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This paper presents a new non-deterministic approach for multiyear distribution network reinforcement planning (DNRP) considering the uncertainty sources pertaining to loads, electricity prices, investment costs, and operation costs. Accordingly, the underlying idea of the information-gap decision theory (IGDT) is used to obtain a robust solution protected against different realizations of each uncertain variable lying in its robust region. The proposed model is capable of adjusting the robustness of the optimal solution in terms of a specific parameter designated as the budget of uncertainty. As the uncertain loads, investment and operation costs competitively tend to maximize their robust regions for a particular value of the budget of uncertainty, the normalized normal constraint (NNC) method as a proficient multi-objective optimization method is exploited in this paper to solve the proposed multiobjective IGDT-based DNRP (IGDT-DNRP) model. Mainly, the NNC method presents a set of Pareto optimal solutions rather than a single optimal solution. Accordingly, a posteriori out-of-sample analysis is introduced in this paper to find the best solution among the set of Pareto optimal solutions. The proposed IGDT-DNRP model is implemented on the IEEE 33-bus distribution network under different circumstances. Simulation results illustrate the effectiveness of the proposed nondeterministic approach. [ABSTRACT FROM AUTHOR]

Midcontinent Independent System Operator (MISO) plans to introduce 30-minute short-term reserve (STR) to address 30 minutes system flexibility needs. Transmission bottlenecks in the power system may inhibit the deliverability of STR. Insufficient deliverable reserve may require additional operator manual adjustments, which may be uneconomic and distort the market price signal. To improve reserve deliverability, event-based zonal STR clearing model and nodal STR clearing model are proposed to distribute reserve across the grid. This paper compares reserve deliverability and market clearing prices between the zonal STR model and the nodal STR model. A new design on penalty function is proposed in this paper to reflect the true value of security constraints for reserve deployment with the consideration of multiple events. Analysis of MISO test cases shows that the zonal approach is imprecise and may not guarantee the actual post-event flows within the physical limits. Nodal STR model can improve the reserve deliverability, market efficiency, and price signal. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-stage model of zonal electricity markets with day-ahead market clearing, and real-time re-dispatch and balancing that accounts for transmission line switching at both stages. We show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse, and present a new algorithm for solving the adversarial max-min problem that obeys the structure of an interdiction game. We apply the model on a realistic instance of the Central Western European system, and comment on the impacts of both proactive, and reactive transmission switching on the operating costs of the system. Part I presents day-ahead models of a short-term zonal electricity market with switching, and describes our algorithmic approach for solving these models efficiently. Part II describes variants of the real-time model, and presents the results of our case study on the Central Western European market. [ABSTRACT FROM AUTHOR]

There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty. [ABSTRACT FROM AUTHOR]

To uncover the mechanism by which voltage-dependent loads (VDLs) influence electromechanical dynamics, this paper mathematically deduces the damping torque induced by VDLs based on a single machine infinite bus system. Moreover, by continuously regulating the terminal voltage of a typical large-scale VDL, i.e., the aluminum electrolysis load, this paper proposes a novel load damping control architecture to dynamically modulate the power consumption of controlled loads so as to eliminate interarea oscillations in power systems. Specifically, the decentralized load damping controllers (LDCs) used in this architecture are designed by a proposed multistage mixed ${{{H}}_{2}} / {{{H}}_\infty }$ control approach to guarantee robustness against uncertainties (e.g., tie-line outages and wind generation fluctuations) as well as to ensure reasonable control efforts of controlled VDLs. Simulation results on the modified New England and New York interconnected system validate the method for analysis of VDLs’ effects on interarea oscillations and show the proposed load damping control strategy can satisfactorily damp interarea oscillations over multiple operating points. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) programs must be able to provide sound operating points for power systems under different conditions while meeting a large number of constraints. These constraints, however, either due to the operating conditions at hand or by construction, can have linearly dependent gradients, thus defining ill-behaved feasible sets. This paper analyzes the use of an alternative set of optimality conditions, derived from the Fritz-John (FJ) conditions, to represent OPF solutions in such critical cases. Results are presented for realistic test systems. [ABSTRACT FROM PUBLISHER]

The increasing penetrations of renewable energy in the electricity sector and plug-in electric vehicles (PEVs) in the transportation sector have increased the interests in introducing new methods to deal with uncertainties in power system studies. In this paper, a new distributionally robust optimization (DRO) via scenario wise ambiguity set is proposed to develop a collaborative bidding strategy for intermittent resources such as hydroelectric generation, wind farms, solar farms and electric vehicle aggregator in the day-ahead energy market. The proposed scenario wise ambiguity set is based on Wasserstein distance and is capable of considering both distributional information and statistical distance metric information in the ambiguity set. In this context, the robust counterpart of proposed DRO applying scenario based affine recourse approximation is developed in this paper. The proposed methodology is applied on a 3-bus test system as well as IEEE 118-bus test system to corroborate the effectiveness of the novel DRO model. [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]

Flexibility is a widely used term in planning process and real-time operation. The existing research on flexibility uses different techniques to study flexibility property from different aspects. While studying a property from various viewpoints increases the understanding on the subject, we need a consistent theoretical framework to consolidate the ideas generated in the field, compare and contrast results, and build on for future analysis. Based on the insights of the nature of flexibility, this paper proposes a unified framework for defining and measuring flexibility in power system. Under the proposed framework, we propose a flexibility metric which evaluates the largest variation range of uncertainty that the system can accommodate. Such a metric takes into account transmission network and system operations constraints, which are critical to assessing flexibility, but are often ignored in literature. A robust optimization technique is used to calculate the proposed metrics. While the illustrative example presented in this paper focuses on the flexibility in real-time system operation in the presence of wind and load uncertainty, this framework can generally be applicable to long-term studies such as system planning. [ABSTRACT FROM AUTHOR]

This paper proposes a probabilistic optimal power flow (POPF) for unbalanced three-phase electrical distribution systems considering robust constraints. Wind velocity, solar irradiation, and demands are considered as exogenous random variables with dissimilar probability distribution functions. The proposed two-stage POPF model determines the optimal generation dispatch that minimizes the average production cost while satisfying probabilistically robust constraints. The robustness of the solution is adjusted through a parameter involving the first two moments of the random state variables. The $2m+1$ point estimate method (PEM) provides the scenarios for the proposed POPF model, which can be solved using commercial solvers. The model's accuracy is evaluated by comparing the results obtained with the PEM and with a classical scenario generator technique. The model is validated through two IEEE distribution feeders with 13 and 123 nodes, comprising dispatchable and renewable generation. Results show that the model can accurately estimate the mean and standard deviation of the state random variables when compared with results obtained through Monte Carlo simulations. Various levels of conservatism are assessed, demonstrating the model's flexibility and applicability. [ABSTRACT FROM AUTHOR]

Customer-level rooftop photovoltaic (PV) has been widely integrated into distribution systems. In most cases, PVs are installed behind-the-meter (BTM), and only the net demand is recorded. Therefore, the native demand and PV generation are unknown to utilities. Separating native demand and solar generation from net demand is critical for improving grid-edge observability. In this paper, a novel approach is proposed for disaggregating customer-level BTM PV generation using low-resolution but widely available hourly smart meter data. The proposed approach exploits the strong correlation between monthly nocturnal and diurnal native demands and the high similarity among PV generation profiles. First, a joint probability density function (PDF) of monthly nocturnal and diurnal native demands is constructed for customers without PVs, using Gaussian mixture modeling (GMM). Deviation from the constructed PDF is utilized to probabilistically assess the monthly solar generation of customers with PVs. Then, to identify hourly BTM solar generation for these customers, their estimated monthly solar generation is decomposed into an hourly timescale; to do this, we have proposed a maximum likelihood estimation (MLE)-based technique that utilizes hourly typical solar exemplars. Leveraging the strong monthly native demand correlation and high PV generation similarity enhances our approach's robustness against the volatility of customers’ hourly load and enables highly-accurate disaggregation. The proposed approach has been verified using real native demand and PV generation data. [ABSTRACT FROM AUTHOR]

Conventionally, power flow equations are used for distribution systems (DS) analysis to find the nodal voltages. For the particular form of the DS reconfiguration problem, however, a direct formulation in terms of branch flows allows a substantial increase in solution efficiency from an optimization point of view. In this paper, a set of linear current flow (LCF) equations are derived for DS. This formulation is then used within the network reconfiguration problem for loss minimization. A mixed-integer quadratically constrained programming (MIQCP) formulation, together with a mixed-integer linear programming (MILP) formulation, are proposed in this paper and assessed through simulations. In these comparisons, the MILP formulation shows computational advantages over the MIQCP version and the preceding literature. The proposed methods are evaluated on several test systems. [ABSTRACT FROM PUBLISHER]

Power systems do not always operate under fully balanced conditions because of unbalanced loads and untransposed transmission lines. Under such conditions, commonly used positive sequence equivalent will no longer be valid. On the other hand, use of full three-phase model will add significant computational burden for the considered application. This paper describes a simple approach to address this issue for the specific application of state estimation. The main idea is to exploit the linearity of the estimation problem when the system is measured solely by phasor measurements. The linear problem lends itself to decoupling via modal transformation unlike the nonlinear formulation with SCADA measurements. A further improvement is introduced via the use of the least absolute value (LAV) estimator, which has the desirable property of automatic bad-data rejection. The paper illustrates how a robust LAV estimator designed for a positive sequence model can be efficiently used for the solution of an unbalanced three-phase state estimation problem. [ABSTRACT FROM PUBLISHER]

This paper describes the modeling and formulation of a variety of deterministic techniques for energy storage devices, namely the PI, H-infinity, and sliding mode controllers. These techniques are defined based on a general, yet detailed, energy storage device model, which is accurate for transient stability analysis. The paper also presents a thorough statistical comparison of the performance and robustness of the considered control techniques, using stochastic dynamic models and a variety of disturbances and scenarios. The case study is based on a 1479-bus model of the all-island Irish transmission system and an energy storage device actually installed in the system. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for determining the day-ahead bidding strategies of a large-scale hybrid electric energy company. The company has both energy generation and energy retailing businesses in a competitive electricity market. Demand response programs are also considered in the retail side of the company in order to hedge the risk of participation in wholesale market. This paper introduces a max-min bilevel mathematical programming with equilibrium constraint model for offering a strategy that manages the risk of uncertain forecasted rivals’ bids by robust optimization. The max-min bilevel model is converted to its equivalent single-level optimization using Karush–Kuhn–Tucker optimality conditions. The duality theory is utilized to find the equivalent ordinary maximization model of the max-min problem. Strong duality theory and big M method are also used to linearize the final model of offering strategy. Applicability of the proposed approach is shown by implementing it on the IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

To deal with the difficulties caused by uncertainty of renewable energy sources in solving transmission constrained unit commitment (TCUC), robust optimization (RO) and scenario-based stochastic optimization (SO) methods have gained popularity in recent years. However, RO formulations have a multilevel (min-max-min or min-max) structure and the solution methods are usually complicated. On the other hand, when SO-based formulation is adopted, a careful balance is often required between accuracy and scale of the formulation, since they are conflicting with each other when determining the number of scenarios. Moreover, nonanticipative constraints on economic dispatch (ED) decisions are sometimes not considered in two-stage stochastic UC formulation. An example is given in this paper to show that this may have a serious consequence. The motivation of this paper is to establish a TCUC formulation that can address the above concerns. In summary, the proposed formulation has three features including: it is single-level rather than multilevel, it is established based on very limited scenarios while the solution is feasible to all scenarios, and finally, nonanticipativity of both UC and ED decisions is guaranteed by the formulation. Numerical testing is also performed and the results show that the proposed formulation is effective. [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]

A robust adaptive backstepping approach is considered in this paper to design excitation controllers for synchronous generators in power systems. The higher-order dynamical models of synchronous generators are considered to design the proposed excitation controller. Since the parameters appearing within these dynamical models (especially the parameters related to the synchronous generators and excitation systems) significantly affect the stability of power systems, these parameters are considered as completely unknown during the proposed controller design process. The parameter adaptation laws are used in this paper to estimate the unknown parameters while maintaining the overall stability of power systems. The effects of external disturbances are also considered in this paper to incorporate the model accuracies and measurement noises, which in turn ensure the robustness of the proposed control scheme. The control Lyapunov functions are used to analyze the stability of the whole system through the negative semi-definiteness of their derivatives. Simulation studies are carried out on an IEEE standard power system, the New England 10-machine 39-bus power system, to further validate the performance of the proposed scheme under different operating conditions. Comparisons are also made with different existing nonlinear excitation controllers sliding mode controller and robust partial feedback linearizing controller, which are designed based on the higher order models as well as with the robust adaptive controller, which is designed based on the traditional one-axis model. Simulations results, under different operating conditions, demonstrate the superiority of the proposed control scheme over all these existing nonlinear excitation controllers. [ABSTRACT FROM AUTHOR]

As the level of uncertain renewable capacity increases on power systems worldwide, industrial and academic researchers alike are seeking a scalable, transparent, and effective approach to unit commitment under uncertainty. This paper presents a statistical ranking methodology that allows adaptive robust stochastic unit commitment using a modular structure, with much-needed flexibility. Specifically, this paper describes a bus ranking methodology that identifies the most critical buses based on a worst-case metric. An important innovation is the ability to identify alternative metrics on which to rank the uncertainty set—for example, to minimize economic dispatch cost or ramping needs, to provide a customized robust unit commitment solution. Compared to traditional robust unit commitment models, the proposed model combines statistical tools with analytical framework of power system networks. The resulting formulation is easily implementable and customizable to the needs of the system operator. The method and its applications are validated against other established approaches, showing equivalent solution to the state-of-the-art approach. Case studies were conducted on the IEEE-30, IEEE-118, and the pegase-1354 networks. In addition, the flexibility of bus ranking formulation is illustrated through implementation of alternative definitions of worst-case metrics. Results show that the bus ranking method performs as well as the best of these methods, with the provision of additional flexibility and potential for parallelization. [ABSTRACT FROM AUTHOR]

This two-paper series introduces a new multistage robust approach for solving the transmission expansion planning (TEP) problem under the uncertainty of loads and wind power productions. The proposed multistage robust TEP model is formulated using mixed binary and linear decision rules, which aims at finding a solution withstanding any realization of the uncertain parameters belonging to a set-based uncertainty model. The robustness of the optimal expansion plan can be adjusted by the budget of uncertainty. The first part of this two-paper series presents the extended and compact formulations for a deterministic TEP problem. Then, the compact formulation of the TEP problem under the uncertainty of loads and wind power productions is introduced as a multistage robust optimization problem, which is reformulated using mixed binary and linear decision rules. The extended formulation of these decision rules, as functions of uncertain parameters, is presented in this part as well. [ABSTRACT FROM AUTHOR]

In the restructured power industry, bulk energy storage may play a crucial role to provide the flexibility required by system operators to cater for the unprecedented levels of uncertainty. Within the context of co-optimized electricity markets for energy and reserves under wind uncertainty, this paper addresses the incorporation of bulk energy storage units in day-ahead network-constrained energy and reserve scheduling. A novel two-stage robust optimization approach is presented whereby the nonconvex and time-coupled operation of storage devices is precisely modeled while accounting for the anticipativity of the two-stage setting. The resulting robust counterpart is cast as a mixed-integer trilevel program with lower-level binary variables. In order to address the nonconvexity of the recourse problem, this paper proposes the application of an exact nested column-and-constraint generation algorithm. Numerical results illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Distribution system operators aim to improve hosting capacity (HC) of distribution networks (DNs) to accommodate more distributed rooftop photovoltaics (PVs). Although PV power generation delivers numerous benefits, power unbalance and voltage rise are two major obstacles that limit the network HC. To mitigate these issues, battery energy storage systems (BESSs) can be applied. Thus, this paper proposes a robustly optimal allocation method for BESSs, which aims to reduce the power unbalance and alleviate the voltage rise, and thus improve the HC of the unbalanced three-phase DNs. Considering that locations and capacities of distributed rooftop PVs are determined by customers, future PV installations are regarded as uncertainties. In addition, to deal with the uncertainties, the proposed BESS allocation problem is formulated as an adaptive robust optimization (ARO) model with integer recourse variables. Accordingly, a solution algorithm which integrates an alternating optimization procedure into a column-and-constraint generation algorithm is developed to efficiently solve the ARO model. With the proposed BESS allocation method, a new perspective on HC improvement is provided, which not only considers the worst power unbalance situation but also satisfies the allowed maximum PV capacity. The simulation results verify high efficiency and solution robustness of the proposed allocation method. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven adjustable robust unit commitment (UC) model for integrated electric-heat systems (IEHSs), where the data-driven, and robustness adjustable features are endowed by the novel uncertainty modeling method. The devised uncertainty set is the intersections of a series of hyperplanes. It combines the merits of the traditional box-like uncertainty set, whose underlying computation burden is moderate, and the convex hull formed by historical data, which would lead to less conservative operation strategies. The boundaries of the bounding high-dimensional rectangle of the uncertainty set are set as decision variables to achieve the balance between the operation costs, and risk. The two-stage decision-making framework is employed in the robust UC model of IEHSs, in which the district heating networks are operated at the variable-flow-variable-temperature mode. The modified column-and-constraint generation (C, and CG) algorithm is employed to solve the proposed robust program, where an additional feasible region reduction step is embedded to decrease the computation burden of the worst case identification. Simulation results on two test systems verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper intends to improve the accuracy of power system State Estimation (SE) by introducing a hybrid linear robust state estimator. To this end, automatic bad data rejection is accomplished through an M-estimator, i.e. a Schweppe-type estimator with Huber loss function. The method of Iteratively Reweighted Least Squares (IRLS) is used to maximize the likelihood function in the M-estimator. Leverage measurements are also treated by a simple yet effective formulation. To run the algorithm for real-world large-scale grids, cumbersome construction of the Jacobian matrix at each iteration is avoided. In addition, convergence to the local minima faced in the large-scale Gauss-Newton algorithm is not a concern as the proposed formulation is linear with no approximation. As observability and redundancy considerations mandate SE to take advantage of traditional SCADA measurements along with available PMU measurements, the linearity of the proposed SE formulation is guaranteed regardless of whether PMU-only, SCADA-only or hybrid SCADA/PMU measurements are utilized. In this regard, covariance matrix for measurements weights is derived for both types of measurements. Thanks to the linear formulation and therefore swiftness of the proposed algorithm, SE could be run for different power systems with a few up to thousands of buses. [ABSTRACT FROM AUTHOR]

In AC microgrids (MGs), the required high control gain for dealing with control faults would reduce the robustness of the secondary control to communication constraints. To tackle with this problem, the subarea physical infrastructure of AC MGs and the two-layer secondary control framework are designed. For the physical infrastructure, the whole AC MG is divided into several areas, where each area is composed of a distributed generator (DG) and several geographical-close loads. Furthermore, by utilizing the advanced metering infrastructure (AMI), loads transmit the local load change information to the DG in the same area. Based on this physical infrastructure, a distributed event-triggered fixed-time fault-tolerant (ET-FTFT) secondary control framework is proposed in this paper to improve the resilience of the secondary control to sensor and actuator faults/attacks, and communication constraints, simultaneously. The adopted two-layer control framework is to decouple the communication constraints and control faults. The event-based strategy is adopted in the upper layer to reduce the communication burden and Zeno behavior can be evaded. Real-time simulations based on the NI-PXI real-time simulator validate the advantages of the distributed ET-FTFT secondary control framework, which are the better robustness to control faults, and the fixed-time convergence to improve the power quality. [ABSTRACT FROM AUTHOR]

In this paper, a technique for designing fixed parameter decentralized power system stabilizers (PSSs) for interconnected power systems is proposed. In the proposed method, local information available at each machine in the multimachine environment, is used to tune parameters of PSS. Conventional design techniques such as P-Vr frequency response approaches, and the method of residues are based on complete system information, wherein phase angles of residues are consistent with the P-Vr phase response and can be used with confidence for design purposes. It is shown that magnitude and phase information of the proposed GEP TF agrees closely with that of P-Vr TF and yields a robust stabilizer. Nonlinear simulation and eigenvalue analysis show the efficacy of the proposed stabilizer to damp out the interarea and local modes of oscillations effectively over a wide range of operating conditions. Superiority of the proposed approach over the conventional approaches is demonstrated with simulation studies on two widely used multimachine systems. [ABSTRACT FROM AUTHOR]

In this paper, the application of the S-iteration process for solving the Power Flow (PF) problemis comprehensively studied. Thus, a combined approach between the S-iteration processand Newton's method (SIP-NR) is adapted for solving PF equations. Moreover, drawbacksshown by SIP-NRunder heavy loading conditions due to its linear convergence are addressed by developing a simple but reliable technique called Modified SIP-NR(MSIP-NR). MSIP-NR uses anon-repeatedly updating Jacobianscheme with the aim toaccelerate the convergence of SIP-NR. The introduced PF techniques are validated using well and ill-conditioned systemsunder several demand scenarios. The obtained results prove the robustness and efficiency of the introducedPF techniquescompared with other well-known methodologies. On the light of the results obtained, the introduced PF techniques may be used for different applications in power system analysis. Some of these potential applications are enumerated and discussed. [ABSTRACT FROM AUTHOR]

The technical virtual power plant (TVPP) is a promising paradigm to facilitate the integration of distributed energy resources (DERs) while incorporating operational constraints of both DERs and networks. Due to the volatility and limited predictability of DER generation and electric loads, the output capability of the TVPP is uncertain. In this regard, this paper proposes the robust capability curve (RCC) of the TVPP, which explicitly characterizes the allowable range of the scheduled power output that is executable for the TVPP under uncertainties. Implementing the RCC can secure the scheduling of the TVPP against unexpected fluctuations of operating conditions when the TVPP participates in the transmission-level dispatch. Mathematically, the RCC is the first-stage feasible set of an adjustable robust optimization problem. An uncertainty set model incorporating the variable correlation and uncertainty budget is employed, which makes the robustness and conservatism of the RCC adjustable. A novel methodology is proposed to estimate the RCC by the convex hull of several points on its perimeter. These perimeter points are obtained by solving a series of multi scenario-optimal power flow problems with worst-case uncertainty realizations identified based on a linearized network configuration. Case studies based on the IEEE-13 test feeder validate the effectiveness of the RCC to ensure the scheduling feasibility while hedging against uncertainties. The computational efficiency of the proposed RCC estimation method is also verified based on larger-scale test systems. [ABSTRACT FROM AUTHOR]

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]

Due to the geographic features and fruitful water resources, the distributed generation of Small Hydropower Generator Stack (SHGS) are vigorously developed in southwest China. As the more concerns about security and stability of power grids with the large amount of SHGS feed into the grid, the accurate models are critical to analyze those potential impacts. With the development of online monitoring technologies in smart grid, PMU based dynamic equivalent modeling for SHGS drawn many attentions. However, field applications reveal that traditional SHGS equivalent model may not be robustness enough to adapt the different disturbances. To overcome this deficiency, method to improve the robustness of SHGS dynamic equivalent modeling is proposed. In the paper, a coherency identification based multi-machine modeling method is introduced to enhance the accuracy of equivalent model. Sensitivity and correlation analysis based key parameters selection scheme is implemented to select the critical parameters, meanwhile avoiding the multiple solutions problem. Moreover, multi-objective optimization algorithm is designed for key parameters identification of the equivalent model. Additionally, hybrid dynamic simulation has adopted into the equivalent process to improve the computational efficiency. The effectiveness of the proposed method has been validated with an actual case from China Southwest grids. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven distributionally robust chance constrained real-time dispatch (DRCC-RTD) considering renewable generation forecasting errors. The proposed DRCC-RTD model minimizes the expected quadratic cost function and guarantees that the two-sided chance constraints are satisfied for any distribution in the ambiguity set. The Wasserstein-distance-based ambiguity set, which is a family of distributions centered at an empirical distribution, is employed to hedge against data perturbations. By applying the reformulation linearization technique (RLT) to relax the quadratic constraints of the worst-case costs and constructing linear reformulations of the DRCCs, the proposed DRCC-RTD model is cast into a deterministic linear programming (LP) problem, which can be solved efficiently by off-the-shelf solvers. Case studies are carried out on a 6-bus system and the IEEE 118-bus system to validate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Recent climate changes have created intense natural disasters, such as windstorms, which can cause significant damages to power grids. System resilience is defined as the ability of the system to withstand such high-impact low-probability events. This paper proposes a robust resilient operational schedule for active distribution networks against windstorms. In order to capture dynamic behaviors of these disasters, zonal disaster-specific uncertainty sets associated with the windstorm are proposed. Additionally, the unavailability uncertainties of N-K contingencies as well as the forecast uncertainties of load demand, wind power, and solar power are taken into account. Instead of committing micro-turbines and energy storage systems in the first stage (here-and-now) of the decision-making process, the proposed model considers these commitment decisions in the second stage (wait-and-see) of the decision-making process, which is more consistent with the fast response time of these units. Since the second stage of the proposed model has binary decision variables, recent KKT-based and duality-based methods are not applicable. Therefore, a new solution method based on block coordinate descent (BCD) and line search (LS) techniques is proposed to solve the bi-level problem. Eventually, IEEE 33-bus distribution test system is used to illustrate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Topology design is a critical task for the reliability, economic operation, and resilience of distribution systems. This paper proposes a distributionally robust optimization (DRO) model for designing the topology of a new distribution system facing random contingencies (e.g., imposed by natural disasters). The proposed DRO model optimally configures the network topology and integrates distributed generation to effectively meet the loads. Moreover, we take into account the uncertainty of contingency. Using the moment information of distribution line failures, we construct an ambiguity set of the contingency probability distribution, and minimize the expected amount of load shedding with regard to the worst-case distribution within the ambiguity set. As compared with a classical robust optimization model, the DRO model explicitly considers the contingency uncertainty and so provides a less conservative configuration, yielding a better out-of-sample performance. We recast the proposed model to facilitate the column-and-constraint generation algorithm. We demonstrate the out-of-sample performance of the proposed approach in numerical case studies. [ABSTRACT FROM AUTHOR]

Wide-area damping controller (WADC) is a very effective tool to damp out the low-frequency oscillation in wide-area power systems. However, the WADC needs communication networks to transmit remote signals; hence, the network-induced delay and packet dropout are inevitably introduced in the communication of wide-area measurement systems (WAMS). In order to effectively compensate delay and packet dropout, in this paper, a new wide-area dynamic damping controller (WADDC) is designed. Firstl the discrete-time model of power system with random delay, packet dropout, and external disturbance is established. Then, the WADDC based on robust H∞ control is designed and the sufficient condition about stability of the closed-loop system is given. Finally, the controller designed in this paper is tested on the two-area four-machine power system and the 16-machine 68-bus system. Simulation results demonstrate the effectiveness the proposed methods for damping out the low-frequency oscillation and compensating the network-induced delay and packet dropout. [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]

Hybrid state estimation determines the states of systems monitored both by conventional SCADA measurements and PMUs. This paper proposes a decentralization method in order to improve the computational performance of hybrid state estimators with minimum loss of accuracy. The proposed method utilizes sensitivity matrix that relates measurement errors to state estimates in order to form the so-called isolated bus groups and observable subislands. Although the proposed decentralization method can be applied to any state estimator, the paper is developed using a least absolute value (LAV) estimator for demonstration purposes, which is known to be robust against bad data. The high computational burden of LAV estimator compared to the well-known weighted least squares estimator is eliminated, thanks to the proposed decentralization method. [ABSTRACT FROM AUTHOR]

This paper presents a distributionally robust planning model to determine the optimal allocation of wind farms in a multi-area power system, so that the expected energy not served (EENS) is minimized under uncertain wind power and generator forced outages. Unlike conventional stochastic programming approaches that rely on detailed information of the exact probability distribution, the proposed method attempts to minimize the expectation term over a collection of distributions characterized by accessible statistical measures, so it is more practical in cases where the detailed distribution data is unavailable. This planning model is formulated as a two-stage problem, where the wind power capacity allocation decisions are determined in the first stage, before the observation of uncertainty outcomes, and operation decisions are made in the second stage under specific uncertainty realizations. In this paper, the second-stage decisions are approximated by linear decision rule functions, so that the distributionally robust model can be reformulated into a tractable second-order cone programming problem. Case studies based on a five-area system are conducted to demonstrate the effectiveness of the proposed method [ABSTRACT FROM PUBLISHER]

Due to rapid expansions of renewable energy (RE) generations, it becomes more important to assess the feasibility of power system operation under limited controllable resources. Especially, exact evaluation of the system reserve for preserving system security is required under erroneous RE output predictions. This paper proposes a method to evaluate the size of the feasible region of power system operation in control space for the examination of the effective system reserve margin under uncertainties. Predicted RE and demands with their confidence intervals (CIs) are specified to formulate a problem for the evaluation of the size of the worst-case feasible region, where positive size implies feasibility, while negative, infeasibility. The method computes the degree of system security, which is referred to as “Robust Power System Security” in this paper. The problem is formulated as bi-level optimization, which is linearized and transformed into the mixed integer linear programming (MILP) problem. This is a new approach in the treatment of uncertainties. We use DC power flow and linear constrained dynamic economic dispatch problem to demonstrate the effectiveness of the proposed method. The proposed approach is useful in power system planning in analyzing the feasibility of dynamic real-time operation in future circumstance. [ABSTRACT FROM PUBLISHER]

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]

Concerning the stochastic excitation caused by wind power fluctuation and the stochastic parameter of virtual inertia caused by wind speed uncertainty, a power system stability analysis method considering the Wiener noise is proposed in this paper. First, based on the reduced-order model of DFIG retaining virtual inertia control and phase-locked loop (phase-locked loop) dynamics, the analytic function relationship between stochastic parameters and elements in the state matrix is derived using the sensitivity analysis method; thus, the model of interconnected system with stochastic parameters considering the Wiener noise is established. And by constructing the Lyapunov functional containing the model of stochastic parameters, the linear matrix inequality (LMI) that satisfies the robust stochastic stability criterion is derived. Furthermore, by transforming the solving of LMI to a feasibility problem, the stability of system is identified. And then, by calculating online system instability probability under the current operating condition, the probability stability analysis method is proposed. On this basis, a system stochastic stability degree index is defined in this paper, which quantifies the effect of stochastic parameters on system small-signal stability, and could provide more effective information for the safe and stable operation of power system. Simulation tests on the IEEE four-generator two-area system and the New England 10-machine 39-bus system verify that the proposed method could effectively identify the small-signal stability of power system under the joint influence of stochastic parameter and stochastic external excitation, and is applicable to complex system with multiple generators. [ABSTRACT FROM PUBLISHER]

This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox. [ABSTRACT FROM PUBLISHER]

This paper presented a combined scheduling and bidding algorithm for constructing the bidding curve of an electric utility that participated in the day-ahead energy markets. Day-ahead market price uncertainty was modeled using non-probabilistic information gap decision theory (IGDT). The considered utility consisted of generation units and a retailer part; the retailer part of the utility and its demand response program (DRP) could affect the utility's profit, which should be considered in the bidding strategy problem. The bidding strategy algorithm proposed in this paper dispatched units by optimizing the demand response programs of the retailer part. In addition, non-decreasing bidding curve was constructed according to the proposed IGDT-based method. Applicability of the proposed method was demonstrated using an illustrative example with 54 thermal units. Results were verified using after-the-fact actual market data. [ABSTRACT FROM PUBLISHER]

With the increasing penetration of variable renewable generations, independent system operators (ISOs)/regional transmission organizations (RTOs) are faced with new challenges for the secure and economic operation of power systems. This paper proposes an effective approach for deriving robust solutions to the security-constrained unit commitment (SCUC) problem, which considers load and wind uncertainties via interval numbers. Different from most robust optimization-based SCUC approaches in literature which explore robust unit commitment (UC) solutions for immunizing against the worst economic scenario in terms of the highest minimum dispatch cost, the proposed robust SCUC model minimizes operation cost for the base case while guaranteeing that the robust UC and dispatch solutions could be adaptively and securely adjusted in response to uncertain intervals. Thus, the proposed model achieves smaller unit commitment costs while maintaining the solution robustness as compared with literature. In addition, the proposed model describes base case dispatches and corrective actions in uncertain intervals, which is more consistent with the current day-ahead and real-time markets. Furthermore, besides budget constraints used in literature, this paper also considers load and wind variability correlations in constructing uncertain intervals, which would eliminate unlike-to-happen scenarios and further limit the level of conservatism of the robust solution. The proposed robust SCUC model is solved by Benders decomposition, which decomposes the original problem into a master UC problem for the base case and subproblems for the base case network evaluation and the security checking for uncertain intervals. Feasibility cuts are generated and fed back to the master problem for further iterations when violations are identified in subproblems. Numerical case studies on the modified IEEE 118-bus system illustrate the effectiveness of the proposed robust SCUC model for the secure and economic operation of power systems under various uncertainties. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel stochastic adaptive robust optimization (SARO) model for determining the optimal self-scheduling plan for VPP’s participation in the day-ahead energy-reserve market. We consider exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind generation, as well as endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution methodology based on modified Benders dual decomposition is developed to effectively solve the proposed SARO model with both DIUs and DDUs. Case studies are conducted to verify the efficiency and applicability of the proposed approach. Comparative results show that the proposed method can mitigate the conservatism of robust strategy by capturing a satisfactory trade-off between profitability and real-time operation feasibility. [ABSTRACT FROM AUTHOR]

This paper presents an equally constrained robust estimator of both the state and the transformer tap positions of a power system able to withstand all types of outliers, including bad leverage points and erroneous zero-injections. The statistical robustness of the estimator stems from the application of the Schweppe-type Huber GM estimator (SHGM) while its numerical robustness originates from the use of an orthogonal iteratively re-weighted least-squares algorithm together with the Van Loan's method for processing the equality constraints. The good performance of the new estimator, termed EC-SHGM estimator for short, is demonstrated on a small test system and on the Brazilian Southern power system with increasing size ranging from 139 buses to 1916 buses. It is shown that it exhibits superior convergence properties in all tested cases while the WLS method may suffer from numerical instabilities or even divergence problems when large weights are assigned to zero power injections modeling false information. [ABSTRACT FROM PUBLISHER]

This paper proposes a robust optimization approach for optimal operation of microgrids. The uncertain output variation of renewable energy sources (RESs) is addressed by collaboratively scheduling of energy storage (ES) and direct load control (DLC) through a two-stage complementary framework: an hour-ahead charging/discharging of ES and a quarter-hour-ahead activation of DLC. The objective is to maximize the total profit of the microgrid considering operation and maintenance costs of ES units, wind turbines and photovoltaics, and transaction with main grid and customer loads. Assuming the power output of RES randomly varies within a bounded uncertainty set, the problem is modeled to a two-stage robust optimization model and solved by a column-and-constraint generation algorithm. Compared with conventional operation methods, the ES and DLC are coordinated in different time-scales, and RES uncertainties are fully addressed during operation decision-making, ensuring the solutions to be optimal and robust for any realization of uncertainty. The proposed methodology is verified on the IEEE 33-bus distribution system through a wide range of different tests. [ABSTRACT FROM AUTHOR]

This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see, made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust model. [ABSTRACT FROM AUTHOR]

Transmission planning is typically faced with a wide range of uncertainty including growth in demand, renewable energy generation and fuel price. The restructuring of the electric power industry, the drive for energy independence and the push for a cleaner environment have led to additional sources of uncertainty in all aspects of power system operations and planning. The more decentralized decision-making implicates uncertainty in future generation investment and retirement of existing units. Such uncertainties are among the biggest challenges in transmission planning in power systems. However, existing approaches in the literature do not fully address this problem. In this paper, we construct a new robust transmission planning model representing generation investment and retirement uncertainty more realistically to improve the quantification and visualization of uncertainty and the impacts of environmental policies. With this model, we can manage the impacts of uncertainty in the time, the size and the location of candidate generation additions as well as the retirement of units. The corresponding algorithm we develop takes advantage of the structural characteristics of the model so as to obtain a computationally efficient solution methodology. We present an extensive numerical study on the WECC 240-bus system and illustrate the effectiveness of our approach. [ABSTRACT FROM PUBLISHER]

Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is largely due to LP technology's superior reliability and computational efficiency, especially in real-time market applications, security-constrained applications, and extensions involving integer variables, in addition to its ability to readily generate locational marginal prices (LMP) for market applications. In the aim of leveraging the advantages of LP while retaining the accuracy of NLP interior-point methods (IPMs), this paper proposes a sequential linear programming (SLP) approach consisting of a sequence of carefully constructed supporting hyperplanes and halfspaces. The algorithm is numerically demonstrated to converge on 138 test cases with up the 3375 buses to feasible high-quality solutions (i) without AC feasibility restoration (i.e., using LP solvers exclusively), (ii) in computation times generally within the same order of magnitude as those from a state-of-the-art NLP solver, and (iii) with robustness against the choice of starting point. In particular, the (relative) optimality gaps and the mean constraint violations are on average around $10^{-3}$ % and $10^{-7}$ , respectively, under a single parameter setting for all the 138 test cases. To the best of our knowledge, the proposed SLP approach is the first to use LP exclusively to reach feasible and high-quality solutions to the nonconvex AC OPF in a reliable way, which paves the way for system and market operators to keep using their LP solvers but now with the ability to accurately capture transmission losses, price reactive power (Q-LMP), and obtain more accurate LMP. [ABSTRACT FROM AUTHOR]

In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this paper, we propose a novel robust contingency analysis approach based on holomorphic embedding (HE). The HE-based simulator provides theoretical convergence guarantee, which is desirable because it avoids the influence of numerical issues and provides a credible security assessment conclusion. In addition, based on the multi-area characteristics of real-world power systems, a partitioned HE (PHE) method is proposed with an interface-based partitioning of HE formulation. The PHE method does not undermine the numerical robustness of HE and significantly reduces the computation burden in large-scale contingency analysis. The PHE method is further enhanced by parallel or distributed computation to become parallel PHE (P2HE). Tests on a 458-bus system, a synthetic 419-bus system and a large-scale 21 447-bus system demonstrate the advantages of the proposed methods in robustness and efficiency. [ABSTRACT FROM AUTHOR]