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Development of smart grid technologies has created a promising atmosphere for smart cities and energy trading markets. Especially, traditional electricity consumers evolve into prosumers who produce as well as consume electricity in modern power electric systems. In this evolution, the electric power industry has tried to introduce the notion of local energy markets for prosumers. In the local energy market, prosumers purchase electricity from distributed energy generators or the other prosumers with surplus electricity via a local power exchange center. For this purpose, this paper proposes joint geometric clustering and truthful auction schemes in the local energy markets. The proposed clustering scheme is designed for distribution fairness of the distributed energy generator for serving prosumers, where the scheme is inspired by expectation and maximization based unsupervised learning. Moreover, this paper proposes an auction mechanism for truthful electricity trading in a local energy market. In order to guarantee truthful electricity trading, the proposed auction mechanism is constructed based on the Vickrey–Clarke–Groves auction, which was proven to guarantee truthful operations. The Hungarian method is also considered in addition to the auction. The simulation results for the auction verify that the utilities of local market energy entities are maximized when the prosumers are truthful. [ABSTRACT FROM AUTHOR]

Droop control is a viable method for the operation of island DC microgrids in a decentralized architecture. This paper presents a mixed-integer conic optimization formulation for the design of generator droop control, comprising the parameters of a piecewise linear droop curve. The mixed-integer formulation originates from a stochastic optimization framework that considers several operating scenarios for finding the optimal design. The convexity of the mixed-integer problem continuous relaxation gives global optimality guarantees for the design problem. The paper presents computational results using a tight polyhedral approximation of the conic program, leading to a mixed-integer linear programming (MILP) problem that is solved using a state-of-the-art commercial solver. The results from the proposed approach are contrasted with both a classic linear droop control design and a recent piecewise linear formulation. The Monte-Carlo simulation results quantify the extent to which the MILP solution is superior in reducing voltage violations and power loss, and the degree to which the loss is close to that from a conic optimal power flow solution. [ABSTRACT FROM AUTHOR]

The generator in generative adversarial networks (GANs) is driven by a discriminator to produce high-quality images through an adversarial game. At the same time, the difficulty of reaching a stable generator has been increased. This paper focuses on non-adversarial generative networks that are trained in a plain manner without adversarial loss. The given limited number of real images could be insufficient to fully represent the real data distribution. We therefore investigate a set of distributions in a Wasserstein ball centred on the distribution induced by the training data and propose to optimize the generator over this Wasserstein ball. We theoretically discuss the solvability of the newly defined objective function and develop a tractable reformulation to learn the generator. The connections and differences between the proposed non-adversarial generative networks and GANs are analyzed. Experimental results on real-world datasets demonstrate that the proposed algorithm can effectively learn image generators in a non-adversarial approach, and the generated images are of comparable quality with those from GANs. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for advanced demand side management (DSM) in the distribution network (DN), catering at the same time for the requirements of the network operator, transmission or distribution, the available flexibility of the demand side, and the preservation of network performance. The basic premise of the study is that the distribution network operator is providing flexibility to the transmission system operator through load shaping. Different, one or more, indicators can be chosen to assess preservation of network performance. In this paper, for illustrative purposes of the methodology, the steady state voltage stability index, namely the load margin, is chosen as the network performance indicator. This is evaluated before and after a DSM action, in order to analyse the possible effect of DSM on network loadability. Load at each DN bus is represented using a realistic composite load model comprising controllable and uncontrollable loads. The DSM is initially performed based on optimal power flow calculation to ensure that the distribution system load profile at the grid supply point follows the required (pre-specified) load profile during a 24 hour period. Following this, a particle swarm optimisation is used to modify DSM program in those time steps of the planning horizon where load margin is reduced. The methodology is illustrated on a number of case studies using modified IEEE 33 bus distribution network model. The results illustrate the extent to which the available flexibility of demand can be used in support of transmission network operation when the preservation of network performance and appropriate load modeling are considered. [ABSTRACT FROM AUTHOR]

This paper considers the problem of releasing optimal power flow (OPF) test cases that preserve the privacy of customers (loads) using the notion of Differential Privacy. It is motivated by the observation that traditional differential privacy algorithms are not suitable for releasing privacy preserving OPF test cases: The added noise fundamentally changes the nature of the underlying optimization and often leads to test cases with no solutions. To remedy this limitation, the paper introduces the OPF Load Indistinguishability (OLI) problem, which guarantees load privacy while satisfying the OPF constraints and remaining close to the optimal dispatch cost. The paper introduces an exact mechanism, based on bilevel optimization, as well as three mechanisms that approximate the OLI problem accurately. These mechanisms enjoy desirable theoretical properties, and the computational experiments show that they produce orders of magnitude improvements over standard approaches on an extensive collection of test cases. [ABSTRACT FROM AUTHOR]

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation. [ABSTRACT FROM AUTHOR]

There is an increasing necessity for new long-term planning models to adequately assess the flexibility requirements of significant levels of short-term operational uncertainty in power systems with large shares of variable renewable energy. In this context, this paper proposes an adaptive robust optimization model for the generation and transmission expansion planning problem. The proposed model has a two-stage structure that separates investment and operational decisions, over a given planning horizon. The key attribute of this model is the representation of daily operational uncertainty through the concept of representative days and the design of uncertainty sets that determine load and renewable power over such days. This setup allows an effective representation of the flexibility requirements of a system with large shares of variable renewable energy, and the consideration of a broad range of operational conditions. To efficiently solve the problem, the column and constraint generation method is employed. Extensive computational experiments on a 20-bus and a 149-bus representation of the Chilean power system over a 20-year horizon show the computational efficiency of the proposed approach, and the advantages as compared to a deterministic model with representative days, due to an effective spatial placement of both variable resources and flexible resources. [ABSTRACT FROM AUTHOR]

This paper presents a study of the effects that the shoe shape of the teeth of electrical machines has on the performance and losses. This is done by considering a concentrated wound, high-speed permanent magnet generator. The paper investigates the influence of the tooth shoe shape on the machine magnetic circuit and the losses distribution based on analytical and finite-element analysis (FEA). A shape coefficient K {t} is proposed to provide an optimized design reference. A comprehensive analytical tool able to study the variations of the machine performance parameters is proposed. The deduced optimization function is normalized using the non-equilibrium relative weighting method, and then, it is processed via a genetic algorithm to achieve the optimized design. FEA is used to validate the proposed analytical tool and the optimum design. [ABSTRACT FROM AUTHOR]

Boosting the resilience of power systems is one of the core requirements of smart grid. In this paper, an integrated resilience response framework is proposed, which not only links the situational awareness with resilience enhancement, but also provides effective and efficient responses in both preventive and emergency states. The core of the proposed framework is a two-stage robust mixed-integer optimization model, whose mathematical formulation is presented in this paper as well. To solve the above model, an algorithm based on the nested column-and-constraint generation decomposition is provided, and computational efficiency improvement techniques are proposed. Preventive response in this paper considers generator re-dispatch and topology switching, while emergency response includes generator re-dispatch, topology switching and load shedding. Several numerical simulations validate the effectiveness of the proposed framework and the efficiency of the solution methodology. Key findings include the following: 1) in terms of enhancing power grid resilience, the integrated resilience response is preferable to both independent preventive response and independent emergency response; 2) the power grid resilience could be further enhanced by utilizing topology switching in the integrated resilience response. [ABSTRACT FROM PUBLISHER]

This is a follow-up study of the cryogen-free superconducting prototype generator with YBCO field windings. The previous paper had introduced the design of the structure, cryogenic system and electromagnetic characteristics of the prototype machine, whose operating temperature was 30 K, maximum field current was 100 A and rotating speed was from 10 to 30 rpm. In this paper, the optimization of the airgap magnetic field and the stability of superconducting magnet have been carried out. For the purpose of increasing utilization of the magnetic field of superconducting windings, its support structure and vacuum chamber of the cryostat had been upgraded in order to reduce the physical airgap between the armature teeth and the vacuum chamber room temperature wall from 10 mm to 2 mm. In addition, a new coil curing method, vacuum impregnation process with paraffin, had been applied while the YBCO coil fabrication, to improve its stability. The performance properties of the optimized system as well as the comparison between FEM simulation and experimental results are finally presented. [ABSTRACT FROM AUTHOR]

As one of the most widely installed utility-scale storage facilities, pumped storage hydro (PSH) plays an essential role in providing flexibility for power systems worldwide. Thus, to accurately quantify the flexibility of PSH units in operational optimization problems is important. The conventional PSH models in the literature rarely consider detailed state transitions due to their hourly-based settings. However, it becomes imperative for operational optimization on short-term intervals, especially with increasing shares of renewable energy in power systems. To this end, this paper presents a novel deterministic PSH model that considers the transition time and trajectory between three states of PSH units in look-ahead dispatch. Moreover, to better characterize the varying efficiency of PSH units with water head and flow rate, this paper proposes to model detailed head-dependent efficiency curves (hereafter called input-output curves) in look-ahead dispatch, which encounters heavy computational burdens when short time intervals are applied. In this work, a zig-zag piece-wise linear approximation method is used for input-output curve modeling. This can enable an accurate quantification for variable efficiency and head dependence in a computationally effective manner. Numerical results are presented to show performances of the proposed PSH model in both flexibility quantification and computation time. [ABSTRACT FROM AUTHOR]

Bulk integrated electricity and gas systems (IEGSs) introduce complex coupling relations and induce synergistic operation challenges. The growing uncertainty arising from the renewable power generation in the IEGS further aggravates the synergistic problems. Considering the availability of historical wind power generation data, this paper adopts a two-stage sample robust optimization (SRO) model, which is equivalent to the two-stage distributionally robust optimization (DRO) model with a ${\text{type}} - \infty $ Wasserstein ambiguity set, to address the wind power penetrated unit commitment optimal energy flow (UC-OEF) problem for the IEGS. Compared to the equivalent DRO model, the two-stage SRO model can be approximately transformed into a computationally efficient form. Specifically, we employ linear decision rules to simplify the proposed UC-OEF model. Moreover, we further enhance the tractability of the simplified model by exploring its structural features and, accordingly, develop a solution method. Simulation results on two IEGSs validate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Power router technology is maturing to the point of becoming a cost-effective enabler of increased transmission asset utilization. Power routers can enable a desirable increase in control of power systems, especially as infrastructure ages and degrades. This paper presents a formal extension to the traditional security-constrained optimal power flow (SCOPF) algorithm, named flexible security-constrained optimal power flow (FSCOPF), which utilizes power router control in the post-contingency timeframe. The operational improvement is enabled by the fast-response capability of FACTS-based power routers to change setpoints in response to power system contingencies. The FSCOPF algorithm, developed in this paper, allows for power routers to be used as a real-time dispatchable resource. We show that further power system savings are achieved when compared to the traditional SCOPF. [ABSTRACT FROM PUBLISHER]

This paper proposes a new congestion management (CM) approach by using the generation rescheduling and load shedding, with the realistic voltage-dependent load modeling. The paper presents several objective functions such as generation and load shedding cost minimization (GLCM)/social welfare maximization including demand response offers (SWM), load shedding minimization (Pshd M), load served maximization (LSM), and load served error minimization. To the best of our knowledge, all previous CM efforts considered constant load models. Using voltage-dependent load models, the paper clearly brings out the inappropriateness of conventional single objectives for CM, such as GLCM/SWM and PshdM, due to the reduction of amount of load served. Therefore, multi-objective optimization is required and the objectives can be judiciously combined depending on the loading condition. Multi-objective strength pareto evolutionary algorithm 2+ has been employed to solve the proposed CM problem. The effectiveness of the developed approach is confirmed from the simulation results on IEEE 30 bus test system. [ABSTRACT FROM AUTHOR]

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained ac optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an ac feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex ac-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the ac feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

Memory-based LT encoders (MBLTEs) have been shown to have better performance than the regular LT encoder in terms of bit error rate (BER) and decoding convergence speed. In this paper, we explore the entire family of MBLTEs for finite block-length codes over the binary erasure channel (BEC). We propose an algorithm to extend the first and second order MBLTE approach to an arbitrary $i$ -th order MBLTE. We analyze the performance of such encoders mathematically by characterizing the expected accumulated number of recovered variable nodes at each decoding round. We define the threshold of the memory-based encoding method (MBEM) and show that the performance of MBLTEs increases as the memory order increases up to the point where this threshold is achieved. Beyond this point, we show that the performance of MBLTEs saturates if the channel erasure probability is zero and degrades otherwise. We formulate an optimization problem to solve for the optimal memory order based on whether or not the MBEM threshold is achieved. We present an extensive set of numerical results. These show agreement between our analysis and computer simulations. They also show that our optimization problem is efficient in determining the optimal memory order of MBLTEs in terms of decoding convergence speed, BER/frame-error-rate, and error floor. [ABSTRACT FROM AUTHOR]

This paper reports on mechanical design, optimization, and experimental testing of a novel piezo-actuated elliptical vibration-assisted cutting (EVC) system constructed by flexure hinges. The stroke and natural frequency were analyzed based on the theoretical modeling. An enhanced central composite design was chosen as the design of experiments methodology to reduce the modeling error, and a nondominated sorted genetic algorithm-II (NSGA-II) was adopted for structure optimization. The optimized EVC generator was manufactured and experimentally tested to investigate practical properties of the proposed EVC system. It shows that the stroke of input end can reach to 30 μ m with a motion resolution of 10 nm, and the first natural frequency can reach to 2600 Hz without considering the manufacturing error. Besides, a relatively small cross-axis coupling ratio (within 0.21%) can be effectively obtained. The developed EVC system is advantageous not only to being equipped with machine tools with various configurations, but also to easily achieving arbitrary vibrations in three-dimensional space through two actuators, which is especially important for the generation of complex structured surfaces. With this paper, it is of great significance to promote industrial application of EVC techniques. [ABSTRACT FROM AUTHOR]

The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved for various inputs to determine robust schedules given a set of contingencies. Unfortunately, the modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs, which are hard to solve. To address this challenge, leveraging the wealth of available historical data, this paper proposes a novel approach that combines deep learning and robust optimization techniques. Unlike recent machine-learning applications where the aim is to mitigate the computational burden of exact solvers, the proposed method predicts directly the SCOPF implementable solution. Feasibility is enforced in two steps. First, during training, a Lagrangian dual method penalizes violations of physical and operations constraints, which are iteratively added as necessary to the machine-learning model by a Column-and-Constraint-Generation Algorithm (CCGA). Second, another different CCGA restores feasibility by finding the closest feasible solution to the prediction. Experiments on large test cases show that the method results in significant time reduction for obtaining feasible solutions with an optimality gap below 0.1%. [ABSTRACT FROM AUTHOR]

The volatility of renewable energy causes mismatch between real-time generation and demand, calling for sufficient backup to compensate such discrepancy. This paper studies the uncertainty mitigation problem at a given operating point, which entails correctively dispatching obligate generators to maintain power balancing and network power flow constraints. The redispatch problem is modeled via a convex quadratic program parameterized in the real-time renewable output, aiming at minimizing the weighted sum of square of generator incremental output. Such an objective leads to a proper allocation of unbalanced power among generators and ensures a unique optimal solution, therefore circumvents model degeneracy. Based on the first-order optimality condition, the analytical expression of the optimal redispatch policy is proven to be piecewise affine: the renewable output set is partitioned into polyhedral regions; in each region, the optimal redispatch policy of generator is an affine function in the incremental output of renewable plants. Provided with the optimal redispatch policy in the analytical form, the nodal-wise flexibility requirements on obligate generators, including the spinning reserve capacity and the ramping capability, can be easily assessed, which is useful in generation scheduling. Case studies on the PJM 5-bus system and the modified IEEE 118-bus system demonstrate the outcome and validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, remarkable progress in zero-shot learning (ZSL) has been achieved by generative adversarial networks (GAN). To compensate for the lack of training samples in ZSL, a surge of GAN architectures have been developed by human experts through trial-and-error testing. Despite their efficacy, however, there is still no guarantee that these hand-crafted models can consistently achieve good performance across diversified datasets or scenarios. Accordingly, in this paper, we turn to neural architecture search (NAS) and make the first attempt to bring NAS techniques into the ZSL realm. Specifically, we propose a differentiable GAN architecture search method over a specifically designed search space for zero-shot learning, referred to as ZeroNAS. Considering the relevance and balance of the generator and discriminator, ZeroNAS jointly searches their architectures in a min-max player game via adversarial training. Extensive experiments conducted on four widely used benchmark datasets demonstrate that ZeroNAS is capable of discovering desirable architectures that perform favorably against state-of-the-art ZSL and generalized zero-shot learning (GZSL) approaches. Source code is at https://github.com/caixiay/ZeroNAS. [ABSTRACT FROM AUTHOR]

Under future low-carbon scenarios, it will be crucial to boost the rapidity in the delivery of frequency response services, especially those provided by conventional generators. This paper proposes a novel framework for the scheduling of frequency response services that incentivizes a rapid response from different system assets, including conventional generators. Differently from other approaches which envisage a fixed delivery time for frequency response services, the proposed methodology implements time-varying delivery intervals, which coincide with the time of frequency nadir occurrence. A relevant set of linearized constraints is embedded in a typical power system scheduling model. Results indicate that the proposed methodology reduces the unnecessary overscheduling associated with traditional methodologies, leading to significant operational cost savings. [ABSTRACT FROM AUTHOR]

Recent years have witnessed significant interest in convex relaxations of the power flows, with several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that ac-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-hard for tree networks. [ABSTRACT FROM AUTHOR]

Emerging smart-grid-enabling technologies will allow an unprecedented degree of observability and control at all levels in a power system. Combined with flexible demand and storage, they could allow procuring energy at minimum cost and environmental impact. That however presupposes real-time coordination of demand of individual households and industries down at the distribution level, with generation at the transmission level. This is closely related with the balancing market economic dispatch (ED) problem, which currently does not take into account distribution network constraints and flexible demand characteristics. Still, assuming a suitably modified form of that problem was available, due to both computational and communications requirements, its centralized solution in its full detail would not be tractable. While there is currently a wealth of literature dealing with distributed optimization applications in power systems, it typically focuses on smaller parts of the overall energy management problem (e.g., transmission area synchronization or electric vehicles management) often without considering its full scale or establishing any association with energy market mechanisms. The target of this paper is twofold: 1) identify a flexible demand and distribution network inclusive formulation for ED and 2) propose a solution method. [ABSTRACT FROM AUTHOR]

Increasing penetration of renewable power sources (RESs) is bringing more uncertainties to power systems. Real-time economic dispatch should be able to handle the fluctuations caused by the load as well as RESs, and obtain new optimal operating points after deviating from original generation schedules. This paper proposes a generation adjustment algorithm based on the base point and participation factor method. The objective of the method is to obtain fast adjustments to generators’ real power outputs in real-time economic dispatch. The proposed method achieves significant and consistent improvements comparing to the original participation factor method by using a more precise model of transmission losses in the optimization process. The computational burden and execution time of the proposed method is much less than OPF and heuristic economic dispatch methods. The proposed method and its effectiveness are tested using IEEE 30-bus system, IEEE 118-bus system, and GuangDong 1018-bus system. Simulation results are demonstrated with comparisons and discussions. [ABSTRACT FROM AUTHOR]

Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This problem becomes more severe when the SCOPF has to be solved not only for a single instance, but for multiple periods, e.g. in the context of electricity market analyses. This paper proposes an algorithm that identifies the minimal set of constraints that exactly define the space of feasible nodal injections for a given network and contingency scenarios. By internalizing the technical limits of the nodal injections and enforcing a minimal worst-case impact of contingencies to line flows, computational effort can be further improved. The case study applies and analyzes the methods on the IEEE 118 and A&M 2000 bus systems, as well as the German and European transmission systems. In all tested cases the proposed algorithm identifies at least 95% of the network and security constraints as redundant, leading to significant SCOPF solve time reductions. Scalability and practical implementation are explicitly discussed. The code and input data of the case study is published supplementary to the paper under an open-source license. [ABSTRACT FROM AUTHOR]

Repetitive high-voltage square pulses are of great importance for producing long-pulse electron beams and high-power microwaves. One of possible technologies for the generation of such pulses is a Marx generator using pulse forming network (PFN) stages, often combined with a pulse sharpening technique to reduce the rise time to a few nanoseconds (peaking stage). This paper presents an innovative design, named the “zigzag design,” for the optimization of the compactness and of the rise time of 400-kV–85-ns PFN-Marx. Thanks to this design, the 16 stages of this generator, which delivers an open circuit output voltage of 720 kV, fit in a 650-mm length. For a slightly overmatched load ($Z_{\mathrm {load}} = 100 ~\Omega$), the output voltage reaches 400 kV with a rise time as less as 5 ns. The inductance reduction associated with the innovative zigzag design, which allows this sharp rise time with no need for a peaking stage, is described. The 85-ns plateau duration of the pulse is given by the PFN construction of each stage, which is based on six ceramic capacitors (2.1 nF–45 kV) connected within a strip line. The 16 PFN stages are housed in a 360-mm diameter gas pressurized vessel. Burst mode operation for a duration of 10 s at a pulse repetition frequency of 100 Hz is reported, for a resistive load and for the electron beam diode of a X-band relativistic backward-wave oscillator (BWO). To reach further compactness, the BWO system is integrated on side of the generator vessel and a U-shaped gas pressurized line connects both systems through a compact conical vacuum insulator. [ABSTRACT FROM AUTHOR]

This paper proposes two second-order continuous-time algorithms to solve the economic power dispatch problem in smart grids. The collective aim is to minimize a sum of generation cost function subject to the power demand and individual generator constraints. First, in the framework of nonsmooth analysis and algebraic graph theory, one distributed second-order algorithm is developed and guaranteed to find an optimal solution. As a result, the power demand constraints can be kept all the time under appropriate initial condition. The second algorithm is under a centralized framework, and the optimal solution is robust in the sense that different initial power conditions do not change the convergence of the optimal solution. Finally, simulation results based on five-unit system, IEEE 30-bus system, and IEEE 300-bus system show the effectiveness and performance of the proposed continuous-time algorithms. The examples also show that the convergence rate of second-order algorithm is faster than that of first-order distributed algorithm. [ABSTRACT FROM AUTHOR]

This paper examines optimal energy market bidding behavior for stochastic resources when energy imbalance payments are determined endogenously from market clearing conditions. Some electricity markets require wind producers to settle day-ahead offers based on their real-time energy production. This is usually justified by economic and cost-causation principles, without considering the effects of these policies on curtailment and system balancing costs. Under these real-time settlement requirements, demand and wind forecast errors impact the effective penalty price, so strategic behavior affects the penalty price paid by producers. This paper formulates a two-stage game where producers place energy bids in the day-ahead market and then choose a curtailment level in real-time, and it derives the symmetric subgame perfect equilibrium strategy for producers. It details how supply curve convexity and resource correlation can lead wind producers to bid conservatively even when they are not risk averse. The results show that market-based pricing mechanisms improve tradeoffs between system efficiency and mean squared bid error as compared to the case where penalty levels are determined by alternative policies, suggesting additional benefits of market-based penalty prices beyond those previously studied. [ABSTRACT FROM AUTHOR]

This paper jointly addresses two major challenges in power system operations: 1) dealing with non-convexity in the power flow equations, and 2) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period AC optimal power flow problem (AC-OPF) with detailed modeling considerations, such as reactive capability curves of conventional and renewable generators and transmission constraints. This paper then applies strong second-order cone programming (SOCP)-based convex relaxations of AC-OPF combined with the use of an alternating direction method to identify worst-case uncertainty realizations, and also presents a speed-up technique based on screening transmission line constraints. Extensive computational experiments show that the solution method is efficient and that the robust AC OPF model has significant advantages both from the economic and reliability standpoints as compared to a deterministic AC-OPF model. [ABSTRACT FROM PUBLISHER]

In this paper, a coordinated adaptive droop control is addressed for DC microgrid to optimize its power distribution. The optimal solution for economical dispatch problem (EDP) of the microgrid is found through a fully distributed hierarchical control. The consensus-based economical regulator calculating the optimal solution for the generator is fully distributed. Thus, it eliminates the requirement of centralized coordinator. The droop controller receives the reference from the economical regulator and ensures the output power converging to the reference while maintaining the power balance of the system. Moreover, the economical regulator can estimate the load information of the system based on the characteristics of droop control. Thus, the information from load or renewable energy source is no longer required to solve the EDP that consequently decreases the number of communication nodes. This will reduce infrastructure cost, enhance the reliability, and fasten the converging speed of algorithm. The dynamic model is established and parameter selection guideline are given in this paper. A low-voltage dc-microgrid prototype platform is utilized to validate the effectiveness of the proposed control. [ABSTRACT FROM PUBLISHER]

In Part II of this paper, we present formulations for three two-settlement market models: Baseline cost-minimization (\textitStoch- \textitOpt); and two sequential market models in which an independent system operator (ISO) runs real-time (RT) balancing markets after making day-ahead (DA) generating unit commitment decisions based upon deterministic wind forecasts, while virtual bidders arbitrage the two markets ( ${{\textit{Seq}}}$ and ${{\textit{Seq}}}$- ${{SS}}$). The latter two models differ in terms of whether some slow-start generators can self-schedule in the DA market while anticipating probabilities of RT prices. Models in ${{\textit{Seq}}}$ and ${{\textit{Seq}}}$- ${{SS}}$ build on components of the two-settlement equilibrium model ( \textitStoch- ${{MP}}$) defined in Part I of this paper [J. Kazempour and B. F. Hobbs, “Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation - Part I: Principles and competitive model,” IEEE Trans. Power Syst., vol. 33, no. 1, pp. 749–759, Jan. 2018]. We then provide numerical results for all four models. A simple single-node case illustrates the economic impacts of flexibility, virtual bidding, and self-schedules, and is followed by a larger case study based on the 24-node IEEE reliability test system. Their results confirm that flexible resources, including fast-start generators and demand response, can reduce expected costs in a sequential two-settlement market. In addition, virtual bidders can also improve the functioning of sequential markets. In some circumstances, virtual bidders (together with self-scheduling by slow-start generators) enable deterministic ISO DA markets to obtain the least (expected) cost unit commitments. [ABSTRACT FROM AUTHOR]

The increasing penetration of variable energy resources has led to more uncertainties in power systems. Flexible Ramping Products (FRP) have been adopted by several electricity markets to manage the uncertainties. We reveal that neglected line congestion for FRP may not only cause infeasibility, but also result in a failure of cost recovery. To address the deliverability issues on FRP, this paper proposes a new concept, Deliverable Robust Ramping Products (DRRP), in real-time markets. The DRRP includes generation ramping reserve and generation capacity reserve. The DRRP is deliverable and immunized against any predefined uncertainty. It also fully addresses the bid cost recovery issue caused by the line congestion in existing FRPs. The prices of DRRP are derived within the Affine Adjustable Robust Optimization (AARO) framework. These prices can be used to identify valuable reserves among available reserves and quantify the values of flexible resources that provide reserves. This paper also proposes a general approach to obtaining the time-decoupled prices for DRRP and generation, which can be used for the market settlement of the first interval only in real-time markets. Simulations on a 3-bus system and the IEEE 118-bus system are performed to illustrate the concept of DRRP and the advantages of DRRP compared to existing FRP. [ABSTRACT FROM PUBLISHER]

This paper discusses the design process of a generator to utilize waste diesel engines in the automotive industry, and presents the results of the design, analysis, and test evaluation of a 78 kW permanent magnet synchronous generator. In the initial design process using the finite-element analysis and space harmonic analysis, the number of poles and slots was determined. Then, the generator characteristics were investigated by the torque per rotor unit volume method and the $d$ , $q$ -axis equivalent circuit. Last, the optimal size of the generator was determined. This process makes it possible to design in consideration of efficiency, inductance, material cost, and temperature characteristics. A prototype of the model was created and tested with uncertainty analysis, and a comparison between the experimental results and the results of the optimization was conducted to validate the analytic approach. [ABSTRACT FROM AUTHOR]

This paper presents an optimized energy management system (OEMS) to control the microgrid of a remote temporary military base (FOB) featuring diesel generators, a battery energy storage system (BESS), and photovoltaic (PV) panels. The information of the expected electric demand is suitably used to improve the sizing and management of the BESS, according to the days of operation. The OEMS includes power electronics to charge the batteries from either the PV source or the diesel generators, and it can function as a current source when it is supplementing the power from one of the generators or as a voltage source when it is the sole source of power for the loads. The new contribution of this paper includes the optimization of a FOB's microgrid, where critical loads must be serviced at all times. The proposed optimization, which uses Special Order Sets for the semicontinuous function handling, also integrates economic evaluations by properly taking into account how the size of BESS affects its charge/discharge cycle; thus, the FOBs’ battery lifetime, in addition to its fuel consumption. Results from optimization are employed by the OEMS to coordinate the energy sources, and match the critical and noncritical loads with the available supply. Fuel savings of \approx \text30\% (and \approx \text50\% adding the PV source) can be achieved with respect to the already improved, but not optimal, solution of a previous work. [ABSTRACT FROM PUBLISHER]

The locally repairable code (LRC) studied in this paper is an [n,k] linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this paper is to determine the largest possible minimum distance for LRCs. First, an integer programming-based upper bound is derived for any LRC. Then, by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters n1>n2 , where n1 = \lceil ({n}/{r+1}) \rceil and n2 = n1 (r+1) - n . Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field \mathbb F2^{m} , where m\geq n1r . Based on these results, the largest possible minimum distance for all LRCs with r \le \sqrt n-1 has been definitely determined, which is of great significance in practical use. [ABSTRACT FROM PUBLISHER]

The dramatic increase of cyber-attacks onenergy systems can cause huge losses, which has drawn extensive attention due to the fast integration of information communication technologies (ICTs). This issue is becoming worse with the integration of electricity and gas systems (IEGS), facilitated by gas generation and new coupling technologies. This paper investigates the risk and mitigation strategies for IEGS under false data injection attacks (FDIA) in a hierarchical two-stage framework. The FDIA on both electricity and gas systems are modelled through injecting falsified data by adversaries. To mitigate the adverse impacts, a novel two-stage distributionally robust optimization (DRO) is proposed: i) day-ahead operationto determine initial operationscheme and ii) real-time corrective operation with the realization of FDIA and renewable generation uncertainties. A semidefinite programming is formulated for the original problemand it is then solved by a convex optimization-based algorithm. A typical IEGS is used fordemonstration, which shows that the proposed model is effective in mitigating the risks caused by potential FDIAand renewable uncertainties, by optimal coordinating energy infrastructures and load shedding.This work provides system operators with a powerful toolto operate the IEGS with enhanced security against malicious cyber-attacks while accommodating increasing renewable energy. The method can also be easily extended to operatingIEGS against other natural attacks. [ABSTRACT FROM AUTHOR]

This paper studies a class of distributed convex optimization problems by a set of agents in which each agent only has access to its own local convex objective function and the estimate of each agent is restricted to both coupling linear constraint and individual box constraints. Our focus is to devise a distributed primal-dual gradient algorithm for working out the problem over a sequence of time-varying general directed graphs. The communications among agents are assumed to be uniformly strongly connected. A column-stochastic mixing matrix and a fixed step-size are applied in the algorithm which exactly steers all the agents to asymptotically converge to a global optimal solution. Based on the standard strong convexity and the smoothness assumptions of the objective functions, we show that the distributed algorithm is capable of driving the whole network to geometrically converge to an optimal solution of the convex optimization problem only if the step-size does not exceed some upper bound. We also give an explicit analysis for the convergence rate of the proposed optimization algorithm. Simulations on economic dispatch problems and demand response problems in power systems are performed to illustrate the effectiveness of the proposed optimization algorithm. [ABSTRACT FROM AUTHOR]

Several parallel restored subsystems exist in the last stage of the build-up restoration process of bulk power systems. The whole system restoration is completed when these subsystems are reconnected and their internal loads are recovered. This paper proposes a robust distributed coordination scheme to achieve reconnection and load recovery of parallel restored subsystems in wind power penetrated transmission systems. First, robust distributed restoration models are constructed considering individual subsystems under uncertain conditions. Then, an inner-outer nested upper-lower (IOUL) iterative algorithm is developed to solve the constructed models. The robust distributed coordination can be realized according to convergence. The proposed algorithm solves the complex non-convex model with uncertain variables by iteratively solving the small-scale mixed-integer linear programming (MILP) problem. The robust distributed restoration scheme allows independent decision-making within subsystems and ensures the feasibility of the distributed restoration strategy under uncertain conditions. The effectiveness of the proposed method is validated using three interconnected 6-bus systems and the IEEE 118-bus system, showing improved computational efficiency and restoration acceleration. [ABSTRACT FROM AUTHOR]

To capture the stochastic characteristics of renewable energy generation output, chance-constrained unit commitment (CCUC) model is widely used. Conventionally, analytical reformulation for CCUC is usually based on simplified probability assumption or neglecting some operational constraints, otherwise scenario-based methods are used to approximate probability with heavy computational burden. In this paper, Gaussian mixture model (GMM) is employed to characterize the correlation between wind farms and probability distribution of their forecast errors. In our model, chance constraints including reserve sufficiency and branch power flow bounds are ensured to be satisfied with predetermined probability. To solve this CCUC problem, we propose a Newton method based procedure to acquire the quantiles and transform chance constraints into deterministic constraints. Therefore, the CCUC model is efficiently solved as a mixed-integer quadratic programming problem. Numerical tests are performed on several systems to illustrate efficiency and scalability of the proposed method. [ABSTRACT FROM AUTHOR]

Due to inherent uncertainty and volatility, large-scale wind power integration requires additional reserves for power balancing. However, it remains an open question as to how to quantify the required reserves corresponding to different uncertainties and penetration scales of wind power. This paper addresses this problem with an improved endogenous reserve determination method. Multiple uncertainties, including wind power outputs, load fluctuations, and generator failures, especially power flow uncertainties caused by wind power fluctuations and generator faults, are comprehensively integrated into a security and network-constrained economic dispatch (S&NCED) model to jointly schedule the generation and reserve. Affinely adjustable robust optimization (AARO) is adopted to address wind power and load uncertainties. Then the model is transformed into a two-stage (normal state optimization and fault verification) S&NCED model for iterative solving with the aid of Benders decomposition, and auxiliary constraints are designed to accelerate the convergence. Results of 6-bus and IEEE118-bus systems show that the proposed method can effectively provide a more economical and robust generation-reserve dispatch scheme and can clearly specify the reserve capacity required by wind power. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for generating restoration sequences in distribution systems and microgrids with emphasis on deriving optimal switching times for remote control switches. Microgrid architecture considered are assumed to be operating in islanded single master mode. Control methods for handling the unbalance inherent in distribution systems using single-phase controlled PQ inverters were developed and incorporated in the proposed method. The problem of considering simultaneously both energy optimization and dynamic stability of the system, which is lacking in existing methods, was addressed by studying the transient behavior of microgrids based on extended electromagnetic transients program (EMTP) simulations and then approximate and incorporate these behaviors into the optimization formulation for restoration. The approach is based on multi-objective optimization of final restored load and total restoration time. The methodology was studied on a modified IEEE 123 node test feeder. An EMTP simulation in PSCAD of the formed microgrids was used to validate the accuracy of the dynamic and steady-state characteristics of the resulting systems. By considering the transient behavior of distributed generators (DGs) during restoration, a better restoration sequence that does not trigger protection relays could be realized. [ABSTRACT FROM AUTHOR]

As the development of tidal turbines attracts more and more attention in recent years, reliable design and efficient control of tidal turbines are becoming increasingly important. However, the majority of existing tidal turbines still utilize traditional fixed ratio geared transmissions and the associated control designs focus on simple feedback controllers that use measurements or possibly estimates of the turbine itself or current local tidal profile. Therefore, the measurement and control are inevitably affected by the inherent delay with respect to the current tidal speeds. This paper proposes a novel tidal turbine with continuously variable speed hydrostatic transmissions and a nonlinear predictive controller that uses short-term predictions of the approaching tidal speed field to enhance the maximum tidal power generations when the tidal speed is below the rated value. The controller is designed based on an offline finite-horizon continuous time minimization of a cost function, and an integral action is incorporated into the control loop to increase the robustness against parameter variations and uncertainties. A smooth second order sliding mode observer is also designed for parameter estimations in the control loop. A 150 kW tidal turbine with hydrostatic transmission is designed and implemented. The results demonstrate that the averaged generator power increases by 6.76% with this preview based nonlinear predictive controller compared with a classical non-predictive controller. [ABSTRACT FROM AUTHOR]

This paper tries to develop a multiagent consensus-based algorithm to handle the energy management problem (EMP) in the smart grids in the presence of dispatchable loads and distributed generators. To this end, the neighbor virtualization concept is employed to improve the system performance by introducing a novel communication structure for distributed algorithms. Accuracy, quickness, and scalability are the most important benefits of this algorithm that make it applicable in real power systems. The increasing penetration of wind turbines and the stochastic nature of load demand can inject much uncertainty in our problem. In order to deal with this issue, unscented transform as a powerful tool is used to model the problem uncertainties. The proposed problem is formulated in the form of a single-objective stochastic optimization framework maximizing the generators and consumers welfare. The feasibility and high performance of the proposed framework are examined on two test systems, including the IEEE 39-bus test system and a large grid with 1305 agents in MATLAB simulation. The simulation results advocate the high capability and effectiveness of the proposed framework for EMP of smart grids. [ABSTRACT FROM AUTHOR]

Flexible ramping product (FRP) has been recently launched in a number of electricity markets to enhance the power grid flexibility and accommodate additional deals of uncertainty introduced by renewable energy resources. The FRP procures additional ramp capacities provided by the dispatchable generating units and consumers in the real-time market (RTM) with the aim to enhance the ability of supply to closely follow the net-load at the next immediate time-interval. An important challenge in widespread adoption of this technology is a key question: Does the available energy capacity of the RTM participants contain sufficient ramp capacity to tackle the net-load uncertainties? Indeed, shortage of the systems ramp capacity may not only jeopardize its flexibility, but also may cause drastic fluctuations in the RTM energy prices. To address this challenge, this paper proposes a novel optimization framework to harness the procured spinning reserve services in the day-ahead market (DAM) for FRP provision in the RTM while meeting the system reliability requirements. On this basis, the FRP will be simultaneously procured from the RTM energy and DAM spinning reserve capacities. Furthermore, a new payment mechanism is proposed to compensate the portion of spinning reserve utilized for FRP procurement in the RTM. The proposed framework is simulated on the IEEE 118-bus test system and the results verify its effectiveness in modern electricity markets. [ABSTRACT FROM AUTHOR]

Intentional controlled islanding (ICI) and black start allocation (BSA) are two examples of problems in the power systems literature that have been formulated as mixed integer programs (MIPs) and allow reconfiguration of the power system topology. A key consideration in both of these problems is that each island that appears after a reconfiguration must have at least one energized generator. In this paper, we examine three alternative MIP formulations for this restriction, show their equivalence, and prove that two of them are stronger in terms of their linear programming relaxation than the formulation most commonly used in the power systems literature. Since the time to solve MIPs can vary significantly between equivalent formulations, we also present computational experiments on the IEEE test systems for the ICI and BSA problems. We observe that a polynomially separable, exponential in size, strong formulation yields the best performance for the BSA problem and exhibits a comparable performance to a linear in size, weak formulation for the ICI problem. [ABSTRACT FROM AUTHOR]

Linear droop control is a standard approach for the decentralized operation of AC microgrids. While the traditional design of the real and reactive power droop functions does not consider economic aspects, recent approaches present modifications to enable least-cost operation. This paper proposes mixed-integer conic programming (MICP) for computing the real and reactive power droop parameters from a stochastic optimization framework that captures several snapshots of the microgrid’s operation. The model permits distributed generation to switch between grid-forming and grid-feeding modes. Unlike previous works, MICP provides droop parameters that are globally optimal for the design scenarios. Numerical results show that using traditional linear cost-based droop design methods may result in voltage magnitude violations. In contrast, the proposed method gives a solution free of violations and is yet more economical. [ABSTRACT FROM AUTHOR]

Wind energy systems are expected to supply the majority of future generation from renewables due to the maturity of technology and the availability of energy resources. In this paper, in order to improve the ability of tracking a desired power reference at high wind speed region, a pitch control strategy based on error-based active disturbance rejection control (ADRC) approach is proposed for variable speed wind turbine system, providing a novel practically appealing control structure. The stability analysis of the proposed pitch controller based on singular perturbation theory is provided. Next, an improved coyote optimization algorithm (COA) fused with L $\rm {\acute{e}}$ vy flight and Sinusoidal map is proposed to address the controller parameters tuning issue. Then, the effectiveness of the proposed solution is verified on a 1.5 MW FAST simulator taking into account both multi-step and IEC turbulence wind conditions. Finally, an analysis in frequency domain of the pitch control system with the proposed control strategy is presented. [ABSTRACT FROM AUTHOR]

With theincreased penetration of renewable sources, power gridsare becoming stressed due to fluctuating generation. To alleviate stress from inconsistent sources, utilities employ energy storage systems alongside renewable sources and rely on dispatching synchronous generators. However, optimal dispatch of such devices is limited by traditional AC optimal power flow methods that do not account for time-dependent constraints, such as the state of charge of energy storage systems and generator ramping constraints. Multi-period optimal power flow is proposed as a large non-convex non-linear problem to optimally dispatch and control generators and energy storage elements across multiple time periods. In this paper, we introduce a scalable, robust framework to solve multi-period optimal power flow using a differential dynamic programming scheme that makes it capable of scaling to large systems containing energy storage devices. We demonstrate the efficacy of this solution by optimizing the SyntheticUSA testcase over a set of time periods. A robust homotopy method is applied to achieve fast simulation times that can be parallelized for further improvements. [ABSTRACT FROM AUTHOR]

Uncertainty arising from renewable energy results in considerable challenges in optimal power flow (OPF) analysis. Various chance-constrained approaches are proposed to address the uncertainty within OPF models. However, most existing approaches either assume that the uncertainty distributions are known a priori or consider individual chance constraint modeling. This paper proposes a distributionally robust (DR) joint chance-constrained OPF model, which ensures that the operational constraints are simultaneously satisfied with a given probability and does not require an assumption of specific probability distributions. An ambiguity set built on the first two moments is used to model the uncertainty. An optimized Bonferroni approximation (OBA) is first introduced to decompose the DR joint chance constraint into DR individual chance constraints. The resulting OBA formulation is strongly nonconvex. Different convex approximations are then proposed to formulate the OBA formulation as tractable forms. The proposed convex approximations can be easily extended to incorporate the structural information associated with uncertainty, and correlations among reserve chance constraints. Case studies demonstrate the effectiveness of the proposed convex approximation methods and their extensions. [ABSTRACT FROM AUTHOR]

The output of renewable generation depends on the real-time weather conditions and changes rapidly; so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters; then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance; this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method; by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively. [ABSTRACT FROM AUTHOR]