Estimation of Optimum Transformer Capacity based on Load Curve

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1 Estimation of Optimum Transformer Capacity based on Load Curve # Lanka Transformers Limited, Moratuwa, * University of Moratuwa Abstract: Tis paper presents te development of a software package tat can be used to select a transformer of optimum capacity for given loading condition and also to ceck te termal parameters of an existing transformer. Te application of a load in excess of nameplate ratings and/or an ambient temperature iger tan designed, involves a degree of risk and accelerated ageing. Tis software package identifies suc risks and indicates ow, witin limitations, transformers may be loaded in excess of te nameplate rating witout adverse effects. Te basis of tis software package is te standard equations given in te IEC 54 Loading guide for oil immersed power transformers. Te program is coded in Turbo/Borland C ++. Te results of te software package are sown to be accurate for any complex sape of load curve. Tis gives a solution to te tedious manual calculations involved wit complex load profiles found in reality. Te load curves analysed on several industries also give an indication of a lack of knowledge of users on te possibilities of loading a transformer beyond its name plate rating. θ a θ θ oi θ on List of Symbols = Ambient temperature = Ultimate (steady state) ot spot temperature = Initial top oil temperature rise = Top oil temp. rise at end of n t interval θ o(n-1) = Top oil temp. rise at end of (n-1) t interval θ or = Top oil rise at rated current θ ot = Top oil temp. rise after time t θ ou = Ultimate top oil temp. rise corresponding to load during time t θ oun = Ultimate top oil temp. rise in n t interval θ td = Temperature difference between ot spot and top oil Hgr = Temperature difference between ot spot and top oil at rated current K = Load factor during t = Load L R t t 1, t 2 T T p Transformer capacity = Loss of Life in per unit days = Loss ratio = Load loss at rated current No load loss = time interval of application of specific load = period under consideration; t 2 - t 1 = T = total time interval of application = Peak duration τ o V x y = Oil time constant = Relative ageing rate = Oil exponent = Winding exponent 1. INTRODUCTION 1.1 Effects of loading beyond name plate rating Te life duration of a transformer depends to a ig degree on extraordinary events, suc as over-voltages, sortcircuits in te system and emergency loading. Te consequences of loading 1,2 a transformer beyond its nameplate rating are as follows. Te temperatures of windings, insulation, oil etc. increase and can reac unacceptable levels. Te leakage flux density outside te core increases, causing additional eddy current eating in metallic parts linked by te flux. As te temperature increases, te moisture and gas content in te insulation and in te oil will increase. Busings, tap-cangers, cable-end connections and current transformers will also be exposed to iger stresses. Due to tese reasons, tere will be a risk of premature failure associated wit te increased currents and temperatures. Tis risk may be of an immediate sort term nature or long term failure due to cumulative deterioration of te transformer over many years Sort term risks Te reduction in dielectric strengt due to te possible presence of gas bubbles in te region of ig electrical stress, (i.e. te windings and leads) is te main risk for sort time failures. Tese bubbles may develop in te paper insulation wen te ot spot temperature rises suddenly above a critical temperature of about C. Te pressure build up in te busings may result in a failure due to oil leakage & gassing in te busings may also occur if te temperature of te insulation exceeds about C Long term risks Cumulative termal deterioration of te mecanical properties of te conductor insulation will accelerate at iger temperatures. Tis deterioration process may ultimately reduce te effective life of te transformer. Te sort term risks normally disappear after te load is reduced to normal level but tat will affect te reliability. 1

2 Te long term risk is te reduction in te effective life of te transformer. 1.2 Scope Tis software package identifies te risks involved wit over-loading and indicates ow, witin limitations transformers may be loaded in excess of teir nameplate rating. Tis is applicable to ONAN type distribution transformers wit a maximum rating of 2500 kva tree pase or 8 kva per limb single pase. Te ig voltage rating is limited to kv and witout on-load tapcanging, complying wit IEC 76 wit normal cyclic loading of duration one day. Tis software package provides guidance for loading of distribution transformers from te point of view of operating temperature and termal ageing. It can be used to acieve two objectives. To select a transformer of optimum capacity for a given loading condition. To ceck weter an existing transformer is operating safely. i.e. If over-loaded ow te load cycle sould be reduced. If under-loaded ow te load cycle can be canged in order to acieve te maximum usage of te transformer. 2. SELECTING A TRANSFORMER BASED ON THERMAL PARAMETERS Te metod of selecting a transformer using te Tables and Graps given in te guide IEC 54 as well as using te software package developed are described in te following section. 2.1 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 Metod of representing an actual load cycle by an equivalent two-step cycle. Load factor K 1 T p a d c 0 24 Time of day Figure Approximation metod 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 b K 2 Te load steps K1 is selected as te average value of te off-peak portion of te curve wile te load step K2 is selected equal to te peak load of te curve. i.e. Area 1 = Area 2 + Area + Area 4 Te peak load duration Tp sould also be selected on an area basis. Area a + Area b = Area c + Area d Te value Tp is owever restricted to a few standard values in te Table and Grap metod. 2.2 Software metod In tis metod te standard equations given in IEC 54 loading guide for oil immersed power transformers ave been used. Tis metod uses te actual load curve and te approximation to two steps is not necessary Top Oil Temperature Rise Any cange in load conditions is treated as a small step function. 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. Te oil temperature rise (eg: for top oil) after time interval t is given by equation (1), θ ot= θ oi+ ( θ ou θ oi )(1 e t/τo ) (1) and te Ultimate top oil temperature rise θ ou is given by equation (2). 2 x 1+ RK θ ou = θ (2) or 1+ R Hot Spot Temperature For ON cooling, te ultimate ot spot temperature (θ ) under any load K can be stated as in equation (). θ = θa + θot + θtd () Since during one cycle of te load tere are variations in te load, te simple metod of using equation (2 ) cannot be applied to obtain top oil temperature rise and ence it cannot be substituted in equation (). To obtain te top oil temperature rise in eac time interval of te load cycle, taking into consideration te different loads before tat particular time interval, some adjustments ave to be made to equation (1). Consider a load cycle wit n number of equal time intervals, eac of duration t. Ten te equation (1) can be modified as equation (4). θon = θo(n-1) + ( θoun θo(n-1))(1 e t/τo ) (4) 2

3 Te temperature difference between ot spot & top oil is given by equation (5). θ td = Hgr K y (5) It is seen tat wit canges in load tis component of ot spot temperature also canges 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. Tis corresponds to operation at an ambient temperature of 20 C and a ot spot temperature rise of 78 C. Te relative ageing rate is given by equation (6). ageing rate at θ ( θ 98 )/ 6 V = = 2 (6) o ageing rate at 98 C Hot spot rise(78 C) = Hot spot to top oil gradient(2 C) + Top oil temperature rise(55 C) Hence for a design ambient temperature oter tan 20 C, te ot spot temperature rise as to be modified accordingly. For example wen te design ambient is 0 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 (7). L 1 t2 = T V dt (7) t1. SOFTWARE DEVELOPMENT Start A: Assign constants and limitations Select Option Case End Case 1 Case 2 B: Find te optimum t/f capacity for given load curve C: Find top oil temp, Hot spot temp, ageing of existing t/f Display Results Need to be Optimised? Find Optimum load curve multiplier Display Results End No Display Results End.1 Flow cart Te flow cart for implementing te termal equations (1) to (7), suitably modified 4, is sown in figure.1. In Module A of te program, te data is assigned. In te Module B te optimum value of te transformer capacity is selected for a given load profile. Figure.1 - Flow Cart Let (1 e t/τo ) = C Tis gives θ on= θ o(n-1) (1 C) + θ oun * C (8) Te Module C finds te optimum load curve multiplier. Load curve multiplier is a factor used to increase or decrease te load profile. To calculate te termal parameters for te load profile as it is, tis factor as to be made equal to unity initially. Afterwards it is varied in order to find te optimum set of termal parameters wic would yield te most optimum load profile..2 Modified calculations Calculating Top Oil Rearranging Equation (4) θ on= θ o(n-1) (e t/τo ) + θ oun (1 e t/τo ) Equation (8) can be extended to represent te total duration of te load cycle by a series of equations, wic will form a matrix equation (9). θ o1 * θ on θ ou1 θ o2 θ o1 θ ou2 = ( 1 C ) + C (9) θ on θ o(n-1) θ oun * Since te load curve is of cyclic nature for te first time duration 1, te initial top oil temperature rise is equal to te final top oil temperature rise.

4 Rearranging equation (9) gives equation (10). θ o1 θ o2 [A] = C [B] (10) were θ on (C-1) θ ou1 (C-1) θ ou2 [A]= 0 (C-1) ,[B] = (C-1) 1 θ oun Equation (10) is solved using LU Decomposition metod, to obtain te top oil temperature rise ( θ on) for eac time interval. From te array of θ on values, te maximum is selected ( θ omax) and te maximum top oil temperature(θ omax) is calculated as follows: θ omax = θ a + θ omax Calculating Hot Spot Wit reference to equation () θ = θ a + θ on + θ td 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 are stored in an array [ θ on], described earlier. Temperature difference between ot spot and top oil is calculated by equation (5). Tus te equation () becomes modified as equation (11). [θ ] = [θ a] + [ θ on] + [Hgr K y ] (11) Wit tese calculations te maximum value of θ from te time intervals is found and stored as te maximum ot spot temperature for calculations (θ max ). Calculating Ageing Relative loss of life is calculated wit reference to equations (6) and (7). To obtain tis te function V was integrated using te Simpson s rule. t 2 V dt = n odd + t1 = 2Vn + 4( Vodd ) + 2( V { V + V + 4( V ) 2( V } 0 even ) { } even since by te caracteristics of te curve of V, V0 = Vn ) If te number n is taken as even, ten t 2 V dt = V odd + V even t1 Hence, relative ageing { 4( ) 2( )} L T { 4V odd + 2V } = even 4. CASE STUDIES & JUSTIFICATION Program testing plays an important role in te software development life cycle. Hence, in order to justify te results of tis software package, te following cases were studied. For case 1 and case 2, te transformer capacity is taken as 1.0 p.u. Tese analyses are valid for any kva rating. Case 1 Tis is a two step load wit load steps of 0.8 & 1.1p.u. as illustrated in figure 4.1. In tis case te values obtained for ot spot temperature (108 0 C) & loss of life (0.74 p.u days) from bot metods are found to be te same. Case 2 Load (p.u) Te load curve in Case 2 as several steps as sown in figure 4.2. Wen approximated to two steps, it is similar to Case 1. Since te actual load curve is different from te approximated curve, te value for ageing obtained from software is 0.9 p.u.days, compared to te value of 0.74 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 damage.. Load (p.u) Time of day Figure 4.1 Load curve for Case Time of day Figure 4.2 Load curve for Case 2 4

5 Case Several industrial loads were also analysed wit te software developed. Two of tem are discussed ere. Te load curve of Lanka Transformers Limited (LTL) was obtained using demand readings at 15min intervals as sown in figure 4.. Te load curve tus obtained is of a complex sape and difficult to approximate to a two-step curve. Te results of te load curve analysis using te software package is given in Display 4.1. Load (kva) Time (rs) Figure 4. - Daily Load Profile of LTL OPTIMIZED PARAMETERS ********************************* Top Oil Temperature (celcius) : (105) Hotspot Temperature (celcius) : (140) Loss of life ( p.u.days ) : (1) OPTIMIZED TRANSFORMER CAPACITY 180 kva Display Optimum Transformer parameters for LTL Te results in Display 4.1 sows tat te required transformer capacity wic satisfy all termal parameters is of 180kVA. Te actual supply transformer in operation at Lanka Transformers is owever of capacity 400kVA. It is seen to be muc more tan required. Te data were ten analysed wit option 2 of software package, and te results obtained are given in displays 4.2 and 4.. T/F THERMAL PARAMETERS *********************************** Top Oil Temperature (celcius) : (105) Hotspot Temperature (celcius) : (140) Loss of life (p.u. days) : (1) Optimise (Y/N)? : Display 4. - Load curve multiplication possibility to existing load profile at LTL Te results indicate tat te existing transformer is under utilised and te load curve multiplier is 2.2 for optimum utilisation. Case 4 Te load curve of anoter industry and its data analysis is illustrated in figure 4.4 and display 4.4 Load (kva) OPTIMIZED PARAMETERS ********************************* Top Oil Temperature (celcius) : (105) Hotspot Temperature (celcius) : (140) Loss of life ( p.u.days ) : (1) Load Curve Multiplier : Time (rs) Figure Load Profile of an Industry OPTIMIZED PARAMETERS ********************************* Top Oil Temperature (celcius) : (105) Hotspot Temperature (celcius) : 11.9 (140) Loss of life ( p.u.days ) : (1) OPTIMIZED TRANSFORMER CAPACITY 165 kva Display Optimum Transformer parameters Te results are similar in tis case too. Te required transformer capacity is 165kVA, were as installed capacity is 400kVA, wic is muc more tan required. Display 4.2 Termal parameters of existing transformer at LTL It is to be noted tat tis does not owever take into account te increased capacity usually installed to cater for unforeseen loads and future expansion. 5

6 5. CONCLUSION From te study carried out (Case 1), it is evident tat te results obtained from bot software & tables are te same wen te load curve is of two-step nature. However, as can be seen (Case 2) wit a load curve of several steps te table and grap metod cannot give sufficiently accurate results for loss of life as from te package. Tis is because of te cange in ot spot temperature is not linearly proportional to cange in load factor, wic is considered equal in te two step metod. As te software package is developed based on te standard equations given in IEC 54 guide, te results of te software package are accurate for 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. Finally Case studies and 4, give an indication of under utilisation of transformers by users due to te lack of knowledge on te possibilities of loading a transformer beyond its name plate rating. 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 54: Loading Guide for Oil Immersed Power Transformers, 2 nd Edition, Press W.H., Flannery B.P., Teukolsky S.A., Vetterling.T., Numerical Recipes in C, Cambridge University Press,

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