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This paper proposes an efficient solution approach based on Benders’ decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders’ approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach. [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]

This paper proposes a novel comprehensive operation and self-healing strategy for a distribution system with both dispatchable and nondispatchable distributed generators (DGs). In the normal operation mode, the control objective of the system is to minimize the operation costs and maximize the revenues. A rolling-horizon optimization method is used to schedule the outputs of dispatchable DGs based on forecasts. In the self-healing mode, the on-outage portion of the distribution system will be optimally sectionalized into networked self-supplied microgrids (MGs) so as to provide reliable power supply to the maximum loads continuously. The outputs of the dispatchable DGs will be rescheduled accordingly too. In order to take into account the uncertainties of DG outputs and load consumptions, we formulate the problems as a stochastic program. A scenario reduction method is applied to achieve a tradeoff between the accuracy of the solution and the computational burden. A modified IEEE 123-node distribution system is used as a test system. The results of case studies demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM PUBLISHER]

Increased penetration of renewable energy leads to increased challenges for the transmission system operators (TSOs) to operate their system in a secure way. Through the limited means available to the TSOs to manage power flows in the system, reliability is jeopardized. Reliability must be managed differently, replacing the current ways of reliability management which fails as uncertainty increases. In this paper, a novel risk-based approach of system operation is proposed that can be helpful for the TSOs to assess the confidence of system operation day-ahead, that is, the probability of the forecasted system to end up in an insecure state is calculated. This paper only focuses on violation of power flow constraints in the system. It also demonstrates the increase of this operation confidence using already installed power flow controlling devices. It is shown that these devices aid in enhancing confidence of system operation by shifting power flows to a more optimal one in the light of generation uncertainty. The main emphasis is laid on preventive action. The proposed approach is demonstrated on test systems. [ABSTRACT FROM PUBLISHER]

This paper proposes a robust control scheme to involve the distributed Battery Energy Storage Systems (BESSs) in Load Frequency Control (LFC) through BESS aggregators with sparse communication networks. In order to cope with the uncertainties associated with system operation, a two-layer Model Predictive Control (MPC) is developed so that more efficient control signals are provided to improve the response of BESSs to make larger contribution to the LFC. The outer layer in the proposed structure produces the command signal for the aggregator based on signals which are produced by the inner layer as well as the signal provided from the actual system. These command signals are provided so as to achieve the least value of error in Area Control Error (ACE) with a minimum control effort taking a variety of operational and physical constraints into consideration. Optimization procedures are also carried out to compute the optimal value of weighting coefficients contained in the objective functions. The capability of controller to cope with uncertainties is compared with a conventional single-layer MPC. In addition, the delay caused by propagation channels in delivering control signals to BESSs is modeled, and its impact on the performance of frequency regulation is evaluated. An intelligent fuzzy coordination control is then developed to coordinate the BESS aggregator and conventional power plants to avoid extra power injection/withdrawal by the conventional power plants in case of long delays. Case studies are conducted to illustrate the effectiveness of the proposed structure in controlling distributed BESSs with diverse energy capacities, rated powers, charging/discharging coefficients and time constants; and State of Charges (SoCs). [ABSTRACT FROM AUTHOR]

The large penetration of renewable energy resources is demanding additional flexibility for the operation of power systems. In this sense, real world applications are proving that wind power units are able to provide part of the required flexibility. Therefore, these new sources of flexibility need to be considered by power system planners in order to make appropriate generation capacity expansion decisions. This paper proposes a generation and storage capacity expansion formulation considering that wind power units are able to participate in the reserve provision service. The proposed model is a stochastic linear program that is solved using a commercial solver. A case study based on the isolated power system of Lanzarote and Fuerteventura in Spain is solved to quantify the impact of considering the reserve provision of wind power in capacity investment decisions. [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]

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]

This paper presents a procedure for the design of a Wide-Area Damping Controller (WADC) towards improving the low-frequency oscillation modes of the power system considering uncertainties in both nominal power system operation condition and time delay on the WADC communication channels. A set of possible operating conditions is linearized around their equilibrium points and used for the construction of the uncertainty model of the system. The lower and upper limits of the time delay are also included in the set. The WADC operation requires remote signals provided by Phasor Measurement Units and highly susceptible to failures or cyber-attacks that may compromise the controller performance. The proposed procedure evaluates in each stage if the resulting controller presents robustness to communication channel permanent failure. Modal analysis and time-domain nonlinear simulations were conducted in the IEEE 68-bus power system. [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]

Voltage stability assessment on a deterministic direction of loading variation may provide misleadingly high values of voltage stability margin due to uncertainties in load forecast. On the other hand, by disregarding loading forecast information and computing the worst case scenario, we may obtain unrealistic and very conservative margin values. This paper proposes a new voltage stability index that takes place between these two approaches. In this proposal, a set of credible loading variation directions is considered and the closest bifurcation point is determined within this set. A fast method for computation of this index is also proposed. The method is able to detect both saddle-node and limit-induced bifurcations. The efficiency of the proposed method is confirmed by means of numerical simulation on different power systems. [ABSTRACT FROM AUTHOR]

The uncertainty has been one of the main obstacles in the operation of distribution systems with renewable energy resources whose power generation is, by nature, highly intermittent, often resulting in the unbalanced conditions of distributed networks. This unbalance degrades voltage profiles and, thus, aggravates power loss consumed in distributed networks. In this sense, the pragmatic coordination scheme between day-ahead and real-time optimization to achieve economic and stable operation is presented in this paper. At the day-ahead optimization stage, the objective aims to minimize operation costs by controlling the energy storage system such as battery systems. This stage is based primarily on historical data about the daily profiles of power demands or renewable distributed generations, so uncertain elements are always inevitable in operational procedures. The real-time monitoring system plays a pivotal role in computing present operating conditions on a real-time basis sufficient to address these uncertainties of renewable energy resources. The operating conditions are, then, utilized to formulate the objective function and relevant constraints to calibrate control orders once decided at the day-ahead optimization stage. This paper explains the proposed coordination scheme with real-time monitoring capability and, then, presents the test results of numerical experiments with a 15-bus test distribution system. [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]

The decision to proceed with a distribution engineering expansion project is often preceded by some form of cost to benefit analysis. The Kaldor–Hicks compensation principle is a criterion that assists in this analysis by the evaluation of net present value over the expected project life. This paper discusses this principle applied to power distribution systems. A probabilistic formulation is proposed to capture uncertainty in cost and benefit data. In effect, the approach models ranges of value of project parameters. While the method does not determine whether to proceed with a given project, it does give a measure of the value of the engineering economic efficiency. The method is especially valuable for cases of “next generation” systems, and this is illustrated in this paper. [ABSTRACT FROM AUTHOR]

The uncertainties of renewable energy may bring impacts to power system reliability. This paper proposes a novel generation rescheduling algorithm, which adjusts generation outputs to mitigate the variations of branch power flows and relieve the overload probability. This algorithm helps prevent power congestion and balance the aggregate renewable generations and loads in power systems. Besides, the paper also proposes a probabilistic method evaluating the system uncertainty issue in the power system considering generation rescheduling operation. The proposed generation rescheduling algorithm has been tested on the Arizona transmission system. The generation rescheduling method enhances power system reliability analysis with a high penetration of renewable energy resources. [ABSTRACT FROM PUBLISHER]

This paper analyzes the benefits of dynamic line rating (DLR) in the system with high penetration of wind generation. A probabilistic forecasting model for the line ratings is incorporated into a two-stage stochastic optimization model. The scheduling model, for the first time, considers the uncertainty associated with wind generation, line ratings, and line outages to co-optimize the energy production and reserve holding levels in the scheduling stage as well as the redispatch actions in the real-time operation stage. Therefore, the benefits of higher utilization of line capacity can be explicitly balanced against the costs of increased holding and utilization of reserve services due to the forecasting error. The computational burden driven by the modeling of multiple sources of uncertainty is tackled by applying an efficient filtering approach. The case studies demonstrate the benefits of the DLR in supporting cost-effective integration of high penetration of wind generation into the existing network. We also highlight the importance of simultaneously considering the multiple sources of uncertainty in understanding the benefits of DLR. Furthermore, this paper analyzes the impact of different operational strategies, the coordination among multiple flexible technologies, and the installed capacity of wind generation on the benefits of DLR. [ABSTRACT FROM PUBLISHER]

In this paper, we model topology control through transmission switching as a recourse action in the day-ahead operation of power systems with large-scale renewable generation resources. We prove that transmission switching could only reduce the linear objective value of direct current optimal power flow when congestion exists. However, we also show, through a simple example, that unit commitment cost could be reduced by transmission switching even in the absence of congestion. To solve the stochastic unit commitment with topology control within reasonable computational time, we proposed a heuristic that first decomposes a practical system into zones and then solves the problem for each zone in parallel. The benefit of topology control recourse is demonstrated on a network representing the Central European System. We compare the costs of the network with different loading and renewable generation conditions. The cost reduction of the test system can reach 3.34% with heavy load and large-scale renewable generation while in a single zone the cost reduction can be above 7%. [ABSTRACT FROM PUBLISHER]

In this paper, we study the optimal location planning of renewable distributed generation (RDG) units by taking into account the random uncertainties of renewable generation and load demand. In presence of the random uncertainties, location planning problem is naturally a two-stage stochastic mixed integer nonlinear programming problem, which is hard to solve efficiently. Instead of using traditional sampling methods or robust optimization methods, we propose a novel analytical approach in this paper to solve the problem efficiently and optimally. In particular, analytical expressions are derived for efficiently evaluating the performance of a candidate RDG placement decision. In this way, the stochastic mixed integer nonlinear programming problem is equivalently transformed into a deterministic integer problem, which can be solved efficiently using off-the-shelf tools. Numerical results show that the optimal RDG placement can save up to $4.2\%$ of the long-term average cost and $80.59\%$ of the line losses on the IEEE 13-bus test feeder. In addition, our proposed approach effectively reduces the computational time by $99.51\%$ on the IEEE 123 node test feeder compared with other traditional sampling-based metaheuristic approaches. [ABSTRACT FROM PUBLISHER]

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]

A basic principle of electricity market design is that cost allocation should follow cost causation as closely as possible. As renewable resources play a larger role in electricity generation, system operators have become increasingly concerned about costs related to variability in net load. While variable generation resources have attracted a great deal of attention along these lines, load is a larger source of variability in most systems. This paper introduces a Shapley value framework to assess the total system cost attributable to electricity market participants that either exacerbate or alleviate net load variability. Furthermore, this paper investigates the extent to which these costs are adequately reflected in wholesale market prices. Numerical tests indicate that the cost of variability on the hourly time scale is in most cases internalized by market-integrated generators and buyers, mitigating concerns that variability imposes a socialized cost from ramping or cycling of thermal generators. [ABSTRACT FROM PUBLISHER]

The uncertain nature of wind power causes difficulties in power system operation scheduling. Probabilistic descriptions of the uncertainty have been studied for decades. However, probabilistic forecasts designed for the regional multiple wind farms are few. Although the traditional methods for the single wind farm can still be used, they have the limitations in capturing the spatial correlations among wind farms, and they are less robust when multivariate observations are not so complete. To improve the forecast quality in this case, we combine the multivariate distribution modeling and probabilistic forecasts in this paper. An advanced model—the regular vine copula, which can describe the wind farms’ dependence structure precisely and flexibly with various bivariate copulas as blocks, is used in this paper. Enough simulation data can be generated from the model, which can be easily used to form the conditional forecast distributions under multiple forecast conditions. A case of 10 wind farms in East China has been used to compare the proposed method with its competitors. The results showed the method's advantages of providing reliable and sharp forecast intervals, especially in the case with limited observations available. [ABSTRACT FROM PUBLISHER]

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 presents a new framework for multistage expansion planning in active power distribution networks, in which the distribution system operator (DSO) considers active network management by clearing the local energy market at the distribution level. The proposed model is formulated as a bi-level optimization problem, where the upper level minimizes the net present value of the total costs imposed to DSO associated with the investment and maintenance of the network assets as well as the network operation, while the lower level on clearing the local energy market captures the participation of distributed energy resource (DER) owners and demand aggregators to maximize the social welfare. The expansion plans consider the investments in DER owners’ assets as well as variety of network assets in which the profitability of DER owners’ investment is guaranteed. The Karush-Kuhn-Tucker optimality conditions and the strong duality theory are employed through which the model is converted to a mixed integer linear programming optimization problem. The implementation of the suggested model on the 24-bus and 86-bus distribution test systems validates its performance and efficacy in making cost-effective planning decisions. [ABSTRACT FROM AUTHOR]

As an efficient tool for uncertainty quantification of renewable energy forecasting, prediction intervals (PIs) provide essential prognosis to power system operator. Merely improving the statistical quality of PIs with respect to calibration and sharpness cannot always contribute to the operational value for specific decision-making issue. In this paper, the cost-oriented prediction intervals are firstly proposed to achieve the joint improvement of forecasting quality and decision performance. In order to bridge the gap between forecasting and decision, a novel cost-oriented machine learning (COML) framework is established, which unifies nonparametric renewable power PI construction and decision-making. Formulated as a bilevel programming model, the COML minimizes the operational costs of decision-making process by adaptively adjusting the quantile proportion pair of PIs resulting from extreme learning machine based quantile regression. The hierarchical optimization model of the COML is equivalently simplified as a single level nonlinear programming problem. Then an enhanced branch-and-contract algorithm with innovative bounds contraction strategy is devised to efficiently capture the optimum of the single level problem with bilinear nonconvexity. Numerical experiments based on actual wind farm data simulate the online forecasting and decision process for wind power offering. Comprehensive comparisons verify the substantial superiority of the proposed COML methodology in terms of forecasting quality, operational value, as well as computational efficiency for practical application. [ABSTRACT FROM AUTHOR]

This paper proposes a machine learning method for the reliability evaluation of integrated power-gas systems (IPGS) under the uncertain component failure probability distributions. The Random Forest (RF) method is designed to select important features to solve the insufficient quantity of data and the curse of dimensionality problems. The Extreme Gradient Boosting (XGBoost) regression algorithm is developed to quantify the relationship between the uncertain parameters and reliability metrics. Moreover, a ten-fold cross-validation method is employed to further improve the accuracy of the regression model. Simulation results on three test systems show that the proposed method can achieve high accuracy for the reliability evaluation. [ABSTRACT FROM AUTHOR]

Distribution systems are becoming more active and provide more power support for transmission systems via their connection points at the transmission-distribution (T-D) interfaces. This paper proposes a chance constrained optimization model to estimate the flexibility area at a T-D interface. In this model, network flexibility is for the first time involved and facilitated by introducing power flow routers (PFRs) into the distribution system. The chance-constrained flexibility area (CCFA) given by the proposed model provides a description of the aggregated power dispatchability of distribution system with the guarantee of low risks of voltage violations under renewable uncertainties. We exploit the mechanism of network flexibility and reveal that it significantly reduces the voltage standard deviations, which cannot be achieved by node power flexibility. To evaluate the CCFA, an efficient two-layer iteration algorithm is designed. The inner layer finds the boundary point of CCFA along a given direction for active and reactive power. The outer layer determines those key directions to be included in the estimation as the corresponding points capture the features of the CCFA boundary. Case studies show that PFRs significantly enlarge the CCFA, which reveals that network flexibility is an important supplement to node power flexibility in T-D interaction. [ABSTRACT FROM AUTHOR]

The paper presents a methodology for estimation of dynamic response of aggregate load at distribution network buses by taking into account daily variation in demand composition and generic dynamic responses of different types of load. Dynamic load models for different load categories obtained from field or laboratory measurements or through appropriate mathematical modeling are used in combination with hourly load composition at the given bus. The load composition is derived based on past demand surveys, and daily loading curves for different classes of customers. Uncertainties in both dynamic load models/responses of individual loads and load compositions at different times of the day are modeled probabilistically. With established dynamic signatures of different load categories and load compositions at different times of the day, Monte Carlo simulations are used to estimate probabilistic real and reactive power responses, including ranges of variation of these responses, for every hour of the day for a given or anticipated mix of demand. [ABSTRACT FROM PUBLISHER]

Time varying prices by motivating customers to reduce their consumption in peak periods propel the electricity industry towards a higher efficiency compared to that of common flat prices. Focusing on time-of-use (TOU) sale prices, this paper establishes a stochastic model for the medium-term decision making problem faced by a distribution company (DisCo). The developed model deals with the DisCo's decisions on the level of involvement in forward contracts and in the pool as well as the sale prices offered to customers. The demand response to TOU prices is captured using a price elasticity matrix (PEM). The objective is to maximize the DisCo's profit while the exposure risk imposed by uncertainties is limited to a given level. The model is formulated as a mixed integer linear programming (MILP) problem that can be effectively solved via commercial software packages. A typical Finnish 20-kV urban distribution network is used to demonstrate the effectiveness of the developed model. [ABSTRACT FROM PUBLISHER]

Integrating wind power into power systems contributes to existing variability in system operations. Current methods to mitigate this variability and uncertainty focus on using conventional generator ramping capability. There is also the option of using wind power itself to mitigate the variability and uncertainty that it introduces into the system. This paper introduces the concept of a flexible dispatch margin as a means for wind to participate in mitigating net variability and net uncertainty. In providing a flexible dispatch margin, wind generators under-schedule in the hour-ahead energy market in order to have additional expected flexibility available for the real-time market. The implementation of the flexible dispatch margin is analyzed in a two-stage optimization model with recourse to the flexible dispatch margin, flexible demand and generator ramping. This modeling framework combines Monte Carlo simulations with AC OPF analysis, using the IEEE 39-bus test system. Results show that use of the flexible dispatch margin decreases the reliance on peaking generators to mitigate net variability and uncertainty, and also decreases the frequency of price spike events, particularly as wind penetration increases from 10% to 30%. The analysis emphasizes the importance of increasing flexible resource capability as power system variability and uncertainty increase. [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]

Uncertainty in consumption is a key challenge at energy utility companies, which are faced with balancing highly stochastic demand with increasingly volatile supply characterized by significant penetration rates of intermittent renewable sources. This paper proposes a methodology to quantify uncertainty in consumption that highlights the dependence of the cost-of-service with volatility in demand. We use a large and rich dataset of consumption time series to provide evidence that there is a substantial degree of high-level structure in the statistics of consumption across users which may be partially explained by certain characteristics of the users. To uncover this structure, we propose a new technique for extracting typical statistical signatures of consumption—energy demand distributions (EDDs)—that is based on clustering distributions using a fast, approximated algorithm. We next study the factors influencing the choice of consumption signature and identify certain types of appliances and behaviors related to appliance operation that are most predictive. Finally, we comment on how structure in consumption statistics may be used to target residential energy efficiency programs to achieve greatest impact in curtailing cost of service. [ABSTRACT FROM AUTHOR]

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]

This paper presents comparative analysis of the performance of three efficient estimation methods when applied to the probabilistic assessment of small-disturbance stability of uncertain power systems. The presence of uncertainty in system operating conditions and parameters results in variations in the damping of critical modes and makes probabilistic assessment of system stability necessary. The conventional Monte Carlo (MC) approach, typically applied in such cases, becomes very computationally demanding for very large power systems with numerous uncertain parameters. Three different efficient estimation techniques are therefore compared in this paper—point estimation methods, an analytical cumulant-based approach, and the probabilistic collocation method—to assess their feasibility for use with probabilistic small disturbance stability analysis of large uncertain power systems. All techniques are compared with each other and with a traditional numerical MC approach, and their performance illustrated on a multi-area meshed power system. [ABSTRACT FROM PUBLISHER]

Real-Time Thermal Rating (RTTR) is a smart-grid technology that allows electrical conductors to operate at an enhanced rating based on local weather conditions. RTTR also provides thermal visibility of the network, making system operators aware if the actual rating drops below the static seasonal rating. This paper investigates how using these enhanced variable ratings affects power network reliability. A methodology has been developed to assess network reliability with variable conductor ratings. The effect of failures and uncertainties in the RTTR system are also considered, and the effect of the correlation between conductor ratings due to common weather conditions is built into the model. State sampling and sequential Monte Carlo simulations are used to estimate the reliability of the RBTS 6-bus test network. At low loading levels, the RTTR appears to reduce network reliability but actually illustrates occasions when the existing ratings are being unknowingly infringed. For higher loading, the network reliability is significantly improved by the use of RTTR, with reductions in loss of load expectation of up to 67%. [ABSTRACT FROM PUBLISHER]

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]

In this paper, a modified frequency control model is proposed, where the demand response (DR) control loop is added to the traditional load frequency control (LFC) model to improve the frequency regulation of the power system. One of the main obstacles for using DR in the frequency regulation is communication delay which exists in transferring data from control center to appliances. To overcome this issue, an adaptive delay compensator (ADC) is used in order to compensate the communication delay in the control loop. In this regard, a weighted combination of several vertex compensators, whose weights are updated according to the measured delay, is employed. Generating the phase lead is the most important strategy for these compensators to eliminate the impact of communication delay. Moreover, to overcome the impact of disturbances and uncertainties in power system, an active disturbance rejection control (ADRC) is utilized as the load frequency controller. Being used instead of a PI controller, this robust controller employs an extended state observer to estimate the disturbances and uncertainties and uses a feedback controller to compensate them. The confined iterative rational Krylov algorithm (CIRKA) is employed to reduce the order of the detailed IEEE 39-bus test system model meticulously and facilitate the controller process design. Therefore, a DR control loop, ADC, and ADRC are employed in the LFC to regulate the frequency of the power system in a more efficient way. The simulation results confirm the effectiveness and robustness of the frequency control in presence of communication delay and model uncertainties. [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]

Renewable energy will become a normal energy source and will be required to participate in the market. The renewable portfolio standards (RPS) together with tradable green certificates (TGC) are considered as an appropriate market mechanism to help recover renewable energy investments. The strategic offering behaviors of renewable energy should be carefully studied, especially with the introduction of TGC. This paper proposed a market equilibrium model with joint consideration on energy and TGC. The model includes two-stages of day-ahead and real-time analysis, to formulate the complex decision processes of strategic renewable energy. The model is built in a bilevel format, with multiple-scenario settings to consider the uncertainty of renewable power output within a day. Then, the bilevel model is reformulated as a single-level nonlinear problem based on KKT theorems. Then, the nonlinearities are linearized based on the strong duality theorem and a binary expansion method. The model has been finally transformed as a mix integer linear problem. Finally, an illustrative example is proposed to analyze the strategic offering behaviors of renewable energy under various market situations. [ABSTRACT FROM AUTHOR]

Successful trading in electricity markets relies on the market actor's ability to accurately forecast the electricity price. The fundamental electricity price models use market information, provided by various price drivers, including the residual that contains a risk premium. In the past, researchers investigating risk premium focused primarily on daily spot price levels, ignoring the intraday information hindering the accurate risk premium determination. This paper presents a new KGB Method for modelling of risk premium, based on “ex-ante” approach focused on a yearly product. The method involves a novel KGB Model and its linearized formulation, the KGB Linear Model, which enables capturing the influence of renewable energy sources on risk premium. The four key drivers of the KGB Linear Model were used providing an insight into the influence of RES generation on risk premium evolution. The method was tested on historical data from the German electricity market. The results for the 2010–2014 period reveal overall influence of PV production share on risk premium is greater than that of wind production share, both increasing the risk premium due to their variability and uncertainty. Using the KGB Method, market actors can forecast risk premium using information readily available to them. [ABSTRACT FROM AUTHOR]

This paper presents a new computational attractive interval power flow (PF) approach with correlated uncertain power injections while maintaining high estimation accuracy. The key idea is to integrate the ellipsoid convex model with the evidence theory. This allows us to effectively account for uncertain power injection correlations and eliminate irrelevant focal elements, yielding significantly improved computational efficiency. Extensive comparisons with other approaches demonstrate its effectiveness under various conditions. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal allocation of the electric spring (ES) smart load device in radial distribution systems for voltage regulation. An ES can transform a connected noncritical load into a smart load providing voltage support and voltage suppression functions. A risk-limiting ES planning method is proposed to obtain the optimal ES configuration (number, locations, capacities, and types) to mitigate the voltage violations caused by uncertainties in renewable distributed generation. The forecasting uncertainties are placed into multi-state discrete levels to reduce scenario numbers. The voltage regulation capability of different types of ES are quantified and compared to determine the optimal allocation model. The optimal ES installation plan is identified as per the minimal total cost and lowest voltage violation risk. The proposed optimal allocation method is validated on a modified IEEE 15-bus distribution network. [ABSTRACT FROM AUTHOR]

This paper has three unique contributions: the proposal of a new security taxonomy not previously seen in the literature; the presentation of a novel and successful approach (see) to solve an important problem encompassing two conflicting security objectives, using an efficient multi-objective Pareto optimization technique; and the proposal and application (see) of two original and very powerful probabilistic security indexes (apparent stability index and probability of instability), which render a sound solution to the consideration of uncertainties in dynamic security problems. All results are obtained based on a detailed representation of the system dynamic behavior. [ABSTRACT FROM AUTHOR]

Constant power loads (CPLs) impose instability issues in DC microgrids due to their negative impedance characteristics. This paper studies the problem of voltage control design of DC microgrids with CPLs. It is assumed that the power of CPLs is uncertain and belongs to a given interval leading to an infinite number of equilibrium points of the system. We develop a polytope model for DC microgrids with uncertain CPLs. Using this model, a robust two-degree-of-freedom feedback-feedforward voltage control framework is then proposed. The voltage controller is obtained by a solution of a set of linear matrix inequalities. The voltage control design strategy for each distributed generation (DG) unit is scalable and independent of the other DGs. The effectiveness of the proposed control approach is evaluated through simulation studies in MATLAB/SimPowerSystems toolbox. [ABSTRACT FROM AUTHOR]

Distribution system state estimation, which provides critical information for system monitoring and control, is being challenged by multiple sources of uncertainties such as random meter errors, stochastic power output of distributed generation (DG), and imprecise network parameters. This paper originally proposes a general interval state estimation (ISE) model to simultaneously formulate these uncertainties in unbalanced distribution systems by interval arithmetic. Moreover, this model can accommodate partially available measurements of DG outputs and inaccurate line parameters. Furthermore, a modified Krawczyk-operator algorithm is proposed to solve the general ISE model efficiently, and effectively provides the upper and lower bounds of state variables under coordinated impacts of these uncertainties. The proposed algorithm is tested on unbalanced IEEE 13-bus and 123-bus systems. Comparison with various methods including Monte Carlo simulation indicates that the proposed algorithm is many orders of magnitude faster and encloses tighter boundaries of state variables. [ABSTRACT FROM AUTHOR]