Life Cycle Assessment and Capitalized Cost of Transformer Overload: A Multi-Regional Study in Ecuador ^†

Abstract

This study presents an integrated thermo-economic framework for evaluating the impact of daily overload on the aging and cost performance of oil-immersed distribution transformers. The methodology combines international transformer thermal aging models, widely accepted in transformer loading guides such as those established by IEEE and IEC, with an equivalent annual cost (EAC) model, enabling a unified assessment of insulation degradation and operational expenditures. Using a residential load profile with 15 min resolution and climate data from three Ecuadorian regions (Quito, Guayaquil, and the Amazon), we analyze the influence of varying overload levels, peak durations, cooling methods Oil Natural Air Natural (ONAN), Oil Natural Air Forced (ONAF), and Oil Forced Air Forced (OFAF), and installation environments (indoor/outdoor) on transformer lifetime and ownership costs. Parametric simulations reveal that ambient temperature is the dominant factor in thermal degradation, with Guayaquil showing service life reductions of up to 70% compared to Quito under identical loading conditions. While larger transformers with forced cooling exhibit enhanced thermal resilience, the economic performance deteriorates non-linearly beyond 120–130% loading due to compounding losses and replacement costs. The results demonstrate that (i) overload tolerance is climate dependent, (ii) indoor installations incur systematic thermal penalties, and (iii) the IEC and IEEE models yield similar outcomes under moderate conditions but diverge under severe stress. The proposed approach provides utilities with a robust decision-support tool to optimize transformer loading strategies, replacement planning, and cooling system upgrades in geographically diverse power systems.

1. Introduction

1.1. Research Motivation

Transformers are critical elements in the value chain of a modern electrical system. They represent critical assets whose value can reach several thousands or millions of dollars, depending on their rated power, and whose traditionally projected useful life is between 20 and 40 years. However, the current operational reality, linked to the current consumption rate, presents unprecedented challenges that significantly compromise this life expectancy, creating a complex problem that requires urgent attention at both the technical and economic levels [1].

The fundamental problem lies in the accelerated aging of the cellulose insulation, which is the main factor limiting the service life of this equipment. The thermal deterioration of the oil-impregnated paper insulation system, subjected to increasingly demanding operating conditions, manifests itself through the molecular degradation of the cellulose, with a consequent loss of mechanical and dielectric properties [2,3]. Multiple factors aggravate this aging process, including high temperatures and the presence of moisture, oxygen, and acids, as well as overload conditions that generate peak temperatures above the design limits [4].

The current operational context significantly exacerbates this situation. In Ecuador, electricity demand has consistently grown by approximately 200–300 MW annually, forcing electricity companies to maximize the use of existing infrastructure [5,6]. This reflects a global trend in which grid operators must increasingly rely on fleets of transformers installed mainly between the 1950s and 2010s, which are now approaching or exceeding their projected useful life [7]. In addition, climate change has introduced additional thermal stresses, with rising ambient temperatures and increasing heat waves documented around the world [8,9]. Recent studies show that high ambient temperatures can reduce the life expectancy of transformers by 30–50% under identical load conditions, creating unprecedented challenges for equipment originally designed for different climate parameters [10,11].

The economic consequences of this problem are considerable and multifaceted. The costs of replacing transformers have increased significantly, as power transformers cost between $2 million and $7.5 million, depending on their capacity, while delivery times can be extended to 120 weeks due to supply chain constraints. In addition, unexpected breakdowns generate associated costs, such as supply interruptions causing losses between $500,000 and $5 million per hour, depending on the sector [12], emergency repair costs, and potential regulatory penalties.

From a technical point of view, the international standards IEEE Std C57.91-2011 [13] and IEC 60076-7:2018 [14] provide methodological frameworks for assessing the impact of operating conditions on the service life of transformers [15]. However, these standards present significant conceptual differences in their thermal approaches and aging criteria, as IEEE establishes a normal service life of 180,000 h at a maximum temperature of 110 °C, while IEC considers 98 °C as the reference temperature for a 30-year service life [16]. This methodological disparity creates uncertainty in the accurate assessment of remaining service life and the economic quantification of the impact of accelerated aging.

The complexity of the problem increases when considering that comprehensive economic analysis must incorporate not only initial acquisition costs but also operating costs associated with energy losses, maintenance, monitoring, and the present value of the valuable life consumed by operation outside of nominal conditions [17,18]. The loss assessment factors A and B used in the calculation of total cost of ownership require integration with accurate thermal models to optimize the cost–benefit ratio between asset utilization and accelerated degradation [19].

This multidimensional problem requires an integrated approach that combines thermal aging models established by international standards with comprehensive economic analysis, enabling network operators to make informed decisions about load capacity strategies, predictive maintenance programs, and replacement planning. The lack of tools that adequately integrate these technical and economic aspects is a significant gap in modern transformation asset management, limiting the ability to simultaneously optimize system reliability, asset utilization, and operational economic efficiency.

1.2. Literature Review on the Service Life of Transformers

Scientific research into the thermal models used to assess the service life of transformers has made significant progress. In this context, the thermal models developed by the IEEE and IEC have been fundamental [13,14]. The following are studies carried out by various authors who have addressed this issue.

1.2.1. IEEE Thermal Models for Life Evaluation

The authors in [15] develop a novel approach for predicting temperature rise in transformers under harmonic current conditions, integrating IEEE thermal models with additional loss analysis. Their research establishes that harmonic currents can increase hot-spot temperatures by up to 15°C above nominal values, with corresponding impacts on aging rates according to the IEEE Factor of Accelerated Aging (FAA).

In the paper [20], they present a deep learning approach for predicting the useful life of transformers considering various aging factors. Their model integrates degradation variables extracted from real operational data with IEEE thermal principles, demonstrating over 92% accuracy in remaining life prediction compared to traditional analytical methods.

The research [21] develops a model of the effect of thermal aging on the electrical characteristics of insulating oil using regression approaches. Their research establishes that after thermal aging, resistivity and breakdown voltage decrease exponentially, while the dielectric dissipation factor increases following experimentally validated predictive models.

1.2.2. IEC Models and Comparative Analysis

The authors of [22] developed an indirect methodology for estimating the useful life of transformers through the evaluation of dielectric materials, integrating IEC standards with polymerization degree analysis. Their research establishes correlations between 2-furfural and paper degradation, estimating an approximate maximum life of 27 years for transformers under specific load and temperature conditions.

The author of [23] detects cellulose degradation and transformer failures by applying an integrated analysis of gases and low-molecular-weight alcohols dissolved in mineral oil. His work establishes that methanol and ethanol provide more sensitive and selective indicators of cellulose degradation compared to CO₂, especially in the early stages of aging.

The authors of [24] develop a comprehensive assessment of transformer oil after thermal aging, proposing mathematical models based on exponential regression to correlate electrical and chemical properties with temperature. Their research demonstrates that exponential models can predict oil degradation with correlation coefficients greater than 0.95.

1.2.3. Integrated Aging Modeling and Economic Analysis

The method used in [25] evaluates the optimal economic life interval for transformers based on adjusted failure rate curves and minimum average annual life cycle cost. This research establishes that the optimal economic life interval for 120 MVA transformers is between 31 and 33 years, considering Weibull failure distribution and interval analysis for uncertainty management.

The authors’ model in [18] considers the life cycle cost (LCC) of transformers by merging life cycle cost theory with relevant transformer expenses. Their analysis shows that selecting transformers having appropriate capacity and stable operation can improve economic efficiency by 15–25% by adjusting the load range of the transformer.

The authors of [17] develop the estimation and analysis of life cycle costs of transformers based on failure rates. Their model establishes that operational costs can represent 2–3 times the initial cost during the useful life, with energy losses being the most significant component of the LCC.

Finally, in [19], the authors use an objective function to optimize costs and transformer lifetime using the NSGA-II genetic algorithm. Their research demonstrates that multi-objective optimization can reduce total costs while minimizing lifetime loss, providing Pareto-optimal solutions for transformer fleet management.

1.2.4. Impact of Climate Change on Transformer Aging

Recent research has established direct correlations between increased ambient temperatures and accelerated transformer aging. The authors of [11] developed an integrated framework to assess the vulnerability of distribution networks to local temperature variations under global climate change. Their study shows that climate change increases the risk of blackouts during peak hours by 4–6%, depending on gross domestic product (GDP) growth, and that more than 20% of the United States will require at least a 10% increase in grid capacity by 2050.

The authors of [10] investigated the effects of climate change on the heating of power transformers at the Shituru high-voltage substation. Their research confirms that rising global temperatures have a direct impact on power transformers, where excessive heat can affect windings, insulation, and other internal components, reducing service life and causing costly service interruptions.

Finally, in [26], the authors integrated machine learning approaches with the assessment of the health index, incorporating environmental variables as primary input for lifetime prediction models. Their findings indicate that traditional thermal models may underestimate the rate of aging in regions experiencing temperature increases above historical norms.

This review shows that while previous work has advanced IEEE/IEC thermal aging models and life cycle cost analyses, few studies integrate both under realistic operating conditions; in particular, studies on the effects of temperature in tropical, coastal, and mountainous environments remain scarce. To address this shortcoming, we combined IEEE Std C57.91-2011 [13] and IEC 60076-7:2018 [14] hot-spot/aging formulations with an equivalent annual cost model explicitly parameterized in the climatic and installation (outdoor/indoor) context in three regions of Ecuador. This enables location-specific estimates of loss of life and cost of ownership under daily overload and generates practical and comparable loading guidelines across different standards.

2. Materials and Methods

The purpose of this study is to quantitatively evaluate the effect of load capacity on the life expectancy and economic performance of oil-insulated transformers under thermal conditions representative of three climatic regions of Ecuador: Sierra, Coast, and Amazon. A combined thermo-economic approach is adopted, based on the guidelines established by standards IEEE Std C57.91-2011 [13] and IEC 60076-7:2018 [14], which link thermal degradation of insulation with the load regime and hot-spot temperature. The methodology uses two complementary computational models developed in Python 3.13: one for massive parametric simulation and the other for detailed economic evaluation.

A typical residential load profile was used, interpolated cubically to obtain a resolution of 96 daily intervals (15 min), adequately representing daily demand variations. This profile was normalized and scaled to simulate base load (e.g., 90%) and overload (e.g., up to 150%) conditions, also considering daily peak durations between 2 and 24 h, in 2 h increments.

For thermal conditions, 24-point ambient temperature curves representative of Quito, Guayaquil, and the Amazon region were adopted, interpolated to 96 daily intervals. The ambient temperature was adjusted for indoor environments by applying a thermal amplification coefficient of 30% to excesses above 20 °C, reflecting conditions in enclosed transformer chambers without forced ventilation, which can lead to higher internal temperatures. It should be noted that Ecuador does not present marked seasonal temperature variations, but only wet and dry periods with relatively small changes in ambient conditions throughout the year. For this reason, temperature seasonality was not modeled. Instead, representative daily temperature profiles for each city were selected according to typical worst-case conditions, as summarized in Appendix A.

2.1. Thermal Model and Estimated Service Life

The service life assessment is based on the calculation of the aging acceleration factor (FAA) which indicates how fast the transformer insulation is aging according to the Arrhenius exponential model shown in Equation (1) [13], using a hot-spot temperature of 110 °C as a reference.

$$FAA\left(t\right)=exp\left(E_R\left({\displaystyle \frac{1}{T_{\mathrm{ref}}}}-{\displaystyle \frac{1}{{\theta }_H\left(t\right)+273.15}}\right)\right);$$

(1)

where

• $FAA\left(t\right)$ is the aging acceleration factor at time t;
• $E_R$ is an insulation type material constant, usually (15,000 K);
• $T_{\mathrm{ref}}$ is the reference hot-spot temperature, $110 °\mathrm{C}=383.15\mathrm{K}$;
• ${\theta }_H\left(t\right)$ is the hot-spot temperature at time t [°C].

The instantaneous temperature of the hot spot is calculated according to Equations (2)–(4) [13].

$${\theta }_H\left(t\right)={\theta }_{\mathrm{amb}}\left(t\right)+\Delta {\theta }_{TO}\left(t\right)+\Delta {\theta }_H\left(t\right);$$

(2)

with

$$\begin{array}{cc}\hfill \Delta {\theta }_{TO}\left(t\right)& =\Delta {\theta }_{TO,\mathrm{rated}}·K{\left(t\right)}^n;\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill \Delta {\theta }_H\left(t\right)& =\Delta {\theta }_{H,\mathrm{rated}}·K{\left(t\right)}^m;\hfill \end{array}$$

(4)

where ${\theta }_{\mathrm{amb}}\left(t\right)$ is the ambient temperature at time t [°C]; $\Delta {\theta }_{TO}\left(t\right)$ is the top-oil temperature rise over ambient [°C]; $\Delta {\theta }_H\left(t\right)$ is the hot-spot temperature rise over top-oil [°C]; $\Delta {\theta }_{TO,\mathrm{rated}}$ is the rated top-oil rise [°C]; $\Delta {\theta }_{H,\mathrm{rated}}$ is the rated hot-spot rise [°C]; $K\left(t\right)$ is the load factor at time t [p.u.]; and $n=0.8$, $m=1.0$ are the empirical thermal exponents.

Remaining life is calculated using Equation (5) [13], integrating the equivalent aging factor (FEQA) over a daily horizon and projecting it annually.

$$FEQA={\displaystyle \frac{1}{24}}\sum _{t=1}^{96}FAA\left(t\right)·\Delta t;$$

(5)

with $\Delta t=0.25$ h being the time interval between samples (96 points/day).

The values of loss of useful life, Equation (6) [13], are expressed in equivalent years, under the IEEE and IEC frameworks, considering 180,000 h and 150,000 h as reference bases, respectively. Temperature increases due to load were estimated using empirical power models with exponents n = 0.8 and m = 1.0, representing the thermal response of the oil and the hot spot, respectively.

$$LOL=\left({\displaystyle \frac{FEQA·24·365}{{\mathit{Life}}_{\mathrm{base}}}}\right)·100;$$

(6)

With ${\mathit{Life}}_{\mathrm{base}}$ expressed in hours (180,000 h for IEEE, 150,000 h for IEC), $LOL$ as the annual percentage of insulation aging, and Estimated Life as the remaining transformer life in years, the value is calculated using Equation (7).

$$\mathit{Estimated}\mathit{Life}={\displaystyle \frac{100}{LOL}};$$

(7)

2.2. Economic Model and Cost Analysis

In addition to thermal aging, the methodology includes an economic assessment of transformer performance under different loading conditions. The analysis is based on the annualized total cost of operation, using the concept of equivalent annual cost (EAC), which aggregates the energy losses, maintenance costs, and capital recovery over the expected transformer service life.

The total annual energy losses $E_{\mathrm{loss}}$ are calculated from the rated iron losses ($P_{\mathrm{fe}}$) and copper losses ($P_{\mathrm{cu}}$), the latter depending quadratically on the load factor $K\left(t\right)$, according to Equation (8) [27].

$$E_{\mathrm{loss}}={\displaystyle \frac{1}{1000}}·\sum _{t=1}^{96}\left[P_{\mathrm{fe}}+P_{\mathrm{cu}}·K{\left(t\right)}^2\right]·\Delta t·365;$$

(8)

where $E_{\mathrm{loss}}$ is total annual energy losses [kWh/year], $P_{\mathrm{fe}}$ is constant core (iron) losses [W], $P_{\mathrm{cu}}$ is winding (copper) losses at rated load [W], $K\left(t\right)$ is load factor at time t [p.u.], $\Delta t=0.25$ h is the time interval (15 min), and 365 is the number of days per year.

The corresponding monetary cost of these losses is given by Equation (9) [17,18]:

$$C_{\mathrm{loss}}=E_{\mathrm{loss}}·C_e;$$

(9)

where $C_e$ is the energy tariff in USD/kWh.

Operation and maintenance costs are estimated as a fixed percentage of the transformer’s capital cost $C_t$, as shown in Equation (10) [18,25]:

$$C_{\mathrm{OM}}=\beta ·C_t;$$

(10)

where $\beta$ is the annual operation and maintenance rate (typically 2%).

The investment cost $C_{\mathrm{inv}}$ is annualized using the capital recovery factor method, assuming a nominal service life of n years and a discount rate i. The annual equivalent of the capital cost is calculated using Equation (11) [25]:

$$C_{\mathrm{inv}}=C_t·{\displaystyle \frac{i{(1+i)}^n}{{(1+i)}^n-1}};$$

(11)

Finally, the total equivalent annual cost (EAC) is obtained as the sum of all the components, according to Equation (12) [17,18,25]:

$$EAC=C_{\mathrm{loss}}+C_{\mathrm{OM}}+C_{\mathrm{inv}};$$

(12)

This cost represents the annual economic burden associated with transformer operation under a given load and thermal scenario. For each case (base load and overload), the model calculates the EAC over the transformer lifetime estimated by the thermal model. In scenarios where the thermal lifetime is less than the nominal design life (e.g., 20 years), early replacements are considered by recalculating the capital annuity over the shortened lifetime.

This integrated thermo-economic framework allows the comparison of different transformer utilization strategies by jointly evaluating their impact on thermal aging and life cycle cost, thus supporting more informed and sustainable planning decisions.

2.3. Parametric Simulation and Processing

Three thermal configurations were considered: Oil Natural Air Natural (ONAN), Oil Natural Air Forced (ONAF), and Oil Forced Air Forced (OFAF), with typical oil elevation and hot-spot values taken from design specifications. The resulting hot-spot temperature profiles were calculated for each combination of city, cooling type, loadability, and condition (interior/exterior). From these, the expected annual service life curves were determined for each simulated case.

The mass simulation model explored 576 scenarios per city (3 types of cooling, 33 overload levels, and 8 peak durations), differentiating between indoor and outdoor conditions. For each case, useful life expectancy matrices were generated in accordance with the IEEE and IEC frameworks. The results were stored and supplemented with comparative graphs showing the influence of load and peak duration on accelerated insulation degradation. The entire process is detailed in pseudocode in Algorithm 1.

Algorithm 1 Transformer Thermal–Economic Assessment (IEEE/IEC)

1: Input data: 2:    Ambient temperature profile ${\theta }_{\mathrm{amb}}\left(t\right)$ 3:    Cooling type $\to \Delta {\theta }_{TO,\mathrm{rated}},\Delta {\theta }_{H,\mathrm{rated}}$ 4:    Transformer parameters $C_t,P_{\mathrm{fe}},P_{\mathrm{cu}},C_e,S_{\mathrm{rated}}$ 5: Load-profile construction: 6: Generate normalized 96-point profile $K_{\mathrm{norm}}\left(t\right)$ 7: Apply $K_{\mathrm{base}}$ and $K_{\mathrm{over}}$ for $h_{\mathrm{peak}}$ hours 8: Thermal aging: 9: for each time step t do 10:     $\Delta {\theta }_{TO}\left(t\right)\leftarrow \Delta {\theta }_{TO,\mathrm{rated}}K{\left(t\right)}^n$ 11:     $\Delta {\theta }_H\left(t\right)\leftarrow \Delta {\theta }_{H,\mathrm{rated}}K{\left(t\right)}^m$ 12:     ${\theta }_H\left(t\right)\leftarrow {\theta }_{\mathrm{amb}}\left(t\right)+\Delta {\theta }_{TO}\left(t\right)+\Delta {\theta }_H\left(t\right)$ 13:     $FAA\left(t\right)\leftarrow exp\left[E_R(1/T_{\mathrm{ref}}-1/({\theta }_H\left(t\right)+273.15))\right]$ 14: end for 15: $FEQA\leftarrow (1/24)\sum FAA\left(t\right)\Delta t$ 16: $LOL\leftarrow FEQA·24·365/{\mathrm{Life}}_{\mathrm{base}}\times 100$ 17: $\mathrm{Estimated}\mathrm{Life}\leftarrow 100/LOL$ 18: Energy losses & costs: 19: $E_{\mathrm{loss}}\leftarrow \sum (P_{\mathrm{fe}}+P_{\mathrm{cu}}K{\left(t\right)}^2)\Delta t·365$ 20: $C_{\mathrm{loss}}\leftarrow E_{\mathrm{loss}}{C}_e$ 21: $C_{\mathrm{inv}}\leftarrow C_t\left[i{(1+i)}^n/({(1+i)}^n-1)\right]$ 22: $C_{\mathrm{OM}}\leftarrow 0.02C_t$ 23: $EAC\leftarrow C_{\mathrm{inv}}+C_{\mathrm{OM}}+C_{\mathrm{loss}}$ 24: Output: Life expectancy, replacements, $E_{\mathrm{loss}}$, $EAC$, plots.

2.4. Studied Cases and Simulation Setup

To evaluate the thermo-economic behavior of different transformers under typical and overloaded daily loading conditions, a parametric simulation framework was developed in Python 3.13. Three representative transformer configurations were considered, differing in rated capacity, thermal characteristics, and cooling method. The rated thermal parameters adopted for this study, namely the top-oil temperature rise over ambient ($\Delta {\theta }_{\mathrm{TO},\mathrm{rated}}$) and the hot-spot temperature rise over top-oil ($\Delta {\theta }_{\mathrm{H},\mathrm{rated}}$), were selected according to typical values reported in the international literature. Both IEEE Std C57.91-2011 [13] and IEC 60076-7:2018 [14] establish that top-oil rises under rated load generally range between 45 °C and 65 °C, while hot-spot rises are typically within the range from 15 °C to 35 °C depending on transformer design and cooling mode. These values are also consistent with recent studies based on extended temperature rise tests of large power transformers, which confirm that the IEC recommended values better reflect average behavior, whereas IEEE guidelines remain more conservative [13,14,27]. Therefore, the selected parameters fall within internationally accepted ranges and are supported by both standard guides and empirical validation. Conversely, the loss parameters (no-load and load losses) and the investment costs assigned to each transformer were derived from a focused market survey of transformer models available in Ecuador, compiled from recent vendor quotations and publicly accessible datasheets (2024–2025); the selected figures reflect typical local offerings and realistic procurement conditions rather than optimized best-case designs.These are summarized as follows:

• Case 1: 1000 kVA, ONAN, $P_{fe}=1.7$ kW, $P_{cu}=11.0$ kW, $\Delta {\theta }_{TO}=55 °$C, $\Delta {\theta }_H=25 °$C, investment cost = USD 22,000.
• Case 2: 10,000 kVA, ONAF, $P_{fe}=12.0$ kW, $P_{cu}=28.0$ kW, $\Delta {\theta }_{TO}=48 °$C, $\Delta {\theta }_H=18 °$C, investment cost = USD 170,000.
• Case 3: 40,000 kVA, OFAF, $P_{fe}=30.0$ kW, $P_{cu}=150.0$ kW, $\Delta {\theta }_{TO}=40 °$C, $\Delta {\theta }_H=12 °$C, investment cost = USD 600,000.

Each transformer was subjected to a normalized residential load profile consisting of 96 values per day (15 min intervals). The base scenario assumed a constant daily peak load of 90% of the rated capacity. Overload scenarios were simulated by increasing the peak load from 100% to 150% in 5% increments. Overloads were applied for a fixed duration of 10 consecutive hours per day, targeting the highest load periods, while preserving the original shape of the remaining daily profile.

Thermal and economic evaluations were performed under ambient temperature conditions from three representative Ecuadorian regions:

• Quito (Andean region)
• Guayaquil (Coastal region)
• Amazon (Rainforest region)

Each ambient temperature profile consisted of 24 h values and was interpolated to 96 points using cubic interpolation to match the temporal resolution of the load profile. For indoor installations, a thermal amplification factor $\alpha =0.3$ was applied to reflect the increase in hotspot temperature due to limited ventilation.

The main simulation parameters adopted in this study are as follows:

• Load and temperature profile resolution: 96 points per day;
• Peak load duration: 10 h per day;
• Energy price: 0.10 USD/kWh;
• Discount rate: 12%;
• Operation and maintenance cost: 2% of investment per year;
• Evaluation horizon: 25 years.

It should be noted that both the residential load profile and the ambient temperature profile were assumed to remain constant during the 25-year evaluation horizon. This assumption was adopted to isolate the thermo-economic impact of daily overload and ambient conditions. The economic model, however, does consider the time horizon through the annualization of costs and the use of the capital recovery factor (CRF).

The simulations were driven by a 15 min resolution daily load profile (96 samples) and climate-specific ambient temperatures for Quito, Guayaquil, and the Amazon. The indoor ambient conditions were derived by applying a thermal amplification factor equal to 0.3 to the temperature excess above 20 °C to represent the transformer rooms. Figure A1 (Appendix A) displays the exact input curves used throughout the study.

3. Results

This section presents the quantitative results of the study: heat maps and iso–life curves linking load capacity and climate, annual losses and costs, and tables showing the technical and economic commitment of three refrigeration systems evaluated under different daily peak durations.

Figure 1 shows that the service life of the transformer depends heavily on the combination of overload level and peak duration, and how this effect varies with climate and cooling system. In all three climates, the color bands shift toward blue values (longer life) as we move from ONAN to ONAF and finally to OFAF, showing that forced cooling can increase life by more than an order of magnitude for the same load condition. However, the gain is more pronounced under prolonged peaks (>16 h) and loads above 130%. Among climates, Quito has the most benign thermal environment: it allows life expectancies to remain above 100 years up to around 120% for 8 h, while Guayaquil, the hottest environment, reduces this threshold to approximately 100% in 8 h with ONAN cooling and only partially recovers with forced cooling. The Amazon region exhibits intermediate behavior, although still 30% lower than Quito for identical profiles. In addition, the almost horizontal colored areas below 105% indicate that, in that operating region, life becomes insensitive to peak duration; in contrast, the steep diagonal gradient from 120% reflects that even brief daily overloads can reduce life by half if sustained above 140% of load capacity.

The iso–life curves in Figure 2 show that, with ONAN cooling, the useful life of the transformer decreases non-linearly as the overload and its duration increase simultaneously; in Quito (a) it can be maintained for 60 years up to approximately 115% for 6 h, while in Guayaquil (b) and the Amazon (c) that same threshold is reduced to values close to 100%—8 h and 105%—7 h, respectively. The horizontal shift between the outdoor (red) and indoor (blue) traces confirms that indoor installation adds a thermal penalty of 3–5 °C, shortening the life by 15% to 25%, and the small differences between thermal models (solid line = IEEE; dotted line = IEC) barely exceed 5% except in extreme scenarios (>130% and >10 h), where the IEC model predicts slightly faster aging.

The thermo-economic results obtained from the parametric simulations for the illustrative case studies are presented in

Table 1. Thermo-economic results for Transformer Case 1 under different load levels and cities.

City	Load (%)	Scenario	E_loss (kWh/yr)	EAC (USD/yr)	Life (yrs)	Replacements
Quito	90	Base	66,787.90	9758.79	25.0	0
	100	Overload	79,428.14	11,022.81	25.0	0
	105	Overload	86,010.89	11,681.09	25.0	0
	110	Overload	92,190.26	12,299.03	25.0	0
	115	Overload	97,777.06	12,857.71	25.0	0
	120	Overload	102,869.11	13,366.95	25.0	0
	125	Overload	107,810.36	13,861.42	25.0	0
	130	Overload	112,629.04	14,345.18	25.0	0
	135	Overload	117,237.64	14,813.56	25.0	0
	140	Overload	121,602.76	15,272.73	25.0	0
	145	Overload	125,709.63	15,737.75	25.0	0
	150	Overload	129,587.64	19,069.35	23.6	1
Guayaquil	90	Base	66,787.90	9758.79	25.0	0
	100	Overload	79,428.14	11,024.07	25.0	0
	105	Overload	86,010.89	11,691.88	25.0	0
	110	Overload	92,190.26	12,341.36	25.0	0
	115	Overload	97,777.06	12,961.98	25.0	0
	120	Overload	102,869.11	16,406.72	23.4	1
	125	Overload	107,810.36	17,190.24	19.0	1
	130	Overload	112,629.04	18,092.45	15.4	1
	135	Overload	117,237.64	22,629.39	12.5	2
	140	Overload	121,602.76	24,269.94	10.0	2
	145	Overload	125,709.63	30,730.37	8.0	3
	150	Overload	129,587.64	33,993.08	6.3	3
Amazon	90	Base	66,787.90	9758.79	25.0	0
	100	Overload	79,428.14	11,023.34	25.0	0
	105	Overload	86,010.89	11,686.94	25.0	0
	110	Overload	92,190.26	12,325.78	25.0	0
	115	Overload	97,777.06	12,930.16	25.0	0
	120	Overload	102,869.11	13,514.88	25.0	0
	125	Overload	107,810.36	17,036.33	21.0	1
	130	Overload	112,629.04	17,877.60	17.0	1
	135	Overload	117,237.64	18,852.89	13.7	1
	140	Overload	121,602.76	23,706.06	11.0	2
	145	Overload	125,709.63	25,576.17	8.8	2
	150	Overload	129,587.64	32,763.81	7.0	3

,

Table 2. Thermo-economic results for Transformer Case 2 under different load levels and cities.

City	Load (%)	Scenario	E_loss (kWh/yr)	EAC (USD/yr)	Life (yrs)	Replacements
Quito	90	Base	237,218.66	47,521.87	25.0	0
	100	Overload	282,874.17	56,722.13	25.0	0
	105	Overload	306,739.89	61,392.40	25.0	0
	110	Overload	328,208.15	65,990.40	25.0	0
	115	Overload	347,993.89	70,097.27	25.0	0
	120	Overload	366,766.79	73,653.36	25.0	0
	125	Overload	384,149.35	76,796.64	25.0	0
	130	Overload	400,002.93	79,613.27	25.0	0
	135	Overload	414,585.78	82,233.13	25.0	0
	140	Overload	427,873.80	84,667.30	25.0	0
	145	Overload	439,922.65	86,909.71	25.0	0
	150	Overload	450,808.50	88,940.63	25.0	0
Guayaquil	90	Base	237,218.66	47,521.87	25.0	0
	100	Overload	282,874.17	56,727.23	25.0	0
	105	Overload	306,739.89	61,411.45	25.0	0
	110	Overload	328,208.15	66,028.75	25.0	0
	115	Overload	347,993.89	70,138.43	25.0	0
	120	Overload	366,766.79	92,950.91	18.4	1
	125	Overload	384,149.35	96,945.20	15.0	1
	130	Overload	400,002.93	101,445.33	12.1	2
	135	Overload	414,585.78	109,121.88	10.0	2
	140	Overload	427,873.80	129,649.79	8.3	3
	145	Overload	439,922.65	138,468.25	6.9	3
	150	Overload	450,808.50	151,166.70	5.8	4
Amazon	90	Base	237,218.66	47,521.87	25.0	0
	100	Overload	282,874.17	56,724.63	25.0	0
	105	Overload	306,739.89	61,394.89	25.0	0
	110	Overload	328,208.15	65,998.74	25.0	0
	115	Overload	347,993.89	70,102.62	25.0	0
	120	Overload	366,766.79	74,256.84	25.0	0
	125	Overload	384,149.35	93,628.55	19.1	1
	130	Overload	400,002.93	98,791.37	15.6	1
	135	Overload	414,585.78	106,490.08	12.8	1
	140	Overload	427,873.80	117,418.01	10.6	2
	145	Overload	439,922.65	131,378.41	8.8	2
	150	Overload	450,808.50	148,267.45	7.4	3

and

Table 3. Thermo-economic results for Transformer Case 3 under different load levels and cities.

City	Load (%)	Scenario	E_loss (kWh/yr)	EAC (USD/yr)	Life (yrs)	Replacements
Quito	90	Base	970,471.41	181,047.14	25.0	0
	100	Overload	1,156,595.75	215,911.45	25.0	0
	105	Overload	1,253,482.96	233,130.63	25.0	0
	110	Overload	1,340,910.54	249,432.74	25.0	0
	115	Overload	1,420,723.45	264,112.57	25.0	0
	120	Overload	1,495,191.52	277,407.06	25.0	0
	125	Overload	1,563,013.91	289,452.71	25.0	0
	130	Overload	1,625,341.01	300,363.44	25.0	0
	135	Overload	1,683,034.49	310,235.30	25.0	0
	140	Overload	1,736,495.60	319,151.60	25.0	0
	145	Overload	1,786,211.21	327,187.85	25.0	0
	150	Overload	1,832,486.76	334,412.17	25.0	0
Guayaquil	90	Base	970,471.41	181,047.14	25.0	0
	100	Overload	1,156,595.75	215,918.02	25.0	0
	105	Overload	1,253,482.96	233,150.88	25.0	0
	110	Overload	1,340,910.54	249,457.96	25.0	0
	115	Overload	1,420,723.45	264,142.33	25.0	0
	120	Overload	1,495,191.52	320,337.85	21.2	1
	125	Overload	1,563,013.91	335,651.78	17.3	1
	130	Overload	1,625,341.01	351,214.60	14.2	1
	135	Overload	1,683,034.49	367,053.65	11.8	2
	140	Overload	1,736,495.60	383,192.10	9.9	2
	145	Overload	1,786,211.21	399,649.56	8.4	2
	150	Overload	1,832,486.76	416,442.56	7.2	3
Amazon	90	Base	970,471.41	181,047.14	25.0	0
	100	Overload	1,156,595.75	215,915.24	25.0	0
	105	Overload	1,253,482.96	233,133.32	25.0	0
	110	Overload	1,340,910.54	249,434.93	25.0	0
	115	Overload	1,420,723.45	264,115.89	25.0	0
	120	Overload	1,495,191.52	278,448.26	25.0	0
	125	Overload	1,563,013.91	292,555.66	25.0	0
	130	Overload	1,625,341.01	306,562.93	25.0	0
	135	Overload	1,683,034.49	320,598.31	25.0	0
	140	Overload	1,736,495.60	334,793.79	25.0	0
	145	Overload	1,786,211.21	349,285.35	25.0	0
	150	Overload	1,832,486.76	364,213.37	25.0	0

. These tables summarize the annual energy losses ($E_{\mathrm{loss}}$), equivalent annual cost (EAC), estimated thermal lifetime, and number of replacements over a 25-year evaluation horizon for each transformer configuration. The analysis includes multiple load levels ranging from 90% to 150% of the rated capacity, under representative climatic conditions for Quito, Guayaquil, and the Amazon. Both the base scenario (90% loading) and daily overload scenarios (100–150% loading for 10 h) are considered. These results serve as a basis for comparing the thermal degradation and economic performance of transformers of different sizes and cooling methods, operating under diverse environmental and loading conditions.

4. Discussion

4.1. Comparative Analysis of Parametric Study of Remanent Life

The quantitative results confirm that daily overload is the decisive factor in the thermal life and total cost of the transformers analyzed. Heat maps of Figure 1 show that, under ONAN cooling, the combination of load capacity and peak duration explains more than 90% of the variation in service life: above 120% and 8 h of overload, the degradation slope becomes almost vertical, reducing service life from decades to a few years. The effect is more severe in hot climates, where the increase in ambient temperature shifts all isocurves toward lower operating margins. With forced cooling (ONAF/OFAF), the same curves shift to the right and allow the peak-hour window to be doubled before reaching the same level of aging. However, the incremental gain between ONAF and OFAF becomes marginal (less than 3 years) as long as the load capacity remains below 115%.

Comparing installations, the thermal penalty for installing equipment indoors translates into a systematic reduction in service life of 15 to 25%, a greater penalty than the discrepancy between the IEEE and IEC models (around 5%). This suggests that the location decision is more critical than the choice of calculation standard.

4.2. Comparative Analysis of Thermo-Economic Results

Table 1, Table 2 and Table 3 summarize the simulated thermo-economic performance of the three transformer cases under daily overload conditions of increasing intensity and constant duration (10 h/day), across three distinct climatic regions of Ecuador. The results highlight how transformer capacity, cooling method, and ambient temperature interact to affect both insulation aging and total ownership costs.

In Case 1 (1000 kVA, ONAN; Table 1), thermal degradation remains negligible under the base scenario and low overload levels in all three regions. However, as the loading increases beyond 120%, the aging behavior begins to diverge depending on the climatic conditions. While in Quito, the transformer retains its full lifetime of 25 years even at 150% loading, in Guayaquil, the life expectancy drops to just 6.3 years at this level, with three replacements required. The Amazon region exhibits intermediate degradation, with a life expectancy of 7.0 years at 150%. These results underscore the influence of ambient temperature on the thermal stress margin of ONAN-cooled transformers. Furthermore, the equivalent annual cost (EAC) increases gradually in Quito (from $9758.79 to $19,069.35). It surges more steeply in Guayaquil (up to $33,993.08), reflecting both the higher losses and the cost of accelerated replacement cycles.

Case 2 (10,000 kVA, ONAF; Table 2) demonstrates improved thermal robustness. In Quito, the transformer maintains its full lifetime across all overload levels without requiring any replacements. In contrast, Guayaquil shows accelerated aging from 120% load onward, requiring four replacements at 150% loading. The Amazon region again displays a moderate response, with three replacements needed at the same load level. This indicates that while increased capacity and active cooling improve thermal performance, they do not eliminate vulnerability to high ambient temperatures under sustained overload conditions. Notably, the EAC in Guayaquil increases from $47,521.87 at 90% to over $151,000 at 150%, illustrating how life cycle costs are disproportionately affected by environmental stressors in high-load applications. The presence of nonlinear increments in EAC, particularly beyond 125%, suggests the compounding effect of aging-induced replacements and loss-related costs.

Case 3 (40,000 kVA, OFAF; Table 3) presents the most resilient performance among all cases. In both Quito and the Amazon, the transformer maintains its 25-year expected life even under the maximum overload level tested (150%), showing no replacements and moderate EAC growth. In Guayaquil, however, aging becomes evident from 120% loading, with up to three replacements required by 150%. Despite this, the relative impact is less severe compared to Cases 1 and 2, given the higher base capacity. The EAC in Guayaquil reaches $416,442.56 at 150%, compared to $334,412.17 in Quito and $364,213.37 in the Amazon. These differences highlight the economic implications of climate-resilient transformer design: although larger units require greater initial investment, they offer improved operational longevity and reduced sensitivity to environmental overload risk—particularly in mild or moderate temperature zones.

From a broader perspective, the results confirm several key insights:

• Ambient temperature is a dominant factor in determining thermal aging rates, even more so than load level, particularly in lower-capacity units with passive cooling.
• Transformer capacity and cooling method jointly determine overload resilience. Transitioning from ONAN to ONAF and OFAF allows transformers to operate safely at higher loads and temperatures before incurring aging-related penalties.
• The cost-effectiveness of overloading depends strongly on location. For example, a 120% overload in Quito may be thermally and economically acceptable, while the same in Guayaquil can result in multiple replacements and substantial increases in EAC.
• Nonlinear economic penalties emerge beyond a threshold. In all cases, a critical point between 120 and 130% can be identified where EAC and replacement frequency begin to escalate rapidly. This highlights the value of determining safe loading limits not only from a thermal standpoint but also from a long-term economic perspective.

These findings emphasize the necessity of integrating both thermal and financial criteria in the planning and operation of distribution transformers, particularly in geographically diverse regions. They also support the use of parametric simulation tools as decision-making aids for transformer sizing, asset management, and overload policy design.

Taken together, the findings highlight three practical implications: (i) overload policies should be specific to each climate region; (ii) forced cooling is justified only for extreme profiles, while (iii) indoor location requires a readjustment of the permissible load capacity or the adoption of ONAF/OFAF systems to compensate for the thermal penalty. These results provide the basis for the formulation of operational loadability curves and asset management strategies that simultaneously optimize service life and total cost. The applied model is based on fixed daily load profiles, average ambient temperature values, and standard IEEE/IEC thermal constants; therefore, it does not capture seasonal variability or thermal transients from irregular overloads. It also does not consider accelerated degradation due to moisture, partial discharge, or chemical aging of the oil, and it assumes static energy and investment costs. Future research should incorporate stochastic load profiles based on real measurements, use coupled modeling of insulation moisture and partial discharge, include dynamic power price curves, and analyze active control strategies (e.g., variable fans or targeted cooling) to optimize service life and total cost in real time simultaneously.

5. Conclusions

This study presented a comprehensive thermo-economic evaluation framework to quantify the impact of daily overload on the service life and cost efficiency of oil-immersed distribution transformers operating under three climatic regions in Ecuador. By integrating the IEEE and IEC thermal aging models with an equivalent annual cost (EAC) analysis, the methodology allows a unified assessment of insulation degradation and operational costs under realistic load and temperature profiles.

The results of the parametric simulations, which considered variations in load level (90–150%), peak duration (10 h), cooling configuration (ONAN, ONAF, OFAF), and installation condition (indoor/outdoor), yield several key conclusions:

• Ambient temperature is a dominant driver of thermal degradation. Under identical overload conditions, transformers operating in Guayaquil exhibited service lives up to 70% shorter than those in Quito, particularly under passive (ONAN) cooling. This highlights the necessity of location-specific overload policies.
• Transformer size and cooling method significantly influence resilience. Larger-capacity units with active cooling (OFAF) showed superior thermal endurance, maintaining full life expectancy even under 150% daily loading in mild climates. In contrast, smaller ONAN units in hot environments reached end-of-life in less than 7 years at the same load level.
• Economic performance deteriorates nonlinearly beyond 120–130% load. The equivalent annual cost (EAC) escalates rapidly beyond this threshold due to the compounding effect of increased energy losses and accelerated replacement frequency. In Guayaquil, Case 1’s EAC nearly tripled when load increased from 120% to 150%.
• Indoor installations incur a systematic thermal penalty. Life expectancy decreased by 15–25% when comparing indoor to outdoor cases due to restricted heat dissipation, which justifies reconsidering location or upgrading to forced cooling for installations in enclosed spaces.
• The IEEE and IEC models provide consistent estimations under moderate loads, with discrepancies under 5%. However, under high overload and high ambient temperature scenarios, the IEC model predicts slightly shorter lifetimes, which may lead to more conservative asset management decisions.

The proposed model proves to be an effective tool for evaluating transformer utilization strategies by jointly optimizing technical and economic performance indicators. The methodology can support utilities in defining safe loading margins, designing context-sensitive overload policies, and prioritizing investments in cooling upgrades or transformer replacements.