Intertemporal Constraints Research Articles

Optimal siting and sizing of battery energy storage systems in unbalanced distribution systems: A multi objective problem under uncertainty

In this paper the siting and sizing problem of battery energy storage systems in unbalanced active distribution systems is formulated as a mixed-integer, non-linear, constrained multi objective (MO) optimization problem under uncertainties. The problem is cumbersome from the computational point of view due to the presence of intertemporal constraints, a great number of state variables and the presence of uncertainties in the problem input data. A new approach based on the trade-off/risk analysis is proposed to obtain with acceptable computational efforts a solution that may not be the optimal solution but represents a reasonable and robust compromise. We use the trade-off/risk analysis, because it was specifically developed for power system planning problems in which we deal with a wide range of options, with possible conflicting objectives, and with uncertainty and risk. The proposed approach includes new procedures to select an adequate set of planning alternatives to be considered in the trade-off/risk analysis framework and to assist the planning engineer when difficulties arise in setting probabilities of the input data. Numerical applications to an IEEE unbalanced test system demonstrate the effectiveness of the proposed procedure and indicate the best alternatives of storage systems in the range from 450 kW to 600 kW globally installed in a reduced set of nodes.

Optimization of distributed energy resources planning and battery energy storage management via large-scale multi-objective evolutionary algorithm

This paper investigates the synergistic integration of renewable energy sources and battery energy storage systems to enhance the sustainability, reliability, and flexibility of modern power systems. Addressing a critical gap in distribution networks, particularly regarding the variability of renewable energy, the study aims to minimize energy costs, emission rates, and reliability indices by optimizing the placement and sizing of wind and solar photovoltaic generators alongside battery energy storage systems. An improved large-scale multi-objective evolutionary algorithm with a bi-directional sampling strategy is employed.Two scenarios are considered. In the first scenario, six study cases are analyzed to determine the optimal number, location, and size of distributed generators at peak load demand. The proposed algorithm outperforms existing state-of-the-art methods for small-scale distributed resource allocation. In the second scenario, a multi-period load demand across various seasons is evaluated, introducing new opportunities for battery energy storage systems. The problem is modeled with intertemporal constraints, creating a large-scale optimization challenge. Results demonstrate significant improvements: cost savings of up to 51.67 %, power reductions of up to 76.78 %, and a 99.9 % improvement in voltage deviation. Emission rates decreased by 99.92 % in case 1, 95.19 % in case 2, and 97.38 % in case 3, compared to the base case. The proposed algorithm shows superior convergence and performance in solving both small- and large-scale optimization problems, outperforming recent multi-objective evolutionary algorithms.This study provides a robust framework for optimizing renewable energy integration and battery energy storage, offering a scalable solution to modern power system challenges.

Peer-to-peer multi-period energy market with flexible scheduling on a scalable and cost-effective blockchain

Peer-to-Peer (P2P) electricity trading is an emerging means for allowing communities to share local energy production and demand response through direct trading. It is projected to play an important role in the future energy market by increasing the incentive to own and operate distributed energy resources (DERs) and participate in demand response (DR). A common approach to implementing P2P trading is with blockchain, however, existing solutions feature limitations. Typically, concerns involve either scalability and high transaction costs or projects implementing a permissioned blockchain that does not provide the trust and decentralization desired. In addition, the majority of market designs are simplified and do not capture the distinct complexity of electricity markets. They do not consider the inter-temporal constraints of appliances and DERs that need to run for multiple periods. Complex market designs that address these issues have not been implemented in blockchain based systems due to the computational limitations of such systems. To improve these two aspects, this paper proposes a market formulation that supports products running multiple periods with flexible scheduling, modeled as a mixed integer linear programming problem that optimizes social welfare. The trading platform is then implemented as a side chain of Polkadot, a network of blockchains designed to be secure, scalable, and economically feasible to foster an ecosystem of application-specific sidechains. This design is demonstrated to improve social welfare and achieve scalability by benchmarking the number of transactions that can be included per second, based upon typical assumptions of the market size. The result is a decentralized and performant system that allows for complex market designs to be implemented in a blockchain environment. This approach simplifies the process for participants, allowing them to bid DER or DR devices, directly and easily, even when this requires constraints across periods.

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A new method for finding global solutions to Synge’s electromagnetic problem

Synge’s problem consists in determining the dynamics of two point electrical charges interacting through their electromagnetic fields, without taking into account the radiation terms due to the self-forces in each charge. We discuss how this problem is related to the question on to establish initial conditions for the electromagnetic fields that are compatible with the two point charges system in isolation, that is, the charges are free from the action of external forces. This problem stems from the existence of inter-temporal constraints for the charges trajectories, which implies that the relativistic Newton equations for the charges is not a system of ordinary differential equations (ODEs), but rather a system of functional differential equations (FDEs). We developed a new method to obtain global solutions that satisfies this system of FDEs and a given initial condition for the charges positions and velocities. This method allows the construction of a recursive numerical algorithm that only use integration methods for ODEs systems. Finally, we apply this algorithm to obtain numerical approximations for the quasi-circular solutions that are predicted in Synge’s problem.

Receding horizon dispatch of multi-period look-ahead market for energy storage integration

Although noteworthy efforts towards energy storage participation in electricity markets have been witnessed worldwide during the last decades, market mechanisms for optimal storage integration are yet to be comprehensively studied. This paper presents a novel approach wherein a multi-period look-ahead market is proposed to progressively solve the optimisation problem over a receding horizon, incorporating intertemporal constraints to enable forward planning. The focus is specifically on modelling the bidding behaviour of energy storage, and to address this, we develop two distinct models for the participation of energy storage in the market. The integrated model aims to schedule the future dispatch of the storage to minimise total operational cost, taking into account the fixed costs of the storage, while the strategic model pursues the dual ambition to maximise storage profit by formulating a bilevel optimisation problem. We validate the viability of our proposed market mechanisms through case studies on the Australian National Electricity Market. We conduct case studies which provide evidence that both the strategic and integrated bidding models effectively address the requirement for forward planning, resulting in reduced market costs and volatility. Notably, the strategic model outperforms in terms of generating higher storage revenue, while the integrated model exhibits a slight advantage in terms of lower market costs compared to the strategic model.

Coal-Biomass Co-firing within Renewable Portfolio Standards: Strategic Adoption by Heterogeneous Firms and Emissions Implications

As electricity from coal declines, co-firing coal plants with biomass has been proposed to extend coal unit life, increase production, and reduce carbon emissions. Previous studies reach conflicting conclusions on whether coal biomass co-firing would result in a net increase or decrease in carbon emissions. We explore whether biomass co-firing would decrease emissions using a novel framework that includes two critical features of electricity markets: strategic adoption decisions by firms and intertemporal constraints on power plant operations. We apply this framework to a case study based on the Midwestern U.S. electricity market and show that profit maximizing firms will retrofit mid-efficiency coal units, rather than the most or least efficient units. We demonstrate that, contrary to expectations, this strategy leads to a net increase in system-wide carbon emissions under high carbon prices because of the other generators displaced by co-firing units.

Discussion on Incentive Compatibility of Multi-Period Temporal Locational Marginal Pricing

In real-time electricity markets, locational marginal prices (LMPs) can be determined by solving multi-interval economic dispatch problems to manage inter-temporal constraints (i.e., ramp rates). Under the current practice, the LMPs for the immediate interval are binding, while the prices for the subsequent intervals are advisory signals. However, a generator may miss the opportunity for higher profits, and compensatory uplift payments are needed at the settlement. To address these issues, the “temporal locational marginal pricing (TLMP)” that augments LMP by incorporating multipliers associated with generators’ reported ramp rates was developed. It was demonstrated that it would result in zero uplift payments, showing great potential as a good pricing scheme. Numerical examples also showed that “the generators had incentives to reveal their ramp rates truthfully”. In this paper, the incentive compatibility of TLMP with respect to ramp-rate reporting is discussed. Our idea is to develop numerical examples to investigate whether reporting the true ramp rates is the best option for generators. The results indicate that TLMP is not incentive compatible, and there are market-clearing scenarios where not reporting true ramp rates may be beneficial.

Intraday markets, wind integration and uplift payments in a regional U.S. power system

U.S. electricity markets adopt a two-settlement structure with day-ahead and real-time markets. Wind power integration poses a challenge for this market structure because day-ahead wind production forecasts are uncertain and significant rescheduling costs may occur in real time, increasing the need for out-of-market uplift payments. We investigate whether a multi-settlement structure with four intraday stages taking place 18 to 3 h before electricity generation reduces uplift payments and system costs, relative to a two-settlement structure. We develop unit commitment and dispatch models that account for intertemporal constraints and solve them on a 36-node test system using historical wind forecasts provided by a Regional Transmission Organization, as well as synthetic wind forecasts reproducing the observed correlation in the historical data. Combining historical and simulated forecasts allows us to account for wind uncertainty and draw more robust conclusions about the relative merits of each market structure. Finally, we compare the performance of market designs under varying levels of wind penetration. Under any level of wind penetration, the proposed multi-settlement market design is more likely to yield higher uplift than the two-settlement market design. Wind forecast accuracy and structural differences between the U.S. and European electricity markets are key drivers of our results.

Pricing Under Uncertainty in Multi-Interval Real-Time Markets

A Novel Practical Stochastic Pricing Model for Multi-Interval Real-Time Markets Practical implementations of economic dispatch with associated pricing systems are crucial for operating electricity markets. Because of the high volatility caused by the increasing integration of renewable energy, consideration of the underlying stochastic problem is becoming more important than ever. It is a challenge to incorporate the uncertain nature of real-time operations into an already complex multi-interval dynamic problem with intertemporal constraints. Because solving a standard multi-stage stochastic programming problem is too burdensome in terms of calculation time for real-time markets, it has been standard practice in electricity markets to use a deterministic approximation with varying degrees of look-ahead. Cho and Papavasiliou, in their article “Pricing Under Uncertainty in Multi-Interval Real-Time Markets”, introduced a practical alternative method for pricing under uncertainty in multi-interval real-time markets. Using slightly different stochastic formulations, these authors propose an approach that preserves the attractive features from both the deterministic formulation (simpler calculation) and the standard stochastic formulation (better performance).

Priority Chronological Time-Period Clustering for Generation and Transmission Expansion Planning Problems With Long-Term Dynamics

The increasing incorporation of renewable generating units into power systems has made it imperative to model variabilities during the resolution of generation and transmission expansion planning problems. This is commonly carried out by considering representative time periods, which are attained using clustering techniques, since the use of all historical data may involve computationally intractable problems. The chronological information concerning the input data should be maintained when representative time periods are used to model inter-temporal constraints. This is the case of long-term storage, which may be critical as regards mitigating the fluctuations related to renewable production. Recent clustering techniques have resolved this drawback at the cost of not ensuring the feasibility of the problem or underestimating extreme values of input data, which may influence investment decisions. This paper proposes a new clustering method that is based on previous techniques, maintains the chronological information regarding the input data throughout the entire time horizon and assigns more priority to the representation of extreme values. Numerical results show that the use of the proposed clustering method involves a reduction in the computational burden, since investment plans closer to the optimal solution are attained while considering less representative time periods than occurs with other methods.

SoHAM: A Sound-Based Human Activity Monitoring Framework for Home Service Robots

Monitoring daily activities is essential for home service robots to take care of the older adults who live alone in their homes. In this article, we proposed a sound-based human activity monitoring (SoHAM) framework by recognizing sound events in a home environment. First, the method of context-aware sound event recognition (CoSER) is developed, which uses contextual information to disambiguate sound events. The locational context of sound events is estimated by fusing the data from the distributed passive infrared (PIR) sensors deployed in the home. A two-level dynamic Bayesian network (DBN) is used to model the intratemporal and intertemporal constraints between the context and the sound events. Second, dynamic sliding time window-based human action recognition (DTW-HaR) is developed to estimate active sound event segments with their labels and durations, then infer actions and their durations. Finally, a conditional random field (CRF) model is proposed to predict human activities based on the recognized action, location, and time. We conducted experiments in our robot-integrated smart home (RiSH) testbed to evaluate the proposed framework. The obtained results show the effectiveness and accuracy of CoSER, action recognition, and human activity monitoring. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the goal to develop companion robots that can assist older adults living alone. Among many capabilities, monitoring human daily activities is an essential one for such robots. Though computer vision or wearable sensors-based methods have been developed by other researchers, they are not practical due to the privacy concern and intrusiveness. Sound-based daily activity recognition can address these concerns and offer a viable solution. In this regard, our proposed method adopts microphones on the robot and a small set of motion sensors distributed in the home. The proposed theoretical framework was tested in a small-scale mock-up apartment with promising results. Before such companion robots can be deployed to real homes for elderly care, there is a need to improve the robustness of the algorithms. More thorough tests in various realistic home environments should be conducted to fully evaluate the performance of the robots. In addition, privacy concern related to audio capture should be further mitigated.

MEDICAL ASSIST FOR ISOLATED WARD PATIENTS IN HOSPITALS

Monitoring daily activities is essential for home service robots to take care of the older adults who live alone in their homes. In this article, we proposed a Medical Assist for isolated ward pateints in hospital framework by recognizing sound events in a home environment. First, the method of context-aware sound event recognition (CoSER) is developed, which uses contextual information to disambiguate sound events. The locational context of sound events is estimated by fusing the data from the distributed passive infrared (PIR) sensors deployed in the home. A two-level dynamic Bayesian network (DBN) is used to model the intratemporal and intertemporal constraints between the context and the sound events. Second, dynamic sliding time window-based human action recognition (DTW-HaR) is developed to estimate active sound event segments with their labels and durations, then infer actions and their durations. Finally, a conditional random field (CRF) model is proposed to predict human activities based on the recognized action, location, and time. We conducted experiments in our robot-integrated smart home (RiSH) testbed to evaluate the proposed framework. The obtained results show the effectiveness and accuracy of CoSER, action recognition, and human activitymonitoring. Key Words: Activity monitoring, context-awareness, elderly care, sound event.

Optimisation methods for dispatch and control of energy storage with renewable integration

Renewable energy integration is an effective measure to resolve environmental problems and implement sustainable development, yet the volatility of wind and solar generation has a profound impact on power system operation, calling for sufficient backup capacity. Energy storage can shift demand over time and mitigate real-time power mismatch and thus help integrate renewable energy resources into power grids. However, the unit capacity price of energy storage is still relatively high, and the capacity of energy storage is usually limited. Given the prominent uncertainty and finite capacity of energy storage, it is crucially important to take full advantage of energy storage units by strategic dispatch and control. From the mathematical point of view, energy storage dispatch and control give rise to a sequential decision-making process involving uncertain parameters and inter-temporal constraints. Multitudinous optimisation methods have been developed for such a problem while they differ in two aspects: the modelling of uncertainty and the mechanism to handle uncertainty. This review aims to draw a methodological picture of historical developments and state-of-the-art advances in this research field. These methods are subsumed into three major categories: multistage optimisation, online optimisation, and multi-timescale optimisation. In addition to introducing the advancements and applications, the authors also explain the motivations and theoretical foundations of these methodologies. The authors hope interested readers can attain a holistic outlook of these sophisticated approaches and choose the most appropriate one for their specific applications.

Multi-Period Optimal Reactive Power Dispatch Using a Mean-Variance Mapping Optimization Algorithm

Optimal reactive power dispatch plays a key role in the safe operation of electric power systems. It consists of the optimal management of the reactive power sources within the system, usually with the aim of reducing system power losses. This paper presents both a new model and a solution approach for the multi-period version of the optimal reactive power dispatch. The main feature of a multi-period approach lies on the incorporation of inter-temporal constraints that allow the number of switching operations in transformer taps and capacitor banks to be limited in order to preserve their lifetime and avoid maintenance cost overruns. The main contribution of the paper is the constraint handling approach which consists of a multiplication of sub-functions which act as penalization and allow simultaneous consideration of both the feasibility and optimality of a given candidate solution. The multi-period optimal reactive power dispatch is an inherently nonconvex and nonlinear problem; therefore, it was solved using the metaheuristic mean-variance mapping optimization algorithm. The IEEE 30-bus and IEEE 57-bus test systems were used to validate the model and solution approach. The results allow concluding that the proposed model guarantees an adequate reactive power management that meets the objective of minimizing power losses and keeping the transformer taps and capacitor bank movements within limits that allow guaranteeing their useful life.

Envisioning security control in renewable dominated power systems through stochastic multi-period AC security constrained optimal power flow

The accelerated penetration rate of renewable energy sources (RES) brings environmental benefits at the expense of increasing operation cost and undermining the satisfaction of N-1 security criterion in transmission systems. To address the latter issue, this paper envisions N-1 security control in RES dominated power systems through stochastic multi-period AC security constrained optimal power flow (SCOPF). The paper extends the state-of-the-art, i.e. deterministic and single time period AC SCOPF, to capture two new dimensions, RES stochasticity and multiple time periods, as well as emerging sources of flexibility such as flexible loads (FL) and energy storage systems (ESS). Accordingly, the paper proposes and solves for the first time a new problem formulation in the form of stochastic multi-period AC SCOPF (S-MP-SCOPF). The S-MP-SCOPF is formulated as a non-linear programming (NLP) problem. It computes optimal setpoints of flexibility resources and other conventional control means for congestion management and voltage control in day-ahead operation. As another salient feature, the proposed model is comprehensive and accurate, using: AC power flow model for both pre-contingency and post-contingency states, inter-temporal constraints for resources such as FL and ESS in a 24-hours time horizon and RES uncertainties. The importance and performance limitation of the proposed model through a direct approach, pushing the problem size up to the solver limit, are illustrated on two test systems of 5 nodes and 60 nodes, respectively. For the 60 node test system, the largest successful case can manage 30 scenarios and is solved in 22,110 s. Future work will develop a tractable solution algorithm.

A Fast Calculation Method for Long-term Security-constrained Unit Commitment of Large-scale Power Systems with Renewable Energy

With the increase in the penetration rate of renewable energy, the planning and operation of power systems will face huge challenges. To ensure the sufficient utilization of renewable energy, the reasonable arrangement for the long-term power generation plan has become more crucial. Security-constrained unit commitment (SCUC) is a critical technical means to optimize the long-term power generation plan. However, the plentiful power sources and the complex grid structure in large-scale power systems will bring great difficulties to long-term SCUC. In this paper, we propose a fast calculation method for long-term SCUC of large-scale power systems with renewable energy. First, a method for unit status reduction based on temporal decomposition is proposed, which will reduce plenty of binary variables and intertemporal constraints in SCUC. Then, an efficient redundant constraint identification (RCI) method is developed to reduce the number of network constraints. Furthermore, a joint accelerated calculation framework for status reduction and RCI is formed, which can reduce the complexity of long-term SCUC while ensuring a high-precision feasible solution. In case studies, numerical results based on two test systems ROTS2017 and NREL-118 are analyzed, which verify the effectiveness and scalability of the proposed calculation method.

Bidding problem of Combined Cooling, Heat, and Power systems to take advantage of their inherent flexibility in service restoration programs of distribution networks

This paper focuses on Combined Cooling, Heating, and Power (CCHP) systems, as the key flexible entities in the distribution networks (DNs) which can present their surplus capacities for dealing with outages through participating in Service Restoration Programs (SRPs). To this end, a three-stage hierarchical market framework is developed to conduct all interactions between CCHPs’ operators and Distribution System Operator (DSO) in normal operating, pre-, and post-outage conditions. The bidding problem of CCHPs for participating in SRPs is investigated in both pre- and post-outage stages. In order to use the full capability of CCHPs, the stored energy in their Energy Storage System (ESS) is incorporated in their bids. An efficient optimization model is proposed to overcome the complexity of the bidding problem related to ESSs’ inter-temporal constraints and to compensate all the imposed costs on CCHPs due to the rescheduling of ESSs. The numerical results confirm the effectiveness of the proposed bidding model in SRPs.

Coordinating Distributed Energy Resources and Utility-Scale Battery Energy Storage System for Power Flexibility Provision Under Uncertainty

Relying on the power flexibility of distributed energy resources (DERs) located in an active distribution network (ADN), this ADN will be able to provide power flexibility to the upper-layer grid at their point of common coupling (PCC). The power flexibility is defined as additional bi-directional active/reactive powers a resource can provide to the grid by adjusting its operating point. In this context, this paper presents a two-stage ADN management method to deliver, at the PCC, the power flexibility that the upper-layer grid operator would request minutes-ahead real-time operation. The first stage updates the power set-points of DERs considering their offer curves as well as the uncertainties stem from the short-term forecast errors of demand and renewable generation profiles. The inter-temporal constraints and losses of the grid are accounted for by exploiting a linearized dynamic optimal power flow model, whereby the first stage is implemented as a linear scenario-based optimization problem. Then, in real-time operation, relying on a linear optimization problem, the second stage adjusts the power flexibility injection of a utility-scale battery energy storage system (ESS) to mitigate the imbalance at the PCC inherent in the above-mentioned uncertainties. The performance of the proposed method is tested in the case of a real ADN located in the city of Aigle in southwest of Switzerland.

A two-stage decomposition method for integrated optimization of islanded AC grid operation scheduling and network reconfiguration

A restructuring of electricity systems promises energy resilience, prosperity, and sustainability for communities. In particular, Reconfigurable networks, such as distribution systems or microgrids, as smart electricity systems are more controllable and flexible compared to traditional systems. In this study, we integrate network reconfiguration decisions into a multi-period grid operation scheduling problem to minimize the operational costs while taking into account both technical and inter-temporal constraints for distributed energy resources, physical constraints on alternating current (AC) network, and system reliability constraints. We develop a comprehensive optimization model for the grid operation planning problem by taking into account the operation scheduling and economic dispatch decisions from earlier cycles and grid operational constraints while determining the optimal network topology. Due to the NP-hard nature of the problem, we introduce a two-stage decomposition algorithm where the solution of the operation scheduling problem (without switching variables) feeds the network reconfiguration problem embedding the dispatch problem for each time period. The performance of the proposed two-stage decomposition algorithm is demonstrated on three different available IEEE testbeds against CPLEX and COUENNE solvers for benchmarking purposes. The selected IEEE testbeds have been widely adopted by previous literature for the aforementioned grid operation planning problem due to their capability in reproducibility. The proposed decomposition algorithm outperforms CPLEX in terms of both solution quality and computational times, particularly our algorithm provides 0.5% and 3.17% better solutions in mid-size and large-size networks, respectively.