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The integration of large-scale renewables into the multienergy system has brought a series of problems and challenges to the optimal dispatch of system, especially how to effectively realize the dispatch and accommodation of wind power. In this article, a dynamic economic dispatch (DED) model of wind/combined heat and power (CHP) hybrid energy system considering uncertainty of multiple wind farms and different dispatch time scales is proposed, which aims to minimize expected total energy generation cost based on the typical scenarios of upper bound of wind farm output. The spatial dependence of hourly output of multiwind farm is modeled by copula-based model and improved scenario reduction technique, and the different adjustment time scales of heating system and power system are modeled as well to achieve more reasonable and accurate system dispatching. In addition, an improved adaptive cuckoo search algorithm (ACSA) is proposed for the solution of the DED model of wind/CHP hybrid energy system with highly nonlinear constraints, and a shared parallel computing platform is employed to realize the acceleration of the ACSA. Finally, the corresponding numerical simulation and comparative analysis are performed on two test systems to verify the validity of the proposed model and method. [ABSTRACT FROM AUTHOR]

We propose a power-based unit commitment formulation with capacity and intra-hour ramp reserves for dealing with intra-hour wind power variability and uncertainty. Although the formulation has an hourly resolution, the intra-hour ramp requirements capture wind power ramp excursions with a time duration below one hour, and thus allows the formulation to consider intra-hourly wind variability and uncertainty. This increases the security of the formulation compared to using hourly ramp reserves and allows more efficient scheduling of units with high ramp rates. We test the formulation with different durations for the intra-hour reserves, and using both hourly and intra-hourly ramp reserves, to find the best reserve formulation. The formulations are evaluated using a 5-min economic dispatch, which simulates the real-time operation of the system, for hundreds of out-of-sample realizations of wind power production. The proposed formulations are then compared to two hourly stochastic formulations and a stochastic formulation with 5-min time resolution. The proposed formulations outperform the stochastic formulations in terms of security, showing that they provide a scheduling which is more robust against intra-hour wind power variations. The proposed formulations also outperform the hourly stochastic formulations in terms of total costs, giving a better trade-off between scheduling costs and security. [ABSTRACT FROM AUTHOR]

The uncertainty of wind power and electricityprice restrict the profitability of wind-storage integrated system (WSS) participating in real-time market (RTM). This paper presents a self-dispatch model for WSS based on deep reinforcement learning (DRL). The designed model is able to learn the integrated bidding and charging policy of WSS from the historical data. Besides, the maximum entropy and distributed prioritized experience replay frame, known as Ape-X, is used in this model. The Ape-X decouples the acting and learning in training by a central shared replay memory to enhance the efficiency and performance of the DRL procedures. Besides, the maximum entropy framework enables the designed agent to explore various optimal possibilities, thus the learned policy is more stable considering the uncertainty of wind power and electricity price. Compared with traditional methods, this model brings more benefits to wind farms while ensuring robustness. [ABSTRACT FROM AUTHOR]

Nowadays, taking into account the intermittency of renewable energy resources such as wind farms and uncertainty of load demand seems helpful to obtain a more reliable strategy for the power systems. Nevertheless, information gap decision theory (IGDT) as a nonprobabilistic method has been employed in numerous papers to address the uncertain behavior of input parameters, the simultaneous optimal values of main objective functions (OF) such as cost and radius of uncertainty cannot be guaranteed. To overcome this issue, Fuzzy- IGDT is used, on the other hand, this approach reports the same value for the radius of uncertainty related to the uncertain resources. To cope with this problem, this article presents an algorithm considering uncertainties of multiple wind farms and load demand by acquiring different uncertain bands based on the decision-maker's preferences. Moreover, it is appropriate for uncertain resources with direct and inverse effects on the OF. In other words, it is more flexible than fuzzy-information gap decision theory. The precision of the proposed framework is evaluated by Monte Carlo simulation, meanwhile, its effectiveness and performances are proved. To guarantee global optimal results with reliable precision, the linearized approximation of the original mix integer nonlinear programming model has been accomplished in the GAMS platform. The performance of presented method is illustrated by utilizing IEEE 30 BUS and IEEE 62 bus systems. [ABSTRACT FROM AUTHOR]

This article proposes a risk-based contingency-constrained optimal power flow model by leveraging the methods of both adjustable uncertainty set and distributionally robust optimization. In the proposed model, an adjustable uncertainty set of wind power is developed with network contingencies explicitly incorporated. Based on this uncertainty set, the proposed model is capable of securing the network against both wind power fluctuations and contingencies in a probabilistic manner with the optimal balance between operation cost and risk. Meanwhile, a data-driven L1-norm-based ambiguity set is employed so that the proposed model is distributionally robust to the ambiguous probability distribution of wind power and the size of the model remains unchanged as the available wind power data increases. A decomposition-based algorithm is also derived so that the proposed model is solvable by off-the-shelf solvers. Numerical studies on IEEE 14- and 118-bus systems are conducted to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Chance constrained economic dispatch (CCED) is widely used to handle uncertainties in power systems with high-proportion renewable energy sources (RESs). However, in such system, the upper and lower limits of reserve or transmission line constraints may be violated simultaneously, which makes single-side CCED (SS-CCED) inapplicable. This letter develops a two-side CCED (TS-CCED) model, in which the Gaussian mixture model (GMM) is used to characterize the correlated non-Gaussian distribution of RESs. We propose a hyperbolic tangent function based approximation method to approach GMM and make the TS-CCED tractable. Numerical studies show the proposed method is more applicable than SS-CCED with high efficiency. [ABSTRACT FROM AUTHOR]

In a deregulated environment, the renewable energy producers will face the challenge of how to increase their revenues under uncertainties of power generation and time-varying electricity price. In traditional power network scheduling, prediction and optimization are two independent processes, which easily leads to information loss and modeling error. To deal with the uncertainty and realize an end-to-end controller, this article proposes an energy storage system control model (ESSCM) in the scene of the combined wind-solar storage system. The proposed ESSCM using deep reinforcement learning (DRL) algorithm is trained by interacting with the massive environment of a power grid without requiring the assumption on the uncertainties. It learns from scratch to realize the coordination operation of with wind power and photovoltaic power in a combined system, further maximize the benefits of the combined system in the electricity market. One state-of-the-art DRL algorithm, namely double deep Q-network, is used to formulate the proposed ESSCM. Numerical results illustrate that the proposed approach can effectively accommodate the uncertainty and bring high revenues to the combined system. [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]

The volatile nature of wind power generation creates challenges in achieving secure power grid operations. It is, therefore, necessary to accurately predict wind power and its uncertainty quantification. Wind power forecasting usually depends on wind speed prediction and the wind-to-power conversion process. However, most current wind power prediction models only consider portions of the uncertainty. This paper develops an integrative framework for predicting wind power density, considering uncertainties arising from both wind speed prediction and the wind-to-power conversion process. Specifically, we model wind speed using the inhomogeneous Geometric Brownian Motion and convert the wind speed prediction density into the wind power density in a closed-form. The resulting wind power density allows quantifying prediction uncertainties through prediction intervals. To forecast the power output, we minimize the expected prediction cost with (unequal) penalties on the overestimation and underestimation. We show the predictive power of the proposed approach using data from multiple operating wind farms located at different sites. [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]

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]

In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional, and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage, and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error, and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency, and robustness of dispatch decisions. [ABSTRACT FROM AUTHOR]

This article proposes a method based on data clustering for the optimal placement and sizing of wind farms (WFs) in radial distribution systems considering the wind uncertainty and the wake effect. The stochastic output of wind turbines makes the optimization problem more challenging. Using the probabilistic methods for such analyses proves efficient to yield more reliable results. The data clustering-based Monte Carlo simulation is used to bunch the output powers of wind farm into clusters. The network loss and voltage profile are then evaluated to achieve the optimal candidate bus for the placement of WF with the optimal number of turbines. To accelerate the procedure, a technical constraint is used so as to eliminate the nonimportant samples in WF size evaluation, which results in a reduction in computational burden. In addition, two methods for load flow calculations are investigated, namely the direct load flow and indirect backward/forward sweep load flow methods to evaluate the time burden of load flow method on the proposed problem. The effectiveness of the proposed methodology is illustated by conducting case studies. [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]

Power-to-gas (P2G) technology is an effective way to provide additional flexibility to electricity systems with high penetration of renewable energy. Effective P2G bidding strategies in electricity markets can bring in arbitrage opportunities. This article proposes a coordinated bidding strategy for wind farms and P2G facilities using a cooperative game approach. A coordination framework for optimizing the profit of wind farms and P2G facilities is presented, in which wind power participates in day-ahead, real-time and reserve markets, and the P2G facilities participate in day-ahead and reserve markets for arbitrage. Wind farms strategically purchase reserve to avoid high imbalance penalties. As a coalition, wind farms can provide energy to P2G facilities and receive reserve capacity in return. The coordinated bidding strategy is modeled on stochastic programming to maximize the expected joint profit of wind farms and P2G facilities. Nucleolus and Shapley-value based methods are proposed to allocate profits to each player in the coalition. Numerical results based on real world market data demonstrate that the proposed bidding strategy can increase the profits of both wind farms and P2G facilities. Strategically purchasing reserve can reduce the imbalance penalties of wind farms, and participating in reserve markets of P2G facilities can increase profit. [ABSTRACT FROM AUTHOR]

This article presents a two-stage adaptive robust coordinated generation and transmission expansion planning model for a wind farm-integrated power system. Also, dynamic thermal rating (DTR) systems, energy storage systems, and optimal line switching maneuvers are considered as various flexible sources to enhance the flexibility of the power system in response to uncertain variations of net system demand. The proposed approach characterizes the uncertainty of demands, wind power, and DTRs in each representative day by a polyhedral uncertainty set. Additionally, the $k$ -means clustering technique is used to obtain upward/downward variations of correlated uncertain parameters in each representative day and to construct the uncertainty set. The proposed model is inherently intractable as it includes infinite constraints modeling enforced techno-economic limitations for all realizations of uncertain parameters. To resolve this limitation, the proposed intractable model is recast as a tractable mixed-integer linear programming problem using affine policies. The proposed approach is implemented on the Garver 6-bus and IEEE 73-bus test systems. Simulation results illustrate its flexibility, practicality, and tractability. [ABSTRACT FROM AUTHOR]

Due to the widely deployment of gas-fired units and the emerging power-to-gas (P2G) technologies, the interdependencies between power systems and gas systems have been enhanced, yet the impacts on the ability of accommodating the uncertain and variable wind generation are unclear. On one hand, the regulation capability of gas-fired units might be restricted due to pipeline congestion or gas supply shortage; on the other hand, the P2G facilities could operate as interruptible electrical loads to enhance the operational flexibility of the power network. This paper aims to revisit the wind generation admissibility assessment problem in view of integrated electric-gas systems. The overall model is established according to the two-stage robust optimization framework. By introducing the stepwise penalty coefficients for power shortage and surplus, the risk preference of the operator can be reflected. The mixed integer linear programming-based approximation methods is adopted to tackle the computational challenging Weymouth equation in the gas network, which requires an additional column-and-constraint (C&CG) loop to solve the second-stage max-min problem, other than the common one to coordinate the first- and second-stage problems, resulting in a nested C&CG algorithmic structure. The effectiveness of the proposed model and solution methods are validated by the simulation results. [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]

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]

The increasing penetration level of wind power challenges robust unit commitment with feasibilities and high computational burden. To meet these challenges, we propose two-fold advances for the two-stage robust unit commitment (TS-RUC), aiming at providing feasible solution and efficient decision tool for the TS-RUC with multiple wind farms. First, the feasibility identification method is proposed to ensure the tractability of the TS-RUC. The feasibility boundaries are determined based on values of two sets of introduced slack variables, the wind power curtailment and load shedding. Second, the disjunctive programming is used to improve the computational efficiency of the max-min problem, which is reformulated with convex hull relaxation (CHR) method to reduce constraints embedding binary uncertainty variables. Simulation results on the modified IEEE-118 bus system and Henan power grid demonstrate that the proposed improvement for the TS-RUC can be implemented for power systems with multiple wind farms and significant wind power. The feasibility identification can guarantee a feasible solution and the use of the CHR can improve computational efficiency. [ABSTRACT FROM AUTHOR]

Using the multi-terminal VSC-HVdc (MTDC) system to collect far-distance offshore wind power into the main onshore ac grid has become one of the ideal transmission approaches for renewable energy integration. However, with traditional fixed dc droop control in MTDC system, the lack of the capability of regulating power flow might pose a great challenge to the system operation. Accordingly, a novel MTDC model has been established in this paper which establishes that the output power of onshore converters can be formulated as a linear function of the control variables, namely power initial set point of each onshore converter. Based on this model, considering the uncertainty from wind power forecast error, a distributionally robust chance-constrained AC-OPF model is proposed for the hybrid AC/MTDC system. Without any presumption on the probability distribution of uncertainty, this model ensures the secure operation by enforcing chance constraints under the worst-case probability distribution over an ambiguity set based on the Wasserstein-Moment metric. Aiming at obtaining a tractable chance-constraint reformulation, we first employ the partial linearization of ac power flow equations to yield a linear model which represents the system response under uncertainties. We then develop an efficient and scalable approach to derive the linear analytical reformulation of distributionally robust chance constraints. The performance of the proposed model is firstly tested on the 14-bus system for an illustrative purpose, and then on the 1354-bus system for demonstrating scalability. [ABSTRACT FROM AUTHOR]

The main idea of this paper is to present a method for offering a power generation rate of wind power plants in the electricity market in the conditions, in which there is a lack or extreme shortage of information. In such a state, methods conventionally used in normal conditions are no more applicable. The methods that have been formerly presented for the conditions with severe uncertainty are mostly applied in local decision making, but in the method proposed in this paper, global decision making is considered. The proposed method is based on Liu's uncertainty theory, and the information related to uncertain variables is provided by experts. After developing a cumulative distribution function for expert data, Liu's distribution is calculated. Then, the values of uncertain variables are determined based on various belief degrees. After converting the uncertain model of the objective function into a certain equivalent model in the Liu space, the profit function should be maximized via the two-stage stochastic programming method. The data used are real and relevant to the Nord Pool market. Investigation of the simulation results for two different and specific days indicates the efficiency of the proposed strategy. [ABSTRACT FROM AUTHOR]

The irregular and truncated probabilistic characteristics of wind power uncertainty lead to unknown influences on the power system operation. In this article, we propose a new probabilistic optimal power flow (POPF) framework, which can cope with such uncertainties, while taking into account the correlations among the wind generation power in multiple wind farms. A truncated multivariate Gaussian mixture model (Trun-MultiGMM) is designed to describe the irregular and multimodal wind power distributions with its typical truncation feature. Then an efficient Markov chain quasi-Monte-Carlo (MCQMC) sampler is developed to deliver wind power samples from the customized Trun-MultiGMM. Numerical simulations are conducted on the publicly available wind generation datasets and multiple benchmark power systems. The results have verified the effectiveness and efficiency of Trun-MultiGMM as well as the proposed POPF framework with MCQMC sampler. [ABSTRACT FROM AUTHOR]

The extensive penetration of wind farms (WFs) presents challenges to the operation of distribution networks (DNs). Building a probability distribution of the aggregated wind power forecast error is of great value for decision making. However, as a result of recent government incentives, many WFs are being newly built with little historical data for training distribution models. Moreover, WFs with different stakeholders may refuse to submit the raw data to a data center for model training. To address these problems, a Gaussian mixture model (GMM) is applied to build the distribution of the aggregated wind power forecast error; then, the maximum a posteriori (MAP) estimation method is adopted to overcome the limited training data problem in GMM parameter estimation. Next, a distributed MAP estimation method is developed based on the average consensus filter algorithm to address the data privacy issue. The distribution control center is introduced into the distributed estimation process to acquire more precise estimation results and better adapt to the DN control architecture. The effectiveness of the proposed algorithm is empirically verified using historical data. [ABSTRACT FROM AUTHOR]

This paper presents a day-ahead coordinated scheduling method of hydro and wind power generation systems (HWPGSs) with consideration of uncertainties. In this method, we first formulate the coordinated scheduling model with two-part price and power flow constraints, which manifests the fixed and variable economic benefits as well as the secure operation of HWPGS, respectively. Then, the interval analysis is used to study the effect of uncertain wind power, water inflow, and electricity load on the coordinated scheduling model. Finally, we use a real test system in a western area of China to conduct simulation studies, which verify the effectiveness of the interval analysis and the effect of price mechanism on the day-ahead coordinated scheduling of HWPGS. [ABSTRACT FROM AUTHOR]

Security-constrained economic dispatch is executed based on consecutive dispatch intervals in real time. The short-term variations of wind power can cause the system to enter an unsecured operating region inside a dispatch interval, which is referred to as the intra-interval security (IIS) problem in this paper. IIS may not be addressed by existing dispatch methods as the traditional dispatch is to ensure the security at the interval end. This can lead to IIS risks in an interval when a high-wind-penetrated system encounters large intra-interval variations (IIVs) of wind power. To address this issue, an IIS preventive dispatch approach is proposed in this study. This approach models the wind power IIVs and develops a preventive dispatch to ensure the IIS over the interval in terms of line overloads while taking into account the tradeoff between security and economics. The proposed approach is implemented in a linear-programming model whose global optimum can be efficiently obtained by adding Benders-like cuts. Case study on the IEEE 118-bus system proves that a high level of nonlinear IIVs can cause the IIS issue (inside of an interval) even with accurate wind forecasts at both interval ends. The simulations show that some lines can have severe overloads inside the dispatch interval in spite of having flows below their capacity limits at both interval ends, and demonstrate that the proposed approach can mitigate such intra-interval overloads even under the worst case IIV scenario. [ABSTRACT FROM AUTHOR]

This paper proposes a new distributionally robust optimization (DRO) framework for unit commitment under uncertain wind power. The proposed framework minimizes the worst-case expected total cost over an ambiguity set of possible probability distributions. Unlike the other DRO models that typically exploits variance and covariance data of random variables, this framework uses a distributional interpretation of uncertainty sets to construct the ambiguity set, and it can be solved as an equivalent problem that resembles a conventional two-stage robust linear program. Case studies demonstrate that the proposed model may effectively capture ambiguous distribution information and improve system performance. [ABSTRACT FROM AUTHOR]

The increasing penetration of wind energy poses great challenges to the operation of power systems in normal and emergency states. However, energy storage technologies can help accommodate wind power uncertainty and variability due to their flexible characteristics. This paper focuses on the restoration phase, and provides a novel coordination strategy of wind and pumped-storage hydro (PSH) units for a faster and reliable self-healing process. The wind-PSH assisted power system restoration is formulated as a two-stage adaptive robust optimization problem. The first-stage problem determines the start-up sequence of generators and the energization times of transmission paths; and the second-stage problem decides load pickup sequences, wind power dispatch levels, and PSH units’ operating modes. The column-and-constraint generation decomposition algorithm is applied to solve the two-stage adaptive robust optimization problem, which has a mixed-integer optimization in the inner-level problem. The developed coordination strategy is tested on the modified IEEE 39-bus system. Numerical results demonstrate that the coordinated wind and PSH units can increase the total energy served, enhance wind power dispatchability, and reduce wind power curtailment. [ABSTRACT FROM AUTHOR]

Due to uncertain nature of wind energy, the profit of a wind producer (WP) is at a notable risk. To overcome the risk associated with the uncertain wind power productions, energy storage systems have attracted an increasing attention. However, due to electricity price forecast errors, storage systems might not be able to efficiently participate in an electricity market as they both purchase and sell energy. Therefore, although the combination of WPs and storage systems can be economically promising, they require a proper offering and bidding strategy, which effectively characterizes the uncertainty associated with both wind power production and price forecast errors. To do so, this paper proposes an adaptive robust self-scheduling model for a WP paired with a compressed air energy storage system to participate in the day-ahead energy market. The proposed model addresses the uncertainties regarding the wind power productions and price forecast errors. Furthermore, the flexibility and the robustness of the proposed method can be controlled using a parameter denominating the budget of uncertainty. Simulation results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, a novel approach for look-ahead dispatch (LAD) considering large-scale wind power integration is proposed. An index designated the conditional value-at-risk of wind power (CVaR-WP) is introduced to evaluate the risk of wind power accommodation. A flexible LAD model is developed to balance the operational costs and the CVaR-WP based on robust optimization (RO). According to the proposed model, the base points, participation factors, and flexible capacity of automatic generation control units are co-optimized. In addition, a reasonable admissible region of wind power on each node can be obtained correspondingly. An efficient algorithm based on the big-M method and the decomposition method is presented to solve the resulting bilinear programing model. The proposed approach combines the advantages of RO and stochastic programing, which can avoid the overconservativeness of RO while maintaining its high computing efficiency. Test results illustrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

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

In the power system stochastic unit commitment (SUC) model, the uncertainty and variability of the renewable energy generation, such as wind power, are usually expressed by multiple scenarios. The performance of SUC is driven by how well the selected scenarios represent the stochastic nature, since too few scenarios may lose or distort the uncertainty or variability characteristics, while too many scenarios usually cause computational difficulty. This paper proposes a novel scenario representation method referred to as scenario mapping technology (SMT), which is able to compact large amount of scenarios while preserving the uncertainty and variability features of wind power as much as possible. Specifically, SMT proposes to combine similar wind power generation into a state at each period and contains the possible multiple transitions linking the states in adjacent periods. A novel two-stage SUC model is proposed based on SMT. The numerical results demonstrate a solid improvement of the performance for the SMT-based SUC model on both cost-efficiency and calculation efficiency, compared with traditional two-stage SUC model based on the scenario reduction technique. [ABSTRACT FROM AUTHOR]

Uncertainties associated with wind power integration challenge the operational adequacy of conventional power systems. A set of wind power ramp limits (WPRLs) is proposed in this paper to evaluate the operational adequacy of power systems with high wind power penetration and to provide operating references to wind farms in the form of a ramp power limit (RPL) and ramp rate limit (RRL). The RPL is used to evaluate the minimum and maximum allowable generation of a wind farm by considering the power reserve capacities of generators and power flow constraints of transmission lines. A robust second-order cone programming RPLs formulation with AC power flow constraints and a column-and-constraint generation based solution method are proposed to maximize the total operating range of all wind farms. Meanwhile, a Pareto optimality based RPLs evaluation approach is proposed to handle the coupled relationship among the operating ranges of the wind farms to achieve a balanced RPLs solution for each wind farm. The RRL is used to evaluate the most rapid wind power ramp behavior that can be handled by system frequency regulation without exceeding the designated frequency range. A comprehensive criterion is proposed to evaluate the RRLs by considering primary and secondary frequency regulation. Finally, the effectiveness of the proposed evaluation approach is verified through case studies. [ABSTRACT FROM PUBLISHER]

As wind power makes an increasing  contribution to power systems, the problems associated with wind power curtailment have become a concern in recent years. Battery energy storage (BES) can reduce the effects of wind power curtailment by peak shaving and wind power forecast error compensation. Accordingly, the operational constraints of power systems and wind power uncertainty should be considered in the optimization of BES capacity installed at wind farms. This paper proposes a two-stage method to determine the optimal power and capacity of BES in systems including thermal plants, wind farms, and BES. In the first stage, the unit commitment of thermal generators and scheduled wind farm output are optimized with ac power flow constraints modeled by second-order cone programming. Time series of the wind farm output generated by Monte Carlo simulations are used for BES optimization. In the second stage, operational strategies for BES are designed. The simulation results indicate that cooperation between the BES and wind farm using the proposed method can reduce the costs of both wind farms and thermal plants. Finally, a sensitivity analysis is performed to assess the influence of the BES unit cost and wind power penetration on the optimal power and capacity of BES. [ABSTRACT FROM PUBLISHER]

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

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

It is important to select an appropriate uncertainty level of the wind power forecast for power system scheduling and electricity market operation. Traditional methods hedge against a predefined level of wind power uncertainty, such as a specific confidence interval or uncertainty set, which leaves the questions of how to best select the appropriate uncertainty levels. To bridge this gap, this paper proposes a model to optimize the forecast uncertainty intervals of wind power for power system scheduling problems, with the aim of achieving the best trade-off between economics and reliability. Then, we reformulate and linearize the models into a mixed integer linear programming (MILP) without strong assumptions on the shape of the probability distribution. In order to invest the impacts on cost, reliability, and prices in a electricity market, we apply the proposed model on a two-settlement electricity market based on a six-bus test system and on a power system representing the U.S. state of Illinois. The results show that the proposed method can not only help to balance the economics and reliability of the power system scheduling, but also help to stabilize the energy prices in electricity market operation. [ABSTRACT FROM PUBLISHER]

In the scheduling of wind farms, the fluctuation of system's power demand is required to track within a certain time period. It benefits to reasonably arrange division of wind turbines and distribution of active power output. This paper proposes a stochastic optimal scheduling method based on scenario analysis for wind farms. While tracking the power demand on the system side, the uncertainty of wind speed and the effect of wake flow in the wind farm are also considered in the model in order to minimize the operating cost. The method of scenario analysis can determine uncertain variables, and the nonuniform segmentation piecewise linearization method is used to linearize the model. The mixed-integer linear programming method is used to figure out the optimal scheduling strategy for the wind farm, thus, greatly increasing the economical operation of the wind farm. This proposed method is proved to be effective on an actual wind farm in East Inner Mongolia of China. [ABSTRACT FROM PUBLISHER]

Owing to the large physical area of a wind farm, some uncertainty and inefficiency issues exist in the related power delivery process. To provide required ancillary services regarding reactive power for the utility grid, further optimization processes are needed to maintain the reliability and efficiency of the entire system. In this paper, we introduce a reactive power assignment strategy that is based on the linearized system components of a wind farm, which comprises a power conversion system. Additionally, we perform realistic assignment processes to verify the effectiveness of this strategy with electromagnetic transients using dc software tool. Reducing the total apparent power flow by utilizing the radial structure of the wind farm is explored by assigning reactive power to nearby wind turbines. The verification process focuses on comparing the loss in output profile of a normal assignment and the proposed method in a designated wind farm. [ABSTRACT FROM AUTHOR]

Power system operation has recently witnessed major challenges, which are often due to large-scale integrations of wind power generation. In this paper, a two-stage robust security-constrained unit commitment (SCUC) model is proposed for managing the wind power uncertainty in the hourly scheduling of power system generation. Different from previous studies on robust SCUC, which considered a predefined uncertainty set, the proposed method applies a flexible uncertainty set for managing the variable wind power generation. The proposed method seeks a feasible and economic dispatch in the flexible uncertainty set, takes into account wind spillage and load curtailment risks, and makes a tradeoff between the optimal wind power absorption and the economic grid operation. Several case studies are applied to the proposed method and the corresponding solutions are analyzed in the paper. The impacts of major factors, including flexible generation resources and power transmission capacity, on the proposed solution are also discussed. The numerical results demonstrate the merits of the proposed method for managing large variations in the hourly wind power generation and lowering the power system operation cost in uncertain conditions. [ABSTRACT FROM PUBLISHER]

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

The impact of wind power forecast uncertainty has been amplified by the deepening wind power penetration. To guarantee system security and reliability, sufficient dispatchable generation and transmission capacities have to be reserved. Currently, research has been carried out to improve system operational performance by optimizing schedules considering uncertainty. However, most methods are designed to cover a given risk level of uncertainty, which is determined ex ante. With the increase in wind power capacity, defining the risk level a priori without considering the unit commitment (UC) may limit the scheduling efficiency. Essentially, there is no absolute standard for acceptable risk exposure. Instead, there is a tradeoff between the risk and the cost of reserve capacity. Therefore, it is necessary to develop a tool to enable a flexible and comprehensive consideration of the risk level. In this paper, by combining chance constrained programming and goal programming, a novel model based on chance constrained goal programming is proposed to optimize the risk adjustable UC problem. To facilitate an efficient solution, the proposed model is transferred into a tractable mixed integer linear programming problem by a deterministic equivalent and piecewise linearization. Case studies are performed on an IEEE 118-bus system to illustrate the effectiveness and efficiency of the model. [ABSTRACT FROM PUBLISHER]

This paper presents an adaptive robust network-constrained AC unit commitment (AC-UC) model. This model is formulated as a min–max–min optimization problem, which allows representing the uncertain nature of wind power productions in terms of bounded intervals. A tri-level decomposition algorithm using primal and dual cutting planes is introduced to solve this AC-UC problem and to find a robust commitment schedule withstanding the worst realizations of uncertain wind power. To reduce the computation burden and to obtain a tractable formulation, the AC power flow equations are convexified using a Signomial transformation. The proposed AC-UC model is illustrated using the IEEE 24-bus reliability test system. Simulation results demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents an adjustable interval optimization model for the energy and reserve clearance while treating the wind power variation and uncertainty. Instead of conventional predicted intervals (PIs), adjustable intervals (AIs) as subsets of PIs are proposed as more judicious choices for economically covering wind uncertainties. Ramp-capability reserve is modeled to ensure the existence of sufficient ramp capability needed to follow up wind power variation within AIs. However, realization of wind power beyond AIs, which is no longer compensable by ramp-capability reserve, would necessarily lead to either load shedding or wind spillage. In order to optimally determine AIs, apart from the energy and reserve procurement costs, the costs associated with load shedding and wind spillage are incorporated in the objective function. The confidence level theory is employed as well for tuning the robustness and conservatism of the final solution. Performance of the proposed method is examined on several case studies on an 8-bus and modified IEEE 118-bus test systems. Sensitivity analyses are conducted to specify the impacts of important parameters on the obtained solution. The results confirm the applicability and effectiveness of the proposed methodology. [ABSTRACT FROM PUBLISHER]

In this paper, we consider dispatchability as the set of all admissible nodal wind power injections that will not cause infeasibility in real-time dispatch (RTD). Our work reveals that the dispatchability of the affine policy based RTD (AF-RTD) is a polytope whose coefficients are linear functions of the generation schedule and the gain matrix of affine policy. Two mathematical formulations of the dispatchability maximized energy and reserve dispatch (DM-ERD) are proposed. The first one maximizes the distance from the forecast to the boundaries of the dispatchability polytope subject to the available production cost or reserve cost. Provided the forecast value and variance of wind power, the generalized Gauss inequality (GGI) is adopted to evaluate the probability of infeasible RTD without the exact probability distribution of wind power. Combining the first formulation and the GGI approach, the second one minimizes the total cost subject to a desired reliability level through dispatchability maximization. Efficient convex optimization based algorithms are developed to solve these two models. Different from the conventional robust optimization method, our model does not rely on the specific uncertainty set of wind generation and directly optimizes the uncertainty accommodation capability of the power system. The proposed method is also compared with the affine policy based robust energy and reserve dispatch (AR-ERD). Case studies on the PJM 5-bus system illustrate the proposed concept and method. Experiments on the IEEE 118-bus system demonstrate the applicability of our method on moderate sized systems and its scalability to large dimensional uncertainty. [ABSTRACT FROM PUBLISHER]

The United States targets to supply 20% of its electricity generation using wind energy by 2030. The expansion of renewable resources, especially weather-based resources such as wind, creates more uncertainty and variability in the operation of the power grid. New methods and approaches in electricity market operations are needed to efficiently manage the continuing increase in variability and uncertainty caused by expanding intermittent wind. This paper proposes an improved stochastic programming approach for incorporating wind uncertainty into energy markets. The proposed formulation improves the two-stage stochastic unit commitment problem by introducing a dynamic decision making approach similar to a multi-stage formulation in the presence of wind power scenarios which are not well represented by a scenario tree. The numerical results present up to 1%–2% decrease in operational costs compared to the two-stage stochastic unit commitment formulation. [ABSTRACT FROM PUBLISHER]

Large-scale wind farms are typically geographically separated from load centers and distributed in different control areas. Therefore, interregional energy dispatch is important for wind power generation via sharing spinning reserve capacity among interconnected systems. However, existing tie-line scheduling methods in China do not provide satisfactory performance in accommodating the recent large-scale integration of wind power. In this paper, we describe a coordination framework for tie-line scheduling and power dispatch to operate multi-area systems. Tie-line flows are updated hourly to hedge uncertainty in the near future, preserving the operational independence of areas. The coordinated tie-line scheduling problem is formulated using two-stage adaptive robust optimization to account for uncertainties in the available wind power and is solved using a column-and-constraint generation method in a coordinate-and-decentralize manner. Comparative simulations show that the method is effective in enabling further wind power penetration and can improve economic efficiency in multi-area systems. A case study using a large-scale power system demonstrates the benefits and scalability of the method in practice. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical-based algorithm to solve the probabilistic power flow problem. Parzen window density estimator is used to efficiently estimate probabilistic characteristics of power flow outputs. Correlations between wind generation, load, and plug-in hybrid electric vehicle charging stations are taken into account. The proposed algorithm works properly for random variables with various probability distribution functions and is very useful when limited information is available for each random variable. The algorithm is tested on the IEEE 14-bus and IEEE 118-bus systems considering correlated and uncorrelated conditions. Comparison between the proposed algorithm with 2n, \text2n + 1 point estimation methods as well as Monte Carlo simulation and linear diffusion method are provided. In addition, probability density and cumulative distribution functions are determined using the proposed algorithm, diffusion method, and the combined Cumulants and Gram-Charlier for \text2n + 1 point estimation method. Error indices are introduced to evaluate all random variables in a single benchmark. Simulation results show the effectiveness of the proposed algorithm to provide complete statistical information for probabilistic power flow outputs. [ABSTRACT FROM PUBLISHER]

Power generation uncertainty is an important characteristic of variable generation (VG) platforms, such as wind and solar power, which brings additional operational costs to the power systems. To manage this uncertainty, responsibilities should be properly allocated to encourage good behaviors of system participants, especially the VG producers. Currently, the imbalance-cost-based mechanism is most commonly used for uncertainty management. Based on this method, we consider a new mechanism in this paper for capturing the uncertainty, which may achieve a better mechanism performance. The basic idea is to allow producers to purchase generation intervals (GIs) for their potential production output. The analysis presented in this paper indicates that producers can be very responsive to this mechanism. With the proper pricing policies, producers can be encouraged to provide additional information on upcoming uncertainties to the system operators. Additionally, three strategies for pricing GIs are included in this paper. Case studies are used to demonstrate the application of the mechanism as well as its effectiveness. [ABSTRACT FROM PUBLISHER]

The unpredictable and volatile nature of wind power is the main obstacle of this generation source in short-term trading. Owing to the ability of demand side to cover wind power imbalances, aggregated loads have been presented in the literature as a good complementary resource for the wind generation. To this end, this paper proposes a technique to obtain the best offering strategy for a hybrid power plant consisting of a wind power producer and a demand response provider in the power market. In addition, conditional value-at-risk is used to limit the risk on profit variability. Finally, a detailed analysis of a realistic case study based on a wind farm in Spain has illustrated that joint operation of wind power producers and demand response providers can increase the expected profit and reduce the potential risks. [ABSTRACT FROM PUBLISHER]