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Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is that quantum noise is highly unstable and thus it is likely to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the quantum approximate optimization algorithm and the variational quantum eigensolver with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step toward improving the reliability of VQAs influenced by shifted noise from the parameter optimization perspective.

Advanced adiabatic compressed air energy storage (AA-CAES) has the advantages of large capacity, long service time, combined heat and power generation (CHP), and does not consume fossil fuels, making it a promising storage technology in a low-carbon society. An appropriate self-scheduling model can guarantee AA-CAES's profit and attract investments. However, very few studies refer to the cogeneration ability of AA-CAES, which enables the possibility to trade in the electricity and heat markets at the same time. In this paper, we propose a multi-market self-scheduling model to make full use of heat produced in compressors. The volatile market price is modeled by a set of inexact distributions based on historical data through ø-divergence. Then, the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory, and equivalently reformulated as a mixed-integer linear program (MILP). The numerical simulation results validate the proposed method and demonstrate that participating in multi-energy markets increases overall profits. The impact of uncertainty parameters is also discussed in the sensibility analysis.

Recent research in deterministic sensor placement optimization technologies has improved the capability of monitoring large-scale field environments with a limited budget. In traditional stochastic mixed-integer linear programming formulations, minimizing the expectation of detection time can lead to a detector placement with good average behavior but unexpected worst case behavior. The uncertainty factors in the complex environment and sensor system significantly challenge the effects of the placement strategy provided by stochastic programming (SP). These factors include unknown leakage rate and location, sensor delay, and primary uncertainty of wind conditions. This article introduces a distributionally robust optimization (DRO) formulation of sensor placement under the uncertainty of wind conditions and improves a sensor network’s detection robustness. The method is demonstrated using the atmospheric simulation with site-specific methane-emission scenarios that capture partial natural wind conditions and emission characteristics. DRO techniques are employed to determine sensor locations that minimize the detection time expectation of the emission scenarios with a significantly better worst case behavior. Experiment results show that the proposed DRO method outperforms the sensor placement methods based on SP. [ABSTRACT FROM AUTHOR]

The increased integration of distributed generators (DGs) has exacerbated voltage violations in active distribution networks (ADNs). Utilizing the var capacity offered by DG inverters presents a potential solution for managing the voltage of ADN. By merging the merits of different hierarchies, the combined voltage control can provide better performances in addressing the variability of DGs. In this paper, a combined central-local voltage control strategy is proposed for DGs to suppress voltage fluctuations. Firstly, the control strategy for DGs is generated for global optimization, considering the coordination of discrete regulation devices and DGs in a long-time scale. Then, the local control curve for DGs is established based on the reactive power value of DGs determined in the central strategy. To further enhance the robustness of the local control curves, a parameter tuning model for the local control curve is built based on the distributionally robust optimization (DRO) method. The voltage violations caused by DG fluctuations can be quickly suppressed by using the local control curve. Finally, the effectiveness of the combined central-local control strategy is substantiated through validation using both the modified IEEE 33-node distribution system and the practical JMF3 80-node distribution system. The proposed method can improve voltage control performance while enhancing the adaptation to DG fluctuation. • A combined central-local voltage control strategy is proposed for DGs in ADN. • The system-wide coordinated optimization is realized in the central stage. • The local control curve for DG is established to cope with frequent fluctuation. • The DG uncertainties is addressed with distributionally robust optimization. [ABSTRACT FROM AUTHOR]

The expansion of solar energy in high density cities highlights the crucial need for optimal capacity planning in building-integrated photovoltaic (BIPV) systems. However, uncertainties present significant challenges for robust planning in these systems. Addressing this challenge, this paper proposes a distributionally robust optimization (DRO) model employing scenario robust ambiguity sets for BIPV system expansion planning to handle uncertainties in both demand and solar irradiance. This model stands out for its comprehensive incorporation of factors including the dynamics of climate change, the properties of building geometry, the intricate non-linear correlation between solar generation potential and global horizontal irradiance and uncertainty handling. The model can be transformed into a tractable formulation using the linear decision rule approach. In evaluating the model's performance in data uncertainty handling, the study compares it against three alternative approaches – deterministic optimization, stochastic programming, and robust optimization – in a case study for BIPV system expansion planning for a college in Singapore. The findings demonstrate the superiority of the proposed model: it achieves a 5%–12% reduction in grid reliance, saves electricity cost by 3%–10% and reduces carbon dioxide (CO 2) emission by 3%–10% compared to the benchmark approaches. These results underscore the capability of the proposed model in effectively handling data uncertainties in demand and irradiance in the BIPV system expansion planning. [Display omitted] • Consider weather patterns and geometry property in demand and solar power estimation. • Formulate power potential with global horizontal irradiance, capturing non-linearity. • Develop a distributionally robust optimization model to handle uncertainties. • Integrate the non-linearization into the optimization model. • Compare the solution performance from the proposed model to other benchmark models. [ABSTRACT FROM AUTHOR]

To ensure a successful bid while maximizing profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. Therefore, distributionally robust optimization (DRO) is a good choice because it can provide an adjustable self-scheduling strategy for GENCOs in an uncertain environment, which can balance robustness and economics well compared to strategies derived from robust optimization and stochastic optimization. In this article, a novel moment-based DRO model with conditional value-at-risk is proposed to solve the self-scheduling problem under electricity price uncertainty. The size of the model mainly depends on the system size, and the computational burden increases sharply as the system size increases. For this drawback, two effective approximate models are proposed: one approximate model based on vector splitting (DRA-VS) and another based on the alternate direction multiplier method (DRA-ADMM). Both can greatly reduce calculation time and resources, while ensuring the quality of the solution, and DRA-ADMM only needs the information of the current area in each step of the solution, thus, private information is guaranteed. Simulations of three IEEE test systems are conducted to demonstrate the correctness and effectiveness of the proposed DRO model and two approximate models. [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]

Any reliable model for scheduling optical space-to-ground communication must factor in cloud cover conditions due to attenuation of the laser beam by water droplets in the clouds. In this article, we provide two alternative models of uncertainty for cloud cover predictions: a robust optimization model with a polyhedral uncertainty set and a distributionally robust optimization model with a moment-based ambiguity set. We computationally analyze their performance over a realistic communication system with one satellite and a network of ground stations located in the U.K. The models are solved to schedule satellite operations for six months utilizing cloud cover predictions from official weather forecasts. We found that the presented formulations with the treatment of uncertainty outperform in the long-term models, in which uncertainty is ignored. Both treatments of uncertainty exhibit similar performance. Nonetheless, the novel variant with the polyhedral uncertainty set is considerably faster to solve. [ABSTRACT FROM AUTHOR]

Seismic events can severely damage both electricity and natural gas systems, causing devastating consequences. Ensuring the secure and reliable operation of the integrated energy system (IES) is of high importance to avoid potential damage to the infrastructure and reduce economic losses. This article proposes a new optimal two-stage optimization to enhance the reliability of IES planning and operation against seismic attacks. In the first stage, hardening investment on the IES is conducted, featuring preventive measures for seismic attacks. The second stage minimizes the expected operation cost of emergency response. The random seismic attack is modeled as uncertainty, which is realized after the first stage. An explicit damage assessment model is developed to define the budget set of the uncertain seismic activity. Based on the survivability of transmission lines and gas pipelines of IES, an optimal system investment plan is developed. The problem is formulated as a two-stage distributionally robust optimization (DRO) model, which is tested on an integrated IEEE 30-bus system and 20-node gas network. Case studies demonstrate that the two-stage DRO outperforms robust optimization and a single-stage optimization model in terms of minimizing the investment cost and expected economic loss. This article can help system operators to make economical hardening and operation strategies to improve the reliability of IES under seismic attacks, thus managing a more robust and secure energy system. [ABSTRACT FROM AUTHOR]

Wind power and pumped storage combined system (WPCS), as an entity integrates multiple energy sources, can provide a reliable overall power supply by optimizing the management of available resources, helping to combat the serious climate change challenges. In order to address the participation of combination system in multiple market operations and multiple uncertainties, this paper proposes a joint declaration strategy for WPCS to participate in the electricity market (EM) and frequency regulation market (FRM). Firstly, the trading mechanism is developed for WPCS to collaborate in power markets. Secondly, a joint declaration and dispatching strategy decision-making model of WPCS is constructed, and the uncertainty of market prices and wind power output in the model is processed by using the information gap decision theory-distribution robust optimization (IGDT-DRO) technique. Finally, simulations implemented on an actual WPCS are delivered to show that: 1) WPCS achieved an expected profit by 8.79% and decrease deviation penalty costs by 58.81% through multi energy complementary operation. 2) Compared with the single market, WPCS can increase the expected profit by 77.5% in the joint declaration of multi-markets.3) IGDT-DRO technology can simultaneously manage the uncertainty of both price and electricity. When the sample size increases tenfold, the runtime increases by less than 40%, which has advantages in data-driven and stable runtime. [Display omitted] • A synergistic trading mode of electric energy and frequency regulation markets is designed. • A declaration-dispatching strategy for wind power and pumped storage participating in EM andFRM is constructed. • The IGDT-DRO technique is used to deal with the uncertainty of market price and wind power generation. • The characteristics of IGDT-DRO model in data-driven feature, non-conservative result and stable run time have been proved. [ABSTRACT FROM AUTHOR]

The Unit commitment (UC) problem in power systems has been studied for a long time; however, many new challenges have emerged in the UC problem with the increasing penetration of renewable generation which is intermittent and uncertain. Compared with the common uncertainty modeling methods including stochastic programming and robust optimization, in this paper, we develop a data-driven distributionally robust chance-constrained (DDRC) UC model. The proposed two-stage UC model focuses on the commitment decision and dispatch plan in the first stage, and considers the worst-case expected cost for possible power imbalance or re-dispatch in the second stage. To capture the uncertainty of wind power distribution, a distance-based ambiguity set is designed which can be constructed in a data-driven manner. Based on the ambiguity set, the original complicated UC problem is reformulated to a tractable optimization problem which is then solved by the column-and-constraint generation (C&CG) algorithm. The performance of the the proposed approach is validated by case studies with different test systems including the IEEE 6-bus test system, modified IEEE 118-bus system and a practical-scale system, especially the value of data in controlling the conservativeness of the problem.

With the increasing penetration of wind power, the uncertainty associated with it brings more challenges to the operation of the integrated energy system (IES), especially the power subsystem. However, the typical strategies to deal with wind power uncertainty have poor performance in balancing economy and robustness. Therefore, this paper proposes a distributionally robust joint chance-constrained dispatch (DR-JCCD) model to coordinate the economy and robustness of the IES with uncertain wind power. The optimization dispatch model is formulated as a two-stage problem to minimize both the day-ahead and the real-time operation costs. Moreover, the ambiguity set is generated using Wasserstein distance, and the joint chance constraints are used to ensure that the safety constraints (e.g., ramping limit and transmission limit) can be satisfied jointly under the worst-case probability distribution of wind power. The model is remodeled as a mixed-integer tractable programming issue, which can be solved efficiently by ready-made solvers using linear decision rules and linearization methods. Case studies on an electricity–gas–heat regional integrated system, which includes a modified IEEE 24-bus system, 20 natural gas-nodes, and 6 heat-node system, are investigated for verification. Numerical simulation results demonstrate that the proposed DR-JCCD approach effectively coordinates the economy and robustness of IES and can offer operators a reasonable energy management scheme with an acceptable risk level.

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]

This paper investigates the scheduling strategy of schedulable load in home energy management system (HEMS) under uncertain environment by proposing a distributionally robust optimization (DRO) method based on receding horizon optimization (RHO-DRO). First, the optimization model of HEMS, which contains uncertain variable outdoor temperature and hot water demand, is established and the scheduling problem is developed into a mixed integer linear programming (MILP) by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables. Combined with RHO, the MILP is solved in a rolling fashion using the latest update data related to uncertain variables. The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort. Furthermore, compared with the robust optimization (RO) method, the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users. [ABSTRACT FROM AUTHOR]

Energy hub system (EHS) incorporating multiple energy carriers, storage, and renewables can efficiently coordinate various energy resources to optimally satisfy energy demand. However, the intermittency of renewable generation poses great challenges on optimal EHS operation. This article proposes an innovative distributionally robust optimization model to operate EHS with an energy storage system (ESS), considering the multimodal forecast errors of photovoltaic (PV) power. Both battery and heat storage are utilized to smooth PV output fluctuation and improve the energy efficiency of EHS. This article proposes a novel multimodal ambiguity set to capture the stochastic characteristics of PV multimodality. A two-stage scheme is adopted, where 1) the first stage optimizes EHS operation cost, and 2) the second stage implements real-time dispatch after the realization of PV output uncertainty. The aim is to overcome the conservatism of multimodal distribution uncertainties modeled by typical ambiguity sets and reduce the operation cost of EHS. The presented model is reformulated as a tractable semidefinite programming problem and solved by a constraint generation algorithm. Its performance is extensively compared with widely used normal and unimodal ambiguity sets. The results from this article justify the effectiveness and performance of the proposed method compared to conventional models, which can help EHS operators to economically consume energy and use ESS wisely through the optimal coordination of multienergy carriers. [ABSTRACT FROM AUTHOR]

Networked microgrids (MGs) are considered as an emerging grid design for the future distribution system (DS). The coordination of the networked MGs is critical in order to further enhance the operation efficiency and reliability of the system. In this paper, a transactive energy (TE) framework is proposed for the coordinated energy management of networked MGs in DS. Instead of direct coordination signals and fixed pricing schemes, the distribution network operator (DNO) organizes a transactive market with the MGs to coordinate the energy management in the operation. Further, a distributionally robust optimization (DRO)-based algorithm is developed to provide a robust solution of the detailed scheduling decisions in the proposed TE framework under uncertainty without being too conservative. Case studies with the proposed framework were conducted with the IEEE 33-bus system with three MGs and the IEEE 123-bus system with nine MGs. The results of the case studies show that the proposed TE-based framework can effectively coordinate the energy scheduling of the MGs. The operational cost of the DS is reduced significantly. Meanwhile, the proposed DRO-based algorithm provides a robust but not over-conservative solution for the operation decisions of the DNO and MGs in the proposed framework. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the challenge of design optimization under uncertainty when the designer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out‐of‐sample performance (ie, performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design problem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design problem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample‐average approximation and multiobjective optimization incorporating a risk reduction objective. In contrast with the multiobjective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather specifies a so‐called ambiguity set of possible distributions and optimizes against the worst‐case distribution in this set. Our results show that the DRO designs, in some cases, significantly outperform those designs found using the sample‐average or the multiobjective approach. [ABSTRACT FROM AUTHOR]

Increasing the complexity of power transmission networks has led power systems to be more vulnerable to cascading failures. Thus, hardening and reliability assessment of such complex networks have become a must. In addition, the commonly used $N-1$ security criterion does not guarantee the reliability of the system against possible cascading failures. In this paper, given a hardening plan, we develop two models to evaluate the reliability of the power transmission system under $N-k$ security criterion. In the first model, we quantify the probability of no load-shedding in the system to assess the possibility of load curtailment. Then, to have a better insight of the amount of load-shed in the second model, we use the conditional value-at-risk as a risk measure to evaluate the reliability of the system. To perform reliability assessment, the information of contingency probabilities is required. However, such probability information is usually unknown and cannot be estimated precisely. Therefore, in this paper, we assume the probability of contingencies as unknown and ambiguous. Then, we construct an ambiguity set for the unknown probability distribution of contingencies. Our approaches are robust because they analyze the reliability of the transmission system with respect to the worst-case distribution in the ambiguity set. We formulate both models as bilevel programs and solve them using the Bender's decomposition technique. Finally, we conduct numerical experiments on 6-bus and IEEE 118-bus test systems to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

With the development of smart grid, energy management becomes critical for reliable and efficient operation of power systems. In this paper, we develop a chance-constrained energy management model for an islanded microgrid, which includes distributed generators, energy storage system (ESS), and renewable generation, such as wind power. The objective function of this model consists of generation cost, emission cost, and ESS degradation cost. To capture the uncertainty of renewable generation, a novel ambiguity set is introduced without knowing its probability distribution or exact moment information. Based on the ambiguity set, the chance constraint can be processed with distributionally robust optimization method and the energy management problem is reformulated as a tractable second-order conic programming problem. The proposed approach is tested with a case study and simulation results indicate that it is effective and reliable. Moreover, the comparison with the method based on known moment information and some other methods is also conducted to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes distributionally robust energy-reserve-storage co-dispatch model and method to facilitate the integration of variable and uncertain renewable energy. The uncertainties of renewable generation forecasting errors are characterized through an ambiguity set, which is a set of probability distributions consistent with observed historical data. The proposed model minimizes the expected operation costs corresponding to the worst case distribution in the ambiguity set. Distributionally robust chance constraints are employed to guarantee reserve and transmission adequacy. The more historical data are available, the smaller the ambiguity set is and the less conservative the solution is. The formulation is finally cast into a mixed integer linear programming whose scale remains unchanged as the number of historical data increases. Inactive constraint identification and convex relaxation techniques are introduced to reduce the computational burden. Numerical results and Monte Carlo simulations on IEEE 118-bus systems demonstrate the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• A synergistic trading mode of electric energy and FRP markets is designed. • A declaration-dispatching strategy for VPP participating in the electric energy and FRP markets is constructed. • The distributionally robust optimization (DRO) technique is used to deal with the uncertainty in VPP. • VPP's declaration strategy and cost-benefits in 96 period are examined. • The characteristics of DRO model in data-driven feature, non-conservative result and stable run time have been proved. The volatility and randomness of renewable energy output make the flexible ramping ability demand of power system more urgent, and flexible ramping product (FRP) can effectively improve the flexibility of the power system. Virtual power plant (VPP) can regulate distributed generation, which is conducive to the regulation potential of flexible resources. To solve the problems of FRP and electric energy markets synergy and the wind power output uncertainty faced by the VPP in the declaration process, this paper proposes a comprehensive declaration strategy for the VPP to participate in the power market considering FRP and uncertainties. Firstly, this paper designs a synergistic trading mode covering flexibility resource demand determination and the virtual bidding curve formation for electric energy and FRP markets, in which the virtual bidding curve can reasonably compensate for the unit opportunity cost. Secondly, a comprehensive declaration-dispatching strategy decision-making model for VPP is constructed, and a two-stage distributed robust optimization (DRO) technology is used to deal with the wind power output uncertainty in the model, and flexible resources such as energy storage are used to mitigate energy deviation in the VPP. Finally, simulations implemented on a typical VPP are delivered to show that: 1) Virtual bidding curve realizes the accurate compensation for the units providing FRP. 2) Compared with the single market, VPP can increase the expected profit by 20.44% and reduce wind curtailment cost by 59.68% in the joint declaration of multi-markets.3) VPP can effectively suppress output uncertainty through energy storage system. 4) DRO model has significant advantages in data-driven, less conservative results and stable running time. [ABSTRACT FROM AUTHOR]

Widespread utilization of electric vehicles (EVs) incurs more uncertainties and impacts on the scheduling of the power-transportation coupled network. This paper investigates optimal power scheduling for a power-transportation coupled network in the day-ahead energy market considering multiple uncertainties related to photovoltaic (PV) generation and the traffic demand of vehicles. The crux of this problem is to model the coupling relation between the two networks in the day-ahead scheduling stage and consider the intra-day spatial uncertainties of the source and load. Meanwhile, the flexible load with a certain adjustment margin is introduced to ensure the balance of supply and demand of power nodes and consume the renewable energy better. Furthermore, we show the interactions between the power system and EV users from a potential game-theoretic perspective, where the uncertainties are characterized by an ambiguity set. In order to ensure the individual optimality of the two networks in a unified framework in day-ahead power scheduling, a two-stage distributionally robust centralized optimization model is established to carry out the equilibrium of power-transportation coupled network. On this basis, a combination of the duality theory and the Benders decomposition is developed to solve the distributionally robust optimization (DRO) model. Simulations demonstrate that the proposed approach can obtain individual optimal and less conservative strategies. • Day-ahead power scheduling for power-transportation coupled network with uncertainty. • Uncertainties were modeled by moment-based ambiguity set. • Reconfiguration method of distributionally robust model based on potential function. • The unified optimization framework improved dispatch profit. [ABSTRACT FROM AUTHOR]

The penetration of renewables on the demand side has recently attracted a large amount of attention. Its dual identity has an important impact on the competition between power producers and market dispatching. This study analyzed the participation of prosumers in the Nash–Cournot model for power market clearing. On this basis, we considered the uncertainty of renewable energy production, under which we used the distributionally robust optimization (DRO) model to produce a market equilibrium. Moreover, the Column-and-Constraint Generation algorithm was employed to solve the model. As a result, the impact of prosumers penetration and their production uncertainty on market equilibria was quantified and analyzed. Numerical simulations on an IEEE-30 bus system investigated the impact of the uncertainty of renewable energy output, the penetration level of wind power, and the demand level on the market equilibria. Test results demonstrate that the social welfare obtained from the proposed DRO model is 6.89% higher than that obtained from traditional robust optimization models. [ABSTRACT FROM AUTHOR]

The rapid development of digital economy has led to a dramatic increasement of internet data centers (IDCs), which consume a large amount of electricity. The diverse data-processing demands, high power consumption and workload uncertainty put forward a high requirement for the economical and secure operation of IDCs. As information technology (IT) devices are driven by direct current (DC), flexible substation (FS) has been gradually utilized to provide DC power for IDCs. This paper proposes robust operation strategies for minimizing IDC power consumption with FS integration. First, the linearized IDC power consumption model based on the technology of dynamic voltage and frequency scaling (DVFS) is proposed to describe the operating state of IT devices. Then, considering the FS-based coordinated operation of IDC, photovoltaic (PV) station and energy storage system (ESS), the deterministic power consumption minimization model of IDCs is established. Considering the workload uncertainty, the operation strategies based on distributionally robust optimization (DRO) for IDCs are further proposed. Finally, the effectiveness of proposed method is validated on a modified practical network with IDCs integrated. Results show that through the dispatch of workload and power flow regulation of FS, the power consumption and dropping workload of IDCs are effectively reduced. • The linearized power consumption model of data centers is proposed. • Variable resources are coordinated with flexible substation integration. • Distributionally robust optimization strategies are proposed for data centers. • The power consumption and dropping workload are effectively reduced. [ABSTRACT FROM AUTHOR]

• A distributionally robust optimization dispatch model is proposed to increase wind power absorption. • A moment-based ambiguity set of fluctuation rate of net load power is determined to consider weather conditions. • The wind curtailment risk due to inadequate dynamic dispatchable resources is measured. • The tradeoff between dispatching economy and robustness is balanced. The power system with high penetration of wind power faces a great challenge for system dispatch due to the high volatility and intermittency of the wind power. This work proposes a day-ahead optimal dispatch model which is formulated for a power system with thermal power, hydropower, and controllable load as dispatchable resources. According to the anti-peak regulation, the system dynamic power regulation margin model considering adjacent time periods is established to address the uncertainty in the fluctuation rate of net load power, and to sufficiently use the dispatchable resources to reduce wind curtailment. However, in some circumstances, curtailing wind has to be considered to ensure secure operation of the system and maintain the economic goal from the total cost point of view. The risk of curtailing wind is formulated using conditional value at risk (CVaR), and is minimized as part of the total operating cost. Another objective function of the proposed dispatch model is to maximize the power regulation margin. Uncertainty in the fluctuation rate of net load power is modelled for different weather conditions using moment-based ambiguity set. The moment information is obtained from large amount of historical data using clustering methodologies. The proposed optimal dispatch model with uncertainty and CVaR formulation is reformulated and solved under the distributionally robust conditional value at risk (DRCVaR) framework. The model is transformed into a semi-definite programming problem through the duality theory and can be solved efficiently by commercial solvers. Simulation results show that the proposed dispatch model can effectively strengthen wind power absorption, ensure secure operation, and improve the robustness of the dispatch strategy facing the uncertainty from the wind power. [ABSTRACT FROM AUTHOR]

With the increasing penetration of wind power, the uncertainty associated with it brings more challenges to the operation of the integrated energy system (IES), especially the power subsystem. However, the typical strategies to deal with wind power uncertainty have poor performance in balancing economy and robustness. Therefore, this paper proposes a distributionally robust joint chance-constrained dispatch (DR-JCCD) model to coordinate the economy and robustness of the IES with uncertain wind power. The optimization dispatch model is formulated as a two-stage problem to minimize both the day-ahead and the real-time operation costs. Moreover, the ambiguity set is generated using Wasserstein distance, and the joint chance constraints are used to ensure that the safety constraints (e.g., ramping limit and transmission limit) can be satisfied jointly under the worst-case probability distribution of wind power. The model is remodeled as a mixed-integer tractable programming issue, which can be solved efficiently by ready-made solvers using linear decision rules and linearization methods. Case studies on an electricity–gas–heat regional integrated system, which includes a modified IEEE 24-bus system, 20 natural gas-nodes, and 6 heat-node system, are investigated for verification. Numerical simulation results demonstrate that the proposed DR-JCCD approach effectively coordinates the economy and robustness of IES and can offer operators a reasonable energy management scheme with an acceptable risk level. [ABSTRACT FROM AUTHOR]