te utilisation of an existing transformer. 1.2 Loading effects on transformer life Te rating of a distribution transformer is usually assigned for continuous operation at tat value. However, extraordinary events, suc as overvoltages, sort-circuits in te system and emergency loading can affect te life of a transformer to a ig degree. Consequences 1,2 of loading a transformer beyond name-plate rating can be as follows. 1. Te temperatures of windings, insulation, oil etc. increase and can reac unacceptable levels. 2. Te leakage flux density outside te core increases, causing additional eddy current eating in metallic parts linked by te flux. 3. Te moisture and gas content in te insulation and in te oil increase wit te temperature increase. 4. Busings, tap-cangers, cable-end connections and current transformers are exposed to iger stresses. Mr. K. B. M. I. Perera, B Sc Eng, Factory Manager, Lanka Transformers Ltd, Moratuwa Prof. J. R. Lucas, BSc Eng, MSc, PD, CEng, FIE(SL), FIEE, MCS(SL), Head of Department of Electrical Engineering, University of Moratuwa Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

2 Tese increase te risk of premature failure, wic may be of an immediate sort term nature or may lead to long term failure due to cumulative deterioration of te transformer over many years Consequential Risks Te main risk for sort time failures is te reduction in dielectric strengt due to te presence of gas bubbles in te region of ig electrical stress. Tese bubbles may develop in te paper insulation wen te ot spot temperature rises suddenly above a critical temperature of about 14 C. Tis affects te reliability of te transformer. Te sort-term risks normally disappear, if failure as not been initiated, after te load is reduced to normal level. Te pressure build up in te busings may also result in a failure due to oil leakage and gassing in te busings, if te temperature of te insulation exceeds te said critical temperature. Cumulative termal deterioration of te mecanical properties of te conductor insulation will accelerate at iger temperatures. Tis deterioration process will ultimately reduce te effective life of te transformer. 2. Transformer Selection Based On Termal Parameters Te IEC Loading guide for oil immersed power transformers 3 gives te standard metod of selecting a transformer using Tables and Graps. It also gives te standard equations for te same purpose. Tese latter equations are used in te software package developed 4 (see Appendix-A for details). 2.1 Software Development Te main flow cart for implementing equations A1 to A6 of te appendix, suitably modified 5, is sown in figure 2.1. In Module A of te program, te data is assigned togeter wit any limitations imposed. In te Module B te optimum value of te transformer capacity is selected for a given load profile. Tis is described more fully in te flow cart of figure 2.2. Eac important block of te flow cart is described in te following sections B1 to B5. Start Module B B1:Get Input Data B2: Initialize variables and calculate initial capacity for given load curve data B3: Calculate top oil temp, ot spot temp & ageing for calculated capacity Max top oil temp. rise Max ot spot temp. Ageing exceeded B4: Decrease Capacity Calculate top oil, ot spot & ageing B5: Increase Capacity Calculate top oil, ot spot & ageing top oil top oil ot spot exceeded ot spot exceeded Ageing exceeded Ageing exceeded Figure Flow Cart for finding Optimum Transformer Capacity Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p Case 1 Case 2 Case 3 Start A: Assign constants and limitations Select Option End B: Find te optimum transformer capacity load for given curve C: Find top oil temp, Hot spot temp, ageing of existing t/f Need to be Optimized Find Optimum load curve multiplier End Figure Main Flow Cart End

3 B1: Get Input Data Te weigted ambient temperature; te Mean montly maximum temperature; te period for wic load data is available; and te load data for eac period are input to te program in tis section B2: Initialize Variables Tis is used to initialize te capacity for termal parameter calculations in case 1. Low - assigned to te minimum load in te cycle Hig - assigned to te maximum load in te cycle Te initial required capacity is selected as te mean of te Low and Hig values. Req_capacity = ( Low + Hig ) / 2 B3: Calculate Top Oil, Hot Spot & Ageing In te program, any cange in te load conditions is treated as a small step cange. Terefore for a continually varying load, te step function as to be applied over small time intervals, trougout te load cycle. Calculation of te top oil temperature rise as well as ot spot temperature trougout te load cycle tus requires te use of a computer program. Calculating Top Oil To obtain te top oil temperature rise in eac time interval of te load cycle, some adjustments ave to be made to te equation A1, taking into consideration te different loads before tat particular time interval, Consider a load cycle wit n number of equal time intervals, eac of duration t. Te equation A1 can be modified as equation (1). θon = θo(n-1) + ( θoun θo(n-1))(1 e t/τo ) (1) Rearranging Equation (1) θon= θo(n-1) (e t/τo ) + θoun(1 e t/τo ) θon = Top oil temp. rise at end of n t interval θo(n-1) = Top oil temp. rise at end of (n-1) t interval θoun = Ultimate top oil temp. rise in n t interval t = time interval of application of specific load τo = Oil time constant Let (1 e t/τo ) = C. Tis gives θon= (1 C) θo(n-1) + C θoun (2) Equation (2) can be extended to represent te total duration of te load cycle by a series of equations, wic will form te matrix equation (3). θo1 θon * θon1 θo2 θo1 θon2 = (1 C) + C (3) θon θo(n-1) θonn * Since te load curve is assumed to be of cyclic nature, for te first time duration, te initial top oil temperature rise is equal to te final top oil temperature rise. Rearranging equation (3) gives equation (4). θo1 θo2 θou1 θou2 [A] = C (4) [ A] θon 1 ( C 1) = : 1 ( C 1) : θoun 1 : : :: : ( C 1) ( C 1) : 1 Equation (4) is solved, to obtain te top oil temperature rise ( θon) for eac time interval, using te standard LU decomposition metod. From te array of θon values, te maximum is selected ( θomax) and te maximum top oil temperature (θomax) is calculated as follows: θomax = θa + θomax Calculating Hot Spot Using equation A3 of te appendix, Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

4 θ = θa + θon + θtd θa = Ambient temperature θ = Ultimate (steady state) ot spot temperature θtd = Temperature difference between ot spot and top oil Hot spot temperature as to be found for eac time interval in te load cycle and stored in an array [θ]. Mean montly maximum temperature is used as ambient temperature for ot spot calculations. Top oil temperature rise for eac time interval as been calculated and is stored in an array [ θon]. Temperature difference between ot spot and top oil is calculated by equation A4. Tus te equation A3 becomes modified as equation (5). [θ] = [θa] + [ θon] + [Hg r K y ] (5) Hg r = Temperature difference between ot spot and top oil at rated current K = Load factor during t = Load Transformer capacity y = Winding exponent Wit tese calculations te maximum value of θ from te time intervals is found and stored as te maximum ot spot temperature for calculations (θmax ). Calculating Ageing Relative loss of life is calculated wit reference to equations A5 and A6. To obtain tis, te relative ageing rate V was integrated using te Simpson s rule. t 2 V dt = n odd + 3 t1 { V + V + 4( V ) 2( V } ) even = { 2Vn + 4( Vodd ) + 2( Veven) } 3 since by te caracteristics of te curve of V, If te number n is taken as even, ten t 2 V dt = V odd + V even 3 t1 Hence, relative L t 1, t 2 T V { 4( ) 2( )} ageing L 3T { 4V odd + 2V } = even = Loss of Life in per unit days = period under consideration; t 2 - t 1 = T = total time interval of application = Relative ageing rate B4: Decrease Capacity If all te limitations are not exceeded, te initial value of te variable ig is re-assigned a value ig = capacity - 1 Te range of capacities tat is being considered is reduced to a new range. Tis loop will continue till te optimum capacity is found. B5: Increase Capacity Wen any one of te limitations is exceeded, te initial value of te variable low is re-assigned a value low = capacity + 1 Te range of capacities is again reduced to a new range. Tis loop too will continue till te optimum capacity is found. Te Module C in figure 2.1 finds te optimum load curve multiplier, wic is described using te flow cart in figure 2.3. Important blocks of te flow cart are described in sections C1 to C3. C1: Load Curve Multiplier (F) Te Load curve multiplier is a factor used to increase or decrease te magnitude of te load profile. To calculate te termal parameters for te load profile, tis factor is made equal to unity initially. Afterwards it is varied in order to find te set of termal parameters, wic would yield te most optimum load profile. V = V n Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

5 C2: Increase F Tis is performed wen all te termal parameters are witin limits. Increase of F is done in two ways. 1. If te program operation as entered tis stage witout performing te decrease of F, F is increased by a significant value (say 1%). 2. If te program operation as entered tis stage after performing te decrease of F initially, F is increased by a muc smaller value (say 1%). C3: Decrease F Decreasing of F is performed wen any of te termal parameters ave exceeded te limitations. Decrease of F is also two folds. 1. If te program operation as entered tis stage witout performing an increase of F, F is decreased by a significant value (say 1%). 2. If te program operation as entered tis stage after performing te increase of F initially, F is decreased by a muc smaller value (say 1%). 3. Inaccuracies In Te Manual Two Step Approximation Te IEC guide requires a two step approximation wit te manual metod. Wen te profile of te load curve canges, suc tat a two step approximation does not follow te actual sape, te results obtained from te software become more accurate. Table 3.1 sows its excess over rated value wit cange in load factor of, 1. Te Ultimate top oil temp. rise ( θ ou - θ our ) 2. Temperature difference between ot spot and top oil ( θ td - θ tdr ) 3. Hot spot temperature (θ -θ r ) From te table 3.1 and te corresponding graps sown in figure 3.1 it is seen tat te increase in ot spot temperature due to increase in load factor beyond 1 p.u. is considerably iger tan decrease in ot spot temperature due to an equal decrease in load factor. Tis effect is taken into account in te software metod and result in accurate results. K θ ou - θ our θ td - θ tdr θ -θ r Table 3.1 Excess in Temp.rises & Hotspot temp. wit load factor Temp. (deg. celcius) Hot spot vs Load factor Load factor Figure 3.1 Excess in Hotspot temperature wit load factor In te two step approximation metod, te effect caused by cange in load factor is linearised for canges in ot spot temperature and can tus lead to significant errors. Tis inaccuracy caused by te two step approximation is furter illustrated in te case studies 1 and 2. Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

6 Case Study 1 Te load curve in Case Study 1 as several steps as sown in figure 3.2. Two step approximation is also sown. Since te actual load curve is different from te approximated curve, te value for ageing obtained from software is.94 p.u.days, compared to te value of.62 p.u.days obtained from te two step curve. Tis inaccurate lower value of ageing from te two step curve can lead to an unexpected early damage of te transformer. If te actual load curve follows te two step curve, te software metod also gives te same result of.62 p.u. days for ageing. Tis proves tat te results from te software are correct. Case Study 2 An industrial load wit an installed transformer capacity of 175kVA, analysed using demand readings at 15min intervals, is sown in figure 3.3. Te load curve is of a complex sape and difficult to approximate to a two-step curve. Te two step approximation drawn in accordance to te guideline is also superimposed on te diagram. Te results of te load curve analysis using te software package are given in 3.1. Load (kva) Load (p.u) Time of day Figure 3.2 Load curve for case study Time (rs) Figure Daily Load Profile of Industrial Load Te results wit two step approximation gives.91 p.u days for ageing against 1.35 p.u. obtained from te software metod. T/F THERMAL PARAMETERS *********************************** Top Oil Temperature (celcius) : (15) Hotspot Temperature (celcius) : (14) Loss of life (p.u. days) : 1.35 (1) Optimise (Y/N) : 3.1 -Termal parameters of existing transformer at te Industrial Load 4. Effects on Performance Some practising engineers may get te feeling tat te loading of a transformer beyond its nameplate rating could give rise to problems in te distribution network, suc as an unacceptable voltage regulation or a marked reduction in te efficiency of industrial loads suc as induction motors. Tis is discussed in te following sections. 4.1 Voltage Regulation on Transformer Analysis is made on te cange in percentage voltage regulation due to loading above nameplate rating. Two transformers of 1kVA, 33kV/415V and 4kVA, 11kV/415V were considered wit typical data. Te standard equation 6 (6) was used for te calculation of percentage voltage regulation at a current loading of a times te rated full load current. ( ) ( cosθ 2 sin θ 2) a R a = a V ( cosθ 2 sin θ 2) 2 r + Vx + Vx Vr 2 (6) θ2 = Power factor angle R(a) = % voltage regulation Vr = % resistance voltage at full load Vx = % leakage reactance voltage at full load Te percentage voltage regulations of bot transformers, at a power factor of.8 lagging, are plotted in figure Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

7 Te calculations sow tat in te 1kVA and 4kVA transformers te percentage regulation is 6.62% and 4.88% respectively even at 15% loading. % V Percentage Voltage Regulation at.8 p.f Load factor 1kVA,33kV/415V 4kVA, 11kV/415V Figure 4.1 Percentage Voltage Regulation at.8 p.f. 4.2 Effects on Motor Efficiency Te efficiency variation due to te reduction in terminal voltage is analysed using a 55kW Induction motor. Te efficiency equation (7) used for te calculation is, Efficiency= losses outputpower (7) Te losses include te stator copper and core losses, rotor copper loss and rotational losses. For te determination of tese losses no-load and block rotor tests were carried out. Te results obtained for motor efficiency wit variable terminal voltage are illustrated in table 4.2. Tis indicates tat even wit 1% reduction in terminal voltage, te effect on te motor performance is of no significance. Voltage, V Efficiency Table 4.2 Variation of efficiency wit reduction in terminal voltage 5. Conclusions Te software package is developed based on te standard equations given in IEC 354 guide. Te software package can be applied to any complex sape of load curve. Hence tis package gives a solution to te tedious manual calculations involved wit complex load profiles found in reality. Te studies made sows tat te results obtained for loss of life is more precise wit te software package, tan wit manual two step approximation. Tis will elp to reduce unexpected damage to te transformer in te future. Te practical results obtained for transformer voltage regulation sows tat it as no significant effect on te distribution network at acceptable loading conditions above nameplate rating. Wit regard to industrial loads suc as induction motors, again te test results sow tat te voltage drops caused by loading transformers above nameplate rating as no major effect on its performance. Tus it is recommended tat maximum utilisation of te transformer be made allowing loading beyond nameplate rating witin specified limits. 6. References 1. Brown P.M., and Wite J.P., Determination of te maximum cyclic rating of ig-voltage power transformers, Power Engineering Journal, Feb 1998, pp Heatcote, M.J., Transformer Ratings, Letters to te Editor, Power Engineering Journal, Jun 1998, pp IEC 354: Loading Guide for Oil Immersed Power Transformers, 2 nd Edition, Perera KBMI, Lucas JR, Kumarasinge KKASD, Dias RLIK, Atukorala UADR, Gunawardana PGA., Optimisation of Transformer Design based on Load Curve, IEE Sri Lanka Annual session, September Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

8 5. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling.T., Numerical Recipes in C, Cambridge University Press, Heatcote Martin J., J & P Transformer Book, Twelft edition, Jonson & Pillips Ltd, Appendix A A.1 Loading Tables & Graps metod In te loading tables & graps metod te load curve is approximated to a two step curve. Wit complex load curves te accuracy of te results depends igly on personal skills of te user. A1.1 Metod of representing an actual load cycle by an equivalent two-step cycle To use te Tables and Graps of te guide te daily load cycle as to be represented by a simplified load cycle as sown in figure A.1.1. Te load steps K 1 is selected as te average value of te off-peak portion of te curve wile te load Load factor K 1 T p a d c T p = Peak duration step K 2 is selected equal to te peak load of te curve. i.e. Area 1 = Area 2 + Area 3 + Area 4 Te peak load duration T p sould also be selected on an area basis. Area a + Area b = Area c + Area d Te value T p is owever restricted to a few standard values in te Table and Grap metod. b K 2 24 Time of day Figure A.1.1- Approximation metod A.2 Software metod Te standard equations given in IEC 354 loading guide for oil immersed power transformers ave been used in te software metod. A.2.1 Top Oil Temperature Rise Te oil temperature rise (e.g.: for top oil) after time interval t is given by equation A1. θot= θoi+ ( θou θoi)(1 e t/τo ) A1 and te Ultimate top oil temperature rise θou is given by equation A2. θ ou R x θoi θor θot θou = θ or 1 + RK 1+ R 2 x = Loss ratio = Load loss at rated current load loss = Oil exponent = Initial top oil temperature rise = Top oil rise at rated current A2 = Top oil temp. rise after time t = Ultimate top oil temp. rise corresponding to load during time t A.2.2 Hot Spot Temperature For ON cooling, te ultimate ot spot temperature (θ) under any load K can be stated as in equation A3 θ = θa + θot + θtd A3 Te temperature difference between ot spot & top oil is given by equation A4 θtd = Hg r K y A4 It is seen tat wit canges in load tis component of ot spot temperature also canges. A.2.3 Termal ageing Relative termal ageing rate Te relative rate of termal ageing for transformers designed in accordance wit IEC 76 is taken to be equal to unity for a ot spot temperature of 98 C. Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p

9 Tis corresponds to operation at an ambient temperature of 2 C and a ot spot temperature rise of 78 C. Te relative ageing rate is given by equation A5. Start Module C C1: Initialize Load curve multiplier F = 1 ageing rateat V = ageing rateat 98 θ θ = o C ( 98) / 6 2 A5 Hot spot rise(78 C) = Hot spot to top oil gradient (23 C) + Top oil temperature rise (55 C) Hence for a design ambient temperature oter tan 2 C, te ot spot temperature rise as to be modified accordingly. For example wen te design ambient is 3 C, te allowable ot spot rise is 68 C. Loss of life calculation Te relative ageing (or relative loss of life ) over a certain period of time is given by equation A6. L 1 t2 = T V dt A6 t1 Max top oil temp. rise not exceeded Max ot spot temp.not Ageing not Hold te values of top oil temp, ot spot temp, ageing & F C2: Increase F Load Cycle * F Calculate top oil, ot spot & ageing top oil ot spot Ageing C3: Decrease F Load Cycle * F Calculate top oil, ot spot & ageing top oil not ot spot not Ageing not Figure Flow Cart for finding Optimum Load Curve Multiplier Loading of Transformers beyond nameplate rating, Engineer, vol 3, 3 September 1999, p