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Utility-scale and small scale wind and solar power installations along with electric vehicle charging stations, and other active sources of energy are increasing at the medium and lower voltage levels in the distribution grid. This situation requires a better understanding of the impact of high penetration of weather-dependent renewable energy sources on the operating conditions of the distribution network at both medium and low voltage levels. Despite the need, a multi-voltage level distribution network model, based on real network data and weather-dependent renewable generation data, has not been presented for distribution grid studies. This paper presents a comprehensive multi-voltage level active distribution network model based on real network data along with load and generation time-series for about a year. The network topology is modelled based on geographical data for various rural, semi-urban, and urban locations. The distribution network is embodied with a large share of renewable generation sources, with generation time-series simulated from meteorological data. The network is also flexible to incorporate other assets such as electric vehicle charging stations, storage, etc. The presented active distribution network model can be used to study, optimize, and control the effects of weather-dependent generation and other network assets in the distribution grid. [ABSTRACT FROM AUTHOR]

An optimal static voltage stability margin (SVSM) control model considering the uncertain wind farm output is proposed, in which the probability distribution of SVSM is required to satisfy the chance and variance constraints. A probabilistic distribution control method is proposed to solve the model. First, a linear weighted sum of B-spline basic functions is introduced to approximate the analytical function between the probability density function (PDF) of SVSM and control variables. Next, the analytical expression of the PDF of SVSM corresponding to a control variables’ sample is derived, and the sample of corresponding B-spline function weights is obtained, thus forming a series of ‘control variables-weights’ samples. Then, the analytic functions between weights and control variables are obtained using the generated samples to train a radial basis function neural-network, and the analytical function between the PDF of SVSM and control variables is obtained. After that, the chance and variance constraints are transformed into general nonlinear constraints with respect to control variables. Moreover, a method of selecting key control variables by calculating sensitivities is proposed to increase computational efficiency. Test results on the IEEE-39 bus system and an actual provincial power grid demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In a wind farm, the interactions between turbines caused by wakes can significantly reduce the power output of the wind farm. Cooperative control among the turbines has the potential to improve the power output. However, existing centralized power optimization methods are computationally expensive and does not scale well for large wind farms, limiting their practical use in real-time control for time-varying wind conditions and turbine configuration (with adding or maintaining of turbines). To address this problem, this paper proposes a fully distributed power optimization method for wind farms using alternating direction method of multipliers (ADMM). The proposed method allows the wind farm power output to be optimized in fully distributed manner with turbine-to-turbine message passing over a mesh network, guarantees the implemented control actions satisfy the control constraints of all turbines, and provably converges to a stationary point of the wind farm power optimization problem. Simulation results demonstrate that the proposed method can significantly reduce the computation time with hardly sacrificing the power gain compared with centralized method and thus is computationally efficient for real-time power optimization of large wind farms. [ABSTRACT FROM AUTHOR]

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stochastic robust real-time power dispatch model considering wind uncertainty. In this dispatch model that incorporates automatic power generation control, system constraints are constructed with affinely adjustable robust optimization to enhance the system security, while the objective concerning the expected value of generation cost is optimized to improve the cost efficiency. The optimized objective is consistent with stochastic optimization, while the formulation for the objective is different. A Nataf conversion-based three-point estimate (NC-TPE) is adopted, which uses an approximating function to formulate the expected generation cost with deterministic estimate points. Compared to traditional stochastic sampling methods, the deterministic assessment method NC-TPE achieves an accurate formulation with more stable and efficient computation performance. The dispatch model is derived as a problem with nonconvex objective and bilinear constraints using the dual theory. To address the highly nonconvex problem, the objective and bilinear constraints are first converted to difference-of-convexity functions, and then a tailored difference-of-convexity optimization is employed to convexify the nonconvex functions, such that the original problem can be solved with an iterative quadratically constrained program. Numerical simulations demonstrate the economic superiority and robustness of the proposed model, as well as the effectiveness of the convexified solution. [ABSTRACT FROM AUTHOR]

This paper applies the principles of distribution locational marginal pricing (DLMP) to unbalanced three-phase distribution networks. We first propose a linear model for AC optimal power flow derived through a series of approximation and reformulation techniques. Then a scenario-generation algorithm is proposed to properly model the uncertain parameters in the linear model. Through a proposed No U-Turn sampler (NUTS) based algorithm, probability density functions (PDFs) of DLMPs are calculated. These PDFs provide statistical information about the locational and temporal price risks. By means of applications to two IEEE unbalanced test networks, the numerical results show promising performance for the proposed linear model and the NUTS-based algorithm in creating PDFs of DLMPs. DLMP price densities will be increasingly useful as distribution system operators seek flexible, low risk solutions from embedded generators and aggregators of distributed energy resources. [ABSTRACT FROM AUTHOR]

With the large-scale wind power integration into the power system, the inertia and damping characteristics of the system have been weakened, which is not conducive to fulfill the grid-friendly operation of wind power. Aiming at this, an adaptive control scheme combining virtual inertia control (VIC) and supplementary damping controller (SDC) is proposed in this paper. Firstly, the mathematical model of wind grid-connected power system with VIC is established. Secondly, the polytopic linear parameter varying (LPV) system is built to describe the uncertainty of system operating points, and the gap metric-based nonlinear evaluation method is used for polytope vertex configuration. Next, Youla-Kucera parametrization are extended to polytopic LPV system to design an adaptive damping control, in which VIC and SDC are coordinated to provide damping and virtual inertia simultaneously. Finally, the proposed adaptive control scheme is compared with several existing control techniques to validate its effectiveness and advantages in suppressing system oscillation in the modified IEEE 39-bus system integrated with 2 wind turbines. [ABSTRACT FROM AUTHOR]

This paper presents a wind turbine (WT) control strategy to deliver frequency response (FR) that is similar to conventional synchronous generators, i.e., to deliver accurate and efficient FR. This is achieved by the coordination of WT’s rotor speed control (RSC) and pitch angle control (PAC), wherein the RSC is the summation of the proposed deloading power point tracking curves and FR signal; the PAC is kept as adjusting its control law according to the WT rotor speed. Through the above coordination, the strategy pre-reserves a portion of wind power and releasing it during underfrequency events. Compared with existing methods, the strategy has two significant advantages: 1) it does not need the switching of WT controls according to the real-time wind speed (WS), nor the identification of the boundaries among high, medium and low WSs according to the required reserved power, ultimately reducing the complexity of applying the strategy to practice; 2) its active power response during FR period is independent of the deviated rotor speed and is equal to the FR signal, ultimately enabling the WT to provide accurate and efficient FR. The simulations focusing on the grid frequency side demonstrated the advantages of the strategy over existing methods. [ABSTRACT FROM AUTHOR]

This letter proposes a novel transient stability criterion for power systems with multi-wind farms, which is deduced from power flow and inertia distribution. The variations of acceleration and deceleration power with and without wind integration, instead of the acceleration and deceleration areas themselves, are calculated, in which the power angle swing direction, the transient stability control of wind turbines, the position of wind farms access, and the unbalanced output of synchronous clusters are also considered. The simulation results show the effectiveness of the proposed criterion to distinguish transient stability. [ABSTRACT FROM AUTHOR]

Fast frequency response (FFR) is an option in maintaining system security under low inertia conditions. Power electronics interfaced energy resources such as wind and photovoltaics have the capability to deliver FFR. At present, almost all installed power electronics interfaced energy resources are connected to the grid by the phase locked loop (PLL)-synchronized voltage source converter (VSC) and they usually implement inertial response by measuring the rate of change of frequency (RoCoF). However, RoCoF measurements are highly susceptible to disturbances in the grid. In this paper, a novel inertia controller is developed for PLL-synchronized VSC interfaced energy resources to implement natural inertial response without measuring RoCoF. A thorough stability analysis is performed to study the impact of proposed inertia controller on the VSC in weak grid. The proposed inertia controller makes the deviation of DC voltage proportional to the deviation of system frequency. Further, a method of primary frequency control is proposed by measuring DC voltage rather than grid frequency. The proposed FFR scheme of inertia and primary frequency control is applied to a direct-drive windfarm connected to a grid, and its correctness and advantages are verified by simulation. [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]

The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency’s nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel constraint from the swing equation to contain the frequency nadir using all of these services. The expected cost of UFLS is found probabilistically to facilitate its comparison to the other frequency services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone (SOC), resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to $\pounds $ 559 m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumptions of random variables. A novel critical region integral method (CRIM) which combines the multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed N-POPF model and CRIM form a new framework of POPF problem for power system analysis and operation. [ABSTRACT FROM AUTHOR]

Recent long term planning studies have demonstrated the important role of variable renewables (VRE) in decarbonising our energy system. However, cost-optimising models do not capture the visual impact of VREs on the landscape which can act to undermine their public acceptability. Here, we use crowd-sourced scenicness data to derive spatially explicit wind energy capacity potentials for three scenarios of public sensitivity to this visual impact. We then use these scenarios in a cost-optimising model of Great Britain's power system to assess their impact on the cost and design of the electricity system in 2050. Our results show that total system costs can increase by up to 14.2% when public sensitivity to visual impact is high compared to low. It is thus essential for policy makers to consider these cost implications and to find mechanisms to ameliorate the visual impact of onshore wind in local communities. [ABSTRACT FROM AUTHOR]

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy. [ABSTRACT FROM AUTHOR]

Power system planning is essential for ensuring development of a safe and stable power system. Articles on power system planning have been published in recent decades. In this paper, bibliometric analysis is applied to power system planning to identify its basic characteristics, and to summarize the research hotspots and trends. A total of 4562 publications were obtained from the Web of Science during 1971–2020. The 4562 publications cover 8136 keywords, 1526 journals, 107 countries/territories, and 2519 institutions. IEEE Transactions on Power Systems is the key journal in power system planning; USA, China, and England are the countries that dominate publication production. Research hotspots and trends were analyzed using author-keyword co-occurrence analysis and keyword burst detection. Four clusters were identified and topics from Cluster I (central nodes as power system stability and transient stability) and Cluster IV (central nodes as power system simulation and economics) are important for power system planning research. However, their relative popularities have declined over the past two decades. This indicates that Cluster II (central nodes as renewable energy, wind power, and energy storage) and Cluster III (central nodes as distributed generation and smart grids) will be the focus of future research. [ABSTRACT FROM AUTHOR]

With Denmark dedicated to maintaining its leading position in the integration of massive shares of wind energy, the construction of new offshore energy islands has been recently approved by the Danish government. These new islands will be zero-inertia systems, meaning that no synchronous generation will be installed in the island and that power imbalances will be shared only among converters. To this end, this paper proposes a methodology to calculate and update the frequency droops gains of the offshore converters in compliance with the N-1 security criterion in case of converter outage. The frequency droop gains are calculated solving an optimization problem which takes into consideration the power limitations of the converters as well as the stability of the system. As a consequence, the proposed controller ensures safe operation of off-shore systems in the event of any power imbalance and allows for greater loadability at pre-fault state, as confirmed by the simulation results. [ABSTRACT FROM AUTHOR]

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

To integrate large-scale islanded onshore wind power with different sizes, this paper proposes an integration system based on the cascaded hybrid HVDC transmission system, which consists of LCC and several MMCs in series connection at the DC side of the rectifier. A large-scale wind farm is connected with one LCC and one MMC while several small-scale wind farms are connected with MMCs directly. Owing to the hierarchical integration arrangement, the operating flexibility can be improved with reduced capacity and the number of step-up interfacing transformers. A resilient DC voltage control is proposed for the integration system to adaptively redistribute power among the converters during wind power fluctuations. Firstly, the topology and operating characteristics of the wind power integration system are introduced. Then, a resilient DC voltage control is proposed to ensure stable operation during wind power curtailments. Finally, a simulation model of the hybrid cascaded HVDC transmission system is built in PSCAD/EMTDC to verify the effectiveness. The research results show that the system provides a new option for long-distance transmission of large-scale islanded wind power. [ABSTRACT FROM AUTHOR]

This manuscript presents a novel control architecture for the E-STATCOM (STATCOM integrated with Energy Storage System (ESS)) that is common for both the Stand-Alone (SA) as well as the Grid-Connected (GC) modes of operation of a microgrid operating under unbalanced conditions. The proposed control architecture fulfils the aim of regulating the E-STATCOM in such a manner so as to smoothen the power fluctuations of a nearby renewable energy source (solar, wind, etc) and also to maintain the voltage and frequency at the Point of Common Coupling (PCC) within the normal range of operation. Hence, the resultant real power injected by the renewable energy source along with the E-STATCOM is constant in magnitude, irrespective of whether the microgrid is in the GC or the SA mode of operation. Dynamically varying limits are introduced to provide inherent VSC over-current protection. In order to illustrate the performance of these control architectures, a model of the IEEE 34 node power distribution network that is being supplied by a solar Photo-Voltaic (PV) Distributed Generation (DG) unit, a wind DG unit and two identical E-STATCOMs (for compensating the power fluctuations from the PV and wind DG units) has been considered for study in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

A joint raw moments-based analytical method (JRMAM) is first proposed herein to deal with probabilistic power flow (PPF) of hybrid AC/VSC-MTDC (Alternate Current/Voltage Source Control-Multiple Terminal Direct Current) power systems with integration of the offshore wind farms. JRMAM is able to overcome the challenges of some existing combined methods in estimating the high order moments of target outputs, and the dramatic time consumption of Monte Carlo simulation method (MCSM) in performing the PPF analysis particularly due to the complication of its deterministic power flow (DPF) model. The proposed JRMAM has a further superiority on efficiency, even compared to the joint cumulants-based analytical method (JCAM). As a preliminary step, discrete Fourier transformation matrix (DFTM) method is applied to calculate the joint raw moments of random inputs which are required by conducting JRMAM, and the probability density function (PDF) of outputs can be estimated by means of the Gram-Charlier expansions (GCE) based on the results obtained from JRMAM. Two modified IEEE test cases connected with DC subsystems through the VSC devices are adopted to verify the effectiveness and the scalability of JRMAM, where the result of MCSM is treated as a reference, and the properties of the hybrid AC/VSC-MTDC power system with these master-slave controlled VSCs are investigated for a further acceleration on PPF analysis. [ABSTRACT FROM AUTHOR]

Modern power systems present low levels of inertia due to the growing shares of converter-interfaced generation. Consequently, renewable energy sources are increasingly requested to provide frequency support. In addition, due to the inertia loss, the requirements regarding frequency containment reserves (FCR) are becoming tough to meet with traditional units such as hydro, whose non-minimum phase (NMP) characteristic reduces the closed-loop stability margins. The shortcomings of traditional synchronous generation motivates new protocols for fast frequency reserves (FFR). In this work, we design a wind turbine (WT) model useful for FFR. It is shown that the dynamical shortcomings of the WT, in providing steady-power or slow FCR support, are suitably described by a first-order transfer function with a slow NMP zero. The WT model is tested in a 5-machine representation of the Nordic synchronous grid. It is shown that the NMP model is useful for designing a controller that coordinates FFR from wind with slow FCR from hydro turbines. By simulating the disconnection of a 1400 MW importing dc link in a detailed nonlinear model, it is shown that the wind–hydro combination not only satisfies the latest regulations, but also presents a smooth response avoiding overshoot and secondary frequency dips during frequency recovery. [ABSTRACT FROM AUTHOR]

Transient stability of a power system can be significantly affected by wind power generators due to their stochastic power output and complex dynamic characteristics. This paper proposes a robust optimization approach for coordinating generation dispatch and emergency load shedding against transient instability under uncertain wind power output. The problem is modelled as a two-stage robust optimization (TSRO) model considering transient stability constraints, where the first-stage is to optimize the generation dispatch (preventive control) before a contingency and the second-stage decision is the emergency load shedding (emergency control) after the contingency occurrence under the worst case of wind power variation. To solve this TSRO problem, this paper also proposes a solution algorithm which integrates transient stability assessment and transient stability constraint construction in a column and constraint generation framework. The proposed method is validated on the New-England 39-bus system and the Nordic32 system, which shows high computational efficiency and stability robustness against uncertain wind power. [ABSTRACT FROM AUTHOR]

The paper develops an optimization method for assessing transmission network vulnerability to small changes in generation (as caused, for example, by wind forecast inaccuracy). The method computes the smallest deviation (in a weighted 2-norm sense) from the nominal generation pattern that would drive a particular line to a specified temperature, over a given time horizon. The 2-norm weighting matrix provides a means of capturing spatial and temporal coupling between generation sites and time intervals. The temperature constraint is second-order in voltage angle differences. The problem is therefore a quadratically-constrained quadratic program (QCQP). Solving the QCQP for each line in the network yields a set of candidate generation deviation patterns which may then be sorted to determine the lines that are most vulnerable to overloading. The paper develops a computationally efficient algorithm for solving this QCQP. An example explores line-overload vulnerability due to changes in wind patterns. Numerical results emphasize the framework’s ability to incorporate evolving ambient and system conditions, as well as computational scaling properties. [ABSTRACT FROM AUTHOR]

In the electricity sector the carbon tax is a common environmental policy aiming to reduce CO2 emissions, but is often regarded as economically unfriendly, especially for areas relying on coal-fire and other carbon-intensive generators. A power grid utilizing an energy storage system can be a promising solution to alleviate the regional economy pressure in a grid where the carbon tax is enforced. With the increasing exploitation of clean energy, e.g., solar and wind power, in this work, we characterize the stochastic emission-aware economic dispatch with a storage system utilizing two frameworks, namely a chance-constrained framework and a robust optimization framework. We highlight their differences and connections by studying the trade-offs between robustness and overall cost. Specifically, we bridge the two frameworks with a novel distributed robust optimization framework that considers practical bounds to estimate the optimal system performance under the reliability requirement. Numerical studies on the six-bus model and the IEEE-118 bus model further justify our findings. [ABSTRACT FROM AUTHOR]

Grid modernization and innovations in clean energy are leading to a rapid increase in the penetration of inverter-based resources (IBRs) like wind power and solar photovoltaic (PV) plants in the bulk power system (BPS). To study the implications on BPS dynamics and mitigate potential risks to grid reliability, the second-generation generic renewable energy system model has been developed earlier. However, this model has three modules with 86 user-defined parameters and eight control flags to facilitate the utility-scale solar PV plant operation in different control modes. It presents a major challenge to the transmission system planning engineers. There is a critical need to identify the key parameters of the dynamic model that are highly sensitive to grid events causing large-scale voltage and frequency disturbances. In this work, a sensitivity analysis based on modified Sobol’ method is proposed for identification of the key parameters in the utility-scale solar PV plant model. The total Sobol’ sensitivity index captures even the higher-order effects of the variations in the parameters. Validation of the identified key parameters was carried out on a modified IEEE 9-bus system and 200-bus synthetic grid using PSS®E for plant-level control and local coordinated control operation of the solar PV plant. The reduced set of parameters identified in this work offer help to utility grid planning teams while conducting dynamic studies to meet the interconnection requirements. [ABSTRACT FROM AUTHOR]

As more variable renewable energy (VRE) and energy storage (ES) facilities are installed, accurate quantification of their contributions to system adequacy becomes crucial. We propose a definition of capacity credit (CC) for valuing adequacy contributions of these resources based on their marginal capability to reduce expected unserved energy. We show that such marginal credits can incentivize system-optimal investments in markets with installed capacity requirements and energy price caps. We simulated such markets using a LP-based capacity expansion planning model with convexified unit commitment (UC) constraints and ES. The impacts of UC and ES on capacity credits are investigated. Furthermore, we analyze technology and system cost distortions resulting from implementing inaccurate CCs in the capacity market. The results show that ignoring UC constraints can overestimate the CCs for VRE and ES. Building ES increases the CCs of VRE resources with higher capacity factors and a negative correlation with load. Assigning the wrong credit to VRE can significantly distort resource mixes and system cost. Implementing the proposed CCs can, in theory, eliminate those distortions and achieve the same overall optimum as a theoretical market without energy price caps. [ABSTRACT FROM AUTHOR]

Rapid growth of gas-fired generators strengthens the interdependency of electricity and natural gas markets. To meet the uncertainty challenge, a robust day-ahead market clearing framework for the integrated electricity and natural gas system (IEGS) is presented. First, a robust security-constrained unit commitment (SCUC) model is built considering the joint dispatch of ancillary services. Regulation-up/down reserve is scheduled to balance electrical load/wind power uncertainties, spinning reserve is to manage N-1 generator outage, and natural gas reserve is to withstand gas load uncertainty and provide fuel for gas-fired electrical reserve. The SCUC model is a two-stage mixed-integer nonlinear optimization problem so that a sequential linear approximation-based Column & Constraint Generation (SLA-based C&CG) algorithm is proposed. Then, according to SCUC solutions, an economic dispatch model is derived to obtain market clearing and pricing results. Based on locational marginal pricing, novel definitions of electrical energy, natural gas and multiple ancillary service prices are proposed, which can reflect network limits and uncertainty effects. Numerical cases on two test IEGSs and a provincial-level IEGS demonstrate the high accuracy of proposed SLA-based C&CG algorithm and the impact of uncertainties on market clearing. [ABSTRACT FROM AUTHOR]

This paper proposes a holistic framework of data-driven distributionally robust joint chance constrained economic dispatch (ED) optimization, which seamlessly incorporates deep learning-based optimization for effective utilization of renewable energy in power systems. By leveraging a deep generative adversarial network (GAN), an f-divergence-based ambiguity set of wind power distributions is constructed as a ball centered around the probability distribution induced by a generator neural network. In particular, the GAN is well suited for capturing complicated spatial and temporal correlations of wind power. Based upon this ambiguity set, a distributionally robust joint chance constrained ED model is developed to hedge against distributional uncertainty present in multiple constraints, without assuming a perfectly known probability distribution. The proposed deep learning based ED optimization framework greatly mitigates the conservatism inflicting on distributionally robust individual chance constrained optimization. Theoretical a priori bound on the required number of synthetic wind power data generated by GAN is explicitly derived for the multi-period ED problem to guarantee a predefined risk level. The effectiveness and scalability of the proposed approach are demonstrated in the six-bus and IEEE 118-bus systems by comparing with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Converting wind energy into ammonia (WtA) has been recognized as a promising pathway to produce “green” ammonia compared with traditional coal-based technologies. As the key part of WtA, Power-to-Ammonia (PtA) has great potential to facilitate the usage of wind generation. This paper proposes a co-planning approach for regional wind resources-based ammonia industry and the electric network (EN). To this end, PtA is first modeled as a flexible power load of power systems with spatial and temporal constraints on hydrogen supply chains (HSC). Then a novel co-planning model of WtA and EN is established to optimize the WtA configuration and the EN expansion. An alternating direction method of multipliers (ADMM) based algorithm is introduced to effectively solve this model. Real data of Inner Mongolia Province in China is adopted to verify the effectiveness and significance of the proposed approach. It is shown that the siting and operation flexibility of PtA with HSC can reduce the expansion burden of EN. The co-planning of WtA and EN can significantly enhance wind power utilization and reduce total investment costs. Furthermore, feasibility analysis on WtA in comparison with coal-to-ammonia (CtA) and ultra-high voltage transmission (UHV) provides helpful guidelines for the realization of WtA. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) has gradually become a key technology to the increasing penetration of renewable energy. The uncertainty and variability of renewable energy and load demand pose significant challenges to the efficiency and stability of VPP's operation. In this paper, a data-driven two-stage stochastic robust optimization (SRO) scheduling model is proposed for a VPP considering wind power, solar power, load demand, and market price uncertainties. The objective is to maximize the profit of the VPP in the energy market and minimize the total system cost of the VPP in the reserve market under the worst-case realization of the uncertainties. The Dirichlet process mixture model (DPMM) and variational inference algorithm are employed for constructing the data-driven uncertainty ambiguity set considering the correlations among multiple uncertainties. The tailored column-and-constraint generation algorithm is developed to solve the SRO model iteratively by reformulating the second stage with the application of the Karush-Kuhn-Tucker conditions. Results from a case study illustrate the effectiveness and superiority of the proposed model. [ABSTRACT FROM AUTHOR]

The significant penetration of renewable energy resources and ever-rising load demand has gradually aggravated the safe operation of the interconnected power system. A generalized extended state observer and fractional-order theory based integral sliding mode control strategy is introduced in the interconnected power system to minimize the frequency deviation by controlling the governor of the generation unit. The generalized extended state observer is designed to estimate the disturbance from system uncertainty, load demand, and wind power fluctuation to improve the robustness of the interconnected power system. The fractional-order integral sliding mode control relieves the chattering of frequency deviation and tie-line power deviation. Besides, the superconducting magnetic energy storage and the wind model, as the ancillary frequency regulation devices, are implemented in the interconnected power system. The novel sliding mode controller based on generalized extended state observer is designed for the interconnected power system with the addition of the superconducting magnetic energy storage and the wind model. Stability proof and simulation comparison with the integer-order sliding mode control and other three control schemes are carried out as well. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewable energy, such as wind power, has brought great challenges to the power system operation due to its uncertainty. Flexibility, which measures the ability of power system to deal with the uncertainties, is critical for power system to adapt to the new era of renewable energy. The rising electrical demand of the water distribution system (WDS) creates opportunities for power system to leverage the flexibility provided by WDS. This paper investigates the water-energy relationship between these two systems and makes full use of the water pumps and tanks in the WDS to enhance the power system flexibility. Current WDS designs did not consider well the role WDS plays in the power system. This hinders the WDS from being fully used by power system to provide flexibility. An optimization model is proposed to determine the optimal tank size of WDS, which may provide the maximum available flexibility of power system. The effect of tank size on water quality is also investigated to ensure that the supplied water quality is not compromised. Moreover, a Benders-based heuristic algorithm is proposed to find the optimization solution more efficiently and to protect the data of each energy system. Results of case study highlight the merit of the proposed optimization design and the advantage of using WDS to provide flexibility for power system. [ABSTRACT FROM AUTHOR]

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

Case-by-case study in the literature has found from the results of numerical computation and simulation that a grid-connected virtual synchronous generator (VSG) can maintain the stability under the condition of extremely weak grid connection. This paper presents the theoretical proof to the finding and thus, generally concludes that the grid-connected VSG is immune to the instability risk under the condition of weak grid connection. In addition, the paper extends the theoretical proof to the case of a grid-connected PMSG wind farm with multiple VSGs. An example grid-connected PMSG wind farm with twenty VSGs is presented to demonstrate and evaluate the theoretical analysis and conclusion made in the paper. [ABSTRACT FROM AUTHOR]

Fast insecurity early warning is the key technique to resist the dynamic insecurity risk, which becomes intractable due to the strong nonlinearity of hybrid AC/DC grids and the high uncertainty of wind generation. Considering dynamic security constraints and wind power uncertainty, this paper presents an insecurity early warning method based on decision tree (DT) and semi-supervised deep learning. First, semi-supervised deep learning is deployed to estimate the dynamic security limit of the critical interface of hybrid AC/DC grids. The system security is assessed by comparing the actual power transfer of the critical interface with the security limit. Then, operating conditions (OCs) are ranked into different insecure levels according to the type of preventive control actions that is needed to ensure the system security. Finally, oblique DT is utilized to identify insecurity classification boundaries in the wind power injection space. Insecure OC sets are constructed based on these classification boundaries. Simulation results of the real-life Jiangsu-Shanghai interconnected grid in east China demonstrate that the proposed method can fast construct the insecure OC sets corresponding to different insecure levels. [ABSTRACT FROM AUTHOR]

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

The rotational inertia and primary frequency response capabilities of power systems are declining as synchronous generators (SGs) are replaced by inverter-based variable renewable energy (VRE) resources. Therefore, when a high VRE proportion is present, it becomes essential to include frequency security constraints in power system planning. Under this circumstance, the decline in SGs would deteriorate the system frequency response performance; thus, inverter-based resources are supposed to provide frequency response support. This paper presents a frequency-constrained stochastic planning method for high VRE share systems. Frequency response support from wind farms is considered in the planning process for the first time, and the unique characteristics of wind power support are addressed. Specifically, the uncertainty of and variations in wind power support capabilities are modeled from the field-measured data, and the optimal combination of various support schemes can be determined by introducing binary variables with novel linear constraints into the planning process. Moreover, the nonlinear frequency constraints are transformed and embedded in the planning model by the proposed computationally efficient adaptive piecewise linearization method. The planning is formulated as a stochastic optimization model to consider the VRE power uncertainty. Finally, case studies on the IEEE 30-bus system validate the proposed method, with results indicating time savings of 22%. Further, compared with the case that only SGs provide frequency support, the results based on the East China system demonstrate that considering wind power support can improve the VRE share from 49.5% to 79.7%. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven chance-constrained optimal gas-power flow (OGPF) calculation method without any prior assumption on the distribution of uncertainties of wind power generation. The Gaussian mixture model is employed to fit the uncertainty distribution, where the Bayesian nonparametric Dirichlet process is adopted to tune the component number. To facilitate the online application of the proposed methods, an online-offline double-track distribution construction approach is established, where the frequency of training the relatively time-consuming Dirichlet process Gaussian mixture model can be reduced. On account of the quadratic gas consumption expression of gas-fired generators as well as the linear decision rule based uncertainty mitigation mechanism, the chance constraints would become quadratic ones with quadratic terms of uncertainties, which makes the proposed model more intractable. An equivalent linear separable counterpart is then provided for the quadratic chance constraints, after which the intractable chance constraints could be converted into traditional linear ones. The convex-concave procedure is used to crack the nonconvex Weymouth equation in the gas network and the auxiliary quadratic equalities. Simulation results on two test systems validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Wind power producers participating in day-ahead electricity markets are compelled to pay imbalance costs if they do not generate the same amount of power as they had bid for. These imbalance costs comprise a significant proportion of their income. To reduce the risk of such financial losses, this paper employs the idea of trading in a separate prediction market, as a hedging method. In prediction markets, participants trade shares associated with a certain outcome of an event. We propose that the wind power producers might participate in a prediction market to trade the future value of the wind power and by taking an opposite position in comparison to the electricity market, the imbalance costs will be offset through payouts in the prediction market. Wind power is modelled as a stochastic variable and an optimal trading strategy is developed where the trading volume in the prediction market is analytically derived and formulated by minimising the maximum possible loss and pricing of shares is determined via indifference utility condition. The results suggest that the proposed method limits the loss values and improves the risk measures. [ABSTRACT FROM AUTHOR]

This paper proposes a new decentralized data-driven load restoration (DDLR) scheme for transmission and distribution (TD) systems with high penetration of wind power. Robust DDLR models are constructed in order to handle uncertainties and ensure the feasibility of decentralized schemes. The Wasserstein metric is used to describe the ambiguity sets of probability distributions in order to build the complete DDLR model and realize computationally tractable formulation. A data-driven model-nested analytical target cascading (DATC) algorithm is developed to obtain the final load restoration result by iteratively solving small-scale mathematical models. The proposed DDLR scheme provides load restoration results with adjustable robustness, and performance efficiency is independent from the amount of data. The DDLR scheme makes full use of the available data while respecting information privacy requirements of independent operated systems, and ensures the feasibility of a decentralized load restoration strategy even in the worst-case condition. The effectiveness of the proposed method is validated using a small-scale TD system and a large-scale system with the IEEE 118-bus TS and thirty IEEE-33 DSs, showing high computational efficiency and superior restoration performance. [ABSTRACT FROM AUTHOR]

High penetration of wind energy has intensified system pressure in balancing supply and demand due to the uncertainty nature of wind velocity. To mitigate the negative impacts brought along by wind power integration, an optimal power regulation scheme for a wind farm is proposed in this work. Specifically, the benefits of the designed wind power regulation scheme is innovatively quantified via the reduction of balancing cost. To handle wind uncertainty while determining generation profile for the wind farm, a robust strategy is introduced in the proposed control. In addition, the aerodynamic interactions among wind turbines are considered. To bypass the nonlinearity and non-convexity involved in the optimization problem and achieve online application, an artificial intelligence aided control is newly designed. Simulation results demonstrate the good performance of the proposed control scheme under multiple operation scenarios. [ABSTRACT FROM AUTHOR]

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

In this paper, an analytical two-machine equivalent method of DFIG-based wind power plants (WPPs) is proposed. Through simulations of a 49.5 MW WPP, the root causes of errors of the single-machine equivalent are identified. Taking a four-machine WPP as an example, analytical expressions of fault-ride through (FRT) behaviors of the WPP model and its single-machine equivalent model are derived, and root causes of errors are revealed in theory including: inconsistent transient power behaviors in the initial FRT stage; unequal quasi-steady-state active power during a fault; and mismatching initial points and ramp rates of active power after the fault clearance. To eliminate equivalent errors, an improved equivalent method is proposed with two steps: 1) Group wind turbines into two clusters by the crowbar actions and represent them as two equivalent machines; 2) Correct their controller reference settings based on the derived FRT behavior expressions of the detailed WPP. Simulation results verify that the proposed method can accurately reproduce FRT behaviors of the WPP under various wind scenarios and voltage dips. [ABSTRACT FROM AUTHOR]

The frequency security problem becomes a critical concern in power systems when the system inertia is lowered due to the high penetration of renewable energy sources (RESs). A wind-storage system (WSS) controlled by power electronics can provide the virtual inertia to guarantee the fast frequency response after a disturbance. However, the provision of virtual inertia might be affected by the variability of wind power generation. To address this concern, we propose a two-stage chance-constrained stochastic optimization (TSCCSO) model to find the optimal thermal unit commitment (i.e., economic operation) and the optimal placement of virtual inertia (i.e., frequency stability) in a power grid using representative power system operation scenarios. An enhanced bilinear Benders decomposition method is employed with strong valid cuts to effectively solve the proposed optimization model. Numerical results on a practical power system show the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Full converter-based wind power generation (FCWG, e.g., a permanent magnet synchronous generator (PMSG)), though normally considered to be decoupled from the external power grid can be actuated as an inertia source to suppress modal resonance in wind generation penetrated power systems by installing auxiliary resonance controllers (ARCs). In this paper, three possible options for ARC installation are first identified based on some derivations of the conventional control model of FCWG. The damping support mechanism of ARC is revealed, a suitable and generic configuration structure of ARC is then established, and optimal parameter tuning is conducted on the basis of this ARC configuration. The three ARC alternatives are equipped to contribute to damping by utilizing the potential energy and dynamics hidden in different inertia source components (i.e., the wind turbine rotor and DC capacitor, respectively) of FCWG. Both modal analysis and simulation results validate the effectiveness of the three proposed ARCs in suppressing modal resonance and improving system oscillation stability. Most importantly, extensive comparison investigations are carried out to fully evaluate the pros and cons of the three ARCs and thus provide constructive application guidance for system operators and wind farm owners. [ABSTRACT FROM AUTHOR]

This paper studies the characteristics of subsynchronous oscillation (SSO) power propagation in power systems with a large-scale wind farm integration. Based on the instantaneous power theory, a novel definition of SSO power is proposed to characterize its propagation. The SSO power contains both DC power components and AC power components. Utilizing SSO power, SSO propagation is quantitatively studied in single oscillation source systems, and further studied in multiple oscillation sources systems. Theoretical analysis reveals that in addition to the recognized impact of line impedance, power flow also affects SSO power propagation significantly. Hence, propagation impact factor is proposed for the determination of the dominant influencing element. To reveal SSO power propagation paths in a network, shunt coefficients of DC power components and AC power components are expressed respectively. Test cases under different operating conditions and a practical case are carried out to demonstrate analysis and conclusions in this paper. [ABSTRACT FROM AUTHOR]

Previous robust transmission expansion planning (RTEP) studies have rarely considered the important question of how large the uncertainty set should be, and hence, how the uncertainty budget can be determined objectively. This study addresses this issue by proposing a novel adaptive optimization method that optimizes the value of the uncertainty budget to minimize the size of the uncertainty set while considering the underlying risk for wind power generation (WPG) fluctuations residing outside of the proposed uncertainty set. As such, the proposed method ensures a good tradeoff between the robustness and costs of RTEP solutions. In addition, the proposed method optimizes investment strategies under forecasted WPG scenarios, while providing a security guarantee under extreme WPG scenarios. The variable-limit integral terms introduced by the proposed method are addressed in the solution process by applying the piecewise linearization approximation method combined with the quadratic Newton-Gregory interpolating polynomial technique, which allows the solution process to be cast as a mixed integer linear programming problem. The good performance and effectiveness of the proposed adaptive uncertainty set optimization method are verified by numerical results. [ABSTRACT FROM AUTHOR]

The large shares of wind power generation in electricity markets motivate higher levels of operating reserves. However, current reserve sizing practices fail to account for important topological aspects that might hinder their deployment, thus resulting in high operating costs. Zonal reserve procurement mitigates such inefficiencies, however, the way the zones are defined is still open to interpretation. This paper challenges the efficiency of predetermined zonal setups that neglect the location of stochastic power production in the system, as well as the availability, cost and accessibility of flexible generating units. To this end, we propose a novel reserve procurement approach, formulated as a two-stage stochastic bilevel model, in which the upper level identifies a number of contiguous reserve zones using dynamic grid partitioning and sets zonal requirements based on the total expected operating costs. Using two standard IEEE reliability test cases, we show how the efficient partitioning of reserve zones can reduce expected system cost and promote the integration of stochastic renewables. [ABSTRACT FROM AUTHOR]

This work explores the benefits of increasing transmission capacity between the US Eastern and Western Interconnections under a high-renewables future. Given the existing “seam” between the two interconnections, a co-optimized infrastructure planning model was developed to assess trade-offs between investments in cross-seam HVDC transmission, AC and DC transmission needs within each interconnection, generation investment costs, and operational costs, at different renewable penetration levels. The model allows existing and candidate generation resources for deliverable planning reserves to be shared throughout the interconnections, a feature which drives identification of least-cost investments. This work is performed using an industry-vetted 169-bus representation of the North American power grid. Results from this analysis indicate that, under high wind/solar growth scenarios, the cost of a macrogrid HVDC transmission is outweighed by the generation-related savings they produce. The presence of other benefits related to grid reliability, resilience, and adaptability, suggest that cross-seam transmission is highly attractive infrastructure. [ABSTRACT FROM AUTHOR]