Wastewater treatment plants can utilize biogas in on-site combined heat and power (CHP) systems to offset electricity and natural gas consumption, but CHP systems are often limited to larger facilities due to economic considerations. However, existing CHP sizing guidelines do not consider the operational flexibility provided by biogas storage or its ability to respond to time-varying electricity prices or other demand response signals. This paper develops optimization frameworks for the operation and design of wastewater treatment CHP and biogas storage under time-varying electricity prices. The proposed frameworks determine the optimal CHP and biogas storage capacities and dispatch schedules. In a realistic case study, we find that CHP reduces annual operating costs by 58.6%, while biogas storage provides an additional 12.4% reduction compared to the CHP-only case. Additionally, we find that load-shifting opportunities alter both technology selection and optimal sizing.

Bibtex data:

@inproceedings{WuCHP2026,
    author = {Marcus Wu and Anna Stuhlmacher},
    title = {Optimal Sizing and Dispatch of Biogas Storage and CHP for Demand Response in Wastewater Treatment Plants},
    booktitle = {Proceedings of the North American Power Symposium (NAPS)},
    address = {Houghton, MI},
    month = {10},
    year = {2026}
}

Soft open points (SOPs) are a promising technology for improving distribution system operation by enabling controllable real and reactive power exchange between feeders. Recent work has shown that integrating battery energy storage at the SOP DC link can provide additional operational flexibility. However, existing studies on SOPs with integrated energy storage have focused on balanced distribution network representations, which do not capture the unbalanced nature of distribution systems. This paper presents a three-phase optimal operation framework for SOPs with integrated energy storage to minimize voltage unbalance. The formulation determines SOP power injections and battery schedules while accounting for three-phase unbalanced power flow, SOP, and battery constraints. The problem is reformulated as a mixed-integer second-order cone program using power flow approximations and convex relaxations. A case study demonstrates that SOPs integrated with storage reduce voltage unbalance by approximately 70% relative to the base case, with minor improvements compared to SOP-only configurations.

Bibtex data:

@inproceedings{MyersESOP2026,
    author = {Genevieve E. Myers and Anna Stuhlmacher},
    title = {Three-Phase Optimal Operation of Soft Open Points with Integrated Energy Storage},
    booktitle = {Proceedings of the North American Power Symposium (NAPS)},
    address = {Houghton, MI},
    month = {10},
    year = {2026}
}

Water distribution systems can provide demand-side flexibility to the power grid. By shifting pumping in time while meeting hydraulic requirements, water utilities can respond to electricity price signals and reduce operating costs. However, the extent to which this flexibility is realized depends on the electricity tariff structure. This paper investigates how time-of-use energy rates and demand charges influence water pumping. An optimal water pumping problem is formulated to minimize electricity costs subject to the hydraulic constraints. A sensitivity analysis is performed to evaluate the impact of time-of-use energy rates, on-peak period duration, and demand charge prices on pump scheduling and load-shifting behavior. We find that time-of-use pricing provides stronger incentives for load shifting than demand charges, achieving up to 100% peak-period energy reductions and 400 kWh of shifted energy for TOU ratios greater than 1.3, whereas demand charges primarily encourage flatter pumping and yield substantially smaller increases in load shifting.

Bibtex data:

@inproceedings{SakibTariff2026,
    author = {Aan Nazmus Sakib and Constance Crozier and Anna Stuhlmacher},
    title = {Assessing the Impact of Electricity Tariff Design on Water Distribution Network Flexibility},
    booktitle = {Proceedings of the North American Power Symposium (NAPS)},
    address = {Houghton, MI},
    month = {10},
    year = {2026}
}

Agrivoltaic systems--photovoltaic panels installed above agricultural land--have emerged as a promising dual-use solution to address competing land demands for food and energy production. In this paper, we propose a model predictive control approach to dual-axis agrivoltaic panel tracking control that dynamically adjusts panel positions in real time to maximize power production and crop yield given solar irradiance and ambient temperature measurements. We apply convex relaxations and shading factor approximations to reformulate the optimization problem as a convex second-order cone program that determines the photovoltaic panel position adjustments away from the sun-tracking trajectory. Through case studies, we demonstrate our approach, exploring the Pareto front between i) an approach that maximizes power production without considering crop needs and ii) crop yield with no agrivoltaics. We also conduct a case study exploring the impact of forecast error on model predictive control performance. We find that dynamically adjusting agrivoltaic panel position helps us actively manage the trade-offs between power production and crop yield, and that active panel control enables the agrivoltaic system to achieve land equivalent ratio values of up to 1.897 for lettuce and 1.689 for tomatoes.

Bibtex data:

@article{StuhlmacherMPC2026,
    author = {Anna Stuhlmacher and Panupong Srisuthankul and Johanna L. Mathieu and Peter Seiler},
    title = {A Model Predictive Control Approach to Dual-Axis Agrivoltaic Panel Tracking},
    journal = {Renewable Energy},
    year = {2026},
    number = {274}, 
    pages = {126155}
}

Flexible interconnection agreements are increasingly used to streamline the distributed generation interconnection process by limiting real power exports and avoiding costly grid upgrades. Agrivoltaic systems--solar photovoltaic (PV) panels installed over agricultural land--can provide added value under these agreements by adjusting the PV panels away from sun tracking while increasing the sunlight available to crops. This technical note investigates the operation of agrivoltaics under flexible interconnection limits and evaluates their impact on both PV energy production and crop outcomes. We formulate an optimization problem that determines the time-varying tilt of a single-axis tracking agrivoltaic system to maximize energy production subject to a real power export limit over an entire growing season. The resulting PV operating schedules are then used to evaluate PV energy production and crop yield. In a case study, we demonstrate that agrivoltaic systems can comply with flexible interconnection agreements through operational adjustments that improve crop yield, distinguishing them from conventional PV systems that rely solely on inverter curtailment.

Bibtex data:

@inproceedings{WuPowerUp2026,
    author = {M. Wu and A. Stuhlmacher},
    title = {Productive Curtailment in Agrivoltaic Systems under Flexible Interconnection Agreements},
    booktitle = {Proceedings of the 2026 PowerUp Conference},
    year = {2026},
    address = {Boulder, CO},
    month = {9}
}

Wastewater treatment plants are large, energy-intensive loads that can be optimally controlled to support grid reliability and reduce operational costs. This paper presents a multi-stage robust optimization framework to control a wastewater treatment plant equipped with a biogas generator and storage tank for participation in California's day-ahead and real-time frequency regulation markets while managing biogas production and regulation signal uncertainty. We solve for day-ahead regulation capacity in the first stage and real-time regulation capacity over the day as the uncertainty is progressively revealed. We propose affine control policies to determine the real-time regulation capacity based on partial uncertainty realizations. This results in a tractable affinely adjustable robust counterpart. In a case study, we evaluate our proposed approach against a day-ahead-only robust formulation and found that our approach increases regulation capacity provision and lowers operational costs.

Bibtex data:

@inproceedings{StuhlmacherHICSS2026,
    author = {A. Stuhlmacher and A. Kody},
    title = {Multi-Stage Robust Optimization of a Wastewater Treatment Biogas Generator Participating in Day-Ahead and Real-Time Regulation Markets},
    booktitle = {Proceedings of the 59th Hawaii International Conference on System Sciences (HICSS)},
    year = {2026},
    address = {Lahaina, Hawaii},
    month = {1}
}

Bibtex data:

@inproceedings{WuNAPS2025,
    author = {M. Wu and A. Stuhlmacher },
    title = {Investigating Agrivoltaic System Design Choices on Shading and Power Production},
    booktitle = {Proceedings of the North American Power Symposium (NAPS)},
    year = {2025},
    address = {Hartford, CT},
    month = {10}
}

Wastewater treatment plants are energy-intensive loads with operational flexibility, which has motivated interest in how these plants can support power grid operation through demand flexibility. Since electricity is often the largest single operating cost for wastewater treatment plants, leveraging demand flexibility could offer significant financial benefits. One approach to reduce and shift the wastewater treatment plant's demand is through the use of biogas, a by-product of anaerobic digestion within the wastewater treatment process. Biogas (composed primarily of methane and carbon dioxide) is a renewable fuel that can be used to produce electricity to offset the plant's demand from the grid. However, many wastewater treatment plants currently flare biogas. The goal of this paper is to determine the optimal use of an on-site biogas storage tank and generator to minimize the costs of a wastewater treatment plant participating in the frequency regulation market. To do this, we formulate the wastewater treatment plant optimization problem subject to biogas and frequency regulation constraints while managing biogas production uncertainty. We solve for the biogas generator schedule and frequency regulation capacity to minimize operational costs. In a case study using data from a California wastewater treatment plant, we demonstrate how our approach can exploit electricity rate structures to reduce electricity costs and effectively participate in the frequency regulation market.

Bibtex data:

@article{StuhlmacherIREP2025,
    author = {A. Stuhlmacher and A. Kody and M. Wu},
    title = {Optimizing Biogas Use in Wastewater Treatment Plants For  Demand Flexibility},
    journal = {Sustainable Energy, Grids and Networks  - Special Issue for the 2025 IREP Symposium on Bulk Power System Dynamics and Control},
    year = {2025},
    month = {6},
    volume = {43},
    pages = {101825},
    address = {Sorrento, Italy}
}

Bibtex data:

@inproceedings{SakibPESGM2025,
    author = {A.N. Sakib and A. Stuhlmacher},
    title = {Leveraging Drinking Water Pumps as Flexible Loads Using Input Convex Neural Networks},
    booktitle = {Proceedings of the IEEE Power and Energy Society General Meeting (PES GM)},
    year = {2025},
    address = {Austin, Texas}
}

Bibtex data:

@article{StuhlmacherTPWRS2025,
    author = {A. Stuhlmacher and S. Guikema and J. L. Mathieu},
    title = {Assessing Power and Water Network Resilience When Water Pumps Provide Frequency Regulation},
    journal = {IEEE Transactions on Power Systems},
    volume = {40},
    number = {5},
    pages = {3833 -- 3845},
    year = {2025}
}

Bibtex data:

@inproceedings{StuhlmacherHICSS2025,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Demand Response Potential of Drinking Water Distribution Networks},
    booktitle = {Proceedings of the 58th Hawaii International Conference on System Sciences (HICSS)},
    year = {2025},
    address = {Waikoloa, Hawaii}
}

Bibtex data:

@inproceedings{StuhlmacherHICSS2024,
    author = {A. Stuhlmacher and J. L. Mathieu and P. Seiler},
    title = {Optimizing Dual-Axis Solar Panel Operation in an Agrivoltaic System and Implications for Power Systems},
    booktitle = {Proceedings of the 57th Hawaii International Conference on System Sciences (HICSS)},
    year = {2024},
    address = {Waikiki, Hawaii},
    month = {1}
}

The electrical grid has undergone significant transformations, which have had a profound impact on its distribution system development and expansion. These changes have been primarily driven by changing load profiles, distributed generation sources, and increasingly extreme weather events. Advancements in sensor and communication technologies have played a pivotal role in addressing and adapting to these changes. These changes have also led to an increased focus on reliability and resilience in planning, with priority placed on ensuring robust grid connectivity and flexibility.

Three decades ago, power distribution systems were primarily radial with unidirectional power flow. Today's electrical distribution systems have distributed energy resources, leading to bidirectional power flow. The utility's geographic information system network, advanced metering infrastructure, and other technologies are leveraged to allow feeders and distributed energy resources to be interconnected. This has facilitated the integration of the electric grid with networked microgrids, which has improved the overall resilience and efficiency of the distribution system.

While there have been notable improvements in grid planning, the power grid remains vulnerable to high-impact, low-frequency events caused by climate change, such as hurricanes and tornadoes. This monograph outlines potential solutions for addressing future electric grid issues, including transformer overloading due to electric vehicles, optimization challenges, advanced feeder reconfiguration, and contingency planning for extreme events. The proposed approaches focus on the implementation and operation of new technologies, such as renewable energy sources, batteries, flexible loads, and advanced sensors, that have the potential to transform distribution network planning and operation. From traditional methods to innovative networked microgrids within existing infrastructure and non-wire alternative strategies, this monograph provides a comprehensive overview of stateof- the-art strategies for future problems.

Bibtex data:

@article{StuhlmacherFnT2023,
    author = {A. Stuhlmacher and C. Ten and L. Dilworth and Y. Tang},
    title = {Operational Planning for Emerging Distribution Systems: A Unique Perspective on Grid Expansion},
    journal = {Foundations and Trends in Electric Energy Systems},
    volume = {7},
    number = {2},
    pages = {63--164},
    year = {2023}
}

Large amounts of renewable energy resources are being added to the electric power grid in a push to mitigate the effects of climate change. Due the intermittent and uncertain nature of these resources, more flexibility is needed to ensure safe operating conditions of the power grid. A growing body of research has shown that real-time control of flexible electric loads can provide flexibility to the power grid. For instance, drinking water distribution networks can be treated as flexible, controllable assets to the power grid by leveraging the power consumption of water supply pumps and storage capabilities of water tanks. Initial research has explored optimizing the operation of water distribution networks to support the power grid; however, the impact of uncertainty on network performance and value has not been considered.

In this dissertation, an integrated power-water optimization problem is developed subject to the water and power network constraints and multiple sources of uncertainty. The operation of water distribution networks is optimized to provide multiple local and system services-such as voltage and frequency regulation-to power networks. The integrated optimization of the water distribution network and power network is challenging because both networks have nonconvex models and experience uncertainty (e.g., water and power demands). Additionally, changes in network operation need to clearly provide value to both system operators as well as maintain or improve upon network resilience. The associated benefits and drawbacks of the integrated water-power optimization framework are investigated, with a particular focus on performance, conservativeness, and computational tractability. First, state and country-wide estimates of the power and energy capacity of water distribution networks as flexible loads are calculated using publicly available water distribution network utility information, indicating that water distribution networks can provide a sizable flexible resource. Second, stochastic and robust optimization frameworks are developed to optimally schedule and control the water distribution network to provide power system services while ensuring the safe operation of the power and water distribution networks given power and water demand uncertainties. Third, to address challenges surrounding problem complexity and scalability, this work develops proofs that the monotonicity properties apply to the water flow constraints under certain assumptions, uses approximation and relaxation techniques to reformulate the power-water problem as a convex program, and proposes an analytically reformulated probabilistic framework that manages uncertainty differently in the power and water network. Fourth, the flexibility of the water distribution network may be underutilized if any one power system service is considered. To prevent this, a formulation is developed where the water network provides multiple services simultaneously. This maximizes the overall benefit to the power grid and increases the value proposition to the water distribution network operator. And fifth, optimal pump operation strategies are evaluated to ensure that the power and water networks can respond and adapt to natural hazard events when the water distribution network is providing grid services.

Case studies demonstrate the capability of the water distribution network pumps to provide services to the power grid. By co-optimizing the power grid and the drinking water distribution network, improvement in costs, reliability, and resiliency can be realized across these two critical infrastructure systems. Additionally, leveraging the water distribution network to provide flexibility to the power grid can allow for greater quantities of renewable energy resources to be incorporated into the grid and reduce carbon emissions.

Bibtex data:

@inproceedings{Stuhlmacher2023,
    author = {A. Stuhlmacher},
    title = {Optimal Scheduling and Control of Uncertain Coupled Power-Water Distribution Networks},
    school = {University of Michigan},
    year = {2023},
    month = {5}
}

Drinking water distribution networks (WDNs) can be operated as flexible, controllable loads. In this paper, we consider using WDNs to provide local and grid level services simultaneously to the power grid. We formulate a robust water pumping problem to determine the amount of voltage support and frequency regulation that can be provided subject to network constraints while managing power demand uncertainty. We tractably reformulate the problem as a sequential optimization problem and solve for the scheduled water pumping operation, the frequency regulation capacity, and the optimal control policy parameters that update the pump operation based on the frequency regulation signal and power distribution network demand forecast error. We demonstrate our approach through detailed case studies. Additionally, we evaluate the performance of the reformulation and discuss the benefits and trade-offs of WDNs providing multiple services.

Bibtex data:

@article{StuhlmacherPSCC2022,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Flexible Drinking Water Pumping to Provide Multiple Grid Services},
    journal = {Electric Power Systems Research - Special Issue for the 2022 Power Systems Computation Conference (PSCC)},
    volume = {212},
    pages = {108491},
    year = {2022},
    month = {6},
    address = {Porto, Portugal}
}

Bibtex data:

@inproceedings{StuhlmacherIREP2022,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Uncertainty-Aware Methods for Leveraging Water Pumping Flexibility for Power Networks},
    booktitle = {Proceedings of the IREP Symposium on Bulk Power System Dynamics and Control},
    year = {2022},
    address = {Banff, Canada},
    month = {8}
}

Bibtex data:

@inproceedings{StuhlmacherCDC2023,
    author = {A. Stuhlmacher and L. A. Roald and J. L. Mathieu},
    title = {Tractable Robust Drinking Water Pumping to Provide Power Network Voltage Support},
    booktitle = {Proceedings of the Conference on Decision and Control (CDC)},
    pages = {4206--4213},
    year = {2021},
    month = {12}
}

Bibtex data:

@article{StuhlmacherIEEE2020,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Chance-Constrained Water Pumping to Manage Water and Power Demand Uncertainty in Distribution Networks},
    journal = {Proceedings of the IEEE},
    volume = {108},
    number = {9},
    pages = {1640--1655},
    year = {2020}
}

Bibtex data:

@article{StuhlmacherPSCC2020,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Water Distribution Networks as Flexible Loads: A Chance-Constrained Programming Approach},
    journal = {Electric Power Systems Research - Special Issue for the 2020 Power Systems Computation Conference (PSCC)},
    volume = {188},
    pages = {106570},
    year = {2020},
    month = {6}
}

Bibtex data:

@inproceedings{StuhlmacherNAPS2019,
    author = {A. Stuhlmacher and J. L. Mathieu},
    title = {Chance-Constrained Water Pumping Managing Power Distribution Network Constraints},
    booktitle = {Proceedings of the North American Power Symposium (NAPS)},
    year = {2019},
    address = {Wichita, KS},
    month = {10}
}