Software Guided Safe Loading of Transformers

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/237625513 SOFTWARE GUIDED SAFE LOADING OF TRANSFORMERS Article CITATIONS READS 0 19 2 authors, including: Rohan Lucas University of Moratuwa 29 PUBLICATIONS 180 CITATIONS SEE PROFILE All content following this page was uploaded by Rohan Lucas on 29 July 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. SOFTWARE GUIDED SAFE LOADING OF TRANSFORMERS K. B. M. I. Perera* and J. R. Lucas# * # Factory Manager, Lanka Transformers Limited, Moratuwa, Sri Lanka Professor in Electrical Engineering, University of Moratuwa, Sri Lanka SYNOPSIS Accelerated ageing occurs in transformers when loads exceed nameplate ratings or ambient temperature exceeds the design value. A software package has been developed by the authors based on IEC 354: Loading guide for oil immersed power transformers. It identifies the risks involved and indicates how transformers may be loaded in excess of the nameplate rating (abnormal loading) without adverse effects for specific load curves. A matrix formulation of top oil temperature allows a near continuous load curve simulation. The relative ageing rate is calculated using Simpson’s rule. Results of the package agree exactly with the two step approach specified in the Loading guide for two step load curves. However, it is shown that the two step approximation gives somewhat inaccurate results for certain practical complex load curves. Thus use of the package could minimise unexpected future damages to transformers. Calculations have been done based on practically obtained data to determine the excess voltage regulation introduced by the abnormal loading and the variation of efficiency of a practical induction motor within this range of voltages. These show that there is no adverse effect on motor efficiency. In addition other general effects of voltage regulation on induction motor characteristics were also considered with the guidance of IEEE standard 141:1993. This shows that while there is no significant change in the full load speed and efficiency the starting and running torque varies as the square of the voltage and can drop to about 81% at a maximum possible voltage drop of 10%. 1. INTRODUCTION It is well known that accelerated ageing occurs when a transformer is overloaded and when the ambient temperature increases above normal. The standard IEC 354: Loading guide for oil immersed power transformers [1] indicates how transformers may be loaded in excess of the nameplate rating (abnormal loading) for load curves with a two step approximation. Based on this guide, a software package [2] has already been developed to provide guidance for daily cyclic loading of ONAN type distribution transformers without on-load tap changing complying with IEC 76: Power Transformers. This package indicates how transformers, with a maximum rating of 2500 kVA three phase and high voltage 33 kV, may be loaded in excess of their nameplate rating, within limitations. It can also be used to select a transformer of optimum capacity for a given loading condition and to check the utilisation of an existing transformer. A distribution transformer is usually rated for continuous operation at that value. However, extraordinary events, such as over-voltages, short-circuits in the system and emergency loading can affect the life of a transformer to a high degree. It has been identified that the consequences [3,4] of loading a transformer beyond name-plate rating are (i) the temperatures of windings, insulation, oil etc. increase and can reach unacceptable levels, (ii) the leakage flux density outside the core increases, causing additional eddy current heating in metallic parts linked by the flux, (iii) the moisture and gas content in the insulation and in the oil increase with the temperature increase, and (iv) bushings, tap-changers, cable-end connections and current transformers are exposed to higher stresses. These increase the risk of premature failure, which may be of an immediate short term nature or may lead to long term failure due to cumulative deterioration of the transformer over many years. 2. EFFECT OF THERMAL PARAMETERS ON TRANSFORMER LOADING The IEC 354 - Loading guide for oil immersed power transformers gives the method of selecting a transformer based on its thermal parameters using Tables and Graphs. The equations given in this standard have been suitably modified and used in the software method. The main thermal parameters are the temperature rise of the top oil, hot spot temperature and ageing. Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 1 2.1 Top Oil Temperature Rise According to the standard, the top oil temperature rise ∆θot, after time interval ‘ t’, is given by equation (1). ∆θot= ∆θoi+ (∆θou−∆θoi)(1−e−t/τo) (1) where ∆θoi = Initial top oil temperature rise, τo = Oil time constant and the Ultimate top oil temperature rise ∆θou is given by equation (2). 1 + RK 2  = ∆θ or    1+ R  ∆θ ou x (2) where ∆θor = Top oil rise at rated current, K = Load factor during 't' = , Load Transformer capacity R = Loss ratio, and X = oil exponent 2.2 Hot Spot Temperature For Oil Natural (ON) cooling, the ultimate hot spot temperature (θh) under any load factor K can be stated as in equation (3). θh = θa + ∆θot +∆θtd where θa is the ambient temperature. equation (4). (3) The temperature difference between hot spot and top oil ∆θtd is given by ∆θtd = Hgr K y (4) where Hgr = Temperature difference between hot spot and top oil at rated current and y = winding exponent It is seen that with changes in load both the top oil temperature rise as well as the hot spot temperature changes. 2.3 Thermal ageing Thermal ageing is the deterioration of the insulation due to thermal processes. For derating purposes, what is important is the relative rate of thermal ageing. For transformers designed in accordance with IEC 76, it is taken to be equal to unity for a hot spot temperature of 98°C. This corresponds to operation at an ambient temperature of 20°C and a hot spot temperature rise of 78°C. The relative ageing rate is given by equation (5). V = ageing rate at θ h ageing rate at 98o C = 2 (θ h −98)/6 (5) o IEC354 gives the hot spot to top oil temperature gradient as 23 C, so that Hot spot rise(78°C) = Hot spot to top oil gradient (23°C) + Top oil temperature rise (55°C) For a design ambient temperature other than 20°C, the hot spot temperature rise has to be modified accordingly. For example when the design ambient temperature is 30°C , the allowable hot spot rise is 68°C. The relative ageing (or relative loss of life ) over a certain period of time is given by equation (6). L= where t2 1 V dt T t∫1 (6) L = Loss of Life in per unit days; t1, t2 = period under consideration; t2- t1 = T = total time interval of application; and V = Relative ageing rate Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 2 2.4 The Manual Two Step Approximation Tp Load factor The IEC guide requires a two step approximation to the Load Curve with the manual method (Figure 2.1). The load step K1 is selected as the average value of the offpeak portion of the curve such that b a 2 1 3 d 4 K2 area 1 = area 2 + area 3 + area 4 K1 while the load step K2 is selected equal to the peak load of the curve. The duration of the peak Tp is calculated such that c 0 area a + area b = area c + area d 24 Time of day Figure 2.1- Two-Step Approximation method When the profile of the load curve changes, such that a two step approximation does not follow the actual shape, the two step approximation ceases to be accurate. A software method then becomes a necessity as it models all levels of load steps and thus becomes more accurate . 3. DEVELOPMENT OF THE COMPUTER PROGRAM Figure 3.1 shows the main flow chart for implementing the equations for determining the top oil temperature rise, the hot spot temperature and the thermal ageing [equations 1 to 6], suitably modified for repetitive calculations. In Module A, the optimum value of the transformer capacity required is selected for a given load profile. In Module B the set of thermal parameters and the optimum load curve multiplier are determined for an already installed transformer. Start Assign constants and limitations Select Option Module A Module b Find the thermal parameter of existing transformers Select initial transformer capacity capacity = (max + min)/2 Display Results Find the thermal parameter for selected capacity increase capacity too high Within tolerance ? Yes Display Results too low decrease capacity No Need to be Optimised ? Yes Find Optimum load curve multiplier Display Results End End Figure 3.1 - Flow Chart for thermal parameters Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 3 3.1 Calculation of the Top Oil & Hot Spot Temperatures In the formulation, any change in the load conditions is treated as a small step change. Therefore for a continually varying load, a step function has to be applied over small time intervals, throughout the load cycle. A computer program thus eases the burden of calculating the thermal parameters throughout the load cycle. To obtain the top oil temperature rise in each time interval of the load cycle, some adjustments have to be made to the equation (1), taking into consideration the different loads before that particular time interval. Consider a load cycle with equal time intervals, each of duration ‘t’ (Figure 3.2). ‘t’ is selected corresponding to availability of data. Load Factor For this the equation (1) can be modified as equation (7). ∆θon = ∆θo(n-1) + (∆θoun − ∆θo(n-1))(1− e−t/τo) (7) Rearranging Equation (7) n-1 n ∆θon= ∆θo(n-1) (e−t/τo ) + ∆θoun(1−e−t/τo) Time of day Figure 3.2 Load Curve where ∆θon = Top oil temp. rise at end of nth interval, ∆θo(n-1) = Top oil temp. rise at end of (n-1)th interval and ∆θoun th = Ultimate top oil temp. rise in n interval Let (1−e−t/τo) = C. This gives ∆θon= (1 – C) ∆θo(n-1) + C ∆θoun (8) Equation (8) can be extended to represent the total duration of the load cycle by a series of equations, which will form the matrix equation (9). ∆θo1 ∆θon* ∆θou1 ∆θo2 ∆θo1 ∆θou2 : = ∆θon : (1–C)+C ∆θo(n-1) : (9) ∆θoun * Since the load curve is assumed to be of cyclic nature, for the first time duration, the initial top oil temperature rise is equal to the final top oil temperature rise. Rearranging equation (9) gives equation (10). 0  1  − (C 1) 1   0 (C − 1)  : :   0 0 (C − 1)   ∆θ o1    0   ∆ θo 2  0   ∆ θo 3  = C   : : : : : :  :  0 − − − (C − 1) 1   ∆θon  0 −−− 0 −−− 1 −−− 0 0 0  ∆θou1   ∆θ   ou 2   ∆θou 3     :   ∆θoun  (10) Equation (10) is solved, to obtain the top oil temperature rise (∆θon) for each time interval, using the standard LU decomposition method. From the array of ∆θon values, the maximum is selected (∆θomax) and the maximum top oil temperature (θomax) is calculated as follows: θomax = θa + ∆θomax The ultimate hot spot temperature θh is calculated using equation (3) θh = θa + ∆θon + ∆θtd The hot spot temperature has to be found for each time interval in the load cycle and stored in an array [θh]. The mean monthly maximum temperature is used as the ambient temperature for hot spot calculations. Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 4 Top oil temperature rise for each time interval is calculated and is stored in an array [∆θon]. The temperature difference between hot spot and top oil is calculated by equation (4). Thus the equation (3) becomes modified as equation (11). y [θh] = [θa] + [∆θon] + [Hgr K ] (11) With these calculations the maximum value of θh from the time intervals is found and stored as the maximum hot spot temperature for calculations (θhmax ). 3.2 Calculation of Ageing Relative loss of life is calculated with reference to equations (5) and (6). To obtain this, the relative ageing rate V was integrated using the Simpson’s rule. t2 ∫V dt = t1 h {V0 + Vn + 4(Vodd ) + 2(V even )} 3 = h {2Vn + 4(Vodd ) + 2(Veven )} 3 since by the characteristics of the curve of V, V0 = Vn t2 If the number n is taken as even, then ∫V dt = t1 Hence, relative ageing L = h 3T {∑ 4V odd h {4(Vodd ) + 2(Veven )} 3 + ∑ 2Veven } 3.3 Load Curve Multiplier The Load curve multiplier (F) is a factor used to increase or decrease the magnitude of the load profile. To calculate the thermal parameters for the load profile, this factor is made equal to unity initially. Afterwards it is varied in order to find the set of thermal parameters, which would yield the most optimum load profile. If all the parameters are within limits, F is increased by a fine or coarse increment dependant on whether a previous decrease has been made or not. Similarly, if any of the thermal parameters have exceeded the limitations, F is decreased by a fine or coarse increment. 3.4 Case Studies 3.4.1 Variation of hot spot temperature with load factor The variation of the excess temperature rise and hot spot temperature can be determined for standard operating o o conditions (∆θour = 55 C, ∆θtdr = Hgr = 23 C, R = 5, x = 0.8, y = 1.6) of IEC354 using equations (2) and (4) and addition of the results. ∆θou-∆θour ∆θtd-∆θtdr θh-θhr 0.5 -24.5 -15.4 -39.9 0.6 -20.5 -12.8 -33.3 0.7 -16.1 -10.0 -26.1 0.8 -11.2 -6.9 -18.1 0.9 -5.8 -3.6 -9.4 1.0 0.0 0.0 0.0 1.1 6.2 3.8 10.0 1.2 12.8 7.8 20.6 1.3 19.7 12.0 31.7 1.4 27 16.4 43.4 1.5 34.7 21.0 55.7 Table 3.1 - Excess in temperature rises and hotspot temperature with load factor 60 Temp. (deg. celcius) K 40 20 0 -20 -40 0.5 0.7 0.9 1.1 1.3 1.5 Load factor Figure 3.3 – Excess in Hotspot temperature with load factor Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 5 Table 3.1 shows the excess in the Ultimate top oil temp. rise (∆θou-∆θour), the temperature difference between hot spot and top oil (∆θtd-∆θtdr), and the hot spot temperature (θh-θhr), over rated value with change in load factor. From the table and the corresponding graph shown in figure 3.3 it is seen that the increase in hot spot temperature due to increase in load factor beyond 1 p.u. is considerably higher than decrease in hot spot temperature due to an equal decrease in load factor. This effect is taken into account in the software method and result in accurate results . 3.4.2 Inaccuracy of the two step approximation In the two step approximation method, the effect caused by change in load factor is linearised for changes in hot spot temperature and can thus lead to significant errors as has been observed by the several case studies performed. This inaccuracy caused by the two step approximation is illustrated by a sample case study presented. An industrial load with an installed transformer capacity of 175kVA, analysed using demand readings at 15min intervals, is shown in figure 3.4. The load curve is of a complex shape and difficult to approximate to a two-step curve. The two step approximation drawn in accordance to the IEC 354 guideline, is superimposed on the diagram. The results of the load curve analysed using the software package are given in Display 3.1. 300 T/F THERMAL PARAMETERS *********************************** Top Oil Temperature (celcius) : 87.75 (105) Load (kVA) 250 200 150 Hotspot Temperature (celcius) : 128.71 100 50 Loss of life (p.u. days) (140) : 1.35 (1) 0 0 2 4 6 8 10 12 14 16 18 20 22 24 Time (hrs) Optimise (Y/N)? : Figure 3.4 - Daily Load Profile of Industrial Load Display 3.1 - Thermal parameters of existing transformer at the Industrial Load The results with two step approximation gives 0.91 p.u days for ageing against 1.35 p.u. obtained from the software method. 4. EFFECTS ON PERFORMANCE Some practising engineers may get the feeling that the loading of a transformer beyond its nameplate rating could give rise to problems in the distribution network, such as an unacceptable voltage regulation or a marked reduction in the efficiency of industrial loads such as induction motors. This is discussed in the following sections. 4.1 Voltage Regulation on Transformer Analysis is made on the change in percentage voltage regulation due to loading above nameplate rating. Two transformers of 100kVA, 33kV/415V and 400kVA, 11kV/415V were considered with typical data. The standard equation (12) was used for the calculation of percentage voltage regulation [5] at a current loading of a times the rated full load current . R (a) = a(Vr cos θ 2 + Vx sin θ 2 ) + a2 200 Percentage Voltage Regulation at 0.8 p.f. (Vx cosθ 2 − Vr sin θ 2)2 7 6 (12) where = = = = Power factor angle % voltage regulation % resistance voltage at full load % leakage reactance voltage at full load The percentage voltage regulations of both transformers, at a power factor of 0.8 lagging, are plotted in figure 4.1. %V θ2 R(a) Vr Vx 5 100kVA, 33kV/415V 4 3 2 400kVA, 11kV/415V 1 0 0 0.5 1 1.5 Load factor Figure 4.1 – Percentage Voltage Regulation at 0.8 pf Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 6 Calculations show that in the 100kVA and 400kVA transformers the percentage regulation is 6.62% and 4.88% respectively even at 150% loading. 4.2 Effects on Motor Efficiency It was observed in section 4.1 that the voltage regulation increases when the load factor increases. The variation in efficiency in motor loads due to this reduction in terminal voltage is presented in this section using a 55 kW squirrel cage type induction motor. The efficiency equation (13) used for the calculation is Efficiency = 1 (13)  losses  1 +  output power   The losses include the stator copper and core losses, rotor copper loss and rotational losses. For the determination of these losses, the tests carried out were the no-load test, short circuit test, ohmic resistance when cold and hot stage and the total loss readings at variable voltage and constant power output. The parameters for the equivalent circuit (figure 4.2) were found using these data. PR r1 j x1 j x´2 Is rc j xm Pst,core r´2/s Protational Vnl 0 375 400 425 Figure 4.2 - Equivalent circuit used for the Figure 4.3 - Variation of rotational loss with induction motor voltage The rotational loss was found using the loss readings at different voltages and extrapolating the graph as shown in figure 4.3. The full-load efficiency calculation was then carried out with a Thevenin’s equivalent circuit for a range of terminal voltages and the results are illustrated in figure 4.4. This indicates that even with 10% reduction in terminal voltage, the effect on the motor efficiency is of no significance (less than 2%). 105% 88.5% 100% % Effect Efficiency 88.0% 87.5% 87.0% 95% 90% 86.5% 85% 86.0% 80% 90% 92% 94% 96% 98% 100% 102% 90% 92% Terminal Voltage efficiency Figure 4.4 - Variation of full-load efficiency with a reduction in terminal voltage 94% 96% 98% Voltage variation speed 100% 102% torque Figure 4.5 – Variation of motor performance with reduction in terminal voltage IEEE Standard 141:1993 gives the general effect of voltage variations on induction motor characteristics. The performance for voltage reductions down to 10% are shown in figure 4.5. It is seen that the full-load efficiency variation is and the full-load speed variations are insignificant. However the starting and maximum running torque decreases to about 81% at a maximum voltage reduction of 10%. This is because the torque is proportional to the square of the voltage. Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 7 5. CONCLUSIONS The software package is developed based on the standard equations given in IEC 354 guide. The software package can be applied to any complex shape of load curve. Hence this package gives a solution to the tedious manual calculations involved with complex load profiles found in reality. The studies made shows that the results obtained for loss of life is more precise with the software package, than with manual two step approximation. This will help to reduce unexpected damage to the transformer in the future. The practical results obtained for transformer voltage regulation shows that it has no significant effect on the distribution network at acceptable loading conditions above nameplate rating. With regard to industrial loads such as induction motors, again the test results show that the voltage drops caused by loading transformers above nameplate rating has no major effect on its performance other than for the reduction in the starting and maximum running torque. Thus it is recommended that maximum utilisation of the transformer be made allowing loading beyond nameplate rating within specified limits. 6.0 REFERENCES nd 1. “IEC 354:1991 Loading Guide for Oil Immersed Power Transformers”, 2 Edition. 2. Perera, K.B.M.I. and Lucas, J.R., “Loading of transformers beyond nameplate rating”, Engineer, Journal of the Institution of Engineers, Sri Lanka, vol XXX, No 3, September1999, pp 58-65 3. Brown, P.M. and White, J.P., “Determination of the maximum cyclic rating of high-voltage power transformers”, Power Engineering Journal, Feb 1998, pp 17-20. 4. Heathcote, M.J., “Transformer Ratings”, Letters to the Editor, Power Engineering Journal, Jun 1998, pp 142. 5. Heathcote Martin J., “J & P Transformer Book”, Twelfth edition, Johnson & Phillips Ltd, 1998. Software Guided Safe Loading of Transformers, New Delhi, April 2000 – JR Lucas & KBMI Perera 8