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Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time. [ABSTRACT FROM AUTHOR]

The ever-increasing integration of variable wind energy requests for a power system with high flexibility. In this paper, we formulate the real-time economic dispatch problem as a multi-stage robust program to leverage flexible resources, especially energy storage systems, in a broader timescale, and also to avoid the risk of high costs in critical scenarios. The multi-stage robust program is decomposed to the dynamic programming form and the fast robust dual dynamic programming (FRDDP) algorithm is developed to solve it efficiently. To tackle the nonconvexities caused by the inter-temporal constraints of ESSs, an estimation-correction method is developed, and measures of the approximation accuracy are presented. Comprehensive case studies comprising units up to 1371 are carried out to verify the effectiveness of the proposed model. Numerical results show that compared with the existing ones, the proposed multi-stage robust model achieves lower cost under the worst-case scenario and shows better scalability in large-scale systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal power flow (OPF) problem. We have recently shown that a convex relaxation based on semidefinite programming (SDP) is able to find a global solution of OPF for IEEE benchmark systems, and moreover this technique is guaranteed to work over acyclic (distribution) networks. The present work studies the potential of the SDP relaxation for OPF over mesh (transmission) networks. First, we consider a simple class of cyclic systems, namely weakly-cyclic networks with cycles of size 3. We show that the success of the SDP relaxation depends on how the line capacities are modeled mathematically. More precisely, the SDP relaxation is proven to succeed if the capacity of each line is modeled in terms of bus voltage difference, as opposed to line active power, apparent power or angle difference. This result elucidates the role of the problem formulation. Our second contribution is to relate the rank of the minimum-rank solution of the SDP relaxation to the network topology. The goal is to understand how the computational complexity of OPF is related to the underlying topology of the power network. To this end, an upper bound is derived on the rank of the SDP solution, which is expected to be small in practice. A penalization method is then applied to the SDP relaxation to enforce the rank of its solution to become 1, leading to a near-optimal solution for OPF with a guaranteed optimality degree. The remarkable performance of this technique is demonstrated on IEEE systems with more than 7000 different cost functions. [ABSTRACT FROM PUBLISHER]

In order to provide the ancillary service for smart grid, this paper proposes a modelling and control protocol design approach for the aggregation of heterogeneous thermostatically controlled loads (TCLs). A 2-D state bin is proposed to model the second-order TCL dynamics in a population model. Detailed procedure of calculating the transition probability in the system matrix is provided. In the controller design, a model predictive control (MPC) scheme is proposed to obtain the optimal control actions along the prediction horizon. In addition, implementation of the control signal for adjusting TCLs' statuses are also investigated with practical situations considered. Simulation results reveal the feasibility and efficacy of the proposed modelling and control approach when applied on a large population of TCLs. Some factors that may affect the service performance are also discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional-order sliding mode controller (FOSMC) for fixed-time stability of multimachine power systems. Fractional calculus has been applied in sliding mode control (SMC) to design FOSMC which can better suppress the chattering phenomenon than the traditional integer-order SMC. Hence, a FOSMC is proposed to regulate the excitation of synchronous generators to improve the transient stability of the power system. In addition, the FOSMC can maintain the multimachine power systems stabilization in an upper bound and measurable convergence time independent of the initial operating conditions of the power system. The Lyapunov function is implemented to demonstrate the stability of multimachine power systems under the FOSMC, and the upper bound convergence time of the power system is generally estimated. The New England 10-machine 39-bus power system is taken into simulation to test the effectiveness and superior performances of the FOSMC than the existing control methods under different operating conditions. Meanwhile, the FOSMC with different orders are presented to verify that the FOSMC can better restrain the chattering phenomenon than traditional integer-order SMC. Simulation results show that the FOSMC can effectively reduce the chattering phenomenon and ensure the power system stabilization in an upper bound time, thus enhancing the dynamic performances of the power system. [ABSTRACT FROM AUTHOR]

This paper presents a method for the optimal siting, and sizing of energy storage systems (ESSs) in active distribution networks (ADNs) to achieve their dispatchability. The problem formulation accounts for the uncertainty inherent to the stochastic nature of distributed energy sources, and loads. Thanks to the operation of ESSs, the main optimization objective is to minimize the dispatch error, which accounts for the mismatch between the realization, and prediction of the power profile at the ADN connecting point to the upper layer grid, while respecting the grid voltages, and ampacity constraints. The proposed formulation relies on the so-called Augmented Relaxed Optimal Power Flow (AR-OPF) method: it expresses a convex full AC optimal power flow, which is proven to provide a global optimal, and exact solution in the case of radial power grids. The AR-OPF is coupled with the proposed dispatching control resulting in a two-level optimization problem. In the first block, the site, and size of the ESSs are decided along with the level of dispatchability that the ADN can achieve. Then, in the second block, the adequacy of the ESS allocations, and the feasibility of the grid operating points are verified over operating scenarios using the Benders decomposition technique. Consequently, the optimal size, and site of the ESSs are adjusted. To validate the proposed method, simulations are conducted on a real Swiss ADN hosting a large amount of stochastic Photovoltaic (PV) generation. [ABSTRACT FROM AUTHOR]

This paper proposes a bi-level branch-and-bound ((B&B) method to solve the economic dispatch problem with prohibited zones and network losses. The approach employs binary variables for each prohibited zone and utilizes the B-coefficient for network losses, which can be transformed into a mixed-integer quadratically constrained quadratic programming (MIQCQP), where linear relaxation technique is applied on each bilinear term. Due to the complexity in solving the MIQCQP problem, this paper proposes a bi-level B&B method to achieve global optimum. A spatial B&B method is utilized in the higher level to solve the quadratically constrained quadratic programming (QCQP) problem, whereas a simple B&B method is employed in the lower level to solve a mixed-integer quadratic programming (MIQP) problem. The bi-level B&B algorithm that combines spatial and simple B&B methods is actually a deterministic optimization method and can produce global optimal solutions. Numerical results on 6-unit, 15-unit, and 40-unit test systems show that the bi-level B&B method can solve the MIQCQP problem with superior solution quality and convergence characteristics. [ABSTRACT FROM PUBLISHER]

The long-term operation planning problem is generally solved by a chain of computational models based on Stochastic Dual Dynamic Programming (SDDP) considering a period of 5–10 years ahead. A recent issue that has arisen concerning this problem is to define a convergence criterion when using conditional value-at-risk (CVaR) with SDDP due to the lack of good upper bound estimators. The main contribution of this paper is to propose a convergence criterion in which including CVaR does not hinder convergence analysis. Also, the proposed method does not increase the computational burden. Moreover, this paper provides a method that allows forward paths to be individually assessed, which can then either be discarded to reduce computational time or even replaced in an alternative resampling scheme in the SDDP. Based on aggregate reservoir representation, the proposed method of convergence was applied on long-term operation planning problems related to the Brazilian Power System. Results showed improvements in both the SDDP technique and the effectiveness of the proposed convergence criterion when CVaR was used. [ABSTRACT FROM AUTHOR]

The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach. [ABSTRACT FROM AUTHOR]

Power flow routing is an emerging control paradigm for the dynamic control of electric power flows. In this paper, we propose a generic model of a power flow router (PFR) and incorporate it into the optimal power flow (OPF) problem. First, a generic PFR architecture is proposed to encapsulate the desired functions of PFRs. Then, the load flow model of PFRs is developed and incorporated into the OPF framework. To pursue global optimality of the non-convex PFR-incorporated OPF (PFR-OPF) problem, we develop a semidefinite programming (SDP) relaxation of PFR-OPF. By introducing the regularization terms that favor a low-rank solution and tuning the penalty coefficients, a rank-1 solution can be obtained and used for recovering an optimal or near-optimal solution of the PFR-OPF and the results are verified in numerical tests. The efficacy of the PFR-OPF framework allows us to investigate the impact of PFR integration. With the system loadability as an example, the numerical results show that remarkable enhancement can be achieved by installing PFRs at certain critical buses of the network. [ABSTRACT FROM AUTHOR]

Direct-current microgrids (DC-MGs) can operate in either grid-connected or stand-alone mode. In particular, stand-alone DC-MG has many distinct applications. However, the optimal power flow problem (OPF) of a stand-alone DC-MG is inherently non-convex. In this paper, the OPF of DC-MG is investigated considering convex relaxation based on second-order cone programming. Mild assumptions are proposed to guarantee the exactness of relaxation, which only require uniform nodal voltage upper bounds and positive network loss. It is revealed that the exactness of second-order conic (SOC) relaxation of DC networks does not rely on topology or operating mode of DC networks, and an optimal solution must be unique if it exists. If line constraints are considered, the exactness of SOC relaxation may not hold. In this regard, two heuristic methods are proposed to give approximate solutions. Numerical experiments confirm the theoretic results. [ABSTRACT FROM AUTHOR]

This paper presents a novel model of voltage source converter (VSC) based energy routers (ERs) in microgrids. The proposed model explicitly describes the circuit laws within the ERs and captures the coupling of control variables among the AC/DC, DC/DC, DC/AC links. Therefore, the proposed model possesses unparalleled control capabilities in the operational parameters of both the AC and DC sides of ERs. By incorporating such a model into the AC-DC optimal power flow formulation, we not only optimize the power flows between the AC and DC sides of ERs, but also strategically schedule the flexible resources. To solve the ERs based AC-DC optimal power flow (ER-OPF) in a distributed fashion, we propose a hierarchical distributed optimization method that decouples the power grids into a master region and several sub-regions. In the master region, we propose a sequence of strong relaxations to transform the problem into a semidefinite program (SDP). We further show that this SDP relaxation is exact. For the sub-regions, we utilize sequential quadratic programming (SQP) to solve multiple small-scale subproblems with non-convex constraints in parallel. Case studies on the IEEE benchmark system show that fuel costs and power losses are reduced dramatically by utilizing ERs in microgrids. In addition, the proposed distributed algorithm can converge faster than alternating direction method of multipliers (ADMM). [ABSTRACT FROM AUTHOR]

Adequate reserves are urgently needed to hedge against wind power forecasting uncertainties in power systems. Traditional reserve quantification sequentially acquires statistical features of wind power and then determines reserve amounts. This paper establishes a novel integrated probabilistic forecasting and decision (IPFD) methodology to simultaneously optimize the wind power prediction intervals (PIs) and probabilistic reserve quantification. Upward and downward reserve quantities are defined to cover the wind power forecasting uncertainties within the PIs. A cost function evaluating the reserve provision payment and deficit penalty is elaborated to realize cost-benefit trade-offs of reserve decision. Nonparametric wind power PIs are constructed based on extreme learning machine, which minimizes the reserve cost function subject to eligible target coverage probability constraint. The confidence level and quantile proportions associated with wind power PIs can be jointly tuned to reduce the operational cost of reserves. Benefited from extreme learning machine, the IPFD model is reformulated as a mixed integer linear programming problem. A feasible region tightening strategy that shrinks the large constant coefficients and eliminates the redundant binary variables is proposed to accelerate model training. Numerical experiments based on actual wind power data demonstrate the remarkable cost-effective advantages of the IPFD based reserve quantification, as well as the high computational efficiency for online application. [ABSTRACT FROM AUTHOR]

The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or can be estimated accurately from empirical data, and/or use separate chance constraints for upper and lower line/bus limits. In this paper, we propose a data driven distributionally robust chance constrained optimal power flow model (DRCC-OPF), which ensures that the worst-case probability of violating both the upper and lower limit of a line/bus capacity under a wide family of distributions is small. Assuming that we can estimate the first and second moments of the underlying distributions based on empirical data, we propose an exact reformulation of DRCC-OPF as a tractable convex program. The key theoretical result behind this reformulation is a second-order cone programming (SOCP) reformulation of a general two-sided distributionally robust chance constrained set by lifting the set to a higher dimensional space. Our numerical study shows that the proposed SOCP formulation can be solved efficiently and that the results of our model are quite robust. [ABSTRACT FROM PUBLISHER]

Active research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of solutions. Although several upper bounds exist, recent studies have hinted that much sharper upper bounds that depend on the topology of underlying power networks may exist. This paper provides a significant refinement of these observations. We also develop a geometric construction called adjacency polytope that accurately captures the topology of a power network and is immensely useful in the computation of the solution bound. Finally, we highlight the significant implications of the development of such solution bounds in numerically solving load flow equations. [ABSTRACT FROM PUBLISHER]

Increasing wind power (WP) integration is forcing conventional units to go through more frequent and significant cycling operations, which would accelerate wear and tear to unit components and eventually affect the unit's lifespan. In this context, this paper proposes a hierarchical scheme to control the power of plug-in electric vehicles (PEVs) to mitigate unit ramp cycling (URC) operations. A general-form representation of the URC operation is proposed for the first time. At the top level of the hierarchical scheme, a system net load variation range (NLVR) is constructed first to capture the uncertainty in WP forecasts, and then the PEV power is scheduled to reshape the NLVR so as to minimize the URC operations that can be caused by the possible net load realizations in the NLVR. Based on updated WP forecasts, the middle-level dispatch model exempts overscheduled anti-URC regulation onus on PEVs to promote PEV charging. At the bottom level, a decentralized PEV charging control strategy is used to implement the PEV power dispatch instruction. Simulation results verify that the proposed scheme can avert the URC operations effectively, while preserve most of the desired PEV charging energy. Simulation results also show that the proposed scheme is more capable of withstanding WP forecast errors compared with its deterministic version and a benchmark scheme. [ABSTRACT FROM PUBLISHER]

This paper presents a unit commitment algorithm that defines each unit discharge given the water head, the total plant downstream flow, the variable discharge upper limit, the unit efficiency curves, and the restricted operating zones in order to maximize power efficiency. This algorithm is part of the preprocessing phase that is intended to approximate a hydro-power production function that represents individualized unit decisions. A compact mixed-integer linear programming formulation, with fewer integer variables, based on an equivalent unit model and a piecewise linear generation function, is proposed. The unit commitment is integrated without increasing the model size and complexity due to the preprocessing phase. Moreover, the optimal aggregate decision is automatically converted to unit decisions by the proposed algorithm. The coordination with mid/long-term planning is performed by taking into account the power demand allocated to the hydro-power plants. Numerical tests on Brazilian hydro-power plants demonstrate that the proposed formulation has lower computational cost than unit individualized models considering a given accuracy level for the generation function approximation. [ABSTRACT FROM PUBLISHER]

With increasing renewable penetration in power systems, considerable research efforts have been focused on how to accommodate the uncertainties from renewables in the Security-Constraint Unit Commitment (SCUC) problem. One of the candidate approaches to handling uncertainties is the two-stage Robust SCUC (RSCUC), which enables system to survive in any scenario. The survivability is guaranteed by the solution optimality of the max-min problem in the second stage. However, as the non-convex max-min problem is NP-hard, it is difficult to get the exact optimal solution in acceptable time. In this paper, we propose a new efficient formulation which recasts the max-min problem to a Mixed Integer Programming (MIP) problem using Binary Expansion (BE). The upper bound of the gap between the new MIP problem and the original max-min problem is derived. The gap, which quantifies the solution optimality of the max-min problem, is controllable. Two effective acceleration techniques are proposed to improve the performance of the MIP problem by eliminating inactive flow constraints and decomposing time-coupled uncertainty budget constraints. Accordingly, the computation burden of solving the max-min problem is reduced tremendously. The simulation results for the IEEE 118-Bus system validate and demonstrate the effectiveness of the new BE-based solution approach to the two-stage RSCUC and the acceleration techniques. [ABSTRACT FROM AUTHOR]

Variability in power generation at multiple consumer-owned renewable energy sources can cause random voltage fluctuations, which may result in voltage violations at multiple nodes in a power distribution system. Traditional methods of voltage control are ineffective to address fast voltage variations. New dynamic methods of voltage control using end-user devices can significantly benefit from the knowledge of the dominant influencer of voltage fluctuation (DIVF). This paper introduces information theoretic metrics to identify DIVF for every node in the power distribution system. A node can be DIVF due to its location in the distribution system and its capacity to generate and change its power. Use of traditional power flow algorithms to identify the DIVF is computationally complex, which limits their use in real-time applications. In this paper, information theoretic indicators of the DIVF are computed analytically in a computationally efficient manner, and their effectiveness to identify the DIVF is tested using the IEEE 69 node test system. From simulations, it is shown that differential entropy, Kullback–Leibler distance, and Frechet distance are effective indicators of the DIVF and can successfully identify the most influential nodes providing the foundation for intelligent voltage control. [ABSTRACT FROM AUTHOR]

This paper investigates load frequency control (LFC) of power systems with probabilistic interval delays. The LFC design specifically takes the probability distribution characteristic of the communication delays into account. Firstly, by considering the probability distribution characteristic of the communication delays in the modeling, the original power systems with a PI-based LFC are transformed into a stochastic closed-loop time-delay system. Secondly, by using the Lyapunov-Krasovskii functional method, sufficient delay-distribution-dependent stability and stabilization criteria are derived for the power systems with a PI-based LFC. Following this, an algorithm is provided to obtain the gain of PI-based LFC and the allowable upper bound of the communication delay simultaneously while preserving the desired H\infty performance. Finally, a case study is applied to illustrate the effectiveness of the proposed delay-distribution-dependent PI-based LFC design method. [ABSTRACT FROM PUBLISHER]

Transitioning from fossil fuel dominated power systems to high penetrations of intermittent renewable generation is affecting classical electricity market designs. Here, a method is proposed to model and assess the absence of co-optimization of energy and reserve that prevails in the European system. Co-optimization is formulated through an optimization problem (COM), and its absence as an equilibrium problem (EQM) built on Karush-Kuhn-Tucker conditions of agents’ optimization and market clearing equations. EQM cannot be reformulated as a single optimization problem. Market distortions are identified by comparing the complementarity conditions of both models. These are then discussed on system with Feed in Premium to wind generation. Parameters in the models allow to represent different market configurations regarding: available wind generation, Feed in Premium to wind, generators’ risk aversion, and required reserve from wind generation. [ABSTRACT FROM AUTHOR]

Incentives to encourage the uptake of renewable energy generation have fostered wind energy in many power systems. These incentives usually take the form of market instruments (e.g., feed-in tariff or premium) that are not directly amenable to optimization representations of the market. In this paper, we propose an equilibrium model of the short-term market to address the impact of wind operation under different structural assumptions. The model is formulated for several price taking, risk averse firms in competition. It accounts for wind generation uncertainty and embeds a representation of the day ahead and balancing mechanisms. The consumer is modeled by a linear inverse demand function. We focus on feed-in premium as the incentive to wind as this is the instrument most favored today in European discussions. The model is formulated as a stochastic equilibrium problem where the Karush-Kuhn-Tucker (KKT) conditions from the optimization problem of each firm are simultaneously solved together with market clearing conditions on energy, capacity for reserve and energy for reserve. The problem for each firm consists of a two-stage stochastic optimization problem with a recourse function based on the conditional value at risk (CVaR\theta ) as a risk measure. Due to price taking assumptions the model is a single stage complementarity problem; it is implemented and solved using the software GAMS. An example based on a stylized simplification of the Spanish power market and motivated by the impact of wind penetration on the revenue of conventional plants is used to illustrate the proposed approach. [ABSTRACT FROM PUBLISHER]

Unsatisfiable transmission constraints (UTCs) may lead to failures in look-ahead dispatch. Hence, the detection of UTCs is a critical issue in power systems, and it may also aid in the discovery of unavailable transmission resources in online look-ahead dispatch. The Lagrangian relaxation (LR) algorithm is a rapid and efficient approach to solving look-ahead dispatch (LD) problems; however, it does not readily handle infeasible problems. Here, we describe criteria and procedures for detecting infeasible LD and for locating and addressing UTCs via an LR framework. The proposed procedures for detecting infeasibility and locating unsatisfiability are incorporated into a conventional LR framework to develop an enhanced LR solution framework without affecting the original computational efficiency. Numerical simulations are carried out using an IEEE 24-bus system, 31-bus system, and several large-scale power systems; the results demonstrate the accuracy, efficiency, and reliability of the methods. [ABSTRACT FROM PUBLISHER]

In this letter, we present an internally induced acceleration method for the branch-and-cut (B&C) process of unit commitment (UC) problem on the basis of general mixed-integer programming (MIP) solvers. The B&C process is internally guided by solving a small-scale induced MIP model formulated by combining the congestion management information with global upper and lower bounds. Based on the test cases of RTS-GMLC and practical utility data, the UC calculation can be accelerated by 2.29 and 2.06 times on average, respectively, with no influence on the solution optimality. [ABSTRACT FROM AUTHOR]

Participants in electricity markets are becoming more proactive owing to the fast deployment of distributed energy resources (DERs) and the further development of demand-side management (DSM), which also boosts the emergence of Peer-to-Peer (P2P) market mechanisms. Moreover, the market is also required to operate in a real-time scheme in response to changes in generation and load to maintain power balance. It is highly desirable to propose and analyse novel approaches suitable for real-time P2P market mechanisms. These are challenging since most often involving a heavy computational burden, while the time available for negotiation in real-time is very short. Our core contribution is to design and analyse a novel asynchronous online optimization framework and related real-time P2P market negotiation mechanism, which can greatly reduce the computation and communication burden from two aspects. First, a novel online consensus alternating direction method of multipliers (ADMM) algorithm is proposed. It significantly reduces computation since only one iteration is performed for each agent at every time period. Second, the market operates in an asynchronous mode so that all agents can freely trade without waiting for idle or inactive neighboring agents. The sublinear regret upper bound is proved for our asynchronous online algorithm, which indicates that social welfare in the market can be maximized in the long run on average (over time). Simulations show that our algorithm enjoys good convergence performance, robustness, and fairness. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power system analysis. To control the maximum influence of linearization error on decision making, it is important to evaluate the worst-case linearization error (i.e., the error bound). This letter theoretically derives the error bound of linear power flow models based on the truncation error analysis of Taylor series expansion. A cold-start approach is proposed to restrain the error bound. Case studies show that 1) the proposed error bound is tight and effective and 2) the maximum linearization error can be successfully reduced using the proposed method. [ABSTRACT FROM AUTHOR]

A unified distributed reinforcement learning (RL) solution is offered for both static and dynamic economic dispatch problems (EDPs). Each agent is assigned with a fixed, discrete, virtual action set, and a projection method generates the feasible, actual actions to satisfy the constraints. A distributed algorithm, based on singularly perturbed system, solves the projection problem. A distributed form of Hysteretic Q-learning achieves coordination among agents. Therein, the Q-values are developed based on the virtual actions, while the rewards are produced by the projected actual actions. The proposed algorithm deals with continuous action space and power loads without using function approximations. Theoretical analysis and comparative simulation studies verify algorithm's convergence and optimality. [ABSTRACT FROM AUTHOR]

In chance-constrained OPF models, joint chance constraints (JCCs) offer a stronger guarantee on security compared to single chance constraints (SCCs). Using Boole's inequality or its improved versions to decompose JCCs into SCCs is popular, yet the conservativeness introduced is still significant. In this letter, a non-parametric iterative framework is proposed to achieve the decomposition of JCCs with negligible conservativeness. An adaptive risk allocation strategy is also proposed and embedded in the framework. Results on IEEE test cases show that the conservativeness using the framework is nearly eliminated, thereby reducing the generation cost considerably. [ABSTRACT FROM AUTHOR]

In this letter, we provide a convex-concave procedure based model to approximate the unbalance operation constraints of three-phase fossil-fuel distributed generation. This model transfers the non-convex unbalanced operation constraints into an iterative convex optimization procedure. The simplicity and convexity make it easy to integrate into a broad range of convex distribution optimal power flow formulations. [ABSTRACT FROM AUTHOR]

We demonstrate that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. Ultimately, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone. [ABSTRACT FROM AUTHOR]

In this letter, we describe and develop edge-based and node-based formulations for combined-cycle units (CCUs) with different levels of accuracy in respect of the physical constraints of each turbine, from no requirement to partially and fully respecting all physical constraints, including min-up/-down time, capacity, and ramping constraints. We develop corresponding models for independent system operators (ISOs) and vertically integrated utilities (VIUs), respectively. These models demonstrate complexity in terms of the size of decision variables and show the tradeoff between accuracy and computational complexity. To the best of our knowledge, this letter provides one of the first models that can capture both configuration transition restrictions and all the physical constraints of each turbine within CCUs, for both ISOs and VIUs. [ABSTRACT FROM AUTHOR]

Presents a closure to the Discussion on the paper, "Interval Power Flow Analysis Using Linear Relaxation and Optimality-Based Bounds Tightening (OBBT) Methods." [ABSTRACT FROM PUBLISHER]