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This paper extends a new concept of energy-water-hydrogen (EWH) nexus, which was recently developed as a solution for reducing carbon emissions from the generation side of power systems, to the distribution side. Under the concept of distribution-level EWH (micro EWH) nexus, renewable energy sources (RES) are utilized to meet the energy needs of a small community. To avoid the uncertainty caused by RESs, this paper aims to investigate the real-time optimal operation of the micro EWH nexus which is however a challenging optimization problem. First, such a large-scale mixed-integer nonlinear programming problem is relaxed into a mixed-integer convex program (MICP) by leveraging the effective convex-hull relaxation technique. Second, a fast data-driven solution method based on active constraint and integer variable prediction is presented, which can solve the MICP problem very fast since it utilizes historical optimization data to quickly predict binary variable values and a limited set of active constraints., Comment: arXiv admin note: text overlap with arXiv:2306.17395

This paper aims to evaluate the economic viability of the energy-water-hydrogen (EWH) nexus as a new solution for reducing carbon emissions from power systems. The urgency around climate change emphasizes the pressing need to mitigate carbon emissions, especially from the electricity sector, which accounts for a significant portion of total emissions in the US. In response, incorporating more renewable energy sources (RESs) and green hydrogen, created through water electrolysis and RES, stands out as a crucial strategy to combat climate challenges. We delve into various aspects of the EWH nexus, including carbon emissions from different power plants, capturing these emissions, and potential options for their reuse or storage. This paper involves modeling different sections of the EWH nexus and conducting an economic analysis across scenarios in power plants to determine optimal water supply methods, suitable chemical products for carbon reuse, and an appropriate carbon emission penalty to encourage emission reduction through the EWH nexus. The results indicate that reusing captured carbon emissions emerges as the most beneficial option across all power plant types. This finding underscores the potential of carbon reuse as a pivotal strategy within the EWH nexus framework for addressing carbon emissions., Comment: 5 pages, 3 figures, 2 tables, conference

This paper focuses on developing a real-time optimal operation model for a new engineering system, wind-to-hydrogen-driven low-carbon critical infrastructure (W2H-LCCI), that utilizes wind power to generate hydrogen through electrolysis and combines it with carbon capture to reduce carbon emissions from the power sector. First, a convex mathematical model for W2H-LCCI is proposed, and then optimization models for its real-time decision-making are developed, which are mixed-integer convex programs (MICPs). Furthermore, since this large-scale MICP problem must be solved in real-time, a fast solution method based on active constraint and integer variable prediction (ACIVP) is presented. ACIVP method predicts the binary variable values and the set of limited-number constraints, which most likely contain all of the active constraints, based on historical optimization data. It results in only a small-scale continuous convex optimization problem needing to be solved by optimization solvers for W2H-LCCI real-time optimal operation. To increase the accuracy of the ACIVP method, feature space expansion (FSE) is employed, and a multi-stage ACIVP-FSE method is proposed. The effects of stage design and stage ordering on ACIVP-FSE performance are also discussed. We validate the effectiveness of the developed system and solution method using two water-energy nexus case studies.

The electric power distribution network (PDN) and the transportation network (TN) are generally operated/coordinated by different entities. However, they are coupled with each other due to electric vehicle charging stations (EVCSs). This paper proposes to coordinate the operation of the two systems via a fully decentralized framework where the PDN and TN operators solve their own operation problems by sharing only limited information. Nevertheless, the operation problems generally are in mixed-integer programming (MIP) form. To the best of our knowledge, the most existing decentralized/distributed optimization algorithms, such as the alternating direction method of multipliers (ADMM), are not always guaranteed to converge for such MIP problems. Therefore, a novel fully decentralized optimization algorithm is proposed, whose contributions include: 1) it is applicable to MIP problems with convergence and optimality guaranteed for mild assumptions, 2) it only requires limited information exchange between PDN and TN operators, which will help preserve the privacy of the two systems and reduce the investment in building communication channels, and 3) it is fully decentralized so that all the computations are carried out by PDN operator and TN coordinator only. Simulations on the test cases show the efficiency and efficacy of the proposed framework and algorithm.

Water and power systems are increasingly interdependent due to the growing number of electricity-driven water facilities. The security of one system can be affected by a contingency in the other system. This paper investigates a security-constrained operation problem of the energy-water nexus (EWN), which is a computationally challenging optimization problem due to the nonlinearity, nonconvexity, and size. We propose a two-step iterative contingency filtering method based on the feasibility and rating of the contingencies to decrease the size of the problem. The optimal power and water flow are obtained in a normal situation by considering the set of contingencies that can not be controlled with corrective actions. The feasibility check of the contingencies is performed in the second step, followed by a rating of the uncontrollable contingencies. Finally, the critical contingencies are obtained and added to the first step for the next iteration. We also employ convex technologies to reduce the computation burden. The proposed method is validated via two case studies. Results indicate that this approach can efficiently attain optimal values.

The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is formulated using the chance-constrained optimization (CCO) modeling paradigm, where the constraints include the nonlinear energy storage and AC power flow models. Based on the emerging scenario optimization method which does not rely on pre-known probability distribution functions, this paper develops a novel solution method for this challenging CCO problem. The proposed meth-od is computationally effective for mainly two reasons. First, the original AC power flow constraints are approximated by a set of learning-assisted quadratic convex inequalities based on a generalized least absolute shrinkage and selection operator. Second, considering the physical patterns of data and motived by learning-based sampling, the strategic sampling method is developed to significantly reduce the required number of scenarios through different sampling strategies. The simulation results on IEEE standard systems indicate that 1) the proposed strategic sampling significantly improves the computational efficiency of the scenario-based approach for solving the chance-constrained optimal PSO problem, 2) the data-driven convex approximation of power flow can be promising alternatives of nonlinear and nonconvex AC power flow.

The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization problems of power flow under uncertainty. This paper develops a novel solution approach for chance-constrained AC optimal power flow (CCACOPF) problem based on the data-driven convexification of power flow and a fast algorithm for scenario technique (FAST). This method is computationally effective for mainly two reasons. First, the original nonconvex AC power flow (ACPF) constraints are approximated by a set of learning-based quadratic convex ones. Second, FAST is an advanced scenario-based solution method (SSM) that doesn't rely on the pre-assumed probability distribution, using far less scenarios than the conventional SSM. Eventually, the CCACOPF is converted into a computationally tractable convex optimization problem. The simulation results on IEEE test cases indicate that 1) the proposed solution method can outperform the conventional SSM in computational efficiency, 2) the data-driven convexification of power flow is effective in approximating original complex AC power flow.

This paper presents a novel solution paradigm of general optimization under both exogenous and endogenous uncertainties. This solution paradigm consists of a probability distribution (PD)-free method of obtaining deterministic equivalents and an innovative approach of scenario reduction. First, dislike the existing methods that use scenarios sampled from pre-known PD functions, the PD-free method uses historical measurements of uncertain variables as input to convert the logical models into a type of deterministic equivalents called General Scenario Program (GSP). Our contributions to the PD-free deterministic equivalent construction reside in generalization (making it applicable to general optimization under uncertainty rather than just chance-constrained optimization) and extension (enabling it to the problems under endogenous uncertainty via developing an iterative and a non-iterative frameworks). Second, this paper reveals some unknown properties of the PD-free deterministic equivalent construction, such as the characteristics of active scenarios and repeated scenarios. Base on this discoveries, we propose a concept and methods of strategic scenario selection which can effectively reduce the required number of scenarios as demonstrated in both mathematical analysis and numerical experiments. Numerical experiments are conducted on two typical smart grid optimization problems under exogenous and endogenous uncertainties., Comment: Subtitle: Applications in Smart Grid Optimization under Both Exogenous and Endogenous Uncertainty

This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.

This paper presents a practical approach to utilizing emergency response resources (ERRs) and post-disaster available distributed energy resources (PDA-DERs) to improve the resilience of power distribution systems against natural disasters. The proposed approach consists of two sequential steps: first, the minimum amount of ERRs is determined in a pre-disaster planning model; second, a post-disaster restoration model is proposed to co-optimize the dispatch of pre-planned ERRs and PDA-DERs to minimize the impact of disasters on customers, i.e., unserved energy for the entire restoration window. Compared with existing restoration strategies using ERRs, the proposed approach is more tractable since 1) in the pre-disaster stage, the needed EERs are determined based on the prediction of energy shortage and disaster-induced damages using machine learning-based algorithms (i.e., cost-sensitive-RFQRF for prediction of outage customers, random forest for prediction of outage duration, and CART for prediction of disaster-induced damages); 2) in the post-disaster stage, the super-node approximation (SNA) and the convex hull relaxation (CHR) of distribution networks are introduced to achieve the best trade-off between computational burden and accuracy. Tests of the proposed approach on IEEE test feeders demonstrated that a combination of SNA and CHR remarkably reduces the solution time of the post-disaster restoration model., Comment: 8 pages, 7 figures!

This paper presents a novel optimization framework of formulating the three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework that is less complex than the existing optimization frameworks involving uncertainty, and 2) convex such that it admits polynomial-time algorithms and mature distributed optimization methods. To construct this UaO framework, a methodology of learning-aided uncertainty-aware modeling, with prediction errors of stochastic variables as the measurement of uncertainty, and a theory of data-driven convexification are proposed. Theoretically, the UaO framework is applicable for modeling general optimization problems under uncertainty., Comment: Accepted for pubication in the IEEE Transactions on Power Systems

This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as a basic learner to capture the linear relationships between the bus voltage as the independent variable and the active or reactive power as the dependent variable in rectangular coordinates. Then, gradient boosting (GB) and bagging as ensemble learning methods are introduced to combine all basic learners to boost the model performance. The fitted linear power flow model is also relaxed to compute the optimal power flow (OPF). The simulating results of standard IEEE cases indicate that (1) ensemble learning methods outperform PR and GB works better than bagging; (2) as for solving OPF, the data-driven model excels the DC model and the SDP relaxation in the computational accuracy, and works faster than ACOPF and SDPOPF., Comment: 5 pages, 9 figures, 3 tables

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for AC power flow equations that differs from the existing convex relaxations. The proposed approach is based on quadratic power flow equations in rectangular coordinates and it can be used in both balanced and unbalanced three-phase power networks. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flows, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional SDP relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails., Comment: 8 pages, 8 figures, 4 tables