The stakes are both environmental and economic. Decommissioned crystalline silicon modules contain lead, cadmium and tin, substances linked to brain disorders, cancers and damage to the lungs, liver, kidneys and prostate if they leach from improper dumps. Yet the same panels are also a treasure chest of recoverable material. IRENA estimates that recycling end-of-life PV panels could unlock roughly 450 million dollars in recoverable value by 2030 and 15 billion dollars by 2050. The problem, the study’s authors Shikha Tiwari, Eshwar Dayal and Lakshay argue, is that existing waste management systems simply fail to capture this stream, because of economic and logistical constraints. Solar installations range from sprawling utility-scale parks to scattered urban rooftops, and that geographic fragmentation drives up the cost of collecting heavy, fragile freight from thousands of dispersed points.

The core of the new work is a bi-level optimization model, a mathematical structure designed for situations where two decision-makers with conflicting goals interact. In this formulation, the collection centre operator acts as the leader, seeking to minimise total cost, which includes fixed facility costs, vehicle routing expenses and the incentives paid out. The end users of solar panels act as followers, rationally choosing whether to hand their retired panels to the formal recycling system and, if so, whether to request a home pickup or deliver the panels themselves to a drop-off point. The lower level of the model maximises the incentives users receive, while the upper level minimises the operator’s total cost. The authors frame this as a Stackelberg game, a classic game-theoretic construct in which the leader anticipates the follower’s best response before committing to its own decision.

What makes the framework distinctive is that it stitches together, in a single model, four elements that previous studies treated largely in isolation: forecasting of future waste volumes, optimisation of facility locations, vehicle routing, and financial incentives. The authors’ comparative analysis of the literature shows that most prior works incorporated at most two of these dimensions. Some optimised facility placement but ignored routing; others modelled incentives but lacked any mathematical backbone for reverse logistics. By contrast, the new model makes incentives endogenous, meaning the payment levels themselves are decision variables that respond to waste volumes and costs, rather than fixed assumptions plugged in from outside.

The forecasting component is built on the Weibull distribution, a statistical function widely used to model failure rates over time. Rather than assuming every panel dies at exactly year 25, the Weibull approach produces a probabilistic retirement curve that rises during operational degradation and accelerates near end of life, which the authors argue is far closer to real-world behaviour than a fixed-lifespan model in which all panels retire simultaneously. The study runs two scenarios: a regular-loss baseline with a shape factor of about 2.49, and an early-loss pessimistic scenario with a shape factor of 5.38, reflecting premature failures from harsh weather or handling damage. Future installed capacity is projected using segmented linear growth rates, declining from 7.8 percent in 2021-2025 to 3.5 percent by 2036-2040, a deliberate choice to avoid the overestimation that exponential extrapolation produces over a 20-year horizon.

That overestimation problem is vividly demonstrated in the results. When an exponential growth assumption with a 14 percent compound annual growth rate is applied to Jaipur district, the model projects more than 2,300 megawatts of installed capacity in a single district by 2040, and a cumulative capacity overestimate of more than 100 percent. Such inflated numbers would lead planners to open unnecessary collection centres, oversize their fleets and set incentive levels for waste that will never materialise. The segmented linear approach, by contrast, produces projections that the authors consider implementable, and it feeds district-level waste estimates for Jaipur from 2021 to 2040, a spatial resolution fine enough to support actual facility location and routing decisions, unlike the national or state-level estimates that dominate the existing literature.

For the case study, Jaipur, the district with the highest installed solar capacity in India’s top solar state, was divided into 95 equal square grids, with each grid centroid serving as a waste generation site. Thirty-seven authorised e-waste collection centres provided the pool of candidate facilities. The routing side of the model is a capacitated vehicle routing problem, solved with Miller-Tucker-Zemlin subtour elimination constraints to ensure that every collection route is a single continuous loop returning to its depot, rather than a set of disconnected fragments. Haversine distances between grid centroids and centres ground the routing calculations in real geography. The model also enforces a profitability rule: revenue from selling collected panels to recyclers must exceed total operating cost by at least 10 percent, a threshold reflecting administrative overhead, price volatility in recovered materials and the need to fund infrastructure investment.

The results reveal an elegant adaptive behaviour. Under regular loss, the model keeps just two collection centres open until 2035, then adds one per year, reaching six by 2039. Under early loss, where cumulative waste over 2021-2030 is roughly 31 times higher than in the regular scenario, the network scales to as many as 14 centres. Crucially, the model remains profitable in every year of both scenarios, adjusting centre counts and incentive levels without any structural redesign. The incentive dynamics are particularly telling: at low waste volumes, pickup incentives sit near their upper limit because door-to-door collection is cheap when there is little to collect, but as volumes surge, the model widens the gap between drop-off and pickup payments, effectively shifting the logistical burden onto end users and encouraging them to deliver panels themselves. Incentive values eventually stabilise at around 2,500 rupees per kilowatt for pickup and 3,500 for drop-off.

The study also derives four key performance indicators that translate the mathematics into measurable outcomes: cost per tonne collected, average haul distance per tonne, waste recovery rate, and carbon dioxide emissions per tonne. The recovery rate holds steady at about 84 percent across all years and scenarios, while emissions per tonne fall dramatically as waste density rises, dropping from over 35 kilograms of CO2 per tonne in the sparse early years to under 2 kilograms by 2039 in the regular-loss case. Sensitivity analysis shows that minimum collection rates above 70 percent yield a healthy profit-to-cost ratio, that collection centre capacities of 40,000 kilograms or more stabilise the network at two facilities, and that vehicle capacities of 4,000 kilograms or more minimise cost. Computationally, the framework scales gracefully: even at 132 grid cells, generating over four million variables, the solver converged in under 42 seconds with optimality gaps below 2.5 percent.

The implications reach well beyond Jaipur. The authors recommend that policymakers provide subsidies or extended producer responsibility funding during the low-volume window of 2026 to 2030, explicitly incentivise self-drop-off since full home pickup is fiscally unviable, and use the model’s quantified costs to set collection targets that are both ambitious and financially realistic. For operators, the message is that flat-rate incentives are inefficient; payments should be dynamically adjusted, centres should open in stages, and the pickup-drop-off gap should widen during waste surges. The framework is designed to be replicated across regions and time frames, and with modifications could extend to other e-waste streams. Future work, the authors note, could incorporate stochastic user behaviour, the informal recycling sector as a competitor, and real-time GIS integration. But the central insight stands: the coming wave of solar waste is not merely a liability to be buried, but a feedstock whose recovery can be engineered, optimised and made to pay for itself.

Subject of Research: Bi-level optimization modeling for sustainable end-of-life solar photovoltaic waste management and reverse logistics within a circular economy framework

Article Title: Development of a bi-level optimization model for sustainable Solar PV Waste management within a circular economy framework

Article References: Tiwari, S., Dayal, E., & Lakshay (2026). Development of a bi-level optimization model for sustainable Solar PV Waste management within a circular economy framework. Cleaner Engineering and Technology, 35, Article 101327. https://doi.org/10.1016/j.clet.2026.101327

Image Credits: AI Generated

DOI: 10.1016/j.clet.2026.101327

Keywords: solar PV waste, bi-level optimization, circular economy, reverse logistics, Weibull distribution, vehicle routing problem, Stackelberg game, recycling incentives, extended producer responsibility, Jaipur case study, e-waste management, renewable energy

The research, led by Kunhao Niu and colleagues, tackles a problem that has grown increasingly urgent as the world electrifies transport. Photovoltaic-energy storage-charging stations, which combine rooftop or canopy solar arrays with on-site batteries and charging hardware, are a cornerstone of the renewable transition. Yet they face a stubborn trio of challenges: solar output is inherently volatile, stationary storage is expensive to cycle, and the charging behavior of thousands of individual drivers is chaotic and hard to predict. Left unmanaged, these factors produce stations that lean heavily on the grid, waste solar energy they cannot absorb, and operate at razor-thin economic margins.

The core innovation of the study lies in how it tames that chaos. Rather than treating every electric vehicle as an individual decision-maker, the researchers introduce an intermediary called an EV aggregator, which bundles vehicles into clusters based on shared characteristics such as arrival times, departure times, and state-of-charge needs. To sort vehicles into these groups, the team deployed a hybrid algorithm combining particle swarm optimization with fuzzy C-means clustering. The fuzzy clustering approach allows each vehicle to belong partially to multiple groups, capturing the fuzzy reality of driver behavior, while the swarm-based global search prevents the algorithm from getting trapped in poor solutions, a known weakness of conventional fuzzy clustering alone.

Once vehicles are clustered, the framework faces a second mathematical hurdle: how to describe the collective flexibility of dozens or hundreds of cars without tracking each one separately. Here the authors borrow an elegant tool from control theory called the zonotope, a convex geometric object that can represent the full range of feasible charging and discharging schedules for a cluster. Because zonotopes have a remarkable property, their combination under the Minkowski sum is simply the sum of their centers and generators, aggregating many clusters becomes a matter of basic linear algebra rather than a computationally explosive high-dimensional optimization. The zonotope representations are then converted into half-space inequality constraints that standard solvers can handle directly, preserving the essential operational features of the fleet while dramatically reducing the computational burden of dispatch.

With the fleet flexibility captured, the study then structures the economics as a bi-level, leader-follower game. At the upper level, the station acts as the leader, setting dynamic charging prices and vehicle-to-grid discharge subsidies to minimize its total operating cost, which includes grid electricity purchases, solar maintenance, penalties for curtailed solar power, storage usage charges, and compensation for battery degradation in customers’ vehicles. At the lower level, the EV aggregator acts as the follower, responding to those prices by scheduling its clusters to minimize the combined charging and discharging expenses of users. The two levels never merge into a single objective; instead, they are coupled purely through the prices the station announces and the load responses the aggregator returns.

Solving such a nested problem requires care, because a commercial solver cannot simply minimize both objectives at once. The researchers employed an iterative best-response procedure implemented with the CPLEX solver in MATLAB: the station announces prices, the aggregator computes its optimal response, the station re-optimizes given that response, and the loop repeats. The procedure converges when prices and costs stop changing between iterations, with a price tolerance of one thousandth of a yuan per kilowatt-hour and a cost tolerance of 0.1 percent. In the case study, the process reached a fixed point, a Stackelberg equilibrium where neither side can improve its own outcome by unilaterally changing its strategy, by the fourth iteration, demonstrating that the framework is not just theoretically sound but computationally practical.

To test the model, the team simulated a real station with 1,500 kilowatts of installed solar capacity, a 500 kilowatt-hour battery system, and two aggregators each managing five vehicle clusters with distinct grid-connection windows and power limits. The battery, with charging and discharging efficiencies of 0.92, was required to return to its initial state of charge by the end of each 24-hour cycle, a constraint that ensures fair economic comparisons between scenarios and prevents the optimizer from artificially draining the battery to flatter the day’s numbers. Time-of-use tariffs ranged from 0.295 yuan per kilowatt-hour off-peak to 0.804 yuan at peak, with the station selling surplus power back at 75 percent of the purchase price.

The comparison between two operating scenarios delivers the study’s headline finding. In the first scenario, vehicles charge in an orderly, unidirectional fashion alongside storage and solar. In the second, vehicles gain bidirectional capability, discharging back to the station when prices and demand warrant. The difference is striking: during the evening peak from 18:00 to 24:00, the station’s maximum grid purchase drops from 200 kilowatts to 150 kilowatts, a 25 percent reduction, while the solar consumption rate climbs from 90.1 percent to 90.8 percent. Those percentages may look modest, but at scale they translate into substantially less solar energy wasted and materially lower operating costs, all while drivers still get their cars charged on schedule.

The cluster-level dispatch profiles reveal how this coordination actually works. Under uncontrolled charging, sharp demand spikes appear at mid-morning, mid-afternoon, and early evening, worsening the peak-valley disparity that plagues power systems. Under the optimized regime, clusters flip their behavior fluidly: they charge deeply during overnight and midday windows when solar generation is abundant or tariffs are low, then discharge during the evening peak to provide peak regulation. Individual clusters adapt to their own constraints, with one cluster absorbing solar energy in the late afternoon while another charges overnight to meet its demand, showing that the aggregation method preserves the granular realities of driver schedules rather than flattening them into an unrealistic average.

Beyond the immediate numbers, the study points toward a broader reimagining of electric vehicles as distributed energy assets. Millions of car batteries sitting in parking lots represent an enormous, largely untapped reservoir of storage capacity, one that could buffer renewable generation without the capital cost of building new grid-scale batteries. The bi-level pricing mechanism at the heart of this framework offers a market-compatible way to unlock that reservoir, compensating drivers for battery wear while giving stations a dispatchable resource. The authors note that future work could extend the model to formal electricity market participation, allowing aggregators to bid their clustered flexibility into energy and reserve markets. If the gap between solar abundance at noon and demand peaks at dusk is the central problem of the renewable era, this research suggests the solution may already be parked in the garage, waiting for the right price signal to plug in.

Subject of Research: Bi-level optimal scheduling of photovoltaic-energy storage-charging stations with electric vehicle aggregators and vehicle-to-grid dispatch

Article Title: Optimal bi-level scheduling of a PV – energy storage – charging station with consideration for EV aggregators

Article References: Optimal bi-level scheduling of a PV – energy storage – charging station with consideration for EV aggregators. (n.d.). https://doi.org/10.1016/j.egyr.2026.109775

Image Credits: AI Generated

DOI: 10.1016/j.egyr.2026.109775

Keywords: electric vehicles, vehicle-to-grid, photovoltaics, energy storage, bi-level optimization, EV aggregator, fuzzy C-means clustering, particle swarm optimization, zonotope, renewable energy, smart charging, Stackelberg equilibrium