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This paper presents a mathematical analysis of how wind generation impacts the slow coherency property of power systems. Slow coherency arises from time-scale separation in the dynamics of synchronous generators, where generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time-scale due to weaker coupling. This time-scale separation is reflected in the form of a spectral separation in the weighted Laplacian matrix describing the swing dynamics of the generators. However, when wind farms with doubly-fed induction generators (DFIG) are integrated into the system then this Laplacian matrix changes based on both the level of wind penetration and the location of the wind farms. The modified Laplacian changes the effective slow eigenspace of the generators. Depending on the penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and propose an equivalent Laplacian matrix to compute the modified coherent areas. Results are validated using the IEEE 68-bus test system with one and multiple wind farms. The model-based slow coherency results are compared with measurement-based principal component analysis to substantiate our derivations. [ABSTRACT FROM AUTHOR]

The flexibility of power systems to manage variability and uncertainties is becoming increasingly important as the penetration of variable renewable energy continues to raise. Synergies from all parts of the existing system and new flexibility providers are required to balance demand and supply. However, because of fundamental limitations, existing test systems cannot fully support detailed and realistic studies. To fill this gap, this paper presents a 213-bus benchmark, called the FTS-213 system, dedicated for power system flexibility studies. This system has more than 38% of VRE penetration and includes real data at 15 minutes and 1 minute resolutions. The resources considered in the system cover all aspects of the generation, network, demand, energy storage and market. Specifically, to capture the intrinsic relationship between flexibility and renewable energy accommodation, the system contains integration grids, regional transmission grids and inter-regional tie lines. These assets reflect the full stack of utility-scale integration, transmission and consumption within and among regions. They cover multiple voltage levels, from 110 to 750 kV AC and $\pm$ 400 to $\pm$ 800 kV DC. The impacts of and the interactions between these flexibility factors are analyzed and three sets of planning results are provided. [ABSTRACT FROM AUTHOR]

We examine the behavior of a strategic firm that invests-in and operates wind, energy storage, and transmission. The capacity of the energy storage and transmission are co-optimized with the firm's wind-supply and energy-storage offers into a centrally dispatched electricity market. We employ a bi-level stochastic optimization model. The upper level determines the capacities and offering strategies to maximize the firm's expected profits. Multiple lower-level problems represent market clearing under different operating conditions, which capture uncertainties. The resulting large-scale optimization model is solved using multi-cut Benders's decomposition. The model is applied to a case study that is based on Alberta's electricity market. [ABSTRACT FROM AUTHOR]

In this paper, three single-stage stochastic programs are proposed and compared for optimal dispatch by a System Operator (SO) into balancing markets (BM).The motivation for the models is to represent a possible requirement to undertake system balancing with increasing amounts of intermittent renewable generation. The proposed optimization models are reformulated as tractable Mixed Integer Linear Programs (MILPs) and these consider both fuel cost and intermittency cost of the generators, when the SO activates the up- or down-regulation bids. These three models are based on the main approaches seen in practice: dual-imbalance pricing, single imbalance pricing and single imbalance pricing with spot reversion. A scenario-generation algorithm based on predictive conditional dynamic density distributions is also proposed. We perform a comparative analysis of these three proposed models in terms of how they help the SO to optimize their balancing market actions considering intermittent-renewable generators. The single imbalance pricing is found to be the most market efficient. [ABSTRACT FROM AUTHOR]

A novel concurrent control scheme of optimal re/active power regulation in a wind farm is proposed in this letter, of which the objective is to minimize the detrimental shortfall of active power during low-voltage-fault events. Distinguished from the existing works, the proposed control scheme incorporates an efficient optimization module into the wind turbine controllers. Specifically, it features the merit that the practical feasibility of tracking the resultant references can be ensured via considering multiple constraints in presence of complex wake interactions. Case studies on a permanent-magnet-synchronous-generator based wind farm built in a joint DIgSILENT-MATLAB platform are carried out to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Chance-constrained program (CCP) is a popular stochastic optimization method in power system planning, and operation problems. Conditional Value-at-Risk (CVaR) provides a convex approximation for chance constraints which are nonconvex. Although CCP assumes an exact empirical distribution, and the optimum of a stochastic programming model is thought to be sensitive in the designated probability distribution, this letter discloses that CVaR reformulation of a chance constraint is intrinsically robust. A pair of indices are proposed to quantify the maximum tolerable perturbation of the probability distribution, and can be computed from a computationally-cheap dichotomy search. An example on the coordinated capacity optimization of energy storage, and transmission line for a remote wind farm validates the main claims. The above results demonstrate that stochastic optimization methods are not necessarily vulnerable to distributional uncertainty, and justify the positive effect of the conservatism brought by the CVaR reformulation. [ABSTRACT FROM AUTHOR]

The legacy Optimal Power Flow (OPF) dispatch in electric power grids with high proliferation of renewables can be at risk due to the lack of awareness on major uncertainties, and sudden changes in renewable outputs. This may, in turn, result in conditions where transmission line power flows are significantly exceeded, and subsequent automatic protective actions take place. This letter presents a new generalized joint chance-constrained model for the OPF problem that effectively captures the stochasticity in renewable power generation in the system. In dealing with the complexity, and non-convexity of the proposed optimization model with probabilistic guarantees, we propose a novel tractable Boolean method to transform the model into an equivalent deterministic mixed-integer linear problem, which can be solved quickly, and efficiently by off-the-shelf solvers. Numerical results verify the effectiveness of the proposed model, and the suggested Boolean methodology. [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]

In power systems with high penetration of renewable energy resources, uncertainty and variability of these stochastic resources introduce additional challenges for the operation of power systems. To improve the power system's reliability in the face of uncertainty, reserves are required as additional generation capacity to rebalance the power system following random disturbances. However, reserve deliverability is not guaranteed, because it may encounter potential transmission line congestion. Zonal reserve requirements can address this issue, but operators lack efficient ways to allocate reserves to zones while accounting for wind power forecast uncertainty. We propose a methodology for probabilistic zonal reserve requirements to address wind power forecast uncertainties. This method estimates the probability distribution of line flows based on the system generation margin and injection shift factor. This estimate is then used to construct pre-defined and post-zonal reserve requirements. Case studies demonstrate that the proposed method efficiently schedules energy and reserves to balance energy and manage deliverability with wind power forecast uncertainty. We also discuss operational implications of the proposed method. [ABSTRACT FROM AUTHOR]

Confronted with considerable intermittence and variability of wind power, prediction intervals (PIs) serve as a crucial tool to assist power system decision-making under uncertainties. Conventional PIs rely on predetermining the lower and upper quantile proportions and therefore suffer from conservative interval width. This paper innovatively develops a chance constrained extreme learning machine (CCELM) model to generate quality nonparametric proportion-free PIs of wind power generation, which minimizes the expected interval width subject to the PI coverage probability constraint. Due to the independency on the preset PI bounds proportions, the proposed CCELM model merits high adaptivity and taps the latent potentialities for PI shortening. The convexity of extreme learning machine renders the sample average approximation counterpart of stochastic CCELM model equivalent to a parameter searching task in parametric optimization problem with polyhedral feasible region. A novel difference of convex functions optimization based bisection search (DCBS) algorithm is proposed to efficiently construct the CCELM model, which successfully realizes machine learning by means of solving linear programming problems sequentially. Comprehensive numerical experiments based on actual wind farm data demonstrate the significant effectiveness and efficiency of the developed CCELM model and DCBS algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model that incorporates dynamics and controls of both synchronous generators and grid-forming inverters. These constraints are then included into a stochastic UC formulation that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. This method is shown to be generally more accurate and computationally more efficient for medium-sized networks than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response. [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]

The integration of full converter-based wind power generation (FCWG, e.g., permanent magnet synchronous generator (PMSG)) not only introduces the PMSG oscillation modes (POMs) but also might excite severe resonances with electromechanical oscillation modes (EOMs) of the power system. In this paper, a two-open-loop-subsystem dynamic model is firstly established to investigate the interactions between the PMSG and the rest of the power system. On this basis, a modal shift evaluation (MSE) method by using bilateral damping torque analysis is proposed to accurately quantify the interaction effect of POMs and EOMs on each other and effectively explain their complex interaction process. Then two important concepts, i.e., modal shift sensitivity (MSS) with respect to various PMSG controller parameters and resonance excitation index (REI) according to a per unit open-loop modal distance indicating the intensity of modal interactions, are derived to dig the essential modal resonance mechanisms. Furthermore, by using MSS and REI as two tools, the modal interaction optimization (MIO) is conducted through POM tuning in order to prevent potential system modal resonance and enhance resonance mode damping for the first time. The optimized modal interaction is validated to be beneficial and effective for the improvement of power system resonance stability. [ABSTRACT FROM AUTHOR]

Inspired from recent insights into the common ground of machine learning, optimization and decision-making, this paper proposes an easy-to-implement, but effective procedure to enhance both the quality of renewable energy forecasts and the competitive edge of renewable energy producers in electricity markets with a dual-price settlement of imbalances. The quality and economic gains brought by the proposed procedure essentially stem from the utilization of valuable predictors (also known as features) in a data-driven newsvendor model that renders a computationally inexpensive linear program. We illustrate the proposed procedure and numerically assess its benefits on a realistic case study that considers the aggregate wind power production in the Danish DK1 bidding zone as the variable to be predicted and traded. Within this context, our procedure leverages, among others, spatial information in the form of wind power forecasts issued by transmission system operators (TSO) in surrounding bidding zones and publicly available in online platforms. We show that our method is able to improve the quality of the wind power forecast issued by the Danish TSO by several percentage points (when measured in terms of the mean absolute or the root mean square error) and to significantly reduce the balancing costs incurred by the wind power producer. [ABSTRACT FROM AUTHOR]

This paper proposes a new coordinated method for preventive generation rescheduling and corrective load shedding to maintain power system transient stability under uncertain wind power variation. A two-step bi-level optimization model is proposed where generation rescheduling and load shedding are coordinated by a risk coordination parameter, which adjusts the total coordination cost in the upper level. Then, based on Extended Equal Area Criterion (EEAC) and trajectory sensitivities, the non-linear risk and stability constraints are converted into the linear form for generation rescheduling cost and load shedding cost optimization in the lower level, respectively. Uncertain wind power output is modeled as a small number of robust test scenarios. Finally, the golden section search is applied to solve the bi-level problem. The proposed method is validated on the New-England 39-bus system by using commercial grade software. The computational efficiency, economic optimality, and stability robustness under random wind power of the method are demonstrated. [ABSTRACT FROM AUTHOR]

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

Unsteady motion of the atmosphere incurs nonlinear and spatiotemporally coupled uncertainties in the wind power prediction (WPP) of multiple wind farms. This brings both opportunities and challenges to wind power probabilistic forecasting (WPPF) of a wind farm cluster or region, particularly when wind power is highly penetrated within the power system. This paper proposes an Improved Deep Mixture Density Network (IDMDN) for short-term WPPF of multiple wind farms and the entire region. In this respect, a deep multi-to-multi (m2m) mapping Neural Network model, which adopts the beta kernel as the mixture component to avoid the density leakage problem, is established to produce probabilistic forecasts in an end-to-end manner. A novel modified activation function and several general training procedures are then introduced to overcome the unstable behavior and NaN (Not a Number) loss issues of the beta kernel function. Verification of IDMDN is based on an open-source dataset collected from seven wind farms, and comparison results show that the proposed model improves the WPPF performance at both wind farm and regional levels. Furthermore, a laconic and accurate probabilistic expression of predicted power at each time step is produced by the proposed model. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic coordination control strategy to enhance the reactive power capability of wind power plants (WPPs) which deploy doubly-fed induction generator-based wind turbines (DFIG-WTs). The proposed control architecture seeks to maximize reactive power availability during grid faults without violating the stable and thermal operational limits of the generator. To achieve this objective, the presented control topology calculates the maximum available reactive power that can be provided by the DFIG-based WPP under any disturbed operation of a power system. The reference value of the required reactive power compensation is thereafter calculated using an adaptive proportional-integral (PI) regulator which outperforms the traditional PI controller. The computed reference value is directly applied to the outer control of the rotor side converter (RSC) to regulate reactive power generation of the stator circuit. Furthermore, the $P-V$ droop characteristics of the induction generator is employed to adjust the active power reference of the RSC converter to increase the reactive power capability during grid faults. Meanwhile, de-rating the active power generation of the DFIG-based WT is accompanied with modifying the pitch angle of the rotor blades to balance the mechanical and electromagnetic torques and to avoid any stresses excreted on the mechanical parts of the WT. If rotor current limits are reached and more reactive power support is still required, the responsible control loop of the grid side converter (GSC) will be activated and augmented to enhance the overall reactive power capability of the DFIG-based WPP. Finally, the proposed control strategy is verified using Two area four machines and IEEE 68 bus test systems. [ABSTRACT FROM AUTHOR]

The construction of the uncertainty set is a key aspect of robust unit commitment (RUC) for the power systems with wind power integrated. The existing uncertainty sets based on the convex hull of historical data are limited to the specific shape of the historical data set or with high computational burden. In this letter, we propose the partition-combine method to build the minimal uncertainty set with the irregularly-distributed historical data. The partition of the box set is used to reduce the size of the uncertainty so that the set can properly adapt the data provided and is no longer limited to a specific shape. The combination of non-empty subsets is used to formulate the model of uncertainty set instead of the extreme points. The scale of uncertainty variables is reduced with quick identification of inner subsets which contain no extreme points. The simulation results validated the enhanced performances of the proposed method from both the conservativeness and computational burden perspectives. [ABSTRACT FROM AUTHOR]

This paper proposes a novel control approach to reduce the rated power of energy storage system (ESS) in the smoothing of wind power output. Wind power generation causes frequency fluctuations in power systems. Therefore, ESSs are used to absorb the fluctuating power of wind generators. Generally, the controller in an ESS is composed of a first-order low-pass filter (FLF) with a large time constant. However, the FLF incurs a high cost because its phase-lag induces an unnecessary increase in the rated power of ESS. This study addresses the reduction in the rated power of ESS without using a complex controller. First, the requirement of the controller is analyzed and its structure is proposed. Then, the absorption of the short-period wind power output is reduced by tuning a gain in the controller until the grid code is violated. The effectiveness of the proposed controller is verified by comparing it to the conventional controllers via scenario simulations using real wind data. [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]

Currently, the increasing wind power penetration, with consequent randomness and variability, presents great challenges to power system planning and operation. Probabilistic power flow (PPF) has been developed to calculate the power flow under uncertain circumstances. However, the current wind power models are subject to specific probability distributions, limiting their accuracies in wider applications. Additionally, the cumulant method (CM)-based PPF, if nonlinear relationship is considered in, would face an impractically high computational complexity. To address these problems in modeling and cumulant calculation, this article proposes a novel generalized density/distribution fitting method (GDFM) combining with the Copula function to establish a joint probability model for wind power generation. A special impulse- mixed probability density (IMPD) integration method is also introduced to derive the input cumulants from the model. Finally, a fast cumulant method (FCM) is proposed to reduce the computational burden of output cumulant calculation while retaining a high accuracy in a nonlinear context. Case study on the IEEE-118 test system validates the effectiveness of the proposed methods, and a real application to a provincial power grid in China provides some useful power flow risk information for decision making. The whole FCM-based PPF scheme can be helpful for future power flow examination in power system planning and operation. [ABSTRACT FROM AUTHOR]

Flexible ramping products (FRPs) have been implemented by several independent system operators (ISOs) to procure adequate flexible resources. Currently, system operators estimate the system level ramping requirements ignoring the spatiotemporal correlations among various uncertainty sources. This leads to overestimates/underestimates of ramping requirements. In addition, the explicit FRPs model considers only the generation ramping limitation. Other security constraints, such as the transmission limits, are not considered, which leads to deliverability issues of FRPs. To deal with these shortcomings of current FRPs models, this paper proposes a deliverable FRPs based on a distributionally-robust chance constrained multi-interval optimal power flow (DRCC-MIOPF) considering the spatiotemporal correlation of wind power and demand uncertainties endogenously. Furthermore, an asymmetrical affine policy (AAP) is proposed to leverage generation flexibility and mitigate the uncertainty in different directions. The pricing mechanism of the FRPs is proposed using a novel uncertainty-contained locational marginal price (U_LMP) which is derived from the proposed AAP-DRCC-MIOPF model. New components representing the price of FRPs are added into the traditional LMP formulation. Finally, the PJM 5-bus, IEEE 39-bus and IEEE 118-bus systems case studies validate the proposed FRPs approach. The payment of uncertain demand and wind power on FRPs are analyzed. [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]

The increasing integration of renewable resources in electricity markets has increased the need for producers to correct their trading position close to real time in order to avoid volatile real-time prices. The closest option to delivery time in European markets is to trade in the continuous intraday market. This market is therefore an attractive trading outlet for assets that target at extracting value from their flexibility. Trading in this market is challenging due to the multistage nature of the problem, its high uncertainty and the fact that decisions need to be reached rapidly, in order to lock in profitable trades. We model the trading problem of a storage unit in the Markov Decision Process framework. We present an approach based on policy function approximation for tackling the problem. We provide relevant parameters for defining our policy, and demonstrate the effectiveness of our approach by comparing it to the rolling intrinsic policy on real historical data. Our proposed approach outperforms the rolling intrinsic policy, which is commonly employed in practice for storage units, by increasing profitability by $\text{17.8}\%$ on out-of-sample testing for a storage with perfect round-trip efficiency and by $\text{13.6}\%$ for a storage unit with a round-trip efficiency of $\text{81}\%$. [ABSTRACT FROM AUTHOR]

This paper presents a derivation of the small-signal stability limit of a grid-connected wind farm with M permanent magnet synchronous generators (PMSGs) as determined by the dynamics of phased locked loops (PLLs). The stability limit reveals the mechanism whereby the PLLs can destabilize the wind farm in the case of a weak grid connection. Computation of the derived stability limit is simple and obviates the need to establish a parametric model of the wind farm. The stability limit can approximately indicate the potential instability risk collectively posed by the PLLs in the wind farm. Case studies are presented to evaluate the analytical conclusions obtained and the derived small-signal stability limit. Application of the stability limit during the planning and operating stages of a grid-connected wind farm is also demonstrated. Various factors that can affect the stability of the wind farm, and that must be considered during planning and operation, are examined and useful conclusions are obtained. These factors include the length of the transmission line connecting the wind farm to the AC grid, the topology of the wind farm, the wind speed, and its distribution over the wind farm, as well as the parameters of the PLLs. [ABSTRACT FROM AUTHOR]

The rapid expansion of wind power has triggered significant wind curtailment because the power system lacks flexibility to deal with the uncertainty and variability of wind power. The operational flexibility of coal-fired power plants is limited by the minimum stable firing rate in the boiler. Steam extraction and thermal energy storage could enable power output adjustment without changing the firing rate in the boiler. Thus, retrofitting existing coal-fired power plants with steam extraction and thermal energy storage is a promising option to accommodate the high penetration of wind power in the power system, especially in coal-dominated power system. This study investigated the operational flexibility of coal-fired power plants retrofitted with steam extraction and thermal energy storage. First, a linear operation model is proposed for retrofitted coal-fired power plants considering new characteristics and technical constraints. Second, a simulation framework based on stochastic unit commitment and rolling economic dispatch is developed to explore the benefits of steam extraction and thermal energy storage in wind-integrated power systems. The forecasted wind power data is used in stochastic unit commitment to evaluate start-up and shut-down cost, while real wind power data is adopted in rolling economic dispatch to calculate the actual production cost. The simulation results on the modified IEEE 24-bus system demonstrate the effectiveness of retrofitting coal-fired power plants with steam extraction and thermal energy storage for mitigating wind curtailment. [ABSTRACT FROM AUTHOR]

This paper develops models for hurricane exposure, fragility curve-based damage to electrical transmission grid components and power generating stations using Monte-Carlo simulation, and restoration cost to predict resiliency factors including power generation capacity lost and the restoration cost for electrical transmission grid and power generation system damages. Synthetic grid data are used to model the Energy Reliability Council of Texas (ERCOT) electrical grid. A case study is developed based on Hurricane Harvey. This work is extended to evaluate the changes to resiliency as the percentage of renewable sources is increased from 2017 levels to levels corresponding to the NREL Futures Study 2050 Texas scenarios for 50% and 80% renewable energy. [ABSTRACT FROM AUTHOR]

Power systems with high penetration of wind resources must cope with significant uncertainties originated from wind power prediction error. This uncertainty might lead to wind power curtailment and load shedding events in the system as a big challenge. Efficient modeling and incorporation of wind power uncertainty in generation and reserve scheduling can prevent these events. This paper presents a new framework for wind power cumulative distribution function (CDF) modeling and its incorporation in a new chance-constrained economic dispatch (CCED) problem. The proposed CDF modeling uses few moments of wind power random samples. To validly capture the actual features of the wind power distribution such as main mass, high skewness, tails, and especially boundaries from the moments, an efficient moment problem is presented and solved using the beta kernel density representation (BKDR) technique. Importantly, a new polynomial cost function for efficient modeling of wind power misestimation costs is proposed for the CCED problem that eliminates the need for an analytical CDF and enables the use of an accurate piecewise linearization technique. Using this technique, the non-linear CCED problem is converted to a mixed-integer linear programming (MILP)-based problem that is convex with respect to the continuous variables of the problem. Therefore, it is solved via off-the-shelf mathematical programming solvers to reach more optimal results. Numerical simulations using the IEEE 118-bus test system show that compared with conventional approaches, the proposed MILP-based model leads to lower power system total cost, and thereby is suggested for practical applications. [ABSTRACT FROM AUTHOR]

The high penetration of renewable energy will substantially change the power system operation. Traditionally, the annual operation of a power system can be represented by some typical operation modes and acts as the basis for the power-system-related analysis. The introduction of highly penetrated renewable energy will make the power system operation mode highly diversified and variable. These modes may not follow traditional empirical patterns. In this paper, we propose a data-driven method based on high-dimensional power system operation data (including power flow, unit generation, and load demand) to identify the pattern of the operation modes and analyze the impact of high renewable penetration. Specifically, the proposed data-driven method is composed of simulation, preprocessing, clustering, dimension reduction, and visualization with the aim to provide an intuitive understanding of the operation mode variety under high renewable penetration. In addition, several indices are introduced to quantify the space dispersion, time variation, and seasonal consistency of operation modes. A case study on actual Qinghai provincial power system in China validates the effectiveness of the proposed data-driven method and indicates that the dispersion and time variation of operation mode will significantly increase in the beginning and then saturate with the increase in renewable penetration level. The operation mode is also less correlated with seasons in renewable energy dominated power system. [ABSTRACT FROM AUTHOR]

In recent years, the continuous growth of grid-integrated wind power generation causes reduction in the inertia of power system, which deteriorates primary frequency regulation (PFR) of grid. Therefore, wind farms (WFs) are recommended to operate at deloaded condition, rather than maximum power point, to provide sufficient primary reserve for improvement of the PFR. To improve PFR, the droop control uses this reserve and the inertia support emulates stored kinetic energy from the rotor of wind turbines. In this paper, a distributed synchronized control (DSC) technique is proposed which uses optimum power share ratio (PSR) and the frequency of each WF at the point of common coupling to calculate the droop. The optimum PSR is based on the ratio of primary reserve at the WF and required change in rotor speed for the WF. An iterative method is proposed to obtain the PSR of each WF. To reduce delay effect on proposed DSC performance, the synchronized droop varies differently with increasing communication delays. The effectiveness of proposed DSC is tested in WF integrated 39-bus New England system and compared with distributed Newton method. The performance of proposed DSC is verified for different false data injection scenarios. [ABSTRACT FROM AUTHOR]

It is hard to obtain precise wind power forecasting due to the chaotic nature of weather systems. Prediction intervals become an efficient tool to quantify the uncertainty involved in wind power forecasting. Traditional central prediction intervals are widely produced by forecasters, however, which might be conservative with respect to interval width and not well fit the practical conditions. This paper develops a novel adaptive bilevel programming (ABP) model, with extreme learning machine based quantile regression as the follower's problem and tuning hyperparameters of quantile proportions as the leader's problem. The proposed ABP model aims at minimizing the average interval width subject to well calibration. In order to overcome the difficulties in disposing of the intractable nested structure of bilevel programming, the ABP model is equivalently transformed into a single-level nonlinear programming problem with bilinear terms. An improved spatial branch-and-bound (ISBB) algorithm is proposed to efficiently solve the reformulated bilinear programming problem. In the ISBB algorithm, an innovative bounds tightening method is developed to tighten the convex relaxation of the bilinear constraint and enhance the convergence. Experimental studies based on actual wind farm of USA under four seasons show the significant effectiveness and high robustness of the developed ABP model, as well as the excellent global optimum attainment and convergence performance of the proposed ISBB algorithm. Moreover, the widely used traditional interval scores are first verified to be prejudiced in probabilistic wind power forecasting evaluation. [ABSTRACT FROM AUTHOR]

Large-scale wind power cluster with distributed wind farms has generated the active power dispatch and control problems in the power system. In this paper, a novel hierarchical model predictive control (HMPC) strategy based on dynamic active power dispatch is proposed to improve wind power schedule and increase wind power accommodation. The strategy consists of four layers with refined time scales, including intra-day dispatch, real-time dispatch, cluster optimization, and wind farm modulation layer. A dynamic grouping strategy is specifically developed to allocate the schedule for wind farms in cluster optimization layer. In order to maximize wind power output, downward spinning reserve and transmission pathway utilization are developed in wind farm modulation layer. Meanwhile, a stratification analysis approach for ultra-short-term wind power forecasting error is presented as feedback correction to increase forecasting accuracy. The proposed strategy is evaluated by a case study in the IEEE Network with wind power cluster integration. Results show that wind power accommodation has been enhanced by use of the proposed HMPC strategy, compared with the conventional dispatch and allocation methods. [ABSTRACT FROM AUTHOR]

With regard to wind farms connected to the main system via dedicated overhead transmission lines, the available wind power absorbed by the system relies on not only the power generation capacity but also the power transmission threshold. Thus, this study centers on the close relationship between environmental conditions and power transfer limits that involve the thermal limit and steady-state stability limit. Simultaneous equations representing both overhead conductors’ heat balance and power transmission operation are established. In addition, formulations of the maximum transmission power for the steady-state stability limit are derived and then expressed as functions of environmental factors and the line length. The presented approach allows one to analyze the threshold considering not only the thermal limit but also the steady-state stability limit, which could be remarkably different under certain environmental and transmission distance conditions. Then, a scheme to identify the primary limitation and obtain the corresponding threshold value is proposed. Moreover, a simple treatment of wind speed correlation is deployed because of the close distance between a wind farm and its tie-line. Case studies demonstrate that, for a certain wind speed level, the process of transmission rather than generation could become the key factor determining the threshold value. [ABSTRACT FROM AUTHOR]

With the increased uncertainty in the power system operation due to growing penetration of highly intermittent energy sources such as wind power, the need for the impact assessment of the renewable penetration on system operating risk and the quantification of benefits of using energy storage technologies is more than ever. A recovery-risk-analysis-based analytical framework for operating risk assessment of wind-integrated bulk power system following a major contingency disturbance is presented in this paper. Two new indices that quantify the recovery risk profile of the bulk power system and its load delivery points following major disturbances are introduced in this paper. The indices obtained from the proposed framework quantify the impact of increasing wind penetration on the system operating risk and the reliability benefits of using fast-responding energy storage system such as flywheel energy storage systems. The proposed methodology is illustrated through several case studies carried out in a test system. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of how to effectively smooth the short-term tie-line power fluctuations for grid-connected industrial microgrids (IMGs) from demand side. A wide-area closed-loop control architecture is proposed by directly and continuously modulating load power consumption, e.g., the aluminum electrolysis load. To optimally design the load smoothing controllers, an output regulation approach combined with LQ optimal control is developed. In particular, dominant frequencies of wind power fluctuations are analyzed and incorporated into the exogenous system that models time-varying disturbances. Simulations are conducted for a real industrial microgrid in the Inner Mongolia, China, to validate the practical feasibility and effectiveness of the proposed smoothing control strategy. It is demonstrated that the demand side control based on output regulation is able to achieve not only zero steady error in rejecting the time-varying wind power disturbance but also guarantee the satisfactory dynamic performance of modulated loads for the grid-connected IMG. [ABSTRACT FROM AUTHOR]

The injection of a significant amount of wind power tends to increase the rate of change of the grid frequency. Therefore, it is a trend for wind farm to participate in the grid frequency regulation. However, during the frequency control process, individual wind generators in a wind farm may prone to instability due to possible over-deceleration. To address this issue, this paper presents a new nonlinear model predictive control (NMPC) scheme for the wind farm frequency response. By incorporating the nonlinear dynamics of each individual wind generator into the NMPC design, it achieves both objectives of dynamically optimal frequency response and wind generator stability. This scheme has a three-layer structure. Based on the linear model predictive control and moving horizon estimation, a top-layer controller computes the overall wind farm power reference to support the frequency control. This overall power reference is fed to the middle-layer NMPC, and is further distributed among multiple wind generators. The dispatched power references are then sent to the bottom-layer wind generators local controllers for execution. Simulation results verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A major restructuring of electricity markets takes place worldwide, pursuing maximum economic efficiency. In most modern electricity markets, including the widely adapted Locational Marginal Price (LMP) market, efficiency is only guaranteed under the assumption of perfect competition. Moreover, market design is heavily focused on deterministic conventional generation. Electricity markets, though, are vulnerable to strategic behaviors and challenged by the increased penetration of renewable energy generation. In this paper, we cope with the aforementioned bottlenecks by investigating the application of Vickrey–Clarke–Groves (VCG) auction in a two-stage stochastic electricity market. The VCG mechanism achieves incentive-compatibility by rewarding market participants for their contribution towards market efficiency, being attractive from both market operation and participants perspectives. Both traditional and VCG market-clearing approaches are explored and compared, investigating as well the impact of increasing wind power penetration. The main shortcoming of VCG, i.e., not ensuring revenue adequacy, is quantified in terms of market budget imbalance for various levels of wind power penetration. To this end, a novel ex-post budget redistribution scheme is proposed, which achieves to partially recover budget deficit. [ABSTRACT FROM AUTHOR]

In this paper, we review the emerging challenges and research opportunities for voltage control in smart grids. For transmission grids, the voltage control for accommodating wind and solar power, fault-induced delayed voltage recovery, and measurement-based Thévenin equivalent for voltage stability analysis are reviewed. For distribution grids, the impact of high penetration of distributed energy resources is analyzed, typical control strategies are reviewed, and the challenges for local inverter Volt–Var control is discussed. In addition, the motivation, state-of-the-art, and future directions of the coordination of transmission system operators (TSO) and distribution system operators (DSO) are also thoroughly discussed. [ABSTRACT FROM AUTHOR]

This paper examines the small-signal angular stability of a power system affected by a virtual synchronous generator (VSG). The examination is based on an interconnected model with two subsystems. The VSG under the examination is modeled as the VSG subsystem. The rest of power system (ROPS) forms the other subsystem. Damping torque analysis is applied to indicate that when an oscillation mode of the VSG subsystem is in the proximity of an electromechanical oscillation mode of the ROPS subsystem on the complex plane, strong dynamic interactions are introduced by the VSG to decrease the small-signal angular stability of the power system. This implies that when the parameters of the VSG are set, modal proximity of the VSG to the electromechanical oscillation mode of the ROPS subsystem should be examined to avoid the detrimental impact of the VSG on power system small-signal angular stability. A method to evade the modal proximity is proposed in this paper for guiding the design of the VSG. Two example power systems with multiple VSGs for the wind power generation and transmission are presented. Study cases demonstrate and evaluate the analysis about the impact of modal proximity and proposed method for guiding the parameters setting of VSGs. [ABSTRACT FROM AUTHOR]

This paper proposed a Wasserstein metric-based distributionally robust approximate framework (WDRA), for unit commitment problem to manage the risk from uncertain wind power forecasted errors. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed framework minimizes the generating cost, start-up cost, shut-down cost, reserve cost, and the expected thermal generation adjusting cost under the worst-case distribution in the ambiguity set. The more historical available, the smaller the ambiguity set is and, hence, the less conservativeness the decision is. The size of the Wasserstein metric based robust counterpart (WDRC) model mainly depends on the size of sample set, which has a computation burden when more historical data are available. To overcome this drawback, this paper proposed an upper approximate of WDRC and verified the condition that makes the approximate model become exact. Comparisons with robust optimization and stochastic optimization illustrate that the proposed model can balance the economy and conservativeness effectively. Monte Carlo simulations on a modified IEEE-118 and a real 703-bus systems show that the proposed WDRA framework could reduce the computational time by several times when compared with WDRC. [ABSTRACT FROM AUTHOR]

Wind power uncertainty poses significant challenges for automatic generation control (AGC) systems. It can enhance control performances to explicitly consider wind power uncertainty distributions within controller design. However, widely accepted wind uncertainties usually follow non-Gaussian distributions, which may lead to complicated stochastic AGC modeling and high computational burdens. To overcome the issue, this paper presents a novel Itô-theory-based model for the stochastic control problem (SCP) of AGC systems, which reduces the computational burden of optimization considering non-Gaussian wind power uncertainty to the same scale as that for deterministic control problems. We present an Itô process model to exactly describe non-Gaussian wind power uncertainty, and then propose an SCP based on the concept of stochastic assessment functions (SAFs). Based on a convergent series expansion of the SAF, the SCP is reformulated as a certain deterministic control problem without sacrificing performance under non-Gaussian wind power uncertainty. The reformulated control problem is proven as a convex optimization, which can be solved efficiently. A case study demonstrates the efficiency and accuracy of the proposed approach compared with several conventional approaches. [ABSTRACT FROM AUTHOR]

Experimental results and performance analyses of wind farms providing secondary frequency regulation is lacking. This is despite the increasing share of variable generators in electrical energy production. As variable generators displace traditional generators that provide ancillary services, there is a growing need for alternate providers of these ancillary services. Wind generators are technologically capable of providing ancillary services, such as frequency regulation. This paper presents experimental results of a secondary frequency regulation test carried out on a 10 MW wind farm with Type-V wind turbines. This is a 5 h test of the wind farm's ability to follow an external, historical automatic generation control signal. 1 MW of power is offered on the regulation market with up-regulation provided via a fixed curtailment value. The performance of the farm is evaluated using the performance score method developed by the Pennsylvania–New Jersey–Maryland (PJM) system operator. Performance scores are used to perform an economic analysis using 2017 hourly PJM price data. This results in an estimated additional income of $\$$ 7200 from participating in the regulation market versus providing energy alone. A sensitivity analysis reveals that profitability is more influenced by the turbine's performance scores than regulation and energy prices. This paper also examines some practical aspects of providing secondary regulation, such as pitch activity, power error, and operating power ranges. [ABSTRACT FROM AUTHOR]

Scenario-based approaches have been widely employed in stochastic economic dispatch with wind power integration. However, due to computational limitations, the number of wind power scenarios usually need to be reduced to a small subset of all available scenarios. The limited number of scenarios could affect the objective performance related to the correlations and uncertainties of wind power, especially when the influence of extreme scenarios needs to be accounted for. To increase the computational efficiency of economic dispatch problem with a large number of scenarios, we propose a Lagrangian relaxation with incremental proximal method to solve the dispatch problem. This approach combines the benefit of Lagrangian relaxation, which allows the problem to be decomposed into a large number of smaller problems and the proximal method, which lead to much faster convergence. In addition, we also propose a multipliers and primal variables initialization method to further reduce the convergence time. Results of case studies show that this framework greatly reduces the computation time and the system cost of economic dispatch compared with the traditional approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a novel data-driven adaptive robust optimization (ARO) framework for the unit commitment (UC) problem integrating wind power into smart grids. By leveraging a Dirichlet process mixture model, a data-driven uncertainty set for wind power forecast errors is constructed as a union of several basic uncertainty sets. Therefore, the proposed uncertainty set can flexibly capture a compact region of uncertainty in a nonparametric fashion. Based on this uncertainty set and wind power forecasts, a data-driven adaptive robust UC problem is then formulated as a four-level optimization problem. A decomposition-based algorithm is further developed. Compared to conventional robust UC models, the proposed approach does not presume single mode, symmetry, or independence in uncertainty. Moreover, it not only substantially withstands wind power forecast errors, but also significantly mitigates the conservatism issue by reducing operational costs. We also compare the proposed approach with the state-of-the-art data-driven ARO method based on principal component analysis and kernel smoothing to assess its performance. The effectiveness of the proposed approach is demonstrated with the six-bus and IEEE 118-bus systems. Computational results show that the proposed approach scales gracefully with problem size and generates solutions that are more cost effective than the existing data-driven ARO method. [ABSTRACT FROM AUTHOR]

With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal tradeoff between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow model in which only the first-order and second-order moments of the uncertain sources’ probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method. [ABSTRACT FROM AUTHOR]

This paper proposes a restorability improvement strategy to accelerate system restoration through the implementation of a wind farm-battery energy storage system (WF-BESS) system. The concept of restorability is introduced and a restorability improvement model (RIM) is proposed and formulated as a mixed integer linear programming problem. To simulate the cylinder temperature drop during outages, the cranking time of a unit is modeled as a stepwise function of its startup time in the RIM. The WF might fail to meet its scheduled generation outputs optimized by the RIM due to the intermittency of wind. To tackle this problem, a linearized control strategy for the BESS (CSBESS) is proposed to minimize the difference between the scheduled wind power outputs and the combined power of the WF-BESS system. An iterative method is employed to efficiently solve the RIM and CSBESS by introducing optimality cuts. An actual power system case is employed to illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a novel model for the day-ahead self-scheduling problem of a virtual power plant trading in both energy and reserve electricity markets. The virtual power plant comprises a conventional power plant, an energy storage facility, a wind power unit, and a flexible demand. This multi-component system participates in energy and reserve electricity markets as a single entity in order to optimize the use of energy resources. As a salient feature, the proposed model considers the uncertainty associated with the virtual power plant being called upon by the system operator to deploy reserves. In addition, uncertainty in available wind power generation and requests for reserve deployment is modeled using confidence bounds and intervals, respectively, while uncertainty in market prices is modeled using scenarios. The resulting model is thus cast as a stochastic adaptive robust optimization problem, which is solved using a column-and-constraint generation algorithm. Results from a case study illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Increasing interdependency between electric power systems and natural gas systems creates additional dimensions of flexibility of system operation; but it may also escalate risk levels if the two systems are managed without proper coordination. This paper presents a robust security region (RSR) for electricity-gas integrated energy systems (IESs). It is a collection of uncertain parameters, especially wind power generations, under which system power flow has at least one feasible solution. First, a nonlinear optimization model is employed to obtain a set of uniformly distributed points on power flow solvability boundaries, from which the IES security region is constructed using a convex hull. Then, the proposed RSR is constructed to provide secure operation for the base-case scenario, where uncertain wind power generation values are replaced with expected values, and provide a feasible redispatch plan for each wind power generation scenario. Other implications of the RSR on IES security assessment are also envisioned. Results for two test systems indicate that the convex hull approach provides a more accurate approximation of the IES security region than a hyperplane approach. Meanwhile, the benefits of RSR are demonstrated by comparing test results with those obtained for a deterministic security region. [ABSTRACT FROM AUTHOR]