Stochastic framework for scheduling preemptive upgrades of distribution transformers

TL;DR

The paper tackles transformer overloading due to residential electrification by integrating a stochastic framework that combines meter-level load forecasts, transformer aging, and upgrade planning. It uses a Monte Carlo approach to propagate uncertainty in HP and EV adoption and per-meter load profiles, deriving time-resolved failure probabilities, which are then fed into a convex mixed-integer optimization to schedule upgrades under annual capacity constraints. Across 100 realizations on a Vermont feeder and three growth scenarios, most transformers show little aging risk, while a minority drive peak risk; higher upgrade capacity limits and timely sizing can substantially reduce expected failures. The work provides a practical, probabilistic method to guide asset management decisions and investment timing for transformer upgrades in the face of uncertain electrification trajectories.

Abstract

Electrification of residential heating and transporta- tion has the potential to overload transformers in distribution feeders. Strategic scheduling of transformer upgrades to antici- pate increasing loads can avoid operational failures and reduce the risk of supply shortages. This work proposes a framework to prioritize transformer upgrades based on predicted loads at each meter, including heat pumps and electric vehicle chargers. The framework follows a Monte Carlo approach to forecasting, generating many possible loading instances and collecting a distribution of failure probabilities for each transformer. In each loading instance, heat pumps and EVs are added stochastically to each meter over time, based on an overall estimated growth rate and factors specific to each customer. We set heat pump load profiles by temperature and EV load profiles based on a stochastic driving model and charging pattern. The load profiles feed into network topology and transformer failure models to calculate failure probabilities.We formulate a cost optimization based on these failure probabilities to schedule transformer upgrades. We demonstrate this approach on a real-world distribution feeder in rural Vermont under low, medium, and high-electrification scenarios. We find generally less than 20% of transformers having substantial risk of failure over a 20-year simulation. Lastly, we develop an optimization routine to schedule upgrades and discuss the expected number of failures.

Figures (4)

• Figure 1: Information flow for one MC realization for one year with hourly timeseries resolution. The load forecast for each device (heat pump or EV) is randomly generated, individually for each meter, in three stages: adoption determines which meters have a device; device type selects the size of heat pump or battery and parameters for EV driving and charging habits; load profile generates the time series based on the device parameters. Weather (temperature) and baseload timeseries are external inputs. Total meter load combines heat pump, EV, and baseload timeseries. The network model links meters to transformers: transformer loads are the sum of loads of the meters they feed. The transformer risk model consists of three deterministic parts: the temperature in the transformer evolves based on loading and temperature; aging is a model of thermal degradation; and failure probability is based on an empirical distribution. Failure probability timeseries for each transformer are the output of each realization.
• Figure 2: Transformer failure probabilities over 100 MC realizations of a 20-year simulation. (a) Overall failure probabilities of each transformer in low (blue), medium (green), and high (red) growth scenarios. The vertical black line marks the 25 top risk transformers. (Note transformer index is not necessarily the same in each scenario.) Failure risk for these 25 transformers is shown in panels (b)-(d) for low, medium, and high-growth scenarios, respectively. Failure probability on the y-axis is cumulative up to year $y$ (not just in year $y$). In (d), many transformers have failure probabilities of essentially 1 by year 20 of the simulation, so the choice of the top 25 is arbitrary (and happens not to include the two "bad" transformers from the other scenarios).
• Figure 3: Transformer failure probabilities under modified scenarios. Increasing all transformer capacities by 50% (corresponding to business as usual upgrade -- increasing to next size up), (a) shows overall failure probabilities and (b) shows failure curves for the medium-growth scenario. Vertical black line in (a) indicate the top 25 aged transformers whose curves are shown in (b).
• Figure 4: Left: Expected number of failures in the medium-growth scenario after accounting for planned upgrades. Increasing $N^{\rm max}$, the annual upgrade limit, decreases the failure rate. Right: Number of planned upgrades for different $N^{\rm max}$. The number of upgrades saturates for a few years around year 10 with $N^{\rm max}=20$; for smaller $N^{\rm max}$, it is saturated from the outset -- in preparation for the upgrades needed in year 10 as failure probabilities rise.